122

CHAPTER 6

PERFORMANCE OF MULTIBEAM MIMO FOR NLOS

MILLIMETER WAVE INDOOR COMMUNICATION

SYSTEMS

123

CHAPTER 6

PERFORMANCE OF MULTIBEAM MIMO FOR NLOS

MILLIMETER WAVE INDOOR COMMUNICATION

SYSTEMS

High data rate video stream using MMW suffer data loss due to fading effects. Multipath

fading being pre-dominant in indoor, Multi Input Multi Output (MIMO) technology is

considered to be the ideal choice compared with the existing single link systems. As spatial

diversity in both transmit and receive enhances the diversity gain, the performance of the

system is further enhanced by introducing transmit beamforming based antenna beam

diversity. In classical 2x2 MIMO, a diversity gain of 4 is achieved, whereas in this work,

Alamouti code and dualbeam 2x2 MIMO with diversity gain 8 is considered. This chapter

has been formulated for a personal communication system in NLOS indoor environment. In

order to compensate the path loss at 60 GHz, high gain antenna array is proposed. This leads

to achieving highly directive beam, requiring LOS condition. LOS is not suitable for indoor

local environment. To overcome this problem, we have proposed multibeam MIMO to create

rich scattering environment. The proposed system configuration may be highly suitable for

MMW-MIMO in indoor local environment, where systems need not be aligned with LOS

condition. The chapter is organized with section 6.1 discussing survey of reported results,

section 6.2 details the TSV channel Non-Line of Sight (NLOS) parameters, section 6.3

describes the MMW MIMO channel model, section 6.4 describes the three cases in

Multibeam MIMO viz. single beam, dual beam and N-beam, section 6.5 presents the

performance comparison of classical MIMO and Multibeam MIMO and section 6.6 presents

the observations and comments.

6.1 Introduction

Omnidirectional versus directive beams

In recent years, considerable attention has been devoted to the design and standardization of

multi-gigabits per second wireless systems operating at 60 GHz band for a large variety of

low cost consumer applications. Compared with the conventional systems operating in the

lower frequency bands like 2.4 GHz, a significant additive challenge is the achievement of

124

sufficient link budget. The main reason for this is the much lower performance of the RF-

sections as well as the much higher propagation losses. On the other hand, it is easier to

establish highly focused antenna beams at both the ends (or only one end) of the link by

means of small antenna structures. In this manner, the lower RF performance and higher

propagation losses can be compensated by a high antenna gain. Consequently, in the context

of 60 GHz radio design, a paradigm – shift has occurred from omnidirectional antenna to

beamforming antenna.

Spatial Multiplexing

The millimeter wave communication has the advantage of the availability of spatial

multiplexing for MIMO links with moderate antenna spacing even with less scattering

environment. This multiplexing helps to increase the spectral efficiency at millimeter wave

frequencies (Torkildson, E. et al., 2011). For a given linear array of constrained size, spatial

degrees of freedom for millimeter wave line-of-sight (LOS) environment based system

architecture was proposed (Sheldon, C. et al., 2008; Sheldon, C. et al., 2009). The

performance of the proposed architecture in terms of link capacity was measured in an indoor

environment. It was found that the positioning of transmit and receive modes play an

important role in the performance enhancement.

Multipath and MIMO capacity

MIMO capacity increases with rich multipath, i.e spatially uncorrelated channel offers

multiple subchannels based on the antenna configuration (Kermoal, J.P. et al., 2002). But

more the number of multipath, higher is the path loss that leads to reduced SNR. MIMO

capacity as a function of SNR, effective degree of freedom that define the number of

multipaths was analyzed in (Wallace, J.W. and Jensen, M.A. 2003). Apart from the

multipath strength, the angle spread, antenna spacing, array topology significantly improve

the MIMO capacity (McKay, M.R. and Collings, I.B. 2006; Forenza, B. and Heath, R.W.

2005).

Path loss compensation

Path loss increase with increase in frequency. The path loss scales as the square of the

wavelength according to the Friis formula. Penetration effects lead to reduction in signal

strength. Increasing the antenna gain at the transmitter or receiver compensates the loss. This

125

compels the use of highly directive antennae. Fortunately it is easy to synthesize directive

antennae for millimetre waves.

Link reliability using spatial diversity

A simple transmit diversity technique proposed by Alamouti for wireless communication

system achieved full transmit diversity, unity code rate with bandwidth efficiency (Alamouti,

S.M., 1998). A generalised design for space time block code with orthogonal code matrix

facilitating full transmit diversity, code rate of ½ and ¾ were extensively studied and

analysed (Tarokh, V. et al., 1999). Code rate less than unity were not bandwidth efficient but

were found to be suitable in poor scattering environment and indoor environments where

highly directive antenna is used. Closed loop orthogonal space time block codes (OSTBC)

proposed for MIMO systems with more receive antenna compared to transmit antenna. This

was suggested as an alternative to Alamouti code that holds good for 2x2 system yielding full

diversity gain. The closed loop OSTBC is based on the feedback of single phase term which

is a function of the channel gains. This family of channel orthogonalized STBC is found to

achieve full rate for N=3, 4 receive antenna. Thus closed loop OSTBC outperforms the open

loop OSTBC at all SNRs (Milleth, J.K., et al., 2004; Milleth, J.K., et al., 2006). Depending

on the bandwidth and application, various space time coding schemes have come into

deployment. Another variant of space time code was space time trellis code, which is found

to have better coding gain and diversity gain (Tarokh, V. et al., 1998; Chen, Z. et al., 2002).

