Waveform Candidate Selection - IS-Wireless · valued complex constellation. The resulting vector denotes a GFDM data block that contains N elements, which can be decomposed into K

The 5GNOW Project Consortium groups the following organizations:

Partner Name Short name Country

FRAUNHOFER-GESELLSCHAFT ZUR FOERDERUNG DER ANGEWANDTEN FORSCHUNG E.V. HHI Germany

ALCATEL LUCENT DEUTSCHLAND AG ALUD Germany

COMMISSARIAT A L ENERGIE ATOMIQUE ET AUX ENERGIES ALTERNATIVES CEA France

IS-WIRELESS ISW Poland

NATIONAL INSTRUMENTS NI Hungary

TECHNISCHE UNIVERSITÄT DRESDEN TUD Germany

Abstract: The screening process of T3.1 will generate a candidate list of waveforms and signal formats, described in this IR3.1.

5G Waveform Candidate Selection

D3.2

‘5GNOW_D3.2_v1.3.docx’

Version: 1.3

Last Update: 08.04.2014

Distribution Level: PU

Distribution level PU = Public, RE = Restricted to a group of the specified Consortium, PP = Restricted to other program participants (including Commission Services), CO= Confidential, only for members of the 5GNOW Consortium (including the Commission Services)

D3.2

5GNOW FP7 – ICT– GA 318555

Page: 2 of 100

The 5GNOW Project Consortium groups the following organizations:

Partner Name Short name Country

FRAUNHOFER-GESELLSCHAFT ZUR FOERDERUNG DER ANGEWANDTEN FORSCHUNG E.V. HHI Germany

ALCATEL LUCENT DEUTSCHLAND AG ALUD Germany

COMMISSARIAT À L’ENERGIE ATOMIQUE ET AUX ENERGIES ALTERNATIVES CEA France

IS-WIRELESS ISW Poland

NATIONAL INSTRUMENTS NI Hungary

TECHNISCHE UNIVERSITÄT DRESDEN TUD Germany

Abstract: Based on the waveform candidates in D3.1, D3.2 will contain intermediate 5GNOW Transceiver and frame structure concept.

Partner Author name

HHI Martin Kasparick, Gerhard Wunder, Peter Jung

ALUD Yejian Chen, Frank Schaich, Thorsten Wild

CEA Jean-Baptiste Doré, Nicolas Cassiau, Vincent Berg and Dimitri Kténas

ISW Marcin Dryjański, Slawomir Pietrzyk

TUD Ivan Simões Gaspar, Nicola Michailow, Maximilian Matte, Luciano Leonel Mendes

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“The research leading to these results has received funding from the European Community's Seventh Framework Programme (FP7/2007-2013) under grant agreement n° 318555”

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Document Identity

Title: 5G Waveform Candidate Selection WP: WP3 – Physical layer design WP Leader ALUD Main Editors Ivan Simoes Gaspar/Nicola Michailow/Luciano Leonel Mendes Number: D3.2 File name: 5GNOW_D3.2_v1.3.docx Last Update: Monday, May 04, 2015

Revision History

No. Version Edition Author(s) Date

1 0.1 Ivan Simões Gaspar (TUD) 28.06.13

Comments: Providing initial template and skeleton

2 0.2 Nicola Michailow (TUD)

Comments: Updated Skeleton

3 0 Ivan Simões Gaspar (TUD) 17.02.14

Comments: Added contributions from partners

4 1.0 Nicola Michailow (TUD) 14.03.14

Comments: Final merged version

5 1.3 Nicola Michailow/Ivan Gaspar (TUD) 26.03.14

Comments: Comments incorporated

6 1.3 Martin Kasparick / Gerhard Wunder 07.04.14

Comments: Final Review

7 Gerhard Wunder 08.04.14

Comments:

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9

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10

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11

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Table of Contents

1 INTRODUCTION ....................................................................................................................................... 7

2 INTERMEDIATE TRANSCEIVER AND FRAME STRUCTURE CONCEPT OF THE CONSIDERED WAVEFORMS .. 8

2.1 GFDM ................................................................................................................................................... 8 2.1.1 GFDM Principles .............................................................................................................................. 8 2.1.2 Waveform engineering .................................................................................................................. 11 2.1.3 Performance analysis .................................................................................................................... 16 2.1.4 MIMO-GFDM aiming diversity ...................................................................................................... 20 2.1.5 Synchronization ............................................................................................................................. 22 2.1.6 Advanced receivers ........................................................................................................................ 23 2.1.7 Application requirements and Frame Design ................................................................................ 25 2.1.8 Summary for GFDM ....................................................................................................................... 28

2.2 UFMC & IDMA .................................................................................................................................... 29 2.2.1 UFMC principles and frame structure aspects ............................................................................... 29 2.2.2 Synchronization, channel estimation and equalization ................................................................. 31 2.2.3 Support of Autonomous Timing Advance ...................................................................................... 33 2.2.4 Performance in scenarios with relaxed synchronism .................................................................... 34 2.2.5 UFMC with multiple signal layers .................................................................................................. 48 2.2.6 UFMC with flexible single carrier support ..................................................................................... 55 2.2.7 Summary for UFMC ....................................................................................................................... 56

2.3 FBMC .................................................................................................................................................. 57 2.3.1 FBMC principles ............................................................................................................................. 57 2.3.2 Frame design ................................................................................................................................. 59 2.3.3 Receiver architecture overview ..................................................................................................... 60 2.3.4 Time synchronization .................................................................................................................... 62 2.3.5 Carrier frequency offset compensation ......................................................................................... 65 2.3.6 Channel estimation and interpolation ........................................................................................... 69 2.3.7 Equalizer ........................................................................................................................................ 77 2.3.8 Summary for FBMC ....................................................................................................................... 81

2.4 BFDM.................................................................................................................................................. 82 2.4.1 BFDM Principles and Frame Design ............................................................................................... 82 2.4.2 Summary of Transmitter and Receiver Structure .......................................................................... 83 2.4.3 Pulse shaped PRACH ...................................................................................................................... 85 2.4.4 Synchronization and Equalization ................................................................................................. 88 2.4.5 Performance Analysis .................................................................................................................... 90 2.4.6 Application Requirements ............................................................................................................. 93 2.4.7 Summary for BFDM ....................................................................................................................... 94

3 CONCLUSION ......................................................................................................................................... 95

4 ABBREVIATIONS AND REFERENCES ....................................................................................................... 96

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Executive Summary

This document is part of the efforts in T3.2 “Transceiver Algorithm Design”. Based on the selected waveform types from D3.1, the intermediate 5GNOW transceiver and frame structure concepts are described for the individual candidates. Initial performance results, e.g. based on simulations, are presented, along with a detailed description of the required signal processing in the respective transmitters and receivers. Building blocks like modulation, synchronization and channel estimation for the candidate transmitters and receivers are presented. With the considered techniques, orthogonal, non-orthogonal, synchronous, and asynchronous user classes are taken into account.

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1 Introduction

This report re-captures the waveform candidates introduced in D3.1 and extends their concepts towards the intermediate transceiver and frame structure concept according to the goals and roadmap of 5GNOW. The main contribution of the document is concentrated in section 2, where GFDM, UFMC, FBMC and BFDM are presented and their initial performance results based on simulations are discussed. Particularly aspects like spectrum emission characteristics, time and frequency synchronization performance, MIMO and asynchronous multiple access are considered. The focus of section 2.1 is GFDM. After presenting the basic principles of this modulation technique, its capabilities to “engineer” specific waveform properties are discussed. The performance of the scheme is analysed in terms of bit and symbol error rates with simulations as well as with analytical expressions. Multi-antenna techniques are investigated in order to potentially increase diversity in the system. The question of how to achieve synchronization in time and frequency is treated and finally the requirements of different application scenarios like Internet of Things (IoT), machine-type-communication (MTC), and Tactile Internet are brought into the context of GFDM parameterization. Section 2.2 develops the principles of UFMC together with IDMA multiple access concepts. Synchronization, channel estimation and equalization are addressed as well as the support of autonomous timing advance. The performance evaluation highlights specific scenarios with relaxed synchronism requirements. Finally, multiple signal layers with the help of IDMA are considered and a flexible way to support flexible communication modes ranging from single-carrier to different multicarrier transmission schemes is presented. The details of FBMC are addressed in section 2.3. First, the basic concepts of this modulation scheme are shortly outlined and aspects of FBMC frame design are discussed. Then, the building blocks for an appropriate transceiver design are presented. Time synchronization as well as carrier frequency offset compensation are addressed, channel estimation and equalization conclude this section. At last, section 2.4 deals with BFDM, where basic principles and frame design are addressed. An appropriate transceiver structure is presented and advantageous properties such as pulse shaping are discussed which is particularly suited in a random access scenario. Synchronization and channel equalization concepts are addressed and the performance of this scheme is analysed through simulation. Finally, application requirements for the IoT and MTC are presented.

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2 Intermediate Transceiver and Frame Structure Concept of the Considered Waveforms

This section presents a detailed description of the four 5G waveforms that are being considered in the scope of 5GNOW. Technical transceiver aspects like time and frequency synchronization or channel equalization are discussed, while also a view on the improvement over OFDM is presented. The feasibility and the performance of the individual approaches are supported with a selection of simulation results.

2.1 GFDM

2.1.1 GFDM Principles

Consider the block diagram depicted in Figure 2.1.1.1.

Figure 2.1.1.1: Block diagram of the transceiver.

A data source provides the binary data vector b , which is encoded to obtain c

b . A mapper, e.g.

quadrature amplitude modulation (QAM), maps sequences of μ encoded bits to symbols d of a 2μ-

valued complex constellation. The resulting vector d denotes a GFDM data block that contains N elements, which can be decomposed into K groups of M symbols according

to 0 1, ,

TT T

Kd d d

and , 0 , 1

, ,T

k k k Md d d

with N = KM. Therein, the individual

elements ,k m

d correspond to the data transmitted on the kth subcarrier and in the mth subsymbol of

the block. In the GFDM modulator, each ,k m

d is transmitted with the corresponding pulse shape

2

,[ ] m o d

nj k

K

k mg n g n m K N e

(2.1.1.1)

with n denoting the sampling index. Each ,

[ ]k m

g n is a time and frequency shifted version of a

prototype filter [ ]g n , where the modulo operation makes ,

[ ]k m

g n a circularly shifted version

of , 0

[ ]k

g n and the complex exponential performs the shifting operation in frequency. The transmit

samples [ ]T

x x n are obtained by superposition of all transmit symbols

1 1

, ,

0 0

[ ] [ ] , 0 , , 1 .

K M

k m k m

k m

x n g n d n N

(2.1.1.2)

Collecting the filter samples in a vector , ,[ ]

T

k m k mg g n allows to formulate (2.1.1.2) as

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,x d A (2.1.1.3)

where A is a KM ×KM transmitter matrix [MKL+12] with a structure according to

0 ,0 1,0 0 ,1 1,1 0 , 1 1, 1.

K K M K Mg g g g g g

A (2.1.1.4)

Figure 2.1.1.2 shows three columns of an example transmitter matrix. As one can see,

1,0 , 2[ ]

ng A and

0 ,1 , 1[ ]

n Kg

A are circularly frequency and time shifted versions of

0 ,0 ,1[ ]

ng A .

At this point, x contains the transmit samples that correspond to the GFDM data block d . Lastly, on

the transmitter side a cyclic prefix of C P

N samples is added to produce x .

Transmission through a wireless channel is modelled by y x w H , where y is the received

counterpart of x . Here, H is a convolution matrix with band-diagonal structure based on a channel

impulse response h which is a realization of a Rayleigh multipath fading channel. Lastly,

C P

2~ ,

w N Nw

0 IN denotes additive white Gaussian noise. At the receiver, time and frequency

synchronization is performed, yielding s

y . Then the cyclic prefix is removed. Under the assumption

of perfect synchronization, i.e. s

y y , the cyclic prefix can be utilized to simplify the model of the

wireless channel to y x w H (2.1.1.5)

by replacing the matrix H with the corresponding circular convolution matrix H . This allows employing zero-forcing channel equalization as efficiently used in OFDM [Bin90]. The overall

transceiver equation can be written as y d w H A . Introducing 1 1z d w d w

H H A H A

as the received signal after channel equalization, linear demodulation of the signal can be expressed as

ˆ ,d z B (2.1.1.6)

where B is a KM ×KM receiver matrix. Several standard receiver options for the GFDM demodulator

are readily available in literature: The matched filter (MF) receiver M F

HB A maximizes the signal-

to-noise ratio (SNR) per subcarrier, but with the effect of introducing self-interference when a non-

orthogonal transmit pulse is applied, i.e. the scalar product 0 ,0 , 0 , 0 ,

,Nk m k m

g g with Kronecker

delta δi,j.

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(a) A transmitter matrix.

(b) Three columns in detail.

Figure 2.1.1.2: Illustration of the GFDM transmitter matrix for N = 28, K = 4, M = 7, using a raised cosine (RC) filter with parameter 0.4.

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The zero-forcing (ZF) receiver 1

Z F

B A on the contrary completely removes any self-interference

at the cost of enhancing the noise. Also, there are cases in which A is ill-conditioned and thus the inverse does not exist. The linear minimum mean square error (MMSE) receiver

2 1

M M S E( )

H H

w

B I A A A makes a trade-off between self-interference and noise enhancement.

(a) OFDM (b) SC-FDE (c) SC-FDM and GFDM

Figure 2.1.1.3: Partitioning of time and frequency, where data occupies different resources depending on the chosen

scheme. (a) with K = N subcarriers and M = 1 subsymbols, (b) with K = 1 subcarriers and M = N subsymbols and (c) with K = 4, M = 3 and N = 12.

Finally, the received symbols d are demapped to produce a sequence of bits c

b at the receiver,

which are then passed to a decoder to obtain b . From the description of the transmitter and receiver, it is clear that GFDM falls into the category of filtered multicarrier systems. The name derives from the fact that the scheme offers more degrees of freedom than traditional OFDM or single carrier with frequency domain equalization (SC-FDE). GFDM

turns into OFDM when 1M , H

NA F and

NB F , where

NF is a N N Fourier matrix. SC-FDE

is obtained when 1K and SC-FDM - a frequency division multiplexing of several SC-FDE signals - is obtained when g is a Dirichlet pulse [MF13]. However, the important property that distinguishes the

proposed scheme from OFDM and SC-FDE is that, like SC-FDM, it allows dividing a given time-frequency resource into K subcarriers and M subsymbols as depicted in Figure 2.1.1.3. Therefore, it is possible to engineer the spectrum according to given requirements and enables pulse shaping on a per subcarrier basis. As a consequence, without changing the sampling rate, GFDM can be configured to cover a portion of bandwidth either with a large number of narrow band subcarriers like in OFDM or with a small number of subcarriers of large individual bandwidth like in SC-FDM. Further it is important to note that although filters are introduced, GFDM is still a block based approach. These aspects are relevant for the scheduling of users in a multiple access scenario [WJK+14] and also when targeting low latency transmissions [Fet14]. Within each block, the signal is designed such that it exhibits a circular structure in time and frequency domain. In combination with a cyclic prefix at the beginning of each GFDM block, this property helps to keep transmitter and receiver complexity low [GMC+13] and eases synchronization and equalization.

2.1.2 Waveform engineering

The flexibility of GFDM allows designing a signal that has a very low out-of-band (OOB) radiation. A detailed theoretical analysis of the OOB radiation of GFDM is shown in this section.

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The choice of the pulse shaping filters strongly influences the spectral properties of the GFDM signal and the symbol error rate. The frequency responses of candidate filters employed are summarized in Table 2.1.2.1(a), whereas the respective impulse responses are calculated by inverse discrete Fourier transform (IDFT). In Table 2.1.2.1(a), linα(x) is a truncated linear function with

| |1

2lin ( ) m in 1, m a x 0 ,

xx

(2.1.2.1)

that is used to systematically describe the roll-off area defined by α in the frequency domain.

Further, 4 4 2 3( ) (3 5 8 4 7 0 2 0 )p x x x x x is a polynomial that maps the range (0,1) onto itself.

TABLE 2.1.2.1: Pulse shaping filters and window functions. (a) Investigated pulse shaping filters. (b) Window functions for block pinching.

(a)

Name Frequency response

RC R C

1[ ] 1 c o s ( lin ( ))

2

f

MG f

Root RC R R C

[ ] [ ]R C

G f G f

1st Xia [X97] lin ( ) s ig n ( )

X ia

1[ ] 1

2

f

Mj f

G f e

4th Xia [X97] 4( lin ( )) s ig n ( )

X ia 4

1[ ] 1

2

f

Mj p f

G f e

(b)

Window Time domain

Rect R ect

[ ] 1w n

Ramp W W

R

2[ ] lin 1

2C P

N K M N nw n

K M K M K M N

RC R C

1[ ] 1 c o s [ ]

2R

w n w n

4th RC

4

R C 4

1[ ] 1 c o s ( [ ])

2R

w n p w n

In GFDM, the kth subcarrier is centered at the normalized frequency /k K and hence, α describes the overlap of the subcarriers in the frequency domain. In particular, for α= 0 all functions in Table 2.1.2.1(a) reduce to a rect and are denoted the Dirichlet filter, since the impulse response is the Mth Dirichlet kernel of the discrete Fourier transform (DFT) of length MK. Figure 2.1.2.2 shows exemplary impulse and frequency responses of the described pulse shaping filters.

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Figure 2.1.2.1: Impulse and frequency response of employed pulse shaping filters. Roll-off α is set to 0.5 except for the

Dirichlet filter (α = 0). Solid and dashed lines denote real and imaginary part, respectively

To measure the out-of-band radiation, the power spectral density (PSD) of the baseband signal can be formulated as [WND+10]

21( ) lim { | { ( )} | }

TT

P f E x tT

F , (2.1.2.2)

where ( )T

x t is the transmit signal that is truncated to the interval (-T∕2,T∕2). In GFDM, ( )T

x t is the

concatenation of multiple GFDM blocks 2

0

, ,

( ) ( )k

Tsj t

T v m k m s

v m k

x t d g t v M T e

(2.1.2.3)

with respective Fourier transform given by

2

, ,

( ) sj v M T f

T v m k m

v m k s

kX f d G f e

T

(2.1.2.4)

Where Ts is the time duration of one subsymbol, v is the block index that ranges from 2

s

T

M T

to

2s

T

M T

, and k,m range over all allocated subcarriers and subsymbols. When assuming i.i.d. data

symbols with unit variance, inserting (2.1.2.4) into (2.1.2.2) yields the PSD of the GFDM system as 2

,

1( ) .

m

k ms s

kP f G f

M T T

(2.1.2.5)

The OOB radiation of the GFDM signal is defined as the ratio between the amount of energy that is

emitted into the frequency range O O B and the amount of energy within the allocated

bandwidth B by

( )| |

· .| | ( )

f

f

P f d f

O

P f d f

O O B

B

B

O O B

(2.1.2.6)

Between B and O O B a number of guard carriers is inserted. Figure 2.1.2.2(a) illustrates the concept of guard carriers for OOB measurement and shows a comparison of the PSD of OFDM and GFDM. By default, due to the abrupt changes of the signal value between GFDM blocks, the OOB radiation of GFDM is not far below OFDM. In order to make the pulse shaping effectively reduce the OOB radiation two suitable techniques are discussed: 1) Inserting Guard Symbols (GS): When using an ISI-free transmission filter (e.g. the RC or Xia filters) and CP with length of rK,r ∈ℕ samples, it is possible to keep the signal value constant at the block boundaries by setting the 0th and (M -r)th subsymbol to a fixed value. Figure 2.1.2.2(a) shows the strongly attenuated OOB radiation of GFDM, when the GS value is set to zero, denoted by GS-GFDM.

For high M the reduction of the spectral efficiency by 2M

M

due to the GS insertion can be neglected

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and furthermore, these subsymbols are free for inserting synchronization signals and pilots. 2) Pinching the Block Boundary: The insertion of the CP of NCP samples introduces redundancy in the transmitted data. In windowed GFDM (W-GFDM) this is exploited at the transmitter side by multiplying each GFDM block with a window function w[n] in the time domain to provide a smooth fade-in and fade-out as illustrated in Figure 2.1.2.2(c). Different window functions are given in Table 2.1.2.1(b), where NW is the number of samples that are included in the linear part of the ramp wR[n]. At the receiver side, the data is recovered from the received W-GFDM block by summing the parts of the CP that were modified by the window. As a result, a noise enhancement

1 0 W1 0 lo g 1 / ( )N K M dB occurs because of the summation of two redundant parts of the signal.