Increasing Multipath for MIMO

Primarily multipath occur based on the environment, that is excited by the omnidirectional or

directional antenna. Secondly, multipath is created by multiple beams radiated from antenna

array as shown in Figure 6.1 below. Link reliability and capacity increase with increase in

multipath and this shows significant advantages over LOS with high SNR. In indoor

environment since the propagation loss and probability of LOS signal being blocked are high,

the choice of omnidirectional and directional antenna is not considered. Antenna array serves

to address the problem by generating multiple beams. This reduces the probability of

blockage by obstacles and compensates for the propagation losses due to increased antenna

gain.

126

(a)

(b)

Figure 6.1 (a) Single beam and (b) Multibeam MIMO in NLOS

127

Figure 6.1 shows a typical NLOS configuration based on the singlebeam and multibeam

antennas employed for MIMO, for an indoor environment. Our proposed method, such as

multibeam based MIMO improves the performance due to large number of multipaths

compared with single beam.

Rich scattering, improved antenna directivity and performance with multibeam antenna array

configuration were considered (Huang, K-C. and Wang, Z., 2011). The multibeam antennas

are antenna array that make use of beamforming network to produce multiple independent

beams pointing to different directions. By offering independent beams, access point will

switch between these beams to select the channel that has the highest received power. This

feature assists the antenna system to maximize the power received in the desired direction

(Huang, K-C. and Wang, Z., 2011).

The directivity of an antenna scales inversely as the square of carrier wavelength. As a result

of these directive antennae, the multipath environment is much sparser compared to lower

carrier frequencies. Directing the antennae at the transmitting and receiving end can be done

either manually or electronically.

Transmit and receive beamforming is another solution, that analyses the direction of

maximum signal strength and steers the beam in the desired direction. Space time block code

(STBC) coupled with mean values of the underlying channel matrix serves as an eigen

beamformer with multiple beams pointing to orthogonal directions and found as an attractive

choice over one-directional beamforming (Zhou, S. and Giannakis, G.B. 2002; Zhou, W. et

al., 2011). Iterative power method was used to find the CSI which increased the complexity

(Sharma, V. and Lambotharan, S. 2006). Iterative algorithm had slow convergence and

hence maximal norm combining was used to find the Channel State Information (CSI) to

steer the MIMO beam, which served as a good tradeoff between complexity and performance

(Lee, H. et al., 2009). To ease the receiver complexity in MIMO systems, space time coding

with transmit antenna selection was analyzed (Coşkun, A.F. et al., 2012). Also an estimation

of the upper and lower bound of symbol error rate for Nagakami-m fading channel have been

performed in (Coşkun, A.F. et al., 2012).

Indoor environment predominate with LOS and reflected paths, transmit and receive

beamforming serves as an ideal choice to select a subset of antenna elements. This

considerably reduces spatial processing (Dong, ke. et al., 2011). The CSI fedback from the

128

receiver to the transmitter, selects the transmitter antenna elements with the help of

beamforming network. This reduces the requirement of multiple RF chains (Dong, ke. et al.,

2011). Time-varying channels are better estimated over specific frames by transmit

beamforming and CSI known to transmitter (Martos-Naya, E. et al., 2007).

Organization of the work

This work addresses the MIMO MMW propagation in NLOS. Owing to the LOS issues, that

do not ensure safe propagation, antenna array with multibeam is considered in this work. The

multibeam antenna sources multipath in addition to the ones generated in the environment.

The amplitude and phase of the multibeam are analyzed for three different cases vis-a-vis (i)

single beam (ii) dual beam and (iii) general N-beam. In this research work, full rate Alamouti

code and uniform linear antenna array with beamforming network based MIMO

configuration is considered. The complex weights of the beamforming network play a critical

role in generating the beams with controlled interference (Hwang, S-S. and Lee, Y-H. 2005).

The performance is then compared with the classical 2x2 MIMO.

6.2 Indoor NLOS channel model

Shoji, Sawada, Saleh (Triple S) and Valenzuela simply called as Triple SV (TSV) channel

model is a cluster based model (Karedal, J. et al., 2010; Rao, T. et al., 2011). Each cluster is

comprised of many rays. This model is contributed by NICT Japan to the 802.15.3c channel

model subgroup. This is a merger of the two-path model and Saleh-Valenzuela (S-V) model.

This model was found to be much suitable for the indoor environment because of its

capability to describe both the LOS and Non-line-of-sight (NLOS) components (Sato, K. et

al., 2007; Skafidas, E. et al., 2005). The impulse response of the S-V model takes into

account only the complex amplitude of each ray and the Time-of-Arrival (ToA) information

of each ray in a cluster. The impulse response of modified S-V model contains AoA

information also along with ToA information (Sawada, H. et al., 2006; Manojna, S.D. et al.,

2011).

The small scale fading channel impulse response of TSV assuming doppler spread to be

negligible is given by

129

11

, ,

0 0

( ) ( ) ( )lML

lm l l m l l m

l m

h t t T

(6.1)

where h(t) is a complex envelope expression of impulse response of received signal, t and

are ToA and AoA, respectively, (.) means delta function. The parameters in CIR of TSV

are given by

l : cluster number

m : ray number within the lth

cluster

L : total number of clusters

Ml : total number of rays within the lth

cluster

Tl : arrival time of the first ray of the lth

cluster

ml , : delay time of the mth

ray within the lth

cluster relative to the first ray arrival time Tl

l Uniform (0, 2 ]: arrival angle of the first ray of the lth

cluster

ml , : arrival angle of the mth

ray within the lth

cluster relative to the first ray arrival time

The amplitude in impulse response is given by

),0( ,

)](1[

0

2

,,

mllr

mkT

ml Gee mll

(6.2)

]2,0(, Uniformml

where

Ωo is the mean value of amplitude of the first coming wave of the delayed wave,

k is the coefficient used to take the Rician-factor for each cluster into account

Gt directivity function of the transmitting antenna

Gr directivity function of the receiving antenna

130

Figure 6.2 Time dispersive characteristics of TSV channel model

The Figure 6.2 shows the time dispersive TSV channel, where Λ is cluster arrival rate, λ is

ray arrival rate, Г is cluster decay factor, and γ is ray decay factor. The assumptions in

modeling the channel are there will be limited scatterers, brick walls, window panes, floor

and ceiling all of which contribute to diffraction, scattering and reflection. Clusters formed

depend on the type of environment. The number of clusters and rays within a cluster are

limited to four and ten as the amplitude levels of these clusters are within the receiver

sensitivity.

As the number of reflections per ray increases, the corresponding amplitude of the ray

decreases, due to reflection loss and free space loss. Hence, the ray amplitude depends on

room dimensions and the magnitude of reflection co-efficient.

Figure 6.3 shows the power delay profile for 10 channel realizations. The PDP in Figure 6.3

indicates the cluster model of the TSV channel. The NLOS components with cluster power

distribution limiting the number rays to 10 in one cluster is evident in Figure 6.3. The

maximum channel realizations supported in TSV is 100, for computational simplicity the

number of rays was limited to 10. Each cluster has an exponential decrease in power. The

number of clusters depends on the superstructure of the room, floor and ceiling material

(Kirthiga, S. and Jayakumar, M. 2011).

131

Figure 6.3 Power delay profile for 10 channel realizations

Small scale fading effects dominated by multipath delay spread is analyzed in Figure 6.3.

The analysis includes the estimation of the time dispersive parameters i.e RMS delay spread

(RDS), maximum delay spread and mean excess delay. The estimated values serve as a

reference to fix the transmitted symbol period in order to realize frequency flat fading

channel i.e transmitted symbol period has to be much greater than RDS.

The power delay and angle profile are depicted in Figure 6.4. The power of multipath

components within the cluster is the same with variations in ToA and AoA. ToA and AoA

statistics closely relate to the nature of the propagation environment. PDP for a specific

channel in indoor environment have been studied extensively (Holloway, C.L. et al., 1999).

Figure 6.4 shows the PDP of ten channels with three clusters and LOS. The decay

characteristics of PDP can be correlated to the effects of variable indoor values and

properties of the surfaces.

132

Figure 6.4 Power delay profile as a function of ToA and AoA information.

AoA information provides immediate insight into local area fading characteristics, also the

position of the source can be calculated. The LOS component in Figure 6.4 has power of -70

dB with ToA 50 ns and AoA 90o and this component acts as a reference for the NLOS AoA

computation. The effect on spatial correlation of multipath components (MPC) with AoA

between 50o and 180

o that comprise one cluster is the same as they have same signal power

but the effect on angle spread is different. Angle spread ranges between 0 and 1, value 0

indicates the MPC come from single direction while value 1 indicates different directions,

that leads to reduced correlation. Higher the angle spread, lesser is the spatial correlation

(Tang, Z. and Mohan, A.S. 2006). The angle spread depends on the spatial separation

between the antenna and for NLOS indoor it varies between 0.63 and 0.81 (Xu, H. et al.,

2002).

From Figure 6.4, the cluster power indicates the influence of near and far field scatterers, that

contribute to varying AoA and ToA with narrow and wide angle spread. The path traced by

the reflected rays is too long such that the overall power is reduced with increase in ToA. The

ToA from Figure 6.4 is found to vary between 110 and 290 ns.

133

6.3 Millimeter Wave MIMO channel model

The spatial isolation due to oxygen absorption at 60 GHz is beneficial for frequency re-use in

an indoor dense networks, enhances the safety and security of the links and reduction in co-

channel interference. The underlying propagation channel imparts blockages to the multipath

signal, to counter this effect MIMO spatial diversity is used. The classical 2x2 MIMO

configuration for NLOS is analyzed.

The classical MIMO for millimeter wave is analyzed with TSV channel model. The capacity

achieved with multiantenna over the same bandwidth and constant transmit power is

compared to the single antenna system. The transmitter and receiver shown in Figure 6.5 has

the information source modulated and encoded using space time block code (STBC) into a

code transmission matrix. The two transmit antenna with Alamouti STBC is used, as the

scheme which achieves full transmit diversity, full rate and is bandwidth efficient (Alamouti,

S.M., 1998). The orthogonal transmissions ensure full transmit diversity of MT where MT is

the number of transmit antenna. The code transmission matrix S is given by

*12

*21

ss

ssS

,

the dot product of the rows is zero, where s1 and s2 are the modulated symbols, *

1s and *

2s are

the complex conjugate of s1 and s2. As the rows are orthogonal, full transmit diversity is

obtained i.e. TM

H IssSS 22

21 , where

TMI is the identity matrix of size MT x MT. The code

rate which is the ratio of number of transmit symbols to the total number of time slots i.e

m

lR , where l is the number of transmit symbols and m is the number of time slots is unity.

In Alamouti scheme, as l=2 and m=2, the code rate R equals unity, which indicates the code

is bandwidth efficient (Jankiraman, M. 2004). In the receiver, channel estimation using TSV

channel model is done. Orthogonal training symbols are used to train the receiver to perform

better in faded channels.

The training based channel estimation, training symbols are known at both transmitter and

receiver and from the output at the receiver, channel estimation is done (Biguesh, M. and

Gershman, A.B. 2006; Chen, Y. and Su, Y.T. 2010). Block containing both training symbols

and data are sent (Hassibi, B. and Areaochwald, B.M.H. 2003).