This noise enhancement can be mitigated by using the square root of the block window at the transmitter and at the receiver which resembles the matched filter approach. Calculations of the OOB power have been carried out with the parameters in Table 2.1.3.1, where different CP lengths have been employed. The results for one and six guard carriers are shown in Figure 2.1.2.2(b). Obviously, any of the presented GFDM configurations has a lower OOB radiation than OFDM. GS-GFDM efficiently reduces the OOB radiation to 32 dB below OFDM with a CP of K samples. For a CP length of K∕4, GS-GFDM performs 20 dB below OFDM. Pinching is most effective in combination with a higher number of guard carriers, since the multiplication with a block window spreads the spectrum of the GFDM signal. The wRC4-window attenuates the OOB radiation with six guard carriers most, but has the least suppression with one guard carrier due to its wide mainlobe in the frequency domain. It can attenuate the OOB radiation to below -100 dB as is shown in Figure 2.1.2.2(b) in the solid blue line. When tolerating six guard carriers, the pinching technique can supress the OOB radiation below -70 dB with a ramp length of only a quarter subsymbol and an RC window.

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(a) PSD of OFDM and GFDM. GFDM employs a CP of length of one subsymbol and the pinching is done with a RC window

with W = K∕4. Regions that are considered in-band and out-of-band are marked with B and O O B , respectively and in between both ranges a number of guard carriers is considered.

(b) OOB radiation of different GFDM configurations

(c) Pinching the block boundary yields W-GFDM.

Figure 2.1.2.2: Waveform engineering results.

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2.1.3 Performance analysis

In this section we analyze the performance of the GFDM system in terms of symbol error rate (SER)

versus 0

/s

E N assuming that a ZF receiver is employed. This means that self-generated interference

is removed on the receiver side but noise enhancement can be introduced, depending on the pulse shape. The SER performance is evaluated considering different scenarios: additive white Gaussian noise (AWGN), static frequency selective channels (FSC) and flat time-variant channels (TVC). We also present a trade-off analysis between noise enhancement and OOB emissions for different pulse shapes. The system parameters used for the simulation are presented in Table 2.1.3.1.

TABLE 2.1.3.1: Simulation parameters.

Parameter Value

Mapping 16-QAM Transmit Filter RC Roll-off (α) 0.1 or 0.9 Number of subcarriers (K) 64 Number of subsymbols (M) 9 CP length (NCP) 16 samples CS length (NCS) 0 samples

The ZF receiver removes the self-generated interference at the cost of enhancing the noise since the receiver filter collects noise outside the desired bandwidth. Figure 2.1.3.1(a) shows the receive filter impulse response for ZF and MF receivers assuming the parameters presented in Table 2.1.3.1 with α = 0.9 to highlight the noise enhancement. Figure 2.1.3.1(b) shows the corresponding frequency response of both filters. As visible, the ZF filter collects noise outside the desired bandwidth, affecting the SER performance of the system.

(a) (b)

Figure 2.1.3.1: (a) Time and (b) frequency characteristics of the ZF and MF receiving filters.

Over flat channels, the noise enhancement factor (NEF) determines the signal-to-noise ratio reduction when using the ZF receiver. It is defined as

1 2

Z F ,

0

,

M K

k n

n

B (2.1.3.1)

which is equal for every k. 1) AWGN Channel: The NEF adjusts the equivalent SNR for GFDM at the receiver side. Consequently, GFDM and OFDM SER performance under AWGN [S01] only differs in the equivalent SNR. Therefore, GFDM SER under AWGN is given by

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2

A W G N

1 1( ) 2 e rfc e rfc ,p e

(2.1.3.2)

where

0 C P C S

3· a n d ,

2 ( 2 1)

sT

T

ER K MR

N K M N N

(2.1.3.3)

μ is the number of bits per QAM symbol, 2

, NCP and NCS are the CP and CS lengths, respectively, Es is the average energy per symbol, and N0 is the noise power density. Figure 2.1.3.2(a) compares the SER performance of GFDM and OFDM under AWGN taking the CP length into account. The figure shows that the pulse shape and, consequently the NEF, plays an important role in the GFDM performance. The noise enhancement can be neglected when a RC filter with α = 0.1 is used and, in this case, the GFDM and OFDM SER curves match. For this reason, only the theoretical OFDM curve has been plotted in Figure 2.1.3.2(a). On the other hand, the GFDM SER performance is severely degraded due the noise enhancement when a RC filter with α = 0.9 is used. The prototype pulse shape must be properly chosen in order to avoid prohibitive performance loss due to noise enhancement. Figure 2.1.3.2(a) also shows that GFDM suffers a smaller performance penalty due to the CP insertion when compared with OFDM. The GFDM performance gain over OFDM is given by

C P C S

C P C S

( )1 0 lo g d B

M K N N

M K N N

. (2.1.3.4)

Hence, a large M must be chosen if spectrum efficiency is an important requirement in the system design. 2) Frequency-selective channel: A low SER performance over FSCs is an important requirement for multicarrier modulations. Following the block diagram presented in Figure 2.1.1.1, the signal at the input of the demapper when the ZF receiver is employed is given by

ˆ ,e q

d d w (2.1.3.5)

where

1

e q

Ww

H

B F

(2.1.3.6)

is the equivalent noise, W is the noise vector in the frequency domain, and H is the vector of the channel frequency response. The variance of the equivalent noise for the lth subcarrier can be evaluated from (18) and leads to

,

21

2 2 2 0

0

[ ]1,

[ ] 2

l m

M KR

l n l n l

k

G k N

M K H k

(2.1.3.7)

Where ,

[ ]l m

RG k is the frequency response of the filter for the lth subcarrier and mth subsymbol and

ξl is the corresponding NEF. Notice that σl2 is the same for every m. Therefore, the position of the

filter in the frequency domain changes the NEF because the channel frequency response is not flat for multipath channels. Hence, the GFDM SER over FSCs is given by

2

1 1

2

F S C

0 0

1 1 1( ) 2 e rfc e rfc ,

K K

l l

l l

Lp e

K K

(2.1.3.8)

where

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0

3· .

2 ( 2 1)

sT

l

l

ER

N

(2.1.3.9)

GFDM has M times more samples per subcarrier when compared to OFDM, which provides a higher spectrum resolution for equalization, allowing GFDM to better mitigate the frequency selectivity per subcarrier. Figure 2.1.3.2(b) compares the performance of GFDM and OFDM over FSC considering a channel delay profile with 16 taps that decay linearly in the logarithm scale from 0 dB to -10 dB. Again, GFDM uses the CP more efficiently when compared to OFDM. Notice that the channel delay profile leads to

a coherence bandwidth of c

/ 2 5 9s

fB and the bandwidth of each subcarrier is sc

/ 6 4s

fB ,

which means that this channel is frequency-selective per subcarrier. In this scenario, the larger number of samples per subcarriers allows GFDM to present a better performance than OFDM, as shown in Figure 2.1.3.2(b). In fact, even a GFDM system employing a RC filter with α = 0.9, which results in a large NEF, presents a SER performance similar to OFDM in this situation. 3) Time-variant channel: In a time-variant channel both instantaneous SNR and instantaneous SER are random variables. Thus, the average symbol error probability over a time-variant channels is an important tool to analyse the system performance. Consider that a time-variant channel can be modelled as multiplicative channel where the amplitude gain is a Rayleigh random variable with parameter σr and phase uniformly distributed between -π and π. It is assumed that the channel remains static during the transmission of one GFDM symbol. In this case, the GFDM SER follows the OFDM SER with the penalty of the noise enhancement when a ZF receiver is employed. It is important to notice that the NEF is constant for all subcarriers. Therefore, the SER of GFDM over time-variant channels is given by

2

T V C

11 1 4( ) 2 1 1 a tan

1 1

r r r

r r r

p e

(2.1.3.10)

where

2

0

3.

2 1

sr T

r

ER

N

(2.1.3.11)

Figure 2.1.3.2(c) shows the GFDM and OFDM SER performance assuming a Rayleigh channel with parameter σr

2 =1/2. Once again, we can observe that the NEF resulting from the chosen pulse shape is neglectable when compared with OFDM for α = 0.1. GFDM benefits from using only one CP for M subsymbols, which results in a better power and spectral efficiency. Closed-form solutions for the SER performance under AWGN of the matched filter receiver are available in [MMG+14]. The MF receiver outperforms the ZF receiver in low SNR regions due to the significant influence of the noise enhancement. However, since the MF receiver suffers from self-interference, it cannot reach the performance of the ZF approach at high SNR values. The MMSE receiver balances the noise enhancement and self-interference so that it converges to the MF receiver for low SNR and to the ZF receiver for high SNR regions. However, no closed form solutions for the SER in Rayleigh fading channels do exist. Simulated SER curves for the MMSE receiver are provided in [MKL+12].

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Figure 2.1.3.2: GFDM and OFDM SER performance in different channels

Figure 2.1.3.3: NEF and OOB for various GFDM filters. OOB radiation was measured with 6 guard carriers. The W-GFDM system uses a RC window with a ramp length of K∕4. The α increases in the direction of the arrows from 0 to 1 in steps

of 0.1.

Figure 2.1.3.3 shows the OOB radiation and NEF of different filters and different roll-off factors for W-GFDM and GS-GFDM assuming the system parameters presented in Table 2.1.3.1. The choice of the pulse shaping filter significantly influences the NEF and, in case of GS-GFDM, also the OOB radiation. For W-GFDM the OOB radiation is nearly independent of the employed filter. The NEF increases with the roll-off factor due to the wider overlapping of the subcarriers. The ZF receiver needs to put more effort into ICI cancellation which is bought for an increased NEF in the range from 0 dB for the Dirichlet filter up to3.5 dB for full roll-off RRC and 1st order Xia filters. The 4th order Xia filter shows the lowest NEF of 1.25 dB with full roll-off. However, for applications, the RC and 4th order Xia filter with lower α in the range of 0 ≤α ≤0.2 are preferable.

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2.1.4 MIMO-GFDM aiming diversity

Transmission diversity [Ala98] is a crucial feature for future wireless networks to achieve the required reliability and robustness under frequency-selective and time-variant channels. The block-structure of GFDM enables the application of time-reversal STC, which has been developed for single carrier systems to achieve diversity under frequency-selective channels [Dha01]. Figure 2.1.4.1 presents the block diagrams of the STC-GFDM transmitter and receiver.

Figure 2.1.4.1: Transceiver block diagram of the STC-GFDM.

In this approach, two data vectors 1

d and 2

d are independently modulated leading to

1 1 2 2an d .x d x d A A (2.1.4.1)

The modulated signals are delivered to the space-time encoder to produce the signals that will be transmitted by the two antennas in two successive time frames, which are presented in Table 2.1.4.1.

TABLE 2.1.4.1: STC signals.

Antenna 1 Antenna 2

Time frame 1 1 1 1

[ ] [ ]x n x n *

2 1 2[ ] [ m o d ( )]x n x n M K

Time frame 2 1 2 2

[ ] [ ]x n x n *

2 2 1[ ] [ m o d ( )]x n x n M K

A CP is appended to each signal before transmission. On the receiver side, the signals at the ith receiving antenna on time frames 1 and 2 are given by

1 1 1 1 2 2 1 1

2 1 1 2 2 2 2 2

i i i i

i i i i

y x x w

y x x w

h h

h h

(2.1.4.2)

where j i

h is the circulant matrix with the impulse response of the channel between the jth

transmitting antenna and the ith receiving antenna, and 1i

w and 2i

w are the noise vectors received

by ith receiving antenna in the time frames 1 and 2, respectively. It is assumed that the channel coherence time is larger than two GFDM symbols. The space-time maximum ratio combining is carried out in the frequency domain to achieve diversity. The combined signals in the frequency domain are given by

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1

* * * *

1 1 2 2 1 1 2 2

1 1

1 1 1

* * * *

1 1 2 2 1 1 2 2

1 1

* * * *

1 2 2 1 1 2 2 1

1 1

2 2

* * * *

1 1 2 2 1 1 2 2

1 1

ˆ

ˆ

I I

i i i i i i i i

i i

e qI I

i i i i i i i i

i i

I I

i i i i i i i i

i i

I I

i i i i i i i i

i i

Y Y W W

X X X W

Y Y W W

X X

H H H H

H H H H H H H H

H H H H

H H H H H H H H

22 e q

X W

(2.1.4.3)

where I is the number of receiving antennas, 1

ji ji

H F h F and

1iY and

2iY are the discrete Fourier

transform of 1i

y and 2i

y , respectively.

The estimated data vectors can be obtained from the combined signals presented in (2.1.4.2), therefore

1ˆ ˆ.

j jd X

B F (2.1.4.4)

Figure 2.1.4.2 compares the SER performance of classical STC-OFDM [LW00] with STC-GFDM considering the system parameters from Table 2.1.3.1 and the frequency selective channel delay profile from Section 2.1.3. However, each tap of the channel impulse response is multiplied by a Rayleigh random variable with parameter σr

2 =1/2. Also, the total transmitting power is kept constant, which means that each antenna transmits with half of the available power. Two transmitting antennas and two receiving antennas have been used in this simulation. Figure 2.1.4.2 shows that STC-GFDM and STC-OFDM have the same diversity gain. In a system setup, α shall be chosen small because the NEF can be neglected. Again, STC-GFDM uses the CP more efficiently which leads to a better performance than STC-OFDM when small α is used. The NEF becomes significant for high values of α, resulting in a performance loss. Nevertheless, the diversity gain of 2I is achieved by STC-GFDM for both transmit pulses analyzed in this section

Figure 2.1.4.2: SER performance of the 2x2 STC-OFDM and STC-GFDM under frequency-selective and time-variant channel.

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2.1.5 Synchronization

Synchronization is a key element in the performance of the signal processing carried out on receivers and can be achieved in GFDM on a block basis. The block structure with its CP allows adaptation of fundamental OFDM solutions to estimate symbol time offset (STO) and carrier frequency offset (CFO) [BSB97] [SC97], but low OOB is a factor to be considered. The algorithm proposed in [AKE08] will be evaluated in this section to achieve one-shot synchronization using a straightforward proposal of a separated W-GFDM preamble, which is defined

with M = 2 and the transmitted data in the kth subcarriers of both subsymbols , 0k

d and ,1k

d are

filled with the same pseudo-noise (PN) sequence, resulting in a signal composed with two identical halves. Low OOB is obtained by pinching the block boundary and Figure 2.1.5.1 illustrates this configuration, where a W-GFDM preamble precedes another W-GFDM, containing only data, and forms a burst with

a double pinching pattern. As described in the Sec. III, different pinching lengths W p

N and W d

N can

be applied respectively to the preamble and data blocks in order to achieve a desired emission mask.

Figure 2.1.5.1: W-GFDM preamble preceding a W-GFDM data block.

Given that r[n] is a set of received samples containing at least one complete W-GFDM preamble, the two identical halves are identified with an autocorrelation metric integrated along the CP and CS length to remove plateau effects [SC97] [MZB00], leading to

C P

0 1*

0

[ ] .2

N

N k

Nn r n k r n k

(2.1.5.1)

The argument that maximizes the absolute value of the metric μ[n] is taken as a coarse STO

cˆ a rg m a x | [ ] |,

n

n n (2.1.5.2)

while the angle of cˆ[ ]n is used to estimate the CFO as given bellow

cˆ[ ]

ˆ .n

ò (2.1.5.3)

The value ò is employed to correct the CFO in the received sequence and a cross-correlation operation is then explored as

ˆ12 ( )

*

0

1[ ] [ ] [ ] ,

Nj n k

N

k

c n r n k e p kN

ò

(2.1.5.4)

where [ ]p k represents the known GFDM preamble.

To suppress side peaks that arise from the two halves and the CP and CS parts, c[n] is combined with μ[n] and an optimized estimation of the STO is obtained by searching the peak value in the

range around the coarse STO estimation c cˆ ˆ/ 2 , / 2n N n N that is

oˆ arg m ax | [ ] || [ ] | .

n

n c n n (2.1.5.5)

This synchronization procedure is robust for single path channels, but in a time-variant FSC, the primary echo can be lower than other echoes and the strongest peak will not represent the correct

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STO. Thus, an additional search before o

n can reveal if there is another yet undetected peak to be

considered as the primary one. For samples that do not belong to the preamble, the output of the cross-correlation can be interpreted as a complex gaussian random sequence and a threshold criteria, depending on an acceptable probability of false alarm pFA, can reveal the presence of

multipaths before o

n .

Considering that the first peak of (2.1.5.4) is within the range o oˆ ˆ( , ]n n , where λ < NCP is an

adjustable parameter, the threshold is defined as

T h F A o

2

4 1ˆln ( ) | [ ] |

22

Nk

T p c n kN

(2.1.5.6)

and the fine STO estimation for the first multipath is finally given by

o o

T h

ˆ ˆ

ˆ a rg firs t | [ ] | .f

n n n

n c n T

(2.1.5.7)

The performance evaluation in terms of variance of normalized STO and CFO estimations is presented in Figure 2.1.5.2 for the W-GFDM preamble following the parameters presented in Table 2.1.3.1 but with M = 2. A wRC[n] window function with NW = 16 is used, λ = 16, pFA = 10-4 and the FSC is set as described in Section 2.1.3. For a SNR range higher than 5 dB the variance of the STO estimation stabilizes within tenths of a sample due the time variant fading effect in the multipath channel. The variance of the CFO estimation starts from thousandths of the subcarrier bandwidth and gets linearly better (in log scale) with increasing SNR. The results obtained with the double pinching configuration shows that burst synchronization can be achieved without penalties when compared to the performance range presented in [AKE08] and without increasing the OOB emission. More advanced schemes can be reached in future investigations combining the subsymbols and the CP to form special pilot sequences, allowing the construction of embedded synchronization sequence in the GFDM block.

Figure 2.1.5.2: Performance evaluation of variance of the fine STO estimation 𝒏𝒇 and CFO estimation �� for the GFDM

preamble in a multipath channel

2.1.6 Advanced receivers

In this section, the previously presented basic matched filter approach is extended by successive interference cancellation (SIC), yielding the MF-SIC receiver. We investigate its performance compared to the ZF receiver in terms of bit error rates (BER) in a setup with error control coding. Although ZF can severely enhance the noise in the system, it can be a reasonable alternative to the iterative approach in some cases, mainly when small values of α and M are employed.

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A non-orthogonal waveform like GFDM inherently introduces correlation across all subcarriers and

subsymbols within a block, which can result in unwanted self-interference among the elements of d , when the MF receiver is employed. Supposed is the iteration index, the main idea is to first detect

all data symbols ( )

d , 0 , based on the received signal z . In the first iteration 1 , these are

then fed back to calculate a cancellation signal ( ) ( 1 )

, , ,

ˆk m k m k m

u d g d

A for each pair of (k,m), which

is based on all but the (k,m)th element of ( 1 )

d

. The received signal is partially cleaned of

interference, producing ( ) ( )

, ,k m k mz z u . Lastly, the (k,m)th data symbol is detected again to obtain

( )d . The th iteration is complete once all pairs of (k,m) are run through. The total number of SIC

iterations shall be denoted by S IC

J .

This method has been shown to be effective, even for high order of QAM mapping [GMC+13]. However, for large K and M this can significantly increase the computational complexity of the receiver. In that case, using a Nyquist filter allows to elimininate self-intersymbol-interference and thus requires to iterate only through the subcarriers in the system. Another option is to define a

threshold for , ,

,H

k m k mg g

with k≠k′ and m≠m′, below which

', 'k md is considered not to have

influence on ,

ˆk m

d .

Additionally, an interesting question is, to what degree can coding help to overcome the impairments of the non-orthogonal waveform. To investigate this, encoder and decoder are introduced in the

transmission chain. The parallel concatenated convolutional code (PC-CC) from [TGP] with 1 / 3R

is considered for this section. On the receiver side, a turbo decoder [BGT93] with T D

J iterations is

employed. In the following, the two configurations depicted in Figure 2.1.6.1 shall be considered. In the first setup, a ZF receiver is utilized in combination with the turbo decoder, while in the second setup MF with several SIC iterations is employed prior to decoding. As a reference, an orthogonal SC-FDM transmission is used. The performance is compared in terms of bit error rates in AWGN, frequency-selective and time-variant channels and the configuration of the GFDM system is based on Table 2.1.3.1. Results can be found in Figure 2.1.6.2.

(a) ZF receiver configuration

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(b) MF-SIC receiver configuration

Figure 2.1.6.1: The considered receiver configurations.

The main objective here is to evaluate the penalty of using a non-orthogonal waveform. Generally, when the transmit filter exhibits little self-interference (α = 0.1), for either of MF and ZF, the PC-CC alone is able to close the gap to the orthogonal system. In a situation where the interference becomes severe (α = 0.9), MF and ZF can strongly deviate from the performance of the orthogonal system. Looking at the AWGN case, noise enhancement appears to have a more severe impact than

the self-interference as MF outperforms ZF. However, with increasing 0

/b

E N in the frequency

selective channel, the MF can only outperform the ZF, when combined with SIC. This behavior is similar in the time-variant channel, however here a waterfall region is absent. Overall, it can be concluded that when operating with little self-interference, ZF should be favored as ZF and MF-SIC show nearly identical performance, but ZF does not the entail the complexity overhead of the SIC iterations. When self-interference is severe, MF-SIC outperforms at the cost of more computational effort.

Figure 2.1.6.2: BER simulation results for a coded system with JTD = 10 and JSIC = 1.

2.1.7 Application requirements and Frame Design

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New scenarios are being foreseen for 5G networks with requirements that cannot be addressed only with throughput increment. The waveform must be flexible enough to address the following scenarios: 1) Bitpipe communication: Currently broadcasting services are experiencing a media shift, where television and radio content are being delivered to the public through Internet protocol. People demand their favorite shows anywhere and smartphones and tablets are major platforms to access these contents. With resolutions on mobile devices beyond high definition, videos and 3D contends will require several tens of Mbps to achieve a good Quality of Experience (QoE). Therefore, next generation networks must rely on advanced digital communication techniques, such as MIMO [Big10] for diversity and multiplexing, highly efficient channel coding, small cell coverage with inter-cell interference management and efficient dynamic spectrum allocation. For waveform engineering, low out-of-band emission is a crucial requirement to allow fragmented and opportunistic spectrum allocation with cognitive radios (CR) [LCL+11]. Orthogonal Frequency Division Multiplexing (OFDM) [Bin90] with -35 dBc OOB emissions will hardly be able to attend the emission mask without additional filtering, which renders the deployment of OFDM questionable in the next generation standards. 2) IoT: Objects are becoming equipped with sensors and increasingly gain the ability to communicate without human interaction. The market and application for IoT is not clear defined yet, but this is being considered one of the biggest breakthrough applications for future wireless networks. There are two major markets foreseen for IoT. The first considers the "Things" as complete systems with only an interface that allows for controlling it using the Internet. The other considers the "Things" as sensors and actuators and all the control system is moved to the cloud. Although the first approach can be implemented shortly, the second one is being seen as the most interesting for large corporations because the more capillarity connected sensors will provide accurate information for Big Data processing, allowing for pattern identification and service offers according with these patterns. Consider a scenario, where sensors are spread out in an environment measuring low time-variant parameters and send the information to a central server. These sensors are typically low cost devices with limited power source, but require a lifetime of several years. The duty cycle is very low, throughput and latency represent less important requirements, while power saving is mandatory. If IoT devices connect to today’s cellular networks, they cannot pass through all the synchronization steps, because this process would consume a large amount of energy. IoT devices must be able to achieve reliable communication with a loose synchronization or even asynchronous. Cyclic prefix and suffix can be used to allow for loose time domain synchronization in a random access channel. OFDM cannot use this solution efficiently since it requires one CP and CS per symbol. 3) Tactile Internet: This is a new application scenario, first envisioned in [Fet14], where the 5G network is used for real-time control applications with at most 1 ms round-trip latency requirements. The low latency requirement is determined by the typical interaction latency for tactile steering and control of real and virtual objects. In fact, most of today’s mobile devices use a touch screen as input interface and future devices will integrate various interfaces for haptic, visual and auditory input and feedback. These new interface devices are also going to be used to interact with the online environment for virtual and augmented reality, health monitoring, smart house controlling, gaming and many different applications. If too large, the round-trip delays between the command insertion, the action in the online environment and the feedback can result in a poor QoE or even cybersickness. Since the overall round-trip system delay cannot be larger than 1 ms, the time budget for the physical layer will be of no more than hundreds of μs. The current frame structure of Long Term Evolution (LTE), based on 70 μs OFDM symbols, has a latency that is at least one order of magnitude above the target for the Tactile Internet.

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4) WRAN: Despite the fact that reasonable Internet access is available in cities, sparsely populated areas suffer from low data rate and unreliable solutions. Wired technologies have limited coverage. Today’s wireless networks have relatively small cell size and operate in licensed frequencies, which makes them economical unfeasible in low populated areas. CR technology addresses this problem by dynamically and opportunistically accessing vacant UHF TV bands. When using OFDM as the air interface, it is a challenge to attend the emission mask imposed by spectrum regulation. Besides this, large cell coverage leads to high delay spread and the conventional OFDM with a CP for every symbol will result in a low spectral efficiency. The next generation network shall address large coverage areas using dynamic channel allocation based on CR with low OOB emissions and efficiently deal with the multipath effects by reducing the impact of the CP in the overall data rate. GFDM flexibility can address the requirements of these application scenarios by configuring the number of subcarriers and subsymbols. However, the channel characteristics, such as coherence

time (c

T ) and coherence bandwidth (c

B ), impose a general restriction to the number of subsymbols

and subcarriers. The coherence time defines an upper boundary for MK, while the coherence bandwidth defines a lower boundary. In other words,

s

c s(1 ) ,

c

RM K T R

B (2.1.7.1)

where Rs is the overall symbol rate. Different approaches can be used to establish the adequate values of K and M based on these restrictions and the scenario requirements. Table 2.1.7.1 present the typical channel parameters and a suggested GFDM configuration for the scenarios described in this section.

TABLE 2.1.7.1: Channel and system parameters for the different scenarios.

Parameters Bitpipe Tactile Internet IoT WRAN

Cell size [km] 4 1 4 100 Delay Spread [μs] 5 1 5 50

cB [kHz] 40 200 40 4 Doppler shift [Hz] 100 10 100 10

cT [ms] 5 50 5 50

Subcarriers K 20,1,2,...,8 64 or 128 1 20,1,...,4 Subsymbols M 1023 ... 5 5 7 1023 ... 127 Receiver type MF-SIC ZF ZF MF-SIC

C PT 7 2 7 80 Symbol duration [μs] ≤5000 ≈ 5 ≈ 500 ≤ 50000 Modulation order 2, 4, 6 or 8 2 or 4 2 2, 4, 6 or 8

WB [MHz] 20 100 (fragmented) 1 5, 10 or 20

Bitpipe communication demands high throughput and high spectrum efficiency. A large M can reduce the impact of the CP length in the overall throughput. Small cell size combined with Coordianted Multipoint transmission [LKL+12] can increase the spectrum re-use without increasing the interference between cells.

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Low latency is the major requirement for Tactile Internet. Short signal duration with large bandwidth can be used to reduce the impact of the PHY layer in the overall system latency, therefore a small MK product is mandatory. The main requirement for the IoT devices is low energy consumption. Throughput is not an important demand, since the device’s duty cycles are low. It means that the Peak to Average Power Ratio (PAPR) [RM13] must be as low as possible allowing a more efficient use of the power amplifiers. The number of subcarriers cannot be high, unless some PAPR reduction technique is employed. Also, energy cannot be wasted on tight synchronization procedures, which means that the devices must be loosely synchronized with the network. Therefore, random access [BMA11] with tolerable timing misalignment shall be allowed. A larger CP (and CS) can loose the time synchronization for multiuser without decreasing the system performance [VWS+13]. Figure 2.1.7.1

illustrates how one LTE resource block could be organized using GFDM to provide a CP and a CS large enough to accommodate timing misalignment. Notice that GFDM is able to increase the size of the CP and introduce a CS without consuming further resources when compared with the LTE approach. WRAN requires large cell sizes, which leads to spread out channel delay profiles. Thus, a long CP is requested to avoid ISI. On the other hand, the user terminals are typically static and Doppler effect plays a small role in this scenario. Slow time-variant channels allow for large M and CP and CS can be efficiently used to avoid ISI.

Figure 2.1.7.1: GFDM and OFDM frame comparison for the IoT scenario.

2.1.8 Summary for GFDM

A novel modulation proposal for a 5G physical layer needs to address the specific requirements. GFDM has been introduced as a candidate waveform modulation scheme for the air interface of 5G networks. It has been shown how the modulation scheme can address the requirements imposed by the different scenarios with a flexible block structure and subcarrier filtering and a suitable parameter configurations for these envisioned application scenarios has been presented. Various configurations with which the error rate performance is not compromised when compared to OFDM and SC-FDE have been found and MIMO has been presented as a mean to obtain diversity in the system. Synchronization was achieved without affecting the spectral properties of the waveform. Certainly, many more issues still need to be resolved. Nevertheless, GFDM is a novel modulation technology with the potential to fulfil the requirements of the next generation of mobile wireless networks.

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2.2 UFMC & IDMA

2.2.1 UFMC principles and frame structure aspects

UFMC is a multi-carrier signal format with orthogonal subcarriers, which can deal very well with loss of orthogonality at the receiver side, e.g. introduced by timing and frequency misalignments [VWS+13]. This is due to improved spectral properties over OFDM. Figure 2.2.1.1 shows the transceiver block diagram with the receiver applying FFT based detection (for the sake of simplicity we leave out the time index).

Figure 2.2.1.1: UFMC transceiver architecture (UL).

Compared to OFDM, additional per sub-band filters are introduced, reducing the spectral side-lobe levels outside this sub-band. This will increase the robustness against any sources of inter-carrier interference and improve the suitability for fragmented spectrum. Related to the Unified Frame Structure vision of 5GNOW, introduced in [D3.1] and [D4.1], those UFMC properties open up the possibilities to handle synchronous traffic and transmissions with relaxed synchronicity within the same band in neighbored frequencies. Note that relaxed synchronicity does not necessarily mean completely asynchronous, as an open-loop synchronization based on downlink signals is always possible, see section 2.2.3 on the concept of Autonomous Timing Advance (ATA). Compared to OFDM, the cyclic prefix is dropped and its additional symbol duration overhead is used to introduce sub-band filters. Note that those filters are much shorter than the per-subcarrier filters of an FBMC system – UFMC filters are in the order of an OFDM cyclic prefix. This property also improves the suitability for communicating in short bursts, compared to FBMC [SWC14].

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So, UFMC can, roughly speaking, be interpreted as a generalization of FBMC and filtered OFDM (though, being more closely related to the latter) [SW14]. The transmit signal can be mathematically described as follows: The time-domain transmit vector xk for a particular multi-carrier symbol of user k is the superposition of the sub-band-wise filtered components, with filter length L and FFT length N:

B

i n

ik

nN

ik

NLN

ik

LN

k

ii1 1)1(1)1(

sVFx (2.2.1.1)

For each of the B sub-bands, indexed i, the ni complex QAM symbols collected in the transmit vector sik are transformed to time-domain by the IDFT-matrix Vik with dimensions [N×ni]. Vik includes the relevant columns of the inverse Fourier matrix according to the respective sub-band position within the overall available frequency range. Fik is a Toeplitz matrix with dimensions [(N+L-1)xN], composed of the filter impulse response, performing the linear convolution. At the receiver side, while OFDM discards the cyclic prefix and thus processes just N samples in an FFT, UFMC uses the multi-carrier symbol duration of N+L-1 samples. Thus, for an FFT-based processing, N-L+1 zeros have to be appended to reach the next larger power of 2. Then a 2N-point FFT can be executed. Each second output can be discarded, containing frequency points in between subcarriers. The remaining N outputs contain the demodulated subcarriers. Those frequency domain complex symbols now can be processed, using all available knowledge from OFDM. Note that UFMC is able to operate with QAM-modulation which allows to use all processing techniques e.g. known from MIMO, while FBMC with offset-QAM is not that straightforward. Before performing the FFT, the received time-domain signal can be weighted with a window wm, e.g. with raised-cosine shape, corresponding to the areas A, B and C in figure 2.2.1.2:

1,12

12

12

cos12

1

2,

21

12

,0

12

cos12

1

NLNL

mL

LNm

NLL

m

Lm

L

m

wm

(2.2.1.2)

The following figure depicts an example for this window with N = 1024 and L = 80:

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Figure 2.2.1.2: Example time domain window (N = 1024, L = 80).

Two impacts are expected:

Windowing in time corresponds to a convolution in frequency domain, so the subcarriers of

the user of interest are broadened accordingly, introducing self-interference.

Out-of-band emissions of the interfering user within the passband of the user of interest are

attenuated.

So when applying the window, with a high degree of synchronization the overall interference is worsened due to self-interference of the user of interest, due to loss of orthogonality between subcarriers. However, with relaxed time synchronicity the reduction of the inter-traffic interference is dominating, resulting in an overall improved performance as shown in section 2.2.4. The FFT-based processing in Figure 2.2.1.1 is a much less complex solution than the time-domain-based approaches which have been discussed in [D3.1]. Frame Structure Aspects UFMC has been designed in order to enable the unified frame structure concept, depicted in [D3.1], for supporting multiple service and device classes within a single radio frame. As mentioned above UFMC supports a traffic mix of synchronous users and users with relaxed synchronicity. Pilot resource elements may either be superimposed or can be based on classical inserted pilots. Even the LTE-based pilot structure, depicted in Figure 2.2.2.1, can be reused in conjunction with UFMC.

2.2.2 Synchronization, channel estimation and equalization

Note that UFMC is per se orthogonal in the complex-valued subcarrier domain and fully supports QAM modulation and efficient frequency domain processing. This allows to re-use all the vast knowledge gained from OFDM, as UFMC has a lot of similarities to OFDM (in fact classical OFDM is a variant of UFMC with filter length L = 1). Constant amplitude zero auto-correlation (CAZAC) sequences, like Zadoff-Chu sequences are used already in the LTE system [3GPPTS36.211]. The CAZAC property brings along a lot of advantages for synchronization, timing offset estimation and channel estimation. Note that CAZAC sequences are complex-valued and thus cannot be used in FBMC-OQAM without losing their important properties. It is suggested to use CAZAC-sequences in the UFMC uplink.

0 200 400 600 800 1000 12000

0.2

0.4

0.6

0.8

1

RC shaped window, N=1024, L=80

Time index m

wm

A

B

C

A: ramp up area

B: main body of pulse

C: ramp down area

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su

bca

rrie

r

OFDM symbol

1 PRB

Pilot Symbol Data Symbol

15

kH

z

1/14 ms

Slot 0 Slot 1

Subframe

Figure 2.2.2.1: Uplink pilot pattern of LTE can be reused for UFMC.

The inserted pilot symbols, as shown in Figure 2.2.2.1, can carry CAZAC sequences which can be used for all synchronization and timing offset estimation purposes due to their advantageous auto-correlation properties. UFMC channel estimation can be executed in the frequency domain. After the FFT, scalar per-subcarrier processing in the frequency domain can be done, which is low complex and can build upon OFDM knowledge. Looking at a particular subcarrier n, in (2.2.2.1) we obtain

(n)YnFnHnSsingleFDCTFPilot

)()(ˆ)( . (2.2.2.1)

So a raw channel estimate for a single resource element can be computed based on the known pilot symbol SPilot(n), known filter frequency response FFD(n) and observed subcarrier received value Ysingle(n) as :

(n)YnFnSnHsingleFDPilotCTF

)()()(ˆ (2.2.2.2)

Compared to OFDM, the impact of the filtering is additionally taken into account. After having achieved the raw channel estimate (2.2.2.2), every subsequent processing, as known from OFDM can be applied. E.g. two-dimensional Wiener filtering in time- and frequency dimension will be identical to OFDM [WNB13]. Using the estimated channel, a per-subcarrier scalar equalizer can be applied, performing an element-wise multiplication of equalizing vector q and frequency response vector Ysingle

singleYqs ˆ (2.2.2.3)

where the circular symbol represents the Hadamard-product, carring out the element-wise multiplication. The equalizing vector takes care for all phase rotations caused by the frequency responses of the respective per-subcarrier filters, including the filter delay phase shifts, as well as the frequency response of the channel HCTF, the so-called channel transfer function. Note that this equalization is similar to OFDM (with additional compensation of the filter). A note on inter-symbol interference (ISI): OFDM, due to cyclic prefix (CP), has a protection against ISI, as long as the delay spreads and timing offsets do not exceed the length of the CP. UFMC has a soft-protection against ISI: As the filtered multi-carrier symbols are non-overlapping, the beginning and end of the multi-carrier symbol, due to the convolution with the sub-band filter, starts with zero

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power. So there is a filter ramp-up and –down which attenuates any ISI caused by delay spreads. This property allows UFMC for low and medium delay spreads to operate with the symbol-wise processing as the ISI is still negligible. For pathological ultra-high-delay spread cases, further research has to be made, e.g. regarding multi-tap equalizers for UFMC.

2.2.3 Support of Autonomous Timing Advance

As outlined in general by 5GNOW, today’s cellular networks, like LTE, operate strictly synchronous, at least within each cell. A device wanting to transmit a few bits of data has to enter the network via the random access procedure. This includes an ongoing closed-loop timing advance control. The 5th generation of wireless systems, in order to support the upcoming internet of things, will include a large fraction of machine-initiated communication. We will have a large number of devices, where many of them only have sporadic traffic. In this case, the extensive random access procedures, like in LTE, generate a painful signaling overhead. Furthermore, existing closed-loop time synchronization consumes a notable amount of energy. This shortens the battery life time of e.g. cheap sensors. On the other hand, completely giving up time alignment of signals is also not efficient. A simple example [R75]: Slotted Aloha is by a factor of 2 more spectrally efficient than pure Aloha (completely asynchronous). Furthermore, in cellular systems, due to transmission of synchronization and pilot signals, there is already some timing information available. The only unknown here is the propagation delay of the channel. Our vision here is to use open-loop synchronization for devices which just have sporadic MTC traffic (type III and IV in the Unified Frame Structure). Furthermore open-loop synchronization may also be used for scheduled access (type II traffic) for energy and overhead saving reasons, multi-cell scenarios applying UL CoMP mechanisms and in the light of user-centric instead of cell-centric networking [BAD12]. The device listens to the downlink and synchronizes itself coarsely. Here, the usage of a multi-carrier waveform helps: The division of the available bandwidth into smaller chunks (sub-carriers) generates comparatively long symbols, improving robustness against delay spread but also against timing misalignments. The symbol duration can be designed such that the misalignments are just fractions of the multi-carrier symbols. Furthermore, the devices may apply some autonomously derived timing advance. This we call Autonomous Timing Advance (ATA). Two variants of ATA are possible.

On the one hand the single devices may estimate the round trip time their signals are

suffering (e.g. based upon GPS data or making use of pathloss estimations) and apply a

respective timing advance. When doing so, performance of the respective transmission is

improved.

Another simpler variant is for all type II/III devices to apply the same timing advance NOL,max/2

with NOL,max being the highest round trip time appearing within the cell (or alternatively e.g.

the 95%-tile of all existing round trip times). When using this technique, inter-traffic

interference at the frequency borders is reduced (in a later section results for the second

variant will be presented). Various means are available for the devices in order to get

knowledge on NOL,max. The most simple one is for the basestation to broadcast the value

based on measurements (e.g. during closed-loop synchronization of type I devices).

The performance for UFMC with ATA is discussed in the next section.

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2.2.4 Performance in scenarios with relaxed synchronism

As outlined earlier the inclusion of massive machine traffic (MMC) and the support of multi-point transmissions (e.g. in the frame work of user-specific networking [BAD12]) can prevent a 5G system from working as tightly synchronized as with LTE and LTE advanced. For once the intense time, energy and transmission resource consuming closed loop procedure applied in LTE and LTE advanced for achieving a tight synchronisation between user transmissions is unfeasible for low-end MMC devices. Secondly, when devices are attached to multiple transmission points, it is impossible for them to be synchronized to all of them, as typically the respective round trip delays are different. With users being less tightly synchronized, multi-user interference occurs between users being located adjacent in frequency in uplink. In the following we compare a system applying CP-OFDM with a system applying UFMC in this respect. Let’s assume a cut out of the multi-service frame presented earlier (unified frame structure):

Figure 2.2.4.1: Multi-user scenario (FDMA).