134

Figure 6.5 MIMO transmitter and receiver with spatial diversity

Optimum number of training symbols with enough data comprises a block. If more amount

of training symbols are sent, then only less data can be transmitted leading to spectrum

inefficiency so a tradeoff has to be maintained which results in good estimate of channel and

also not compromising on data rate. During the transmission of the data the channel is

assumed to be constant. The PDP of the TSV is used to calculate the delay spread. The delay

spread serves as a reference to calculate the symbol time.

6.3.1 Calculation of symbol period with delay spread parameter

The PDP in Figure 6.3 is analyzed to determine the symbol period. As the symbol period has

to be greater than the delay spread for flat fading characteristic. RMS delay spread using

equation (4.21) and equation (4.22) is determined. The RMS delay spread is found to be

10ns. Since the symbol period should be at least greater than ten times the RMS delay spread,

the symbol period is taken as 1ms and hence block length size is fixed as 1000 bits i.e

h22

Interference

Information

source

BPSK

Modulation

ML Detector

Zero Forcing

Equalizer

Channel

estimation (Least

Squares)

Combiner

Alamouti

Space time

coder

h11

h12 h21

Desired

135

channel is assumed to be constant for this period. Based on this block size, the channel is

estimated.

6.3.2 Combiner

The multiple copies of the same signal are linearly combined to increase the SNR of the

received signal. The three techniques namely selection gain combining, equal gain

combining and maximal ratio combining are the linear combiner techniques. Selection gain

combining selects the signal with maximum SNR and it is further processed by the receiver.

Equal gain combining, combines all the signals with equal gain which is then processed.

Maximal ratio combiner weights the received signal and then combines for further

processing. MRC is preferred as the phase shifts encountered by the signals are co-phased

before combining operation. This increases the SNR. The channel estimation of the

combined signal is performed later.

6.3.3 Channel estimation

6.3.3.1 Least Square channel estimation

The MMW MIMO channel is a frequency flat with delay spread smaller than the symbol

period as discussed in section 6.3.1 and slow fading with doppler spread smaller compared to

transmitted signal bandwidth as in equation (6.1). Flat slow fading channel are best estimated

using LS and MMSE techniques. Training symbols forming part of the transmission are used

for estimating the channel. The complex received signal vector is expressed as y = sH+n,

where s is the training symbol of size MT x 1. To estimate the channel matrix, let N ≥ MT

training signal vectors [s1, s2, ..sN] be transmitted. The corresponding MR x N matrix Y = [y1, y2

…yN] of the received signal is expressed in equation (6.3).

The LS method does not require knowledge of the channel parameters and hence is a little

less efficient (Biguesh, M. and Gershman, A.B. 2006). In LS, channel estimates are found by

minimizing the following squared error quantity

^

HSY (6.3)

YHSYHSYHS

H2

YYYHSHSYHSHS H

H

H

H

^

136

where Y is the received signal, S is the training symbol matrix S= [s1, s2, ..sN] of size MT x N

and ^

H is the estimate of H,

After differentiating with respect to

^

H and equating it to zero, ^

H is obtained

YSHSS HH

YSSSH HH 1

(6.4)

The given solution is further simplified to

Where K = SH

S

6.3.3.2 MMSE channel estimation

The channel estimate H obtained using LS is used in MMSE, to calculate the channel

correlation R. A linear estimator that minimizes mean square error (MSE) of H is expressed

as

HMMSE =YAo (6.5)

Where Y is the output when training symbols are transmitted and Ao has to be obtained so

that the MSE is minimized (Biguesh, M. and Gershman, A.B. 2006).

(6.6)

From equation (6.6) the estimation error can be expressed as

(6.7)

Differentiating equation (6.7) with respect to A,

(6.8)

Using equation (6.8) in equation (6.5), the linear MMSE estimator H can be written as

YS

KH H1^

2^

minargF

o HHEA

2minarg

Fo YAHEA

}{2

FYAHE

H

H

RnH

H

o RSIMPRSA 12 )(

137

(6.9)

where RH is the channel correlation matrix, 2

n - Noise vector at the receiver, 2||.|| Fis the

Squared Frobenius norm.

From the expressions of both the techniques it can be found that MMSE channel estimate

takes both the channel correlation matrix and noise vector at the receiver which results in a

better estimate when compared to that of LS estimate. Equalization is performed on the

channel estimate followed with decoding. BER can be calculated for various values of SNRs.

6.3.4 Maximum Likelihood (ML) decoder

The ML decoder computes the squared euclidean distance between the received signal and

the various combinations of the transmitted signal to estimate the transmitted signal

(Alamouti, S.M., 1998). The ML principle is given as

2

}......,{

^

minarg21 kssss Hsys

TMk

where y is the received signal, H is the channel matrix and s is the transmitted signal. The

search space being 4 for 2x2 MIMO system with transmitted data modulated using BPSK.

6.4 Multibeam MIMO

At MMW range, multibeam antenna systems are widely used with multibeam patterns

forming in space and providing probing signal transmission in the set of desired directions.

This serves to address the MMW propagation in NLOS conditions. Mathematically, the

multibeam is realized by its weight vectors and the direction varies according to the weight

vectors. Multibeam MIMO is analyzed for three special cases (i) Single beam MIMO (ii)

Dualbeam MIMO and (iii) General N-beam MIMO.

6.4.1 Single beam MIMO

For simplicity in performance analysis, a 2x2 MIMO system is considered. The information

source is modulated and encoded using Alamouti STBC that gives two symbols [x1, x2] in a

specific time slot (Jankiraman, M., 2004).