Figure 2.2.4.1 depicts 3 user bursts being placed at the edge between type I transmissions (i.e. transmissions tightly synchronized via the closed loop procedure) and type II or type III transmissions (i.e. synchronized via open-loop mechanisms). The burst depicted in blue is perfectly time and frequency aligned, while the bursts depicted in orange potentially are impaired by timing and frequency offsets. Two major impacts are observable:

1. For the detection of type II and III transmissions more sophisticated mechanisms may be required (depending on the actual magnitude of the offsets) at the base station to achieve signal reception with high quality (e.g. phase compensation, interference suppression ...).

2. Multi-user interference occurs: A. Inter-traffic interference: distortions from type II/III transmissions to type I

transmissions B. Intra-traffic interference: distortions between type II/III transmissions

In the following we concentrate on the second distortion. More sophisticated receiver concepts are future work.

frequencyoffset

timingoffset

Type I burst,closed-loop synched

Type II/III burst, open-loop synched

Type II/III burst, open-loop synched

time

frequency

D3.2


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We start with evaluating the mean squared error (in dB) the user of interest is suffering (interference power) due to an adjacent user being delayed relative to the user of interest (no channel). The system settings are as follows:

Table 2.2.4.1: Simulation settings

Simulation Parameter Value

Subcarriers per sub-band 12

FFT size (N) 1024

No. of allocated sub-bands, (user of interest/interfering user)

3/9, adjacent in frequency

Filter type Dolph-Chebyshev with 40 dB sidelobe attenuation

UFMC filter length L OFDM CP length LCP

[80, 90, 100] 79

Carrier Frequency Offset (CFO) in subcarrier spacings

[0, 0.05, 0.1]

Number of frequency guards [0, 1, 2, 5] subcarriers

Receiver type FFT based w/ and w/o time domain windowing (for UFMC)

Power control ideal, i.e. all transmissions arrive at the base station with unit energy

The following figures 2.2.4.2 – 2.2.4.7 depict the mean squared error (in dB) the user of interest is suffering due to an adjacent user being delayed relative to the user of interest (x-axis) for various system settings (black curves: CP-OFDM , blue/red/green curves: UFMC).

Figure 2.2.4.2: Interference power depending on the timing offset, no CFO, no time domain windowing (black: OFDM, blue/red/green: UFMC).

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

-36

-34

-32

-30

-28

-26

-24

-22

-20

-18OFDM vs. UFMC, no CFO, no windowing

Ndelay

/N

MS

E [

dB

]

continuous: no guards

dashed: 1 subcarrier as guard

dotted: 2 subcarriers as guard

dash-dotted: 5 subcarriers as guard

L = 80

L = 90

L = 100

LCP

= 79

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Page: 36 of 100

Figure 2.2.4.3: Interference power depending on the timing offset, no CFO, RC shaped time domain windowing (black: OFDM, blue/red/green: UFMC).

Figure 2.2.4.4: Interference power depending on the timing offset, 5% CFO, no time domain windowing (black: OFDM, blue/red/green: UFMC).

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

-36

-34

-32

-30

-28

-26

-24

-22

-20

-18OFDM vs. UFMC, no CFO, RC shaped windowing (for UFMC)

Ndelay

/N

MS

E [

dB

]





L = 80

L = 90

L = 100

LCP

= 79

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

-36

-34

-32

-30

-28

-26

-24

-22

-20

-18OFDM vs. UFMC, CFO 5%, no windowing

Ndelay

/N

MS

E [

dB

]





L = 80

L = 90

L = 100

LCP

= 79

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Page: 37 of 100

Figure 2.2.4.5: Interference power depending on the timing offset, 5% CFO, RC shaped time domain windowing (black: OFDM, blue/red/green: UFMC).

Figure 2.2.4.6: Interference power depending on the timing offset, 10% CFO, no time domain windowing (black: OFDM, blue/red/green: UFMC).

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

-36

-34

-32

-30

-28

-26

-24

-22

-20

-18OFDM vs. UFMC, CFO 5%, RC shaped windowing (for UFMC)

Ndelay

/N

MS

E [

dB

]





L = 80

L = 90

L = 100

LCP

= 79

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

-36

-34

-32

-30

-28

-26

-24

-22

-20

-18OFDM vs. UFMC, CFO 10%, no windowing

Ndelay

/N

MS

E [

dB

]





L = 80

L = 90

L = 100

LCP

= 79

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Page: 38 of 100

Figure 2.2.4.7: Interference power depending on the timing offset, 10% CFO, RC shaped time domain windowing (black: OFDM, blue/red/green: UFMC).

Obviously, UFMC outperforms CP-OFDM as soon as the cyclic prefix is exceeded. Additionally, UFMC is less susceptible to CFO. To transport the results given so far into a more tangible setting describing an actual cellular use case, we evaluate in the following the mean squared error a user of interest is suffering in average with the interfering user being delayed randomly between Nmin and Nmax. By doing so, we model the type II/III device being placed randomly within the cell. To evaluate the average distortion due to inter-traffic interference, we have to apply the following metric:

max

min

N

NN

N

N

NpE

delay

delay

delay

interMSEMSE (2.2.4.1)

Ndelay is the actual delay of the interfering user relative to the detection window, pNdelay is the probability density of the respective delays to occur within a given cellular setting (more on that later) and MSE(Ndelay/N) are the measurements given within the figures above. If no ATA is applied Nmin = 0 and Nmax = NOL,max (NOL,max is the highest occurring delay related to the highest occurring round trip time) holds, if type 2 ATA is applied with NTA = 0.5NOL,max, we have Nmin = -0.5NOL,max and Nmax = +0.5NOL,max. To determine pNdelay, we assume a single cell being a sector of a circle with radius Rmax and opening angle α, as shown in figure 2.2.4.8.

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

-36

-34

-32

-30

-28

-26

-24

-22

-20

-18OFDM vs. UFMC, CFO 10%, RC shaped windowing (for UFMC)

Ndelay

/N

MS

E [

dB

]





L = 80

L = 90

L = 100

LCP

= 79

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Page: 39 of 100

Figure 2.2.4.8: Cell shape.

Assuming potential placements of type II/III devices being uniformly distributed within the cell, we are able to derive the probability density function (PDF) pr of the distance of these placements to the base station: The PDF we are looking for is proportional to the arc of the circle at distance r:

rrp

rp

r

r

0

(2.2.4.2)

To calculate the proportionality coefficient r0, we make use of the fact, that the integral of any PDF over its whole range equals 1:

2

max

0

2

max0

0

2

0

0

0

0

2

122

maxmaxmax

Rr

Rrrrrdrrdrp

RRR

r

(2.2.4.3)

So, we get:

otherwise

with

0

,022

max2

max

2

max

RrR

r

R

r

pr

(2.2.4.4)

Figure 2.2.4.9 depicts the shape of this PDF.

Rmaxα

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Figure 2.2.4.9: PDF pr of a device to have distance r to the basestation.

Ultimately, we are interested in the PDF of the occurring delays Ndelay (pndelay). For simplicity we assume a linear relation between the distance of the device and the delay of its transmission at the basestation. This perfectly holds true, if we assume

1. the nodes to be able to perfectly synchronise themselves to the downlink synchronization signal (i.e. perfect synch. at the device antennas is achieved)

2. line-of-sight transmissions. If the first point does not hold, the actual delay inhibits an additional jitter due to estimation errors. If the second point does not hold, the actual behaviour may be slightly deformed, as the effective de-routing factor due to non-line-of-sight transmission may depend on the actual position of the device. Assuming 1 and 2 are true, we get:

rNpp

delay (2.2.4.5)

The following figures 2.2.4.10 - 2.2.4.12 depict the average distortion the user of interest (type I device) is suffering under the assumptions given above and with various system settings (0%, 5% and 10% CFO; w/ Type 2 ATA applying NTA=0.5NOL,max, w/ and w/o time domain windowing, FFT based detection).

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5

3

r/Rmax

pr

cell edge

cell center

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Figure 2.2.4.10: Inter-traffic interference, no CFO.

Figure 2.2.4.11: Inter-traffic interference, 5% CFO.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2-35

-30

-25

-20

NOL,max

/N

E[M

SE

inte

r] [d

B]

OFDM vs. UFMC, no CFO, w/ type 2 ATA applying NTA

=0.5NOL,max

OFDM, LCP

=79

L = 80, no Guards

L = 80, 1 Subc. Guard

L = 80, 2 Subc. Guards


blue: UFMC w/ RC shaped windowing

red: UFMC w/o windowing

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2-35

-30

-25

-20

NOL,max

/N

E[M

SE

inte

r] [d

B]

OFDM vs. UFMC, 5% CFO, w/ type 2 ATA applying NTA

=0.5NOL,max

OFDM, LCP

=79

L = 80, no Guards






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Figure 2.2.4.12: Inter-traffic interference, 10% CFO.

UFMC is able to outperform CP-OFDM significantly. Especially, the use of ATA type 2 and the application of time domain windowing (for NOL,max being above 10% of the overall symbol duration) is recommended. Key take-away is the fact that UFMC is able to support both close-loop synchronized traffic (e.g. smart phone traffic) and open-loop synchronized traffic (e.g. low-cost MMC transmissions) within a single frame more efficiently than OFDM and with negligible distortions enabling a highly scalable system. Taking the shape of pNdelay into account it becomes obvious, that the higher delays (before ATA) are more often occurring than the lower once (this is related to the fact that the arc of a circle grows with its radius). This indicates that a slightly higher common timing advance would further reduce the inter-traffic interference. The following figure 2.2.4.13 confirms this.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2-35

-30

-25

-20

NOL,max

/N

E[M

SE

inte

r] [d

B]

OFDM vs. UFMC, 10% CFO, w/ type 2 ATA applying NTA

=0.5NOL,max

OFDM, LCP

=79

L = 80, no Guards






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Figure 2.2.4.13: Inter-traffic interference, depandance on NTA.

The higher NOL,max is, the higher the applied timing advance NTA is to be chosen indicated by the fact, that the minima of the curves are shifted to the left. So, by choosing the appropriate timing advance ATA type 2 is improving the system even more. If implemented into a real system, the basestation is able to estimate the optimal value based upon prior measurements done during the adjustment of type I devices and broadcast this value every once in a time. As outlined earlier another relevant aspect to evaluate is the intra-traffic interference. For doing so we have to apply the following metric:

max

minN

pE MSEMSEintra (2.2.4.6)

Δ = (Ndelay,1- Ndelay,2) is the delay difference between the two type II/III users (user 1 being the user of interest and user 2 being the interfering user). pΔ is the probability density of these delay differences to occur within the given cellular setting and MSE(Δ/N) are again the measurements given within the figures above. Δmin equals to –NOL,max and corresponds to the case of the user of interest being located at the cell center (and thus having zero delay) and the interfering user being located at the cell edge (and thus having delay NOL,max). Finally, Δmax equals to NOL,max and corresponds the opposite case. To determine pΔ we need to reformulate Δ a bit:

delay,2delay,1delay,2delay,1

NNNN (2.2.4.7)

With the right side of the equation, it becomes obvious, that pΔ is easily determined as follows:

rrNNNN

ppppppp

delaydelaydelay,2delay,1

(2.2.4.8)

So, to determine pΔ a simple convolution needs to be carried out, as shown in figure 2.2.4.14.

-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08-45

-40

-35

-30

-25

-20UFMC, L=80, no CFO, RC shaped windowing, no Guards

(NTA

+NOL,max

/2)/N

E[M

SE

inte

r] [d

B]

NOL,max

= 20

NOL,max

= 40

NOL,max

= 60

NOL,max

= 80

NOL,max

= 100

NOL,max

= 120

NOL,max

= 140

NOL,max

= 160

NOL,max

= 180

NOL,max

= 200

NTA

=0

NTA

=NOL,max N

TA=0.5N

OL,max

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Figure 2.2.4.14: PDF pΔ of two devices to have delay difference Δ.

The following figures 2.2.4.15 - 2.2.4.20 depict the average distortion the user of interest (type II/III device) is suffering under the assumptions given above and with various system settings (0%, 5% and 10% CFO; w/ Type 2 ATA applying NTA=0.5NOL,max, w/ and w/o time domain windowing, FFT based detection).

Figure 2.2.4.151: Intra-traffic interference, no CFO, no time domain windowing (black: OFDM, blue/red/green: UFMC).

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 10

0.01

0.02

0.03

0.04

0.05

0.06

p

both users are colocated

user 1 at cell center

user 2 at cell edge

user 2 at cell center

user 1 at cell edge

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22-35

-30

-25

-20OFDM vs. UFMC, no CFO, no windowing

NOL,max

/N

E[M

SE

intr

a]

[dB

]



L = 80

L = 90

L = 100

LCP

= 79

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Figure 2.2.4.16: Intra-traffic interference, no CFO, RC shaped time domain windowing (black: OFDM, blue/red/green: UFMC).

Figure 2.2.4.17: Intra-traffic interference, 5% CFO, no time domain windowing (black: OFDM, blue/red/green: UFMC).

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22-35

-30

-25

-20OFDM vs. UFMC, no CFO, RC shaped windowing

NOL,max

/N

E[M

SE

intr

a]

[dB

]



L = 80

L = 90

L = 100

LCP

= 79

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22-35

-30

-25

-20OFDM vs. UFMC, 5% CFO, no windowing

NOL,max

/N

E[M

SE

intr

a]

[dB

]



L = 80

L = 90

L = 100

LCP

= 79

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Figure 2.2.4.18: Intra-traffic interference, 5% CFO, RC shaped time domain windowing (black: OFDM, blue/red/green: UFMC).

Figure 2.2.4.19: Intra-traffic interference, 10% CFO, no time domain windowing (black: OFDM, blue/red/green: UFMC).

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22-35

-30

-25

-20OFDM vs. UFMC, 5% CFO, RC shaped windowing

NOL,max

/N

E[M

SE

intr

a]

[dB

]



L = 80

L = 90

L = 100

LCP

= 79

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22-35

-30

-25

-20OFDM vs. UFMC, 10% CFO, no windowing

NOL,max

/N

E[M

SE

intr

a]

[dB

]



L = 80

L = 90

L = 100

LCP

= 79

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Page: 47 of 100

Figure 2.2.4.20: Intra-traffic interference, 10% CFO, RC shaped time domain windowing (black: OFDM, blue/red/green: UFMC).

Again UFMC is outperforming OFDM significantly.

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22-35

-30

-25

-20OFDM vs. UFMC, 10% CFO, RC shaped windowing

NOL,max

/N

E[M

SE

intr

a]

[dB

]



L = 80

L = 90

L = 100

LCP

= 79

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2.2.5 UFMC with multiple signal layers

In this section, we consider an uplink scenario, in which the users with Relaxed Synchronicity (RS) are embedded into a large frame with synchronous users, and produce Inter-Carrier Interference (ICI). We investigate the capability of the UFMC system to support multiple signal layers, by adopting Interleave-Division Multiple Access (IDMA), which is able to separate and detect the superimposed signals of individual RS users [CSW14]. As being a reference solution, the conventional multi-carrier waveform, Orthogonal Frequency Division Multiplexing (OFDM), is supported by Frequency Division Multiple Access (FDMA) to separate the RS users in a classical way. This allows us to study the coded Bit Error Rate (BER) behaviour of UFMC-IDMA and OFDM-FDMA system, if the Forward Error Correction (FEC), e.g. Low-Density Parity-Check (LDPC) channel decoder, is considered. (On the other side, we have the degrees of freedom, to investigate the performance of UFMC-FDMA or OFDM-IDMA, as well.)

Figure 2.2.5.1: A generic UFMC-IDMA transceiver structure

In Figure 2.2.5.1, the basic UFMC modulator and IDMA transceiver structure are presented. The multiple user uplink scenario is the information-theoretic Multiple Access Channel (MAC) problem. The capacity can be described in a two-user rate region [COV06]. A classical and simple approach is

D3.2


Page: 49 of 100

FDMA. While FDMA can achieve the single-user corner points of this rate region, its hull can in general only be achieved when both users transmit simultaneously using joint decoding. In order to exploit this point, a multiple access scheme different to FDMA is required, e.g. Interleave-Division Multiple Access (IDMA). In [PLW06], this new concept was proposed by Li Ping et al., which originally targeted to the performance enhancement for asynchronous Code Division Multiple Access (CDMA). Further studies in [KBU12] revealed the different characteristics of IDMA and CDMA with respect to complexity of the receiver, robustness against asynchronicity and tolerance upon users’ overloading. Being recognized by both [PLW06] and [KBU12], the receiver, denoted as Elementary Signal Estimator (ESE) by Li Ping et al. or denoted as soft rake detector by Kusume et al., turns out to be simple and effective. Firstly, let’s depict the IDMA concept in conjunction with UFMC modulation. For a particular user k the data bits dk are encoded, obtaining coded bits ck. Each user uses its own interleaver Πk. After interleaving, the M-QAM modulated data symbols rk can be segmented to the per sub-band input vector si,k of the UFMC modulator. This provides

kl

nlnlnlnknknknzrFHrFHY

,,,,,, (2.2.5.1)

where rk,n denotes the QAM symbol of user k at subcarrier n after user-specific interleaving, Hk,n denotes the channel transfer function, Fk,n stands for the subband filter frequency response and z models Additive White Gaussian Noise (AWGN) with power spectral density N0. At the receiver side, the ESE is able to deliver the Log-Likelihood-Ratio (LLR) for the m-th bit of the transmit symbol rk,n with

1

0

0

2

,,

0

2

,,

)(

,

)out(

,ESE

exp

exp

ln)(

m

m

a

I

nknk

a

I

nknk

m

nkk

NN

aFHY

NN

aFHY

r

A

A

L (2.2.5.2)

where 0

mA and 1

mA denote the subsets of the QAM constellation candidates, whose m-th bit is 0 and

1, respectively. Notation NI denotes the variance of the interference from other IDMA users. Further, it holds

kl

nlnlnlrEFHYY

,,, (2.2.5.3)

),...,()out(

,,DEC

)out(

1,,DEC,, Ml

kl

lnlnlFHY LLQ

where operator )( Q represents to a soft QAM-mapper for symbol rl,n based on the LLRs from the

decoder. For the output of ESE, the user-specific de-interleaver Πk-1 and FEC decoder basically collect

the diversity and coding gain, which can significantly improve the reliability and coding gain, which can improve the reliability of cancellation in (2.2.5.3). Furthermore, the ESE performance (2.2.5.2) is as well improved, by introducing several IDMA iterations. The user signal layers 1 to k can be successfully separated even within, e.g. 5 IDMA iterations.

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Figure 2.2.5.2: A scenario for performance comparison

In Figure 2.2.5.2, a scenario for performance comparison between FDMA and IDMA is provided. In FDMA, each user is allocated to a relatively narrow frequency bandwidth F/K, considering an FEC rate Rc, frame-length T, and modulation order MF. The achievable throughput per user is RcMF(T·F/K). In IDMA, all of the users are allowed to share the complete bandwidth F. Those increased number of multi-carrier resource elements can be used in various manners, e.g. either by reducing the FEC rate to Rc/K, or by reducing the modulation order (in MI bits per symbol) or by using a repetition code with rate Rr, or any combination of those possible parameters. The achievable throughput per user is thus (Rc/K)MIRr(F·T). Notice that we have the degrees of freedom to adjust the parameters Rc, MF, MI, K and Rr. In our investigations, we chose the parameters such that the achievable throughput is identical for both FDMA and IDMA, which provides a fair comparison. On the other side, the framing design can significantly benefit the IDMA scheme, due to the high potential of frequency diversity and low ICI introduced by adjacent users. Especially, the reduced FEC rate can guarantee a robust IDMA performance. Throughout this section, each user is exactly assigned one layer. The users of interest are assumed to have identical time offsets relative to the fully synchronized user, namely Δτ1=Δτ2=...=Δτk 0. In future work, a much more sophisticated model could be considered. Then, let’s exploit uplink link level simulations for two users of interest, in order to compare different combinations of multi-carrier waveform solutions and multiple access schemes, such as OFDM-FDMA, OFDM-IDMA, UFMC-FDMA and UFMC-IDMA. In Table 2.2.5.1, the simulation parameters are summarized.

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Table 2.2.5.1: Link level simulation parameters

Simulation Parameter Value

Multi-carrier symbols per TTI (Transmission Time Interval) 9

FFT size (N) 1024

Subcarrier spacing 15 kHz

UFMC filter length L 80

Filter type Dolph-Chebyshev with 40 dB sidelobe attenuation

Subcarriers per sub-band 12

Nr. of allocated sub-bands for user of interest (FDMA/IDMA)

5/10

Nr. of allocated sub-bands for interfering users 9

Receiver type FFT based w/o time domain pre-processing

Carrier frequency 2 GHz

Carrier Frequency Offset (CFO) in subcarrier spacings 0

Relative delays between adjacent users )45.0,0(

N

Ndelay

Channel model i.i.d. Rayleigh (blockfading) Pedestrian B, 3 km/h

Power control ideal, i.e. all transmissions arrive at the base station with unit energy

Subcarrier modulation schemes BPSK, QPSK, 16QAM

Number of IDMA iterations 5

Number of FDMA/IDMA users 2

Repetition rate Rr 1

FEC DVD-S2, LDPC code

FEC rate Rc 1/4, 3/4

Iterations in LDPC decoder 50

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(a)

(b)

Figure 2.2.5.3: Performance comparison: OFDM-FDMA with QPSK vs. OFDM-IDMA with BPSK for 2 layers (a), and UFMC-FDMA with QPSK vs. UFMC-IDMAwith BPSK for 2 layers (b)

We adopt the LDPC code specified in the second generation satellite Digital Video Broadcasting (DVB-S2) [ETS04] to enhance the channel coding for IDMA. In Figure 2.2.5.3, the FDMA and IDMA related

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schemes are QPSK and BPSK modulated, respectively, so that the two-user overall achievable throughput is equivalent for both schemes. And for the same reason, the FDMA and IDMA related schemes are 16QAM and QPSK modulated in Figure 2.2.5.4 similarly. In order to consider the influence by delay, we specify a definition “relative delay” Ndelay/N with Ndelay being the delay in time domain with respect to the number of samples. It can be observed that IDMA turns out to be the better solution for lower code rates (e.g. 1/4), and outperforms FDMA by roughly 1-2 dB (at coded BER 10-3). One of the most important reasons to understand the gain is that IDMA can potentially exploit frequency diversity due to wider frequency allocation size, as depicted in Figure 2.2.5.2, and suffers less ICI from adjacent users. Notice that the loss of FDMA scheme user Pedestrian B channel is bigger than that of IDMA scheme. This is an indirect evidence that IDMA scheme is capable of better collecting frequency diversity gain. Due to the computational limitation for the numerical simulation, we do not consider the framing for K>2 users. Nevertheless, significant performance enhancement can be expected, if more users are involved in the framing, so that the potential frequency diversity will further increase the performance gain between IDMA and FDMA.

(a)

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(b)

Figure 2.2.5.4: Performance comparison: OFDM-FDMA with 16QAM vs. OFDM-IDMA with QPSK for 2 layers (a), and UFMC-FDMA with 16QAM vs.UFMC-IDMA with QPSK for 2 layers (b)

On the other side, expected by us, as well concluded in the pioneer works, e.g. [PLW06], IDMA can only enhance the performance within systems applying low rate codes. Thus, FDMA shows better performance for higher code rates. For this reason, we do not provide the IDMA performance in Figure 2.2.5.4 for FEC rate 3/4. Additionally, for low code rates in both multiple access schemes, UFMC slightly outperforms OFDM. Furthermore, in high Eb/N0 areas (e.g. in the higher Eb/N0 operation points for 16QAM with code rate 3/4), especially in the presence of timing delays, the performance gain of UFMC exceeds 1.5dB over OFDM, with respect to Eb/N0 at BER 10-3. This is due to the higher robustness of UFMC to time delay as shown in section 2.2.4. From these results it seems that UFMC is a candidate scheme potentially capable of replacing OFDM. For users transmitting with low code rates, IDMA is preferable over FDMA and can be combined well with UFMC. Even when users are in low-rate operation points, where distortions due to multi-user interference are far beyond the noise floor, the filters help to protect neighbour users from ICI and provide additional benefits, like increased suitability to fragmented spectrum. Throughout this section, equal power per user is assumed, which is the best case for ICI and cannot always be guaranteed for contention-based access. In unbalanced power situation, ICI robustness becomes more important, thus UFMC gain will be much stronger.

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2.2.6 UFMC with flexible single carrier support

This section discusses a hybrid signal structure with multi-carrier and single-carrier building blocks, embedded into the UFMC signal format. The basic idea consists of constructing filtered signal modules, which either contain filtered single carrier transmissions or (e.g. block-wise) filtered multi-carrier signals. Depending on the traffic mix the available subband slots may be dedicated to either of those transmission types. For energy-efficient communication, required in e.g. low-end MTC devices, the single carrier signal format, due to its improved PAPR properties is more power amplifier friendly. UFMC consists of a modular structure with filtered subband-blocks, see Figure 2.2.6.1. The embedded filtering functionality of UFMC applied similarly to the single-carrier modules enables a highly flexible and scalable air interface with high resource efficiency. When applying this approach we are able to dynamically replace UFMC multi-carrier subband modules and instead embed single-carrier signals, optionally with spreading, e.g. spread spectrum or time-spreading, see Figure 2.2.6.2. The embedded single carrier signals are spectrally shaped (preferably already when constructing the digital baseband signal) with filters which align to the UFMC signal structure, e.g. using the same prototype filters of UFMC in a frequency-shifted manner. The single carrier signals can (but do not have to) be constructed using DFT-precoded UFMC (thus SC-FDMA based on UFMC), similar as DFT-precoded OFDM in the LTE uplink.

Figure 2.2.6.1: Embedded into UFMC: Hybrid single-carrier / multi-carrier transmitter, where single carrier is used in its

pure form.

Figure 2.2.6.2: Embedded into UFMC: Hybrid single-carrier / multi-carrier transmitter, where the single carrier contains a

spread spectrum signal. The Serial-to-parallel conversion before spreading allows using multi-code transmission (the usage of several superimposed spread signals)

Naturally, in the uplink low-rate devices can now use single carrier signals, high-rate devices can use multi-carrier signals, all under the umbrella of the UFMC signal structure, e.g. using the same

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subband-filters, both for SC or MC. The system can dynamically adapt the resource blocks to the different SC/MC formats via control signalling.

2.2.7 Summary for UFMC

We have described the basic signal properties of UFMC in section 2.2.1. Its spectral properties are clearly advantageous over OFDM and thus increased robustness against sources of inter-carrier interference are provided. Additionally UFMC subcarriers are orthogonal in the complex domain. Section 2.2.2 shows that, due to the fact that UFMC is very closely related to OFDM, equalization and channel estimation have low complexity and can built upon the vast knowledge base of OFDM. Section 2.2.3 introduces an open-loop timing advance method which is tailored to UFMC. Performance results of this Autonomous Timing Advance (ATA) are demonstrated in section 2.2.4, showing that UFMC is able to operate with relaxed synchronicity very well. Section 2.2.5 introduces the usage of multiple signal layers in conjunction with UFMC, based upon IDMA. This exploits the rate region of the multiple access channel and thus leads to higher throughputs, which was demonstrated by simulations for low code rates. It was also shown that IDMA and UFMC complement each other well. While IDMA especially brings benefits with low code rates, thus in the low Eb/N0 region outperforming FDMA, UFMC brings benefits in higher modulation and coding schemes, always being superior over OFDM. Section 2.2.6 illustrates that UFMC, due to its subband-filtering structure, can easily embed single-carrier signals (either SC-FDMA or a GSM-like “true single carrier” signal) within its multi-carrier signal format. This is especially beneficial in the uplink, when low-end devices require a specially low PAPR, while high-rate devices benefit from the multi-carrier modulation.

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2.3 FBMC

In this chapter, bold letters denote vectors and matrices. Upper-case and lower-case letters denote frequency domain and time domain variables respectively. The following notations are used:

- ( . )T Transpose

- H) . ( Hermitian transform

- ] . [E Expectation operator

- ] . [tr Trace operator

- || . || l -norm

F stands for the NN -DFT (Discrete Fourier transform) matrix defined as:

1)1)((1)2(1

12

1

1

1111

1=

NN

N

N

N

N

N

N

NNN

www

www

N

F

where Nj

New

2

= . Matlab notation was used to index the matrix. Therefore ):(:,1= UBA means

that A is built with the first U columns and all the rows of B .

2.3.1 FBMC principles

A multicarrier system can be described by a synthesis-analysis filter bank, i.e. a transmultiplexer structure. The synthesis filter bank is composed of all the parallel transmit filters and the analysis filter bank consists in all the matched receive filters, as shown in Figure 2.3.1.1 where 𝑝𝑇𝑥(𝑡) and 𝑝𝑅𝑥(𝑡) are respectively the transmit and receive prototype filters. For subcarrier 𝑘, the filter is the

prototype filter phase shifted by 𝑒𝑗2𝜋𝑓𝑘𝑡. This phase shift in the time domain implies a frequency shift of 𝑓𝑘 in the frequency domain. In this figure, the data signal is defined by Eq. (2.3.1):

k k

n

s t s n t n T

(2.3.1)

with 𝑠𝑘[𝑛] the data symbols for subcarrier 𝑘, 𝑇 the symbol period, 𝑛 the symbol number and Nc the number of subchannels.

Figure 2.3.1.1: Block diagram of a multicarrier transceiver.

The most widely used multicarrier technique is CP-OFDM, based on the use of inverse and forward DFT for the analysis and the synthesis filter banks. The prototype filter is a rectangular window whose size is equal to the Fourier Transform. At the receiver, perfect signal recovery is possible under ideal channel conditions thanks to the orthogonality of the subchannel filters. Nevertheless

0s t 02j f t

Txp t e

1s t 12j f t

Txp t e

1Ncs t 12 Ncj f t

Txp t e

+ Channel

02j f t

Rxp t e

12j f t

Rxp t e

12 Ncj f t

Rxp t e

0s n

1s n

1ˆ

Ncs n

transmitter receiver

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under real multipath channels a data rate loss is induced by the mandatory use of a Cyclic Prefix (CP), longer than the impulse response of the channel. With FBMC, the CP can be removed and subcarriers can be better localized, thanks to more advanced prototype filter design. The FBMC prototype filter can be designed in many ways, trying to satisfy different constraints. In general, it is chosen to be:

- complex modulated for good spectral efficiency - uniform to equally divide the available channel bandwidth - with finite Impulse Response for ease of design and implementation - orthogonal, to have a single prototype filter - with Nearly Perfect Reconstruction (NPR) : certain amount of filter bank distortions can be

tolerated as long as they are negligible compared to those caused by the transmission channel

In this document the prototype filter is designed using the frequency sampling technique. This technique provides the advantage of reducing the number of filter coefficients. In other words, the prototype filter coefficients should be given using a closed-form representation that includes only a few adjustable design parameters. The coefficients of the prototype filter for an overlapping factor K equal to 4 are [Bel10]:

2

0:3 11, 0 .9 7 1 9 5 9 8 3 ,1 2 , 1P P

(2.3.2)

The KNc-1 length time response of this filter is computed thanks to:

1

0

1

22 1 c o s 1 , 0 : 2

Kk

m k c

k c

kp P P m m K N

K N

(2.3.3)

The stopband attenuation exceeds 60 dB for the frequency range above 10 channel subcarriers spacings (Figure 2.3.1.2).

Figure 2.3.1.2: FBMC - filters for subcarriers 0 (blue) and 1 (red), 𝑵𝒄 = 𝟓𝟏𝟐,𝑲 = 𝟒

As shown in Figure 2.3.1.2, adjacent carriers significantly overlap. In order to keep adjacent carriers and symbols orthogonal, real and pure imaginary values alternate on carriers and on symbols at the transmitter side. This so-called OQAM (Offset QAM) modulation implies a rate loss of a factor of 2. This efficiency loss of OQAM modulation is compensated by doubling the symbol period 𝑇. 𝐾 is frequently called the overlapping factor: indeed the symbol period is 𝑇/2 and the symbol length is 𝐾𝑇 − 1 samples; each FBMC symbol at the channel input is then overlapped with 2(2𝐾 − 1) other FBMC symbols. The transmitter of FBMC can be represented by Figure 2.3.1.3, with the filtering operation (block ‘frequency spreading’) done in the frequency domain. In this figure:

𝐝𝑚 ∈ ℂ1×𝑁𝑐 is the vector containing the data to transmit for the 𝑚th FBMC symbol.

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𝐗𝑚 = 𝐝𝑚��, ∈ ℂ1×𝐾𝑁𝑐 is the vector of data for the 𝑚th FBMC symbol filtered in the

frequency domain.

𝐆 ∈ ℝ𝑁𝑐×𝐾𝑁𝑐 is the matrix of filtering vectors given by Eq. (2.3.4), with 𝐆 ∈ ℝ1×2𝐾−1, the filtering vector, i.e. the frequency response of the filter given by Eq. (2.3.2):

(2.3.4)

𝐱𝑚 ∈ ℂ1×𝐾𝑁𝑐 is the vector of data for the 𝑚th FBMC in the time domain.

The IFFT has a size of 𝐾𝑁𝑐 samples. The transmit signal is composed of the overlapping of symbols 𝐱𝑚 with a factor of 𝑁𝑐/2.

Figure 2.3.1.3: FBMC transmitter with filtering in the frequency domain

The frequency spreading operation is further described by Figure 2.3.1.4 where each carrier of 𝐝𝑚 is spread on 2𝐾 − 1 carriers on 𝐗𝑚. Here 𝐾 = 4. As can be seen from Figure 2.3.1.3, FBMC symbols overlap in the time domain and as Figure 2.3.1.4 shows, adjacent carriers in the vector 𝐝𝑚 significantly overlap in the vector 𝐗𝑚.

Figure 2.3.1.4: Frequency spreading

The FBMC waveform with its spectrally well shaped prototype filters and overlapped time symbols has some inherent features which makes it a natural choice for some of the anticipated 5G application scenarios. First of all it does not require a cyclic prefix and has an almost perfect separation of frequency subbands without the need for strict synchronization. Consequently its properties make it especially suited for fragmented spectrum and Coordinated Multi Point (CoMP) Transmission/Reception.

2.3.2 Frame design

In order to keep a flexible frequency and time resource block allocation, a preamble based burst approach is considered. Synchronization and channel estimation is performed using the training sequence. Its structure has been defined and is given in Figure 2.3.2.1.

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Figure 2.3.2.1: FBMC burst structure

It is composed of a preamble of duration P-FBMC symbols (P is set to 4 in Figure 2.3.2.1). The preamble has been designed to accurately detect the start of the burst and give an estimate of the channel frequency response while preserving the localization properties of the FBMC signal. It is mainly composed of pilot carriers spaced every D active carriers for the whole duration of the preamble (D is set to 4 in the Figure 2.3.2.1). The pilot carriers are designed so that the signal transmitted on each pilot carrier is constant for the duration of the preamble. Synchronization carriers are added on the first multicarrier symbol but are more sparsely distributed than pilot carriers. These are designed to accurately estimate the start of burst.

2.3.3 Receiver architecture overview

A flexible architecture for multiuser asynchronous reception on fragmented spectrum is able to exploit the advantages of FBMC if the signal is efficiently demodulated in the frequency domain without a priori knowledge of the FFT timing alignment (i.e. the location of the FFT block, this property is called asynchronous FFT). A receiver architecture based on this assumption is depicted in Figure 2.3.3.1. An asynchronous FFT

of size KN is processed every block of /2N samples generating KN points, i.e. if m

r is the thm

received vector, a KN -point FFT is computed for samples /2)(= Nmnk with

1,0,1,= NKn . These successive KN points are stored in a memory unit. The position of the

FFT window is not aligned with the received multi-carrier symbols of the user.

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Figure 2.3.3.1: Block diagram of the proposed receiver

The detection of a start of burst is then realized on the frequency domain (i.e. at the output of the FFT) using a priori information from the preamble. CFO is first estimated using the pilot subcarrier information of the preamble by computing the phase of the product between two consecutive FBMC symbols at the location of the pilot subcarriers. The propagation channel is assumed static for the duration of the burst. As described in [CDK13], when large CFO correction is required, a first step in the estimation process consists of scanning the subcarriers around the pilot subcarrier locations to determine the subcarrier with the highest energy. A tracking algorithm of the CFO may complete the synchronization process when the duration of the burst is large and the accuracy of the preamble based detection algorithm does not meet the required level [AF10]. CFO compensation is then performed in the frequency domain using a feed-forward approach. The channel coefficients may be estimated on the pilot subcarriers of the preamble. [FPT09][Bel10] have already considered a similar approach by introducing a phase term to correct the CFO. In section 2.3.5, this technique is completed by an efficient algorithm that compensates inter-carrier interference. The channel is then estimated on the pilot subcarriers before being interpolated on

every active subcarrier. The use of a KN -point FFT makes the interpolation particularly specific to this receiver and a description of the proposed algorithm is detailed in section 2.3.6. Once the channel is estimated on all the active subcarriers, a one-tap per subcarrier equalizer is applied before filtering by the FBMC prototype filter (section 2.3.7). Then down-sampling by a factor of K is done and O-QAM inverse transform is processed. Demapping and Log-Likelihood Ratio (LLR) computation complete the inner receiver architecture. A soft-input Forward Error Correction (FEC) decoder recovers finally the original message. The asynchronous frequency domain processing of the receiver combined with the high stop-band attenuation of the FBMC prototype filter provides a receiver architecture that allows for multiuser asynchronous reception (considering a frequency guard band of only one carrier). FFT and Memory Unit are common modules, while the remaining of the receiver should be duplicated as many times the number of parallel asynchronous users the system may tolerate in the uplink. In the downlink, the same receiver may be used but without duplicating the blocks at the output of the FFT.

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2.3.4 Time synchronization

2.3.4.1 Introduction

As described previously all the synchronization processes are done in the frequency domain. The main synchronization parameters to be estimated are:

- a flag indicating the presence of the signal since an asynchronous burst mode transmission is considered

- the starting time of the burst. The case of the KN-FFT architecture is a bit specific compared to time domain synchronization algorithms. While for time domain algorithms the start time controls the FFT processor, in the proposed scheme the start time indicates which output FFT block corresponds to the beginning of the burst.

The scheme proposed for symbol-timing synchronization is depicted in Figure 2.3.4.1.1 where a specifically designed training symbol is used (see section 2.3.2).

Figure 2.3.4.1.1: Proposed synchronization scheme

First, coarse timing estimation is performed based on a metric computed from pilot carriers and an appropriate threshold. The decision on the presence of the signal is also performed by analyzing this metric. It should be mentioned that the signal detection can be helped by an AGC (automatic gain control) metric. This feature is not in the scope of this deliverable. Consequently we assume that no information about the presence of the signal is available at the coarse time step of the synchronization scheme. The fine synchronization procedure is performed based on a new metric calculated from the synchronization carriers. An accurate estimation of the beginning of the burst is provided. Information about the position of the FFT window over the FBMC symbol of interest is extracted. This information helps for the channel interpolation by positioning correctly the channel impulse response on the middle of the interpolation filter. Hence the frequency offset is estimated based on pilots. Channel estimation on corrected pilots is then realized.

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2.3.4.2 Coarse time synchronization

The first step in the coarse time synchronization process is to determine the presence of a signal in the frequency band allocated to the desired users. In the frequency domain, energy detection is performed. The false alarm probability target is intentionally set to a high level. Consequently the probability of missed detection is low. Indeed a second algorithm was designed to detect the preamble and check the energy detection results. A schematic overview of the proposed algorithm for energy detection is depicted in Figure 2.3.4.2.1. The optimization of the threshold T is for further study and will be described in the next WP3 deliverable.

Figure 2.3.4.2.1: Architecture of user detection module

The confirmation of the detection is realized by an analysis of a new metric based on pilot carriers denoted “coarse time metric”. The coarse time metric is computed from the distributed pilot of the preamble as depicted in Figure 2.3.4.1.1. First, subcarriers are filtered in the frequency domain by the prototype filter to form N carriers. Then, resource block demultiplexing is performed to separate the users orthogonally distributed over the carriers. Pilot carriers are then extracted. The architecture of the multiuser coarse time synchronization algorithm is depicted in Figure 2.3.4.2.2.