.)( 12^

H

H

RnH

HMMSE RSIMSRSYH

138

Figure 6.6 (a) MIMO with single beam transmitter and single beam receiver and (b) Antenna

array of λ\2 spacing with same amplitude, same frequency and equal phase

3 4

2 1 Antenna

elements

elements

Corporate feed

feed Digital phase shifter

w11

w21

Data

from

STBC

encoder

Input Data

QPSK

Modulation

STBC

Encoder

w11

w21

w12

w22

Linear

Combiner

Channel

Estimation

Equalizer

Demodulator

ML

Detector

h22

h11

TSV Channel

Beamforming

Network

139

The coded symbols are fed to the antenna array that generates single beam per array with the

help of beamforming network (BFN) as shown in Figure 6.6. The weight vectors of the BFN

are of the same amplitude, frequency and equal phase, so as to generate single beam. This

analysis is the same as the classical 2x2 MIMO, which has been discussed in section 6.3. The

radiation pattern obtained with the antenna array is shown below

Figure 6.7 Single main lobe and back lobe obtained using weight vectors of the same

amplitude, frequency and equal phase.

Figure 6.7 shows the single beam generated using antenna array in Figure 6.6b where the

weight vectors w11 and w21 are of the same amplitude, frequency and equal phase.

5 10 15 20

30

210

60

240

90 270

120

300

150

330

180

0

gain (dB)

140

6.4.2 Dualbeam MIMO

For simplicity in performance analysis, a 2x2 MIMO system with dualbeam is studied. The

system model for the proposed concept is depicted in Figure 6.8a and Figure 6.8b. The

information source is modulated and encoded using Alamouti code generating two symbols

[x1, x2]. The baseband symbols are then processed by the RF module and finally by the

beamforming network. The input data to the beamformer has to be ensured zero degree

phase shift. This is required to generate two beams. The weight vector of the beamforming

network is 180 degree out of phase as to reduce the interference between the beams. The

weights are assumed out of phase so as include a null between the two beams which also

reduces the interference between the beams.

(a)

The antenna array shown in dotted lines is expanded in Figure 6.8b.

Input Data

QPSK

Modulation

STBC

Encoder

w11

w21

w12

w22

Linear

Combiner Channel

Estimation

Equalizer

Demodulator

ML

Detector

q22

h22

q11

h11

TSV

Channel Beamforming

Network

141

(b)

Figure 6.8 (a) MIMO with dualbeam transmitter and singlebeam receiver and (b) Antenna

array of λ\2 antenna spacing with out of phase feed configuration (w21= -w11)

In Figure 6.8, the dualbeam of each antenna pair is defined by weight vectors w1 = [w11, w21]T

for the first antenna pair and w2 =[w12 ,w22] T

for the second antenna pair and the TSV

channel co-efficient are h11, q11, h22, q22. Generation of random beams is considered where the

multiple beams interfere in a controlled level. Orthogonal beams do not provide enough

capacity gain so random beam generation through multi-user diversity and multiplexing

(MUDAM) scheme is considered (Hwang, S-S and Lee, Y-H., 2005). The random weight

vector w1 is given by

m=1,2 (6.10)

Where

α – Amplitude of the beam varies from 0 to 1

θ – Angle of beam varies from 0 to 2π.

The four antenna elements in Figure 6.8b, generate two beams. RF signal x1 is fed to antenna

elements 1,2,3 and 4. Weights of the antenna elements 1 and 2 are w11 and w21 is the weight

of the antenna elements 3 and 4. w21 is considered 180o out of phase with respect to w11. The

weight vector W2 is also generated using equation (6.10) and this processes RF signal x2. As

CSI is unknown at the transmitter, equal power is allocated to all the antenna elements. The

3 4

2 1 Antenna

elements

elements

Corporate feed

Digital phase shifter

w11

w21

Data

from

STBC

encoder

1,

1,1,mj

mm ew

142

dual beam radiation pattern obtained using beamforming network (BFN) and antenna array is

shown in Figure 6.9.

Figure 6.9 Two main lobes and two back lobes obtained using out of phase weight vectors.

Generally, 2x2 MIMO systems have channel matrix H with 2x2 elements, so the output at

the receiver is given by

y = Hx + n (6.11)

Where x is the data transmitted and n is the additive white Gaussian noise.

In the proposed work with two sets of dualbeam, four paths exist between the transmit-

receive pair, hence channel matrix in dualbeam comprises of eight elements [h11, q11, h12, q12,

h21, q21, h22, q22 ]. Here, h11 is channel seen by the first beam of the first transmit antenna

array and received by 1st receive antenna and q11 is channel seen by the second beam of the

first transmit antenna array and received by the first receive antenna as shown in Figure 6.8a.

Similarly, h22 is channel seen by the first beam of the second transmit antenna array and

received by 1st receive antenna and q22 is channel seen by the second beam of the second

5 10 15 20

30

210

60

240

90 270

120

300

150

330

180

0

gain (dB)

143

transmit antenna array and received by the second receive antenna as shown in Figure 6.8a.

The remaining channel co-efficients h12, q12, h21 and q21 act as interference co-efficients. Thus

the dualbeam MIMO has four desired paths and four interference paths that increase the

diversity gain from four in classical 2x2 MIMO to eight in the proposed system.

Considering receiver in Figure 6.8a, the received signal y1 by the first receive antenna is

y1 = h11 x1 w11 + q11 x1 w21 + h12 x2 w12 + q12 x2 w22 + n1 (6.12)

STBC encoded data Interference from AWGN Noise

second transmit antenna array

Where

h11, h12 - Elements of channel matrix H

q11, q12 - Elements of channel matrix Q

x1, x2 - RF signal

w11 w21 - Weight vector W1 of first transmit antenna array

w12 w22 - Weight vector W2 of second transmit antenna array

y1 - Received signal of first antenna

Thus the received signals in dualbeam MIMO transmitter with single beam receiver is as

follows

y1 = h11 x1 w11 + q11 x1 w21 + h12 x2 w12 + q12 x2 w22 + n1

y2 = h21 x1 w11 + q21 x1 w21 + h22 x2 w12 + q22 x2 w22 + n2

Putting the above equations in matrix form

2

1

2

2

1

1

2222122221211121

2212121221111111

2

1

n

n

x

x

x

x

wqwhwqwh

wqwhwqwh

y

y

Therefore, the received vector can be expressed as

y = Bx + n (6.13)

Where y is 2x1 vector, B = [H Q] is 2x4 channel matrix, x is 4x1 vector and n is 2x1 vector

144

So this gives an improved diversity gain to the system with multiple copies sent at different

paths and having maximal ratio combiner (MRC) and channel estimation implemented at the

receiver, the performance certainly enhances at the decoder.

Diversity gain for the proposed dualbeam MIMO is 8 obtained from nMTMR, where n is the

number of antenna elements per array which is 2, MT number of transmit antenna equal to 2

and MR is the number of receive antenna equal to 2 (nMTMR =4x2=8). The diversity order of

dualbeam 2x2 MIMO is two times greater than that of the classical 2x2 MIMO. This

significantly improves the power gain and lowers the error rate.

Selection combining is to the elements what switched beamforming was to beams. As each

element is an independent sample of the fading process, the element with the greatest SNR is

chosen for further processing. In selection combining therefore,

otherwise

wn

0

max1 (6.14)

Since the element chosen is the one with the maximum SNR, the output SNR of the selection

diversity scheme is n max , where γn is the SNR of individual branch. Such a scheme

would need only a measurement of signal power, phase shifters or variable gains are not

required. In the above formulation of selection diversity, the element with the best SNR is

chosen. This is clearly not the optimal solution as signals with low SNR are ignored. But,

maximal ratio combining (MRC) obtains the weights that maximize the output SNR, i.e., it is

optimal in terms of SNR.

MRC is applied to equation (6.13) by weighting the received signal and its output is R. The

weights take care of the SNR of the received signal.

NGBXGYGR HHH (6.15)

where G is the weight of each branch of dimension 2x4, the weights are chosen in such a way

that the MRC produces the largest possible value of instantaneous output signal-to-noise ratio

(Jankiraman. M. 2004; Haykin. S. and Moher. M, 2005).

145

The instantaneous output SNR γc of MRC is

R

R

n

M

n

n

M

n

j

nn

o

Xc

g

ebg

N

E

1

2

2

1

(6.16)

Where Ex/No is the symbol energy to noise spectral density ratio, the row vectors of the

weight matrix G and channel matrix B are indicated as gn and bn , bejθ

is the channel fading

component i.e. magnitude and phase.

As γc is to be maximized, which is carried out using standard differentiation procedure,

recognizing that the weighting parameter G is complex, a simpler procedure based on

Cauchy – Schwarz inequality is used. Applying Cauchy-Schwarz inequality to instantaneous

output SNR in equation (6.16) (Haykin. S. and Moher. M, 2005).

R

R R

n

M

n

n

M

n

M

n

j

nn

xc

g

ebg

N

E

1

2

1 1

22

0

(6.17)

Cancelling common terms in equation (6.17) yields

RM

n

n

o

xc b

N

E

1

2 (6.18)

Equation (6.18) proves that in general γc cannot exceed n

n where 2

n

o

xn b

N

E . The equality

in equation (6.18) holds for R

j

n

j

nn Mnwhereebcebcg nn ....2,1)( * , c is some

arbitrary complex constant. Equation (6.18) defines the complex weighting parameters of the

maximal ratio combiner. The weight values of G matrix are proportional to the channel

amplitude B and a phase that cancels the channel phase to within some value that is identical

for all MR branches. Thus permitting coherent addition of the MR receiver outputs by the

linear combiner. Equation (6.18) with the equality sign defines the instantaneous output

signal-to-noise ratio of the MRC which is written as

146

RM

n

n

o

xMRC b

N

E

1

2 (6.19)

Thus the MRC produces an instantaneous output signal-to-noise ratio that is the sum of the

instantaneous signal-to-noise ratios of the individual branches

RM

n

nMRC

1

(6.20)

The MRC is the most optimal diversity combining scheme at the receiver to improve the

performance of the system. The combiner output is then processed by the channel estimation

and channel equalization. MMSE channel estimation based on training symbols is performed.

The second order channel statistics and noise are accounted in MMSE channel estimation.

Zero forcing equalization discussed in section 4.3 is used to equalize the channel effects. As

the codes used for spatial diversity is linear, ML decoder is used. ML decoder computes the

Euclidean distance between the received signal and the actual signal (Jankiraman, M. 2004).

6.4.3 General N-beam MIMO

The system model in Figure 6.8a and Figure 6.8b is considered. The information is space

time encoded using Alamouti code and fed to the RF module. The arbitrary phase of the RF

signal when fed to the beamformer, leads to multibeam generation. Except for the arbitrary

phase of the incoming RF signal, the analysis of N-beam is the same as that of dual beam.

More the number of beams, larger is the number of multipaths. The probability of signal loss

due to blockages is reduced as the multibeam introduces NLOS paths. As a tradeoff between

transmit power and computational complexity, our analysis was restricted to dualbeam.