Figure 2.3.4.2.2: Architecture of the multi-user coarse time synchronization algorithm

The signal at the output of the pilot carrier demultiplexing can be expressed as (assuming Additive white Gaussian noise (AWGN) channel):

),(),(),,(),,( mkimknumkpumkrp

(2.3.4.1)

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Where: o k is the index of the pilot carrier o m is the index of the FFT block o u is the index of the user o rp(k,m,u) is the received kth pilot carrier for user u o p(k,m,u) is the emitted kth pilot carrier for user u o n(k,m) is the AWGN noise o i(k,m) is the interference term due to built-in OQAM interference term and

due to synchronization mismatch between TX and RX FFT. The decision metric is computed as follows:

2

*),1,(),,(),( umkrumkrumd

p

k

p (2.3.4.2)

The pilot pattern was designed in such a way that d(m,u) is constant during the preamble duration. As an example, the decision variable is depicted in Figure 2.3.4.2.3 for various timing offsets between TX and RX FFT, δ, expressed in number of samples. The decision metric is plotted in decibel. Preamble, payload and noise can be, in that case, easily distinguished each other. It should be mentioned that it exists a margin of 18dB between preamble decision term and payload decision term.

Figure 2.3.4.2.3 – Illustration of the decision metric (dB) for various time offsets (δ). δ is expressed in number of samples. The time axis corresponds to the number of FFT output blocks

When a signal is detected by the energy detection module, the coarse time metric is computed on a window centered on the position derived from the energy detection module. The optimization of the decision threshold is for further study and will be described in the next WP3 deliverable.

2.3.4.3 Fine time synchronization

Once the coarse time synchronization is acquired a fine time synchronization metric is computed to detect the beginning of the preamble. The fine time metric is computed from the synchronization carrier of the preamble as depicted in Figure 2.3.4.2.1. First, subcarriers are filtered in the frequency domain by the prototype filter to form N carriers. Then, resource block demultiplexing is performed to separate the users orthogonally distributed over the carriers. Synchronization carriers are then

time samples

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extracted. Synchronization carriers are located on the first preamble symbol. Consequently, power estimation at synchronization carrier location gives an accurate estimation of the beginning of the burst. As an example, the decision variable is depicted in Figure 2.3.4.3.1 for various timing offsets between TX and RX FFT, δ, expressed in number of samples.

Figure 2.3.4.3.1: Illustration of the fine time decision metric for various time offsets (δ). δ is expressed in number of samples. The time axis corresponds to the number of FFT output blocks

The architecture of the multiuser fine time synchronization algorithm is depicted in Figure 2.3.4.3.2.

Figure 2.3.4.3.2: Architecture of the fine time synchronization algorithm

The optimization of the decision threshold is for further study and will be described in the next WP3 deliverable.

2.3.5 Carrier frequency offset compensation

2.3.5.1 Problem formulation

When the received symbol CFO

mr is affected by CFO, the signal CFO

mr can be written as:

time samples

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m

i

m

iCFO

mzrdr

)(2

=i

mi

j

i

e (2.3.5.1)

where 1

KNC

CFO

mr is the received time domain vectors, 1

KN

Ci

mr is the time domain vector

associated with user i , i is the CFO for user i relative to the carrier spacing (assuming N carriers),

i is a random phase for user i ,

mz the noise vector KNKN

Ci

d a diagonal matrix defined for

user i by:

N

ik

j

ekk

2

=],[i

d (2.3.5.2)

The considered scenario is an uplink asynchronous access with multiple different CFOs. Since CFOs associated with different users are different, correction must be performed separatly for each user. The correction of the CFO for one given user cannot then be realized in the time domain with reasonable complexity as described by the authors of [CLL0]. For this reason we propose a frequency domain processing that can be also applied in the downlink. Thanks to the very good frequency localization of the FBMC carriers, the asynchronous time reception of users does not cause any frequency interference between users (providing a frequency guard band of only one carrier). Thus, after FFT, the correction of the CFO in the frequency domain is described without loss of generality

for one user. In the following, subscript index i is dropped. After KN fast Fourier transform, (2.3.5.1) becomes:

mmZCRR

)(2=ˆ mj

me

(2.3.5.3)

where 1

KNC

mZ is the additive white Gaussian noise vector and KNKN

CC is a Toeplitz matrix

defined by: H

FdFC = (2.3.5.4)

The coefficients of C measure the level of Inter-Carrier Interference (ICI) and may be written as:

N

kiKNj

e

N

kiKsinc

kiKsincki

))(1)((

))(

(

))((=],[

C (2.3.5.5)

From equation (2.3.5.5), it can be noted that when ZqqK ,= , C is a subdiagonal matrix. q is

denoted interger part of the CFO. The fractional part is labeled . The parameter may then be decomposed into its integer and its fractional part:

K

q= (2.3.5.6)

Zq and R with )[);1/(21/(2[ KK . Regardless of the integer part, q , ICI is only present

when 0 . Assuming q is known, the required range of detection for may be very small. For

instance, in the case of FBMC with a prototype filter of duration 4=K , the maximum level of ICI is

introduced when 12.5%= .

2.3.5.2 Proposed correction scheme

As described in the previous section, CFO may be decomposed into integer and fractional parts. The

integer part is easily corrected by a shift of q subcarriers at the output of the KN -point FFT. The

phase term should then be compensated by a phase correction factor. A simple and efficient way to reduce ICI introduced by the factional part of the CFO, , may be realized by complex filtering of the

received sequence. In order to derive the complex coefficients of filter W that mitigates ICI, two criteria are considered:

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• Zero-Forcing criterion (ZF): using Equation (2.3.5.3), and omitting the phase term, which

has been corrected, we define W such as: IWC = (2.3.5.7)

By substituting C with the expression in (2.3.5.4), (2.3.5.7) may be rewritten as:

IWFdF =H (2.3.5.8)

As IFFFF ==HH and Idd =

H , the filter W may be derived by:

HH

FFdW = (2.3.5.9)

• Minimum Mean Square Error criterion (MMSE): the filter may also be optimized to minimize the Mean Square Error (MSE), taking the noise level at the receiver into account:

2

ârgmin=mmWest

RRWW (2.3.5.10)

By taking the derivative of the expectation of the trace, the minimization problem becomes:

0= HHHH

HHHHH

trE

WCRRRWCR

WZWZWCRWCRW

mmmm

mmmm

(2.3.5.11)

In presence of Additive White Gaussian Noise (AWGN), IZZmm

2=

n

H

E and if R

Ω is defined by

Rmm

ΩRR =H

E , (2.3.5.11) becomes:

0=2

RRCΩWWCCΩ

H

n

HH (2.3.5.12)

When IΩR

2=

R , the solution is straightforward, and can be expressed by:

HH

nR

RFFdW

22

2

=

(2.3.5.13)

For both cases, the matrix W is Toeplitz and is therefore characterized by only KN complex

coefficients. In general R

Ω is not a diagonal matrix but rather a band diagonal matrix and depends

on the FBMC prototype filter that is considered. A closed-form expression of W may be obtained if

and only if R

Ω is invertible. However W may be derived by a non-linear optimization process or by

a using a pseudo-inverse based for instance on singular value decomposition.

The correction of the fractional part of the CFO with either ZF or MMSE filters requires a KN complex-tap filter. Nevertheless the complexity may be significantly reduced as ICI introduced by the CFO rapidly decreases with the index of the interfering subcarriers (since )1/(2|<| K ). In Figure

2.3.5.2.1, the power of the W coefficients for a 256-point FFT and a CFO of 10% is plotted. In that example, almost all the power is located around the diagonal. We proposed to approximate matrix

W by a sparse band Toeplitz matrix with 12 Q terms on each column and centred on the diagonal.

This is done by forcing all the other coefficients to 0. A trade-off between complexity and accuracy of the frequency offset correction should be found for parameter Q . The 12 Q coefficients may be

extracted from W through equation (2.3.5.11) or (2.3.5.13).

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Figure 2.3.5.2.1: Block power of matrix W coefficients normalized by the highest value (dB).

2.3.5.3 Performance of the CFO correction algorithm

The performance of the proposed algorithm is analysed in this section using the following FBMC

parameters: 1024=N and 4=K . Figure 2.3.5.2.2 gives the architecture of the proposed implementation. The first step, performed by the Shift module, consists in correcting the integer part

q . The result is then filtered by the 12 Q -tap filter W . A phase correction performed on each

FBMC symbol completes the CFO correction process.

Figure 2.3.5.2.2: Block diagram of the proposed CFO correction scheme

The Relative Mean Square Error (RMSE) for values from 1% to 12% and for different values of Q

is given in Figure 2.3.5.2.3 W is derived using the truncated ZF method, i.e. truncated (finite) length approximation. RMSE has been defined by:

(dB)

ˆ

log10=RMSE2

2

10

m

mm

R

RRW

E

E

(2.3.5.14)

RMSE is a measure of the signal to interference level as seen on the constellation. In the example, a QPSK modulation has been considered and RMSE decreases as Q becomes larger.

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Figure 2.3.5.2.3: RMSE performance of the proposed filtering scheme.

When 0=Q , the algorithm only performs phase correction. The benefit of ICI mitigation is clearly

demonstrated. Parameter Q could be chosen as a function of the system Signal to Noise Ratio (SNR)

so as to limit the system by thermal noise but not by interference. In practice, the estimation of the CFO is never perfect. As illustrated in Figure 2.3.5.2.3, a residual

CFO of 1% generated by the correction mismatch exhibits a RMSE power level below 30 dB and does not degrade performance significantly.

2.3.6 Channel estimation and interpolation

Another important function that should be performed in the frequency domain is to recover the channel coefficients on each active subcarrier. This operation is realized after the channel coefficients have been estimated on the pilot subcarrier location. For most interpolation schemes, the channel is poorly interpolated on the carrier frequencies located at the edges of the frequency band. This effect may be neglected when the number of carriers per contiguous frequency band is large but may lead to significant performance degradation of the overall system when the multicarrier modulation is applied to a fragmented spectrum. A robust interpolation scheme for the complete spectrum, including the edges is therefore critical. A stable and robust scheme based on interpolation filters in the frequency-domain is proposed in this sub-section. The interpolation is performed by introducing different interpolation filters on the edges. A theoretical problem description helps to derive a set of key optimization equations used for filter construction. The potential gain of this new method is then simulated for Filterbank Multicarrier (FBMC) modulations.

2.3.6.1 Problem formulation

One of the main advantages of multicarrier modulation techniques over single carrier modulation is a greatly simplified equalization process. In the case of OFDM, as long as the duration of the channel impulse response is shorter than the guard interval and the channel is constant over the duration of the OFDM symbol, a frequency-selective wideband channel converts to a number of subcarrier channel with flat fading. For FBMC, Hirosaki [Hir81] showed that this property may be preserved if the equalizer at each subcarrier channel is fractionally spaced. Therefore under these assumptions the received vector R may be written after Fourier transform as:

ZXHR diag= (2.3.6.1)

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where Hdiag is a HH

NN diagonal matrix of the channel frequency response, X the 1H

N

vector of symbols to transmit and Z the 1H

N vector of additive white Gaussian noise. H

N is the

number of active subcarriers.

We labelled P

U , the indices of the pilots (located at the central location, as a KN -points FFT is

considered at the front end of the receiver) and H

U , the indices of the active subcarriers. p

N is the

number of pilot subcarriers. The LS channel estimation of P , the pilot vector, at indices P

U is given

by [BES+95]:

t

p

p

N

N

1][

1])[(

[1]

[1])(

[0]

[0])(=ˆ

P

UR

P

UR

P

URP

PPP (2.3.6.2)

Accurate estimation, H , of the channel coefficients H may be derived from the observation of P

using an interpolation filter W of size pH

NN .

PWH ˆ=ˆ (2.3.6.3)

To construct the filter W , the following minimization problem should be solved:

2

ˆmin= HPWW

West

Earg (2.3.6.4)

Let be defined as:

2

ˆ= HPWE

(2.3.6.5)

Then, since P is a least square estimate of P , the following equation may be written:

P

ZPP =ˆ (2.3.6.6)

where p

Z is a 1p

N noise vector. Equation (22) may then be rewritten as:

HHH

HHHHH

H

trE

trE

E

WZWZHH

WHPWPHWWPP

HZPWHZPW

HZPW

PP

PP

P

=

)()(=

)(=2

(2.3.6.7)

Then, if h is the 1N vector of the channel impulse response, H and P may be expressed as:

hF:)h,F(UPP

UP== (2.3.6.8)

hF:)h,F(UHH

UH== (2.3.6.9)

Finally (2.3.6.5) may be rewritten as:

H

pZ

HHH

HHH

tr

WW

FΦFWFΦF

FΦWFWFΦWF

HUh

HU

PUh

HU

HUh

PU

PUh

PU

2

=

(2.3.6.10)

where h

Φ is the time domain channel autocorrelation matrix of size NN and 2

PZ

the noise

power. By taking the partial derivative of with respect to W and making it equal to zero, (2.3.6.9) becomes:

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HH

pZ

H

HUh

PU

Δ

PUh

PU

FΦFWIFΦF

W

)(=0

0=

2

(2.3.6.11)

where I is the identity matrix of size pp

NN . In many cases, the matrix Δ is ill-conditioned and

impossible to invert. However, a pseudo inverse using a Singular Value Decomposition (SVD) may be

computed to derive W but this method may lead to an unstable result. The power distribution of

matrix W coefficients is given in Figure 2.3.6.1.1 for a channel distribution with a square delay

profile in the time domain ( 256=H

N and 64=p

N ). The matrix was derived using (2.3.6.11). A

pseudo-inverse matrix inversion based on SVD has been computed.

Figure 2.3.6.1.1: Power of matrix W coefficients (dB).

In this example, the power distribution of matrix W coefficients is mainly located around the diagonal. It should be noted that the coefficients located at the center of the matrix have very similar values. On the contrary, at the edges of the matrix, the coefficients are significantly different. This property has been exploited to construct a new optimization criterion. The criterion imposes

complexity constraints on matrix W coefficients as a function of their location within the matrix. From a practical point of view, implementing a complex filter with a large set of complex coefficients may be extremely costly. The overall complexity should often be kept under control in order to fit implementation area constraints. The following constraints have thus been added to the minimization problem:

• W is a matrix with real Q coefficients per row instead of complex p

N coefficients per

row

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• The pilot carrier distribution follows a regular pattern, i.e. the sampling of the channel is uniform1

• At least Q pilots are active per set of contiguous subcarriers

The structure of matrix W is divided into three sub-filter blocks, a left sub-filter block, a middle sub-

filter block, and a right sub-filter block, so that matrix W may be rewritten as:

|||

|||

||||

||||

||||

||

||

||

=

r

m

m

m

m

m

l

W0

W00

0W0

0W0

0W0

00W

0W

W

(2.3.6.12)

where l

W is the QNl matrix representing the left sub-filter block,

mW is the QN

m matrix

representing the middle sub-filter block and r

W is the QNr matrix representing the right sub-

filter block. The minimization problem of (2.3.6.9) may then be decomposed into three constraint minimization

problems function of the three sub-filter blocks l

W , m

W and r

W . Further constraints on the

coefficients may be added on the minimization algorithm to guarantee stability. This optimization process may be computationally demanding but allows for a control of the complexity of the

implemented interpolation process. Filters l

W , m

W and r

W are obtained through the following

minimization problem by using a priori knowledge of Δ and 2

Z :

minimize

2

):(1):(1ˆl

NQE HPWl

minimize

2

):1():1(ˆrHlp

NNNQNQE HPWm

(2.3.6.13)

minimize

2

):1():1(ˆHrHpp

NNNNQNE HPWr

By applying (2.3.6.10) into (2.3.6.13), the minimization may be realized considering an a priori knowledge of the autocorrelation matrix of the time domain channel impulse response. By applying this constraint, the level of implementation complexity may be traded off against the target performance of the channel estimation module. The optimization process is not necessarily implemented on the real time system. A stable and efficient interpolation scheme adapted to the channel conditions is provided while complexity is kept under control.

1The proposed method also applies to non-uniform sampling, but the problem is more complex to formulate.

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2.3.6.2 Application to the proposed preamble structure

The estimation of the channel coefficients is performed before applying the FBMC prototype filtering. The LS estimates of the channel coefficients are computed by applying a CFO phase correction on the received signal according to the location of the pilot symbol on the prototype filter. Performance may be further improved by considering all the positions of the prototype filter and by applying a maximum ratio combining algorithm after interpolation. Therefore, by considering LS estimates at the center of the FBMC prototype filter, the structure of the pilot pattern is depicted in Figure 2.3.6.2.1. A pilot subcarrier is located every KD active subcarriers (a blue box corresponds to the location of a pilot subcarrier). The first pilot is located on subcarrier 1K . No pilot subcarrier is active on the right edge of the spectrum, therefore DK 1 channel coefficients should be derived. The number of active subcarriers is equal to

KDNKNpH

1)2(= where p

N is the number of active pilots.

Figure 2.3.6.2.1: Structure of the considered pilot pattern.

Under these assumptions, and considering Q is even, r

N , m

N and l

N may be expressed as follows:

2

1

21=

=

2

1

21=

KDKDQKN

KDN

KDKDQKN

r

m

l

(2.3.6.14)

The channel taps are assumed to be uncorrelated and as a consequence h

Φ is a diagonal matrix. The

most difficult task of the problem formulation consists in defining the a priori time domain channel autocorrelation delay profile. Different profiles may be considered and Figure 2.3.6.2.2 gives

examples of possible distributions. For instance, an a priori autocorrelation h

Φ profile adapted to

single frequency network is characterized by a 0 dB echo channel and is given in Figure 2.3.6.2.2 (d). The most conservative shape, the rectangular distribution (see Figure 2.3.6.2.2 (a)), has been considered in the following of the paper.

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Figure 2.3.6.2.2: Examples of considered autocorrelation channel delay profiles. (a) square (b) low decay (c)

exponential decay (d) 0 dB echo.

The optimization process is computationally intensive making it difficult for a real time implementation. In order to maximize the interpolation performance while maintaining a reasonable level of complexity, the interpolation architecture depicted in Figure 2.3.6.2.3 has been considered. A set of x filters is optimized according to a target SNR, time domain channel duration, time domain profile, etc... The choice of the filter to apply is controlled by an entity that estimates the received channel conditions and decides which filter is the most suitable to the channel conditions measured at the receiver. Estimated pilot subcarriers are fed through the three filter blocks and generate three interpolated channel estimates. The choice of the channel estimate is controlled by a multiplexer according to the subcarrier index.

Figure 2.3.6.2.3: Proposed architecture for adaptive frequency domain channel interpolation.

2.3.6.3 Performance results

The following parameters have been taken for a numerical evaluation: • 4=K • 4=D

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• 1024=N The RMSE of the channel frequency response versus the channel delay spread expressed in time

samples for a SNR of 15 dB is given in Figure 2.3.6.3.1. The filter blocks were designed for a channel delay spread of length 64 time samples, a SNR of 15 dB and for 10=Q . Channel length in the figure

stands for the channel dealy spread expressed in time samples. The RMSE is defined by:

(dB)

ˆ

log10=RMSE2

2

10

H

HPW

E

E

(2.3.6.15)

The performance is estimated using a Monte-Carlo simulation based on the draw of 1000 randomly generated channels with rectangular time profiles.

Figure 2.3.6.3.1: RMSE versus channel delay spread for a SNR of 15 dB.

The RMSE is below the noise level for the three filter blocks. However, only a marginal gain is achieved for the right filter block. This is explained by the pattern considered in the pilot scheme; on the right edge, 1 KKD channel coefficients have to be interpolated while no pilot subcarriers are located at the edge. From a practical point of view, it is interesting to determine the number of coefficients required depending on the channel delay spread. In Figure 2.3.6.3.2, the variation of RMSE versus channel

delay spread for filter block designed for a channel delay spread of length 64 time samples, SNR15= dB and for various interpolation length Q is given. When filter interpolation length Q is

increased, performance improves. Right filter blocks designed with 4=Q and 6=Q exhibit poor

performance due to the channel delay spread. On the other hand, for left filter blocks, the variation on performance is much smaller and less than 1 dB between the case 4=Q and the case 10=Q .

Increasing interpolation length Q also increases the number of coefficients to store. This number of

coefficient exhibits polynomial complexity in )(2

QO making large numbers of Q costly for

implementation.

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Figure 2.3.6.3.2: RMSE versus channel delay spread for a SNR of 15 dB for various interpolation filter lengths

Q from 4 to 10 .

The influence of the SNR on the channel estimation is given in Figure 2.3.6.3.3. Three filter blocks

have been designed for a channel delay spread of length 16 time samples and SNR values of 15 , 25

and 60 dB. The distance between the thermal noise and RMSE is given as a function of the SNR. For

low SNR of 0dB, a gain of 5 dB is given by a filter block optimized for a SNR of 15 dB. As the noise

level is increased, the filter blocks optimized for a SNR of 25 dB become more optimal up to around 36 dB, when the filter blocks optimized for 60 dB become more appropriate. These results showed the importance of using filter blocks with key characteristics designed around the actual working SNR in order to maximize channel estimation performance.

Figure 2.3.6.3.3: Filtering gain versus SNR for different filter blocks.

To conclude this section, a set of filter blocks for a channel delay spread of length 16 , 32 and 64 time samples at a SNR=15 dB and with 8=Q has been optimized. The RMSE across the active

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subcarrier band (this includes the left and right edges) as a function of the channel delay spread for a

fragment of 262 active subcarriers has been plotted in Figure 2.3.6.3.4. When the channel delay spread is short, the use of an adequate filter block improves the RMSE of the interpolated channel. This figure illustrates the gain offered by the filtering approach if the channel delay spread is known and/or estimated. A comparison between an interpolation structure based on the state of the art and the proposed filter block structure adapted to the edges of the active spectrum is also given. The

proposed method gives a performance improvement of up to 7 dB on the RMSE of the estimated channel. Interpolation errors at the edge of the fragment dominate the RMSE. For large frequency fragment the gain becomes negligible. Performance improvement is mainly due to the small number of pilot subcarriers located in the frequency fragment making the proposed approach particularly adapted to multiuser asynchronous fragmented spectrum usage.

Figure 2.3.6.3.4: RMSE as a function of the channel delay spread for a SNR of 15 dB and for different

interpolation filter blocks.

2.3.7 Equalizer

The proposed equalizer is realized directly after the FFT but before the FBMC prototype filtering. This strategy enables for asynchronous processing of multiuser in the frequency domain using a shared

FFT processor. Assuming the channel delay spread, L , small compared to the KN -point FFT, the symbols at the output of the FFT may be written as follows:

),(),(),()(=),( pkZpkZpkXkHpkRI

(2.3.7.1)

where k is the subcarrier index, p the index of the FBMC symbol, )( kH the complex channel

coefficients for subcarrier k , ),( pkZ the AWGN sample and ),( pkZI

the inter-symbol

interference (ISI) contribution. The channel is here again assumed static for the duration of the burst. When the matrix is diagonal, the ISI term can be omitted. This assumption is a good approximation when the delay spread of the channel is small compare to size of the FFT. To illustrate the validity of this assumption, we depicted in Figure 2.3.7.1 the power of the channel matrix coefficients in dB for

a channel delay spread of size /64KN and /16KN time samples ( KN is set to 512 ). An average

over 1000 channel realizations was done, each tap following a Rayleigh process.

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Figure 2.3.7.1: Average power of the channel matrix coefficients for different channel delay spread.

When the channel is short, the power is located on the diagonal term validating the proposed assumption. When the channel is longer, power spreads over the diagonal term of the matrix and as a result performance of the one-tap equalizer starts showing its limitations. The goal of the equalizer is to recover ),( pkX from the observation ),( pkR and the estimated

channel coefficient )( kH . Zero forcing (ZF) or Minimum Mean Square Error (MMSE) criteria are

classically used and may be expressed as followed:

),()(

)(=),(ˆ

*

pkRkQ

kHpkX (2.3.7.2)

where )( kQ is the optimized factor according to the ZF or MMSE criterion:

2|)(=|)( kHkQ

ZF (2.3.7.3)

)(

)(|)(=|)(

2

2

2

k

kkHkQ

X

Z

MMSE

(2.3.7.4)

where )(2

kX

is the expectation of the power of X on subcarrier k and 2

Z is the expectation of

the power of Z on subcarrier k . For the following, noise power is assumed to be constant over all the subcarriers. The proposed equalization scheme has been evaluated by simulation using the parameters derived

from the LTE mode 10 MHz parameters and can be found in 2.3.7.1.

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Table 2.3.7.1: Simulated System Parameters.

Prototype filter 4=K

,1/2,0.971962{0.235147,=G

7,0}/2,0.2351420.97196,

N 1024

eF 15.36 MHz

Active Carriers 601 ( 9 MHz)

Modulation QPSK

FEC

CC 1/2 , 7=k

1944=FEC

N bits

2/3=R

SOVA algorithm

Channel estimation 8=Q

First, the effects of timing offset (i.e. location of the FFT) on the proposed equalizer has been simulated. The MSE of a QPSK constellation with ZF equalization has been estimated using the

proposed equalization technique for various time offset of the KN -point FFT location. The following channel has thus been considered:

)(=)(

e

k

F

ktth (2.3.7.5)

where parameter k is the timing offset introduced by the FFT processor. An interpolation filter

optimized for a SNR of dB15 and a delay spread of e

F1/32 was considered for channel estimation.

The simulation results are depicted in Figure 2.3.7.2.

Figure 2.3.7.2: Effects of the timing offset on the RMSE on a QPSK modulation.

The MSE on the constellation depends on the timing offset. The worst-case MSE is found when k is

equal to /4N ; in this case the receiver is affected the most by the interference from the previous or next multicarrier symbols. The best-case comes as expected when the FFT is perfectly aligned, i.e. timing offset is close to pNp /2 . This confirms that the proposed frequency domain equalizer

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scheme combined with channel estimation does not require FFT synchronization and is therefore adapted to asynchronous multiuser reception.

The combined performance of the proposed receiver algorithm is then evaluated. A working SNR of

dB5 has been considered and the Bit Error Rate (BER) after Viterbi decoding for various channel delay spread of length L time samples has been measured. The channel impulse response has been defined as:

)(1=)(

2

e

i

L

i

L

F

itth

(2.3.7.6)

where L is the number of taps in the channel impulse response and i

are complex coefficients

following a Rayleigh distribution. With these assumptions, the delay spread of the channel is equal to

eFL / . The resulting BER at the output of the receiver has been evaluated and averaged for 10000

channel realizations. Figure 2.3.7.3 gives the simulated performance of the receiver for various channel interpolation filters as a function of the channel delay spread. Interpolation filters were optimized for

a SNR of dB15 and a channel delay spread of respectively )/(32e

FN , )/(1289e

FN , )/(8e

FN and

)/(4e

FN . Equivalent CP durations (Guard Interval, GI) have been added for reference.

Figure 2.3.7.3: Performance of the proposed receiver for various interpolation filters as a function of channel

delay spread.

The performance obtained with the interpolation filter optimized for a channel delay spread of

length )/(4e

FN time samples is of particular interest as it demonstrated the limitations of the

proposed scheme. When the delay spread of the channel is greater than e

FN /0.15 performance is

limited by the proposed equalization scheme rather than the channel estimation processing as the one-tap equalizer becomes inefficient. On the other hand, for channel delay spread below

eFN /0.15 , one-tap equalization is sufficient and channel estimation performs beyond requirement

when an appropriate interpolation filter is considered. These results compare with the performance

of an OFDM receiver with a guard interval length of at least N1/8 . In Figure 2.3.6.2.2, the guard

interval length for an equivalent OFDM system with a FFT size of N is given. Performance of the receiver may be further improved by considering multi-tap equalization.

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The choice of the interpolation filter also impacted on performance. When a filter optimized for a channel exhibiting a large delay spread is applied to a channel with a short delay spread, a significant amount of noise is not filtered. Performance is then better if the interpolation filter is adapted to the actual channel delay spread. The proposed frequency domain receiver architecture seems very attractive for asynchronous multiuser processing. Fair performance has been obtained by the proposed equalizer scheme; the receiver is robust for large delay spread environment. As a comparison the normal LTE guard interval

is set to s4.69 or approximately N1/14 .

2.3.8 Summary for FBMC

This chapter presented the architecture and algorithms for the considered FBMC transceiver. All the baseband signal processing functions at the receiver are implemented in the frequency domain and no strict synchronization requirement on the FFT, the first element of the receiver, is required. This asynchronous frequency domain processing of the receiver combined with the high stop-band attenuation of the FBMC prototype filter provides a receiver architecture that allows for multiuser asynchronous reception. Particular attention has been paid to CFO compensation in order to relax synchronism requirements beyond one carrier spacing. An algorithm to mitigate ICI has been proposed and simulated. Depending on the receiver target SNR, complexity may be traded-off to keep RMSE introduced by CFO below thermal noise. Channel interpolation has also been carefully considered. As multiuser asynchronous FDMA generates heavily fragmented spectrum blocks, channel estimation should be optimized for the edges of the receiver active carrier bands. A performance improvement of up to 7dB on the RMSE of the estimated channel may result on some simulated scenarios. Finally, a new equalizer scheme has been thoroughly presented. Its complexity is contained while good performance for channel exhibiting large delay spread is achieved. As a comparison, using the

MHz10 LTE parameters, the receiver performs well for channels with delay spread of up to s8.3 .

This compares with standard LTE that been design for channels with delay spread of up to s4.7 .

Moreover, we have demonstrated that the proposed equalizer does not required FFT synchronization and is therefore adapted to asynchronous multiuser reception. Further work should consider implementation performance and complexity estimation with a comparison to similar flexible systems using traditional OFDM techniques. Eventual cost overhead of FBMC implementation and finite precision effects in this context would further complete the study. An analysis in terms of signalling reduction with respect to OFDM will be also conducted and performance comparison between OFDM and FBMC will be performed with respect to asynchronicity (carrier frequency offset and timing misalignement).

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2.4 BFDM

The material presented in this section is largely based on [KWJ+14].

2.4.1 BFDM Principles and Frame Design

In the following we describe a waveform design approach based on bi-orthogonal frequency division multiplexing (BFDM). In this approach, we replace orthogonality of the set of transmit and receive pulses with bi-orthogonality, which is a weaker form of orthogonality. In particular, time--frequency representations of the transmit and receive pulses are pairwise (not individually) orthogonal. Thus, there is more flexibility in designing a transmit prototype, e.g., in terms of side-lobe suppression. The BFDM approach is well suited to sporadic traffic, since the PRACH symbols are relatively long so that i.) transmission is very robust to (even negative) time offsets and, b.) side effects such as spectral regrowth due to periodic setting when calculating the bi-orthogonal pulses are negligible. In addition, BFDM is also more robust to frequency offsets in the transmission which, as well-known, typically sets a limit to the symbol duration in OFDM transmission. Finally, the concatenation of BFDM and several OFDM symbols together requires a good tail behavior of the transmit pulse in order to keep the distortion to the payload carrying subcarriers in PUSCH small. Conversely, the dual pulse which accounts for the distortion of PUSCH onto PRACH can be controlled by iterative interference cancellation (if necessary). This alleviates the typical problem of controlling time/spectral localization of pulse and dual pulse. The excellent and controllable tradeoff between performance degradation due to time and frequency offsets is the main advantage of BFDM. To illustrate the advantages of BFDM, we consider a simple uplink model of a single cell network, where each mobile station and the base station are equipped with a single antenna. We assume there exist two channels--in LTE terminology--the PUSCH and the PRACH. On the PUSCH, the data bearing signals are transmitted from synchronized users to the base station using Single Carrier Frequency Division Multiple Access (SC-FDMA). A small part of the resources is reserved for PRACH, in which, at the first step of the RACH procedure, users send preambles that contain unique signatures. (The percentage of resources for PRACH depends on the overall bandwidth, i.e., since PRACH always uses 6 PRBs, e.g., for 1.4 MHz it occupies 100% of the particular subframe carrying PRACH, and for 20MHz it occupies 6% of the resources of the particular subframe.) Our goal is not only to design suitable waveforms for asynchronous PRACH operations, but also to leave PUSCH operations as unaffected as possible. The general frame structure that we consider, more precisely, the time-frequency resource grid for the described channels is illustrated schematically in Figure 2.4.2. To minimize the interference between the channels, several subcarriers on both sides of the PRACH are usually left zeros as a guard band. The specific PRACH structure and dimensions in LTE are illustrated in Figure 2.4.1.

Figure 2.4.1 LTE PRACH Time/Frequency structure and comparison to PUSCH subframe of 6PRBs.

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In this paper, however, we will exploit the PRACH to carry some data on the guard bands. These users, however, may be completely asynchronous which can be a serious challenge. Specific system parameters can be found in Table 2.4.1 or in LTE specifications [STB09]. Assuming an AWGN channel and one user transmitting its preamble signal on the PRACH, the base station obtains the superposition of data bearing signals, preamble signal, and noise as

𝑟[𝑛] = 𝑠𝑃𝑈[𝑛] + 𝑠𝑃𝑅[𝑛] + 𝑛0[𝑛], (2.4.1)

where 𝑠𝑃𝑈 is the PUSCH data transmit signals, 𝑠𝑃𝑅 is the PRACH preamble transmit signal, and 𝑛0 is Gaussian noise.

In the following, let 𝑇𝑠 denote the sampling period, which is equal to 1

𝑓𝑠, with 𝑓𝑠 being the sampling

frequency. Moreover, Δ𝑓 denotes the subcarrier spacing. Furthermore, we use 𝑇𝑢 to denote the symbol duration and 𝑁 to denote its discrete counterpart. Let 𝑁𝐹𝐹𝑇 be the FFT-length in PRACH.

Figure 2.4.2: PRACH (blue) and PUSCH (red) regions. A guard interval (GI) separates PUSCH from PRACH in LTE (gray). A part of this area is used to support data transmission of asynchronous users (green) in a novel D-PRACH. The D-PRACH

size can be variably determined by MAC.

2.4.2 Summary of Transmitter and Receiver Structure

2.4.2.1 Transmitter

For the pulse shaped PRACH, additional processing is needed, compared to standard OFDM. In contrast to standard processing, we process more than one symbol interval, even if we use only one symbol to carry the preamble. We refer to [SMH02] for implementation details. A pulse 𝑔 is used to shape the spectrum of the preamble signal, e.g., to allow the use of PRACH guard bands with acceptable interference. Let 𝑃 be the length of pulse 𝑔. We extend the output signal 𝑠[𝑛] after the IFFT stage by repeating it and taking modulo 𝑃 to get the same length as the pulse 𝑔. Given 𝐾 symbols, we stack each symbol 𝑠𝑘[𝑛]] as rows in a matrix

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𝑆 =

(

𝑠0[𝑛]

𝑠1[𝑛]⋮

𝑠𝐾−1[𝑛])

∈ ℂ𝐾×𝑃

Each of these vectors is pointwise multiplied by the shifted pulse 𝑔 and superimposed by overlap add, such that we get the base band pulse shaped PRACH transmit signal

𝑠𝑃𝑅𝑝𝑠 [𝑛] = ∑ 𝑠𝑘[𝑛]𝑔[𝑛 − 𝑘𝑁]

𝐾−1

𝑘=0

.

In greater detail, this can be also written as

𝑠𝑃𝑅𝑝𝑠 [𝑛] = 𝛽∑ ∑ ��𝑘,𝑙𝑔[𝑛 − 𝑘𝑁]𝑒

𝑗2𝜋𝑛𝑙

𝑁𝐹𝐹𝑇 ,

where ��𝑘,𝑙 is the Fourier transformed ZC-sequence of length 𝑁𝑍𝐶 at the 𝑘th symbol and 𝑙th subcarrier, 𝑚 is the guard band subcarriers occupied by messages, and 𝛽 is an amplitude scaling factor for customizing the transmit power. The BFDM-based transmitter structure is illustrated schematically in Figure 2.4.3.

Figure 2.4.3 BFDM based pulse shaped PRACH transmitter

2.4.2.2 Receiver

The only difference to the standard PRACH receiver is the processing before the FFT. In standard PRACH processing, the cyclic prefix is first removed from the received signal 𝑟𝑃𝑅[𝑛] and then the FFT is performed. In the pulse shaped PRACH, an operation to invert the (transmitter side) pulse shaping has to be carried out first. To be more precise, first the 𝐾 symbols of the received signal 𝑟𝑃𝑅[𝑛] are arranged as row vectors in matrix

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𝑅 =

(

𝑟0[𝑛]

𝑟1[𝑛]⋮

𝑟𝐾−1[𝑛])

∈ ℂ𝐾×𝑃

Second, each row is pointwise multiplied by the shifted biorthogonal pulse 𝛾, such that we have

𝑟𝑘𝛾[𝑛] = 𝑟𝑘[𝑛]𝛾[𝑛 − 𝑘𝑁].

Subsequently, we perform a kind of prealiasing operation to each windowed 𝑟𝑘𝛾[𝑛]

��𝑘𝛾[𝑛] = ∑ 𝑟𝑘

𝛾[𝑛 − 𝑙𝑁𝐹𝐹𝑇]

𝑃/𝑁𝐹𝐹𝑇−1

𝑙=0

,

such that we obtain the Fourier transformed preamble sequence at the 𝑘th symbol and 𝑙th subcarrier after the FFT operation

��𝑘,𝑙 =∑ ��𝑘𝛾[𝑛]𝑒

−𝑗2𝜋𝑛𝑙𝑁𝐹𝐹𝑇

𝑁𝐹𝐹𝑇−1

𝑛=0.

Although we do not employ a cyclic prefix as in standard PRACH, the time--frequency product of 𝑇𝐹 = 1.25 allows the signal to have temporal and frequency guard regions as well. This time- frequency guard regions and the overlapping of the pulses evoke the received signal to be cyclostationary [Bol01], which gives the same benefit as the cyclostationarity made by cyclic prefix. Furthermore, it is also shown in [Bol01], that the biorthogonality condition of the pulses is sufficient for the cyclostationarity and makes it possible to estimate the symbol timing offset from its correlation function. The BFDM-based PRACH receiver is illustrated schematically in Figure 2.4.4.

Figure 2.4.4 BFDM based pulse shaped PRACH receiver

2.4.3 Pulse shaped PRACH

We adopt a pulse shaping Biorthogonal Frequency Division Multiplexing (BFDM) scheme for PRACH transmissions. The underlying principle is to transmit the symbols according to a set of shifted pulses on time-frequency lattice points (𝑘𝑇, 𝑙𝐹), where 𝑇 is the time shift period and 𝐹 is the frequency

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shift period and 𝑘, 𝑙 ∈ ℤ. As stated in [KM98], the only requirement of perfect symbol reconstruction is that the set of transmit pulses 𝑔𝑘,𝑙 and the set of receive pulses 𝛾𝑘,𝑙 form biorthogonal Riesz

bases. The determining factors to meet that condition are, first, the properties of the pulses itself, and second, the time-frequency product 𝑇𝐹 being greater than one. We choose 𝑇𝐹 = 1.25. As mentioned before, the used pulses 𝑔 and 𝛾 play a key role and should therefore be carefully designed. Since we consider here the BFDM approach, we setup the transmit pulse 𝑔 according to system requirements and compute from 𝑔 the receive pulse 𝛾 as the canonical dual (biorthogonal) pulse. For this computation we follow here the method already used, for example, in [JW07] (see also the further references cited therein). Briefly explained, biorthogonality in a stable sense means that 𝑔 should generate a Gabor Riesz basis and 𝛾 generates the corresponding dual Gabor Riesz basis. From the Ron--Shen duality principle [RS97] follows that 𝛾 has the desired property if it generates on the so called adjoint time--frequency lattice a Gabor (Weyl--Heisenberg) frame which is dual to the frame generated by 𝑔. However, this can be achieved with the 𝑆−1--trick explained in [Dau92]. As a rough and well--known guideline for well-conditioning of this procedure, the ratio of the time and frequency pulse widths (variances) 𝜎𝑡 and 𝜎𝑓 should be approximately matched to the time

frequency grid ratio:

𝑇

𝐹≈ √

𝜎𝑡

𝜎𝑓, (2.4.2)

and this should also be in the order of the channel's dispersion ratio [JW07]. However, here we consider only the first part (2.4.2) of this rule since we focus on a design being close to the conventional LTE PUSCH and PRACH. We propose to construct the pulse 𝑔 based on the 𝐵-splines in the frequency domain. 𝐵-splines have been investigated in the Gabor (Weyl--Heisenberg) setting for example in [Pre99]. The main reason for using the 𝐵-spline pulses is that convolution of such pulses have excellent tail properties with respect to the 𝐿1-norm, which is beneficial with respect to the overlap of PRACH to the PUSCH symbols. We also believe that they trade off well the time offset for the frequency offset performance degradation but this is part of further on-going investigations and beyond the conceptional approach here. Because of its fast decay in time, we choose a second order 𝐵-spline (the ''tent''--function) in frequency domain given by

𝐵2(𝑓) = 𝐵1(𝑓) ∗ 𝐵1(𝑓), where 𝐵1(𝑓) ≔ χ[−1

2,12](𝑓)

It has been shown in [Pre99] that 𝐵2(𝑓) generates a Gabor frame for the (𝑎, 𝑏)-grid (translating 𝐵2

on 𝑎ℤ and its Fourier transform on 𝑏ℤ) if (due to its compact support) 𝑎 < 2 and 𝑏 ≤1

2 and fails to be

frame in the region:

{𝑎 ≥ 2, 𝑏 > 0} ∪ {𝑎 > 0,1 < 𝑏 ∈ ℕ}.