147

Figure 6.10 Multiple main lobes and multiple back lobes obtained using weight vectors of

random phase i.e 45o

Figure 6.10 shows the three beams generated using the antenna array in Figure 6.6b with

weight vectors of random phase 45o

6.4.4 Relation between scattering environment and antenna spacing

The channel matrix of the multibeam antenna varies depending on three cases (i) critically

spaced (ii) densely spaced and (iii) sparsely spaced. The antenna spacing for indoor system

depends on the scattering mechanism. If the scattering environment is rich enough then

scattered waves coming from all directions can be easily resolved when the antenna spacing

is λ\2. If the scattering is clustered in certain directions then the antenna spacing has be

greater than λ\2. Antenna spacing less than λ\2 caters to directional channels i.e channel that

use high gain directional antenna. The spatial degrees of freedom increase with less spatial

correlation between the channels. Spatial correlation is minimum for antenna spacing equal

to λ\2, hence this increases the rank of the channel matrix and equals the number of receiver

5 10 15 20

30

210

60

240

90 270

120

300

150

330

180

0

gain (dB)

148

antenna. Thus the channel matrix achieves the full rank condition in critically spaced case for

indoor environment.

6.5 Results and Discussion

Classical and Multibeam MIMO performances are analyzed for an indoor environment. More

the number of multipaths, better the system performance i.e fading is completely mitigated in

the presence of infinite diversity (Paulraj, A., 2003). In this work, multipath is introduced in

the form of spatial diversity and multiple beams in addition to that provided by propagation

mechanisms such as scattering, reflection and shadowing. The classical MIMO and

multibeam MIMO are simulated using random samples drawn from the uniform distribution

and noise signal is generated using normal distribution of zero mean and unit variance. The

samples drawn from the distribution are taken to be equiprobable for simple and efficient

decoding.

6.5.1 Classical 2x2 MIMO and Single beam MIMO performance analysis using TSV

A 2x2 MIMO of diversity gain 4 is analyzed using TSV channel. The parameters in Table 6.1

are considered for the simulation. These parameters hold good for analysis of one case in

multibeam MIMO namely single beam.

Simulation parameter Value

Input data 106 bits

Modulation scheme MPSK

Code rate of STBC 1

Transmitting Antenna 2

Receiving Antenna 2

Separation between the transmit and

receive antennas as per NICT standard

3m

Tx and Rx beamwidth 30o

TSV Channel Realizations 10

Combiner MRC

Channel estimation LS and MMSE

Equalizer Zero Forcing

Decoder ML

Table 6.1: Simulation parameters used in 2x2 MIMO using TSV channel

Table 6.1, specifies the parameters used to model the transmitter and receiver of classical

MIMO and single beam 2x2 MIMO and 4x4 MIMO. BPSK is used since spectral efficiency

149

is not matter of concern as MMW has huge bandwidth and ensures reduced probability of

error. Alamouti code of code rate unity is considered to ensure orthogonal space time code.

The transmit and receive beamwidth of 30o is maintained to ensure directional beam. The ten

channel realizations ensure that the delay spread doesn‘t exceed the symbol period in order to

realize flat fading channel. The reason behind considering combiner, channel estimation,

equalization and detection technique is explained in section 6.3.2, section 6.3.3 and section

6.3.4.

Figure 6.11 2x2 MIMO using LS and MMSE techniques employing BPSK modulation

using TSV model.

The orthogonal training symbols are used to train and track the channel. The channel

characterisitics depicted in Figure 6.4 are estimated using LS and MMSE. The channel is

assumed to be constant for a block of 1000 symbols, the block size was determined from the

parameters obtained in Figure 6.3. In Figure 6.11, at SNR greater than 2dB, MMSE

performs better compared to LS. This is due to the fact that the channel correlation and noise

are accounted while computing the channel estimate using MMSE, whereas in LS it is not so,

as expected in section 6.3.3.1.

-2 -1 0 1 2 3 4 5 6 7 810

-6

10-5

10-4

10-3

10-2

10-1

Eb/No,dB

BE

R

LS

MMSE

150

Diversity gain increases with increase in number of antenna, but the increase in antenna leads

to interference. Trading off interference with diversity gain, an optimum multiantenna

configuration i.e 4x4 is considered. In Figure 6.12, the parameters in Table 6.1 are used

except that the number of transmitting and receiving antenna is 4. This analysis is performed

for classical 4x4 MIMO system.

Figure 6.12 4x4 MIMO using LS and MMSE techniques employing MPSK modulation

using TSV model.

Complex code matrix (Tarokh, V., 1999) is used for 4x4 configuration. As the design of the

code matrix satisfies orthogonality criteria, the space time encoder acheives full transmit

diversity, which is 4 equalling the number of tranmit antenna. But the code rate R is 1/2

with number of transmitting symbols equal to 4 and number of time slots equalling 8 and

hence bandwidth is found inefficient. The above features enables linear processing in the

receiver with MRC linear combiner and ML decoder computing the decision metric using the

squared euclidean distance between the received signal and the weighted output versions of

the combiner.

151

6.5.2 MIMO dualbeam transmitter and singlebeam receiver using TSV and Rayleigh

Multibeam MIMO special case dualbeam is analysed. More the number of beams, more is

the number of multipaths, but this leads to reduction in SNR and increased computational

complexity. As a tradeoff between SNR and computational complexity, dualbeam MIMO is

studied. A MIMO 2x2 with dualbeam transmitter of diversity gain 8 is considered and its

performance analysed using TSV and Rayleigh channel models using parameters in Table

6.2.

Simulation parameter Value

Input data 106 bits

Transmit Antenna Array 2 (2 antenna elements per array

with λ/2 spacing)

Weight vector of the antenna

elements (w11,w21 and w12, w22)

Equal amplitude and 180 degree

out of phase

Receiving Antenna 2

Separation between the transmit and

receive antennas as per NICT

3m

Tx and Rx beamwidth 30o and 60

o

Modulation BPSK

Code rate of STBC 1

Channel TSV and Rayleigh

Channel Realizations 10

Diversity Linear Combiner MRC

Channel Estimation LS

Equalizer Zero Forcing

Decoder ML

Table 6.2: Simulation parameters used in dualbeam MIMO using TSV and Rayleigh channel

The parameters discussed as part of Table 6.1 is applicable to Table 6.2, except that each

transmit antenna is replaced with antenna array whose weight vectors are 180o out of phase

to reduce interference between the beams as discussed in section 6.4.2. The directivity of the

transmit and receive antenna is ensured since the beamwidth are 30o and 60

o respectively.

Since Rayleigh channel is the most widely used model for NLOS environment, the

performance of the dualbeam MIMO using TSV and Rayleigh is compared.

152

Figure 6.13 2x2 MIMO dualbeam transmitter and singlebeam receiver using TSV and

Rayleigh channel.

Figure 6.13 analyses the performance of the proposed design using TSV and Rayleigh

channel model. In Figure 6.13, the performance of dualbeam MIMO using TSV is better

compared to dualbeam MIMO using Rayleigh. Typically at high SNR, spatial correlation

between the antenna elements reduces the rank of the channel matrix and leads to Inter

Symbol Interference (ISI). TSV compared to Rayleigh is cluster based model, whose channel

impulse response takes into account the LOS and NLOS along with ToA and AoA of ray and

cluster discussed in section 6.2. The respective power delay and power angle profiles are

depicted in Figure 6.3 and Figure 6.4.

The angle spread in Figure 6.4 is a clear indication of well conditioned indoor channel. The

smaller the angle spread, more is the spatial correlation which tends to reduce the MIMO

channel capacity (Jankiraman, M. 2004; Paulraj, A. et al., 2003). The clustering effect in

TSV model spreads the AoA and hence performance of dualbeam MIMO using TSV is better

-2 -1 0 1 2 3 4 5 6 7 810

-6

10-5

10-4

10-3

10-2

10-1

100

Eb/No (dB)

BE

R

Dualbeam MIMO 2x2 using Rayleigh

Dualbeam MIMO 2x2 using TSV

153

compared to dualbeam MIMO using Rayleigh. This is evident from Figure 6.13, BER of 10-3

at 2.5 dB is achieved with TSV as against 4.5 dB with Rayleigh. The correlation effect can be

reduced with Rayleigh model with λ/2 antenna element spacing. Thus for high attenuation,

rich scattering indoor environment, dualbeam MIMO using TSV is found to be a better

choice compared to dualbeam MIMO using Rayleigh.

6.5.3 Comparison of MIMO dualbeam and Classical MIMO using TSV

The proposed dualbeam performance is compared with classical MIMO under the

assumption that CSI is unknown to the transmitter. The orthogonal space time code of unity

code rate and full transmit diversity and parameters in Table 6.3 are considered.

Simulation parameter Value

Input data 106 bits

Transmitting Antenna Array 2 (2 antenna elements per array

with λ/2 spacing) for dualbeam

MIMO configuration.

2 antennae for classical MIMO

configuration.

Receiving Antenna 2

Separation between the transmit and

receive antenna as per NICT

3m

Tx and Rx beamwidth 30o and 60

o

Modulation BPSK

Code rate of STBC 1

Channel TSV

Channel Realizations 10

Diversity Linear Combiner MRC

Channel Estimation LS

Equalizer Zero Forcing

Decoder ML

Table 6.3: Simulation parameters used in dualbeam MIMO and Classical MIMO

The parameters discussed in Table 6.2 is applicable for Table 6.3 except that the transmit

antenna with and without antenna array using TSV is analyzed.

154

Figure 6.14 Bit Error Rate of Dualbeam MIMO and Classical MIMO using TSV

The dualbeam MIMO with transmit antenna array uses Alamouti code (Alamouti, S.M.,

1998). The receiver decodes the transmitted symbol after two transmission periods. The

number of independent paths between the transmitter and receiver for dualbeam MIMO is 8,

as the elements in the antenna array have out of phase feed configuration. This leads to

generation of two beams from antenna array. In the case of classical MIMO number of

independent paths is 4. The dualbeam exhibits a power gain of 1.6dB compared to classical

single beam MIMO. It is noted in Figure 6.14, that at a BER of 10-3

, the proposed dualbeam

MIMO gains about 1.6 dB relative to the classical MIMO, which can be further improved if

CSI is known to the transmitter.

-2 -1 0 1 2 3 4 5 6 7 810

-6

10-5

10-4

10-3

10-2

10-1

Eb/No (dB)

BE

R

Classical MIMO 2x2

Dualbeam MIMO 2x2

155

MIMO

configuration

Classical

MIMO using

TSV

Single beam

MIMO using

TSV

Dual beam

MIMO using

TSV

Dual beam

MIMO using

Rayleigh

Eb/N0

5 dB 8 dB 5 dB 8 dB 5 dB 8 dB 5 dB 8 dB

BER

2x2 10

-3.6

10-5.6

10-3.6

10-5.6

10-4.7

10-6

10-3.6

10-5

Table 6.4 Comparison of Classical and Multibeam MIMO

A simple 2x2 configuration is considered for comparing classical and multibeam MIMO with

TSV channel model. Also, dualbeam MIMO using TSV and Rayleigh channel model is

analyzed. From Table 6.4, reduction in BER is observed in dualbeam because the two beams

carrying the same data interfere less with each other due to the null between them. And the

same fact contributes to two paths from the transmitter in the place of one path as in the case

of classical and single beam transmitter