Recall, that by Ron--Shen duality [RS97] it follows that the same pulse prototype 𝐵2(𝑓) generates a

Riesz basis on the adjoint (1

𝑏,1

𝑎) -grid. In our setting we will effectively translate the frequency

domain pulse 𝐵2(𝑓) by half of its support which corresponds to 1

𝐵=3

2 and we will use

1

𝑏⋅1

𝑎=5

4=

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1.25 (see here also Table 2.4.1) such that 𝑎 =6

5. It follows therefore that our operation point

(𝑎, 𝑏) = (6

5,2

3)is not in any of two explicit (𝑎, 𝑏)-regions given above. But for 1.1 ≤ 𝑎 ≤ 1.95 a

further estimate has been computed explicitly for 𝐵2(𝑓) [Table 2.3 on p.560, Pre99] ensuring the

Gabor frame property up to 𝑏 ≤1

𝑎. Finally, we like to mention that for 𝑎𝑏 ≤

1

2 the dual prototypes

can be expressed again as finite linear combinations of 𝐵-splines, i.e. explicit formulas exists in [Lau09]. However, in practice 𝑔 has to be of finite duration, i.e. the transmit pulse in time domain will be smoothly truncated:

𝑔(𝑡) = (sin(𝐵𝜋𝑡)

𝐵𝜋𝑡)2𝜒(𝑡), (2.4.3)

where 𝐵 is chosen equal to Δ𝑓. Theoretically, a (smooth) truncation in (2.4.3) would imply again a limitation on the maximal frequency spacing 𝐵 [CKK12]. Although the finite setting is used in our application, the frame condition (and therefore the Riesz-basis condition) is a desired feature since it will asymptotically ensure the stability of the computation of the dual pulse 𝛾 and its smoothness properties. To observe the pulse's properties regarding time-frequency distortions we depict in Figure 2.4.5 the discrete cross-ambiguity function 𝐴𝑔𝛾 between pulse 𝑔 and 𝛾 which is given as:

𝐴𝑔𝛾(𝜏, 𝜈) =∑𝑔[𝑛]𝛾∗[𝑛 − 𝜏]𝑒𝑗2𝜋𝜈𝑛

𝑛

.

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Figure 2.4.5 The cross-ambiguity function 𝐀𝐠𝛄(𝛎, 𝛕).

It can be observed, that the value at the neighboring symbol is already far below 10−3. Obviously, the bi-orthogonality condition states 𝐴𝑔𝛾(𝑘𝑇, 𝑙𝐹) = 𝛿𝑘,0𝛿𝑡,0 and ensures perfect symbol recovery in

the absence of channel and noise. However, the sensibility with respect time-frequency distortions is related to the slope shape of 𝐴𝑔𝛾 around the grid points. Depending on the loading strategies for

these grid points it is possible to obtain numerically performance estimates using, for example, the integration methods presented in [JW07].

2.4.4 Synchronization and Equalization

Due to the Random Access Scenario that we consider, exact synchronizsation is not needed. In fact, a major design target is to enable asynchronous access and data transmission. Nevertheless, we of course have at least a course synchronization due to the reference signals of the base station in downlink. For the discussion of channel estimation and equalization, we first summarize the user detection procedure in PRACH.

2.4.4.1 User Detection

User detection in PRACH is based on suitably chosen preamble sequences, which are generated as follows. The preamble is constructed from a Zadoff-Chu (ZC) sequence [Chu72], which is defined as

𝑥𝑢[𝑚] = exp {−𝑗𝜋𝑢𝑚(𝑚 + 1)

𝑁𝑍𝐶} , 0 ≤ 𝑚 ≤ 𝑁𝑍𝐶 − 1,

where 𝑢 is the root index and 𝑁𝑍𝐶 is the length of the sequence. We consider here the case of contention-based RACH, where every user wanting to send a preamble chooses a signature randomly

from the set of available signatures 𝒮 = {1,… ,64 − 𝑁𝑐𝑓}, with 𝑁𝑐𝑓 being a given number of reserved

signatures for contention free RACH. Every element of 𝒮 is assigned to index (𝑢, 𝑣), such that the preamble for each user is obtained by cyclic shifting the 𝑢th Zadoff-Chu sequence according to

𝑥𝑢,𝑣[𝑚] = 𝑥𝑢[(𝑚 + 𝑣𝑁𝐶𝑆)𝑚𝑜𝑑 𝑁𝑍𝐶],

where 𝑣 = 1,… , ⌊𝑁𝑍𝐶

𝑁𝐶𝑆⌋ is the cyclic shift index, 𝑁𝐶𝑆 is the cyclic shift size and 𝑁𝑍𝐶 is the preamble

length which is fixed for all users. Since there can only exist ⌊𝑁𝑍𝐶

𝑁𝐶𝑆⌋ preambles that can be generated

from the root 𝑢, the assignment from 𝒮 to (𝑢, 𝑣) depends on 𝑁𝐶𝑆 and the size of set 𝒮. The signatures of different users can be detected as follows. Given the received signal (2.4.1), the PRACH receiver observes the fraction 𝑦 that lies in the PRACH region to obtain the preamble. The receiver stores all available Zadoff--Chu roots as a reference. These root sequences are transformed to frequency domain and each of them is multiplied with the received preamble. The result is

𝑍𝑢[𝑤] = 𝑌[𝑤]𝑋𝑢∗[𝑤],

where 𝑌[𝑤] is the received preamble and 𝑋𝑢[𝑤] is the 𝑢th ZC sequence in frequency domain respectively. Using the convolution property of the Fourier transform it is easy to show that 𝑍𝑢[𝑤] is equal to the inverse Fourier transform of any cross correlation function 𝑧𝑢[𝑑] at lag 𝑑. Because the

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preamble is constructed by cyclic shifting the Zadoff--Chu sequence, ideally we can detect the signature by observing a peak from the power delay profile, given by

|𝑧𝑢[𝑑]|2 = |∑ 𝑦[𝑛 + 𝑑]𝑥∗[𝑛]

𝑁𝑍𝐶−1𝑛=0 |

2. (2.4.4)

Let 𝑉 = ⌊𝑁𝑍𝐶

𝑁𝐶𝑆⌋ be the maximum number of preambles which can be generated from one root. Then

the number of roots that we require to generate 64 − 𝑁𝑐𝑓 preambles will be 𝑁𝑟𝑜𝑜𝑡 = ⌊64−𝑁𝑐𝑓

𝑉⌋. The

signature and the delay of user 𝑖, denoted by 𝑆𝑖 and 𝑑𝑖, respectively, are obtained by the following operation

𝑆𝑖 = 𝑉𝑢 + ⌊𝜏𝑙𝑁𝐶𝑆⌋ , 0 ≤ 𝑢 ≤ 𝑁𝑟𝑜𝑜𝑡 ,

𝑑𝑖 = (𝜏𝑙 𝑚𝑜𝑑 𝑁𝑐𝑠) ⋅𝑁𝐹𝐹𝑇𝑁𝑍𝐶

𝑇𝑠,

where 𝜏𝑙 is the location of the largest peak in (2.4.4).

2.4.4.2 Channel Estimation

The question remains how to obtain an estimation for the channel also on the new D-PRACH subcarriers. Assume the received preamble signal can be written as

𝑦 = 𝐷 ⋅ 𝑊⏟ Φ

⋅ ℎ.

Thereby, 𝐷 is a diagonal matrix constructed from the coefficients of the Fourier transformed preamble and 𝑊 = 𝐹(ℐ𝑝, ℐℎ). The matrix 𝐹 is a ℂ𝑀×𝑀 FFT-matrix, the set ℐℎ ≔ {1,… , 𝑛ℎ} contains

the indices of the first 𝑛ℎ columns, and ℐ𝑝 = {1,… , 𝑖𝑁𝑍𝐶} contains the indices of the central 𝑁𝑍𝐶 rows

of 𝐹. Furthermore, 𝑀 is the length of the subframe without CP and guard interval, and we assume a maximum length 𝑛ℎ of the channel ℎ. For simplicity, we consider simple least-squares channel estimation, i.e., we have to solve the

estimation (normal) equation Φ𝐻Φ ℎ = Φ𝐻ℎ. To handle cases where Φ is ill-conditioned, we use Tikhonov regularization. This popular method replaces the general problem of minx‖𝐴𝑥 − 𝑏‖

2 by min𝑥‖𝐴𝑥 − 𝑏‖

2 + ‖Γ𝑥‖2, with the regularization matrix Γ. In particular, in place of the pseudo-inverse, we use

ℎ = (Φ𝐻Φ+ Γ𝐻Γ)−1Φ𝐻𝑦, where Γ is a multiple of the identity matrix. The idea is, that the estimated channel is also valid for subcarriers that are adjacent to the region for which we actually estimate the channel. Numerical experiments indicate that the estimator is an unbiased estimator (with MSE smaller then 10−4) for up to 200 subcarriers outside the region 𝑊.

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2.4.5 Performance Analysis

In this section we verify, using numerical experiments, that using the PRACH guard bands to carry messages is indeed practicable. We compare the standard (LTE) PRACH implementation to our proposed spline pulse shaped PRACH.

2.4.5.1 Simulation Setup

The simulation parameters, chosen according to LTE specifications, are provided in Table 2.4.1. For the computation of 𝛾 we use the LTFAT toolbox which implements an efficient algorithm [Son12]. Due to the properties of the pulses, and to fit the strict LTE frequency specification, we allow a small spillover effect from PRACH to PUSCH in time. Due to the PRACH pulse length of 4 ms, as depicted in Figure 2.4.2, we simulate the PUSCH over this time interval. Furthermore we use the maximal available LTE bandwidth of 20 MHz.

Table 2.4.1: System Specification

PUSCH Std. PRACH Pulse-Shaped PRACH

Bandwidth 20 MHz 1.08 MHz 1.08 MHz

Symbol duration 𝑇𝑢 0.67 µs 800 µs 1 ms

Subcarrier spacing Δ𝑓 15 kHz 1.25 kHz 1.25 Khz

Sampling frequency 𝑓𝑠 30.72 MHz 30.72 MHz 20.72 MHz

Length of FFT 𝑁𝐹𝐹𝑇 2048 24576 24576

Number of subcarrier 𝐿 1200 839 839

Cyclic prefix length 𝑇𝐶𝑃 160 𝑇𝑠 (1st) 144 𝑇𝑠 (else)

3168 𝑇𝑠 0

Guard time 𝑇𝑔 0 2976 𝑇𝑠 0

Pulse length 𝑃 - - 4 ms

Number of symbols 𝐾 14 1 1

Time-freq. product 𝑇𝐹 1.073 1.25 1.25

In the LTE standard, the power of PRACH is variable and is incrementally increased according to a complicated procedure. To allow a meaningful comparison without having to implement to complete PRACH procedure, we choose the power of the PRACH such that approximately the same power spectral density as in PUSCH is achieved, as depicted in Figure 2.4.6. We simulate multipath channels with a fixed number of three channel taps. Moreover, we assume a maximum length of 𝑛 = 300, which corresponds to a delay spread of roughly 5 𝜇𝑠, and which implies a maximum cell radius of 1.5 km.

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Figure 2.4.6: Power spectral density. The power of the PRACH is chosen to achieve a similar PSD as PUSCH.

2.4.5.2 Data transmission in PRACH

Naturally, using the guard bands for data transmission causes an increased interference level in PUSCH. In Figure 2.4.7, we show the effect on PUSCH symbol error rate caused by data transmission on a variable number of D-PRACH subcarriers, given the standard LTE PRACH and the new BFDM-based PRACH approach.

Figure 2.4.7: Symbol error rate in PUSCH (averaged over all (1200) subcarriers) plotted over the number of D-PRACH subcarriers. The BFDM-based approach slightly reduces the symbol error rate. This effect is stronger when no DFT

spreading is performed in PUSCH.

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Clearly, the performance of PUSCH does not deteriorate due to the proposed BFDM-based PRACH. By contrast, it can be observed that irrespective of the actual number of subcarriers used for data transmission, the BFDM-based approach leads to a slightly reduced interference level in PUSCH. Due to the strong influence of the D-PRACH on neighboring subcarriers in PUSCH, this effect is stronger when no DFT-spreading is used in PUSCH. The reason why larger gains, which could be expected from Figure 2.4.6, cannot be realized is the PUSCH receiver procedure, which cuts out individual OFDM symbols from the received data.

2.4.5.3 Asynchronous users

Asynchronous data transmission is a major challenge that comes with MTC and the Internet of Things. Therefore, we now consider a second, completely asynchronous, user that transmits data in the PRACH. Thereby we assign half of the subcarriers available for PRACH data transmission to this second user. However, we still evaluate only the performance of the original `ùser of interest'' (and consequently we carry out channel estimation and decoding only for this user), which is assumed to transmit at the `ìnner'' subcarriers close to the control PRACH. Thereby, we compare two waveforms, OFDM and the proposed spline approach. Figure 2.4.8shows the results.

Figure 2.4.8: Symbol error rate using 16-QAM in PRACH averaged over 10 out of 20 data subcarriers vs. the time offset of a second user. The other subcarriers are used by the second (asynchronous) user. The black line shows the CP length in

LTE PRACH.

It can be observed, that for completely asynchronous users, i.e., offsets larger than the CP (in which case OFDM loses its orthogonality property), the new pulse shaped approach reduced the symbol error rate up to a factor of almost one half. Nevertheless, the resulting symbol error rate may still seem excessive. However, as Figure 2.4.9 shows, this effect can be compensated by allowing small guard bands (GB) in between the users. Figure 2.4.9 compares the performance of no GB and a GB of only two subcarriers, which already drastically reduces the symbol error rate.

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Figure 2.4.9: Symbol error rate using 16-QAM in PRACH over SNR with presence of a second asynchronous user. Here, the second user has a time offset of 200 µs. The spline based approach outperforms OFDM with or without a small guard

band of two subcarriers.

2.4.6 Application Requirements

The IoT is expected to foster the development of 5G wireless networks and requires efficient access of sporadic traffic generating devices. Such devices are most of the time inactive but regularly access the Internet for minor/incremental updates with no human interaction, e.g. MTC. Sporadic traffic will dramatically increase in the 5G market and, obviously, cannot be handled with the bulky 4G random access procedures [WJK+14]. Our new, conceptional, approach is to use an extended physical layer random access channel (PRACH) which achieves device acquisition and (possibly small) payload transmission "in one shot". Similar to the implementation in UMTS, the goal is to transmit small user data packets using the PRACH, without maintaining a continuous connection. So far, this is not possible in LTE, where data is only carried using the physical uplink shared channel (PUSCH) so that the resulting control signaling effort renders scalable sporadic traffic (e.g., several hundred nodes in the cell) infeasible. By contrast, in our design a data section is introduced between synchronous PUSCH and standard PRACH, called D-PRACH (data PRACH) supporting asynchronous data transmission. E.g., in the simplest approach the D-PRACH uses the guard bands between PRACH and PUSCH. Clearly, by doing so, sporadic traffic is removed from standard uplink data pipes resulting in drastically reduced signaling overhead. Another issue that is closely related to the signaling overhead is the complexity and power consumption of the devices. We show that waveform design in such a setting is necessary since LTE OFDM waveform cannot handle the highly asynchronous access of different devices with possible negative delays or delays beyond the cyclic prefix (CP). Clearly, guards could be introduced between the individual (small) data sections which, though, makes the approach again very inefficient. Moreover, giving up guard bands for transmitting data will naturally lead to increased interference for PUSCH users which must be also handled with waveform design.

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2.4.7 Summary for BFDM

We proposed and evaluated a novel pulse shaped random access scheme based on BFDM, which is especially suited in random access scenarios due to very long symbol lengths. It turns out, that the proposed approach is well suited to support data transmission within a 5G PRACH. In particular, numerical results indicate that the BFDM-based approach does not interfere with PUSCH operations, in fact, it even leads to a slightly reduced interference in PUSCH when using (previously unused) guard bands for data transmission, irrespective of the number of subcarriers used for data transmission. Even more importantly, completely asynchronous users, with time offsets larger than the cyclic prefix duration in standard PRACH, can be far better supported using the BFDM based approach than using standard OFDM/SCFDMA. The presented results will help to cope with the upcoming challenges of 5G wireless networks and the Internet of Things such as sporadic traffic.

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3 Conclusion

This report presents intermediate 5NOW transceiver and frame structure concept. The principles of GFDM, UFDC, FBMC and BFDM are described as well the mechanism for basic synchronization, channel estimation and equalization. Initial performance results, e.g. based on simulations, are presented and a detailed summary is provided for each candidate waveform in its own subsection. GFDM has been introduced as a candidate waveform for the air interface of 5G networks and it has been shown how the modulation scheme can address the requirements imposed by the different scenarios. Various configurations with which the error rate performance is not compromised when compared to OFDM and SC-FDE have been found and MIMO has been presented as a mean to obtain diversity in the system. Synchronization was achieved without affecting the spectral properties of the waveform. The basic signal properties of UFMC have been described. Its spectral properties are clearly advantageous over OFDM and thus increase robustness against sources of inter-carrier interference. Additionally, UFMC subcarriers are orthogonal in the complex domain. Equalization and channel estimation have low complexity and can build upon OFDM techniques. Further, an open-loop timing advance method is tailored to UFMC. Performance results show that UFMC is able to operate with relaxed synchronicity. The usage of multiple signal layers in conjunction with UFMC is possible based upon IDMA. The waveform can also easily embed single-carrier signals within its multi-carrier signal format. All the baseband signal processing functions at the receiver of FBMC have been implemented in the frequency domain where no strict synchronization requirement on the FFT is required. This asynchronous frequency domain processing of the receiver combined with the high stop-band attenuation of the FBMC prototype filter provides a receiver architecture that allows for multiuser asynchronous reception. Particular attention has been paid to CFO compensation in order to relax synchronism requirements beyond one carrier spacing. An algorithm to mitigate ICI has been proposed. Channel interpolation has also been carefully considered and a new equalizer scheme with contained complexity and good performance has been presented. Finally, a novel pulse shaped random access scheme based on BFDM was proposed, which is especially suited in random access scenarios due to very long symbol lengths. In particular, numerical results indicate that this approach does not interfere with PUSCH operations. Even more importantly, completely asynchronous users, with time offsets larger than the cyclic prefix duration in standard PRACH, can be far better supported using the BFDM based approach than using standard OFDM/SCFDMA. The presented results will help to cope with the upcoming challenges of 5G wireless networks and the Internet of Things such as sporadic traffic.

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4 Abbreviations and References

3GPP 3rd Generation Partnership Project 4G Fourth Generation 5G Fifth Generation 5GNOW 5th Generation Non-orthogonal Waveforms for Asynchronous

Signaling ADC Analog-to-Digital Converter BER Bit Error Rate BS Base Station CoMP Coordinated Multipoint DAC Digital-to-Analog Converter EXALTED Expanding LTE for Devices FBMC Filter Bank Multi-Carrier FP7 7th Framework Programme GFDM Generalized Frequency Division Multiplexing GSM Global System for Mobile Communications H2H Human-to-Human ICI Inter-Carrier Interference KPI Key Performance Indicato LTE Long Term Evolution LTE-A Long Term Evolution Advanced MAC Medium Access (layer) MTC Machine Type Communication IoT Internet of Things

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Waveform Candidate Selection - IS-Wireless · valued complex constellation. The resulting vector denotes a GFDM data block that contains N elements, which can be decomposed into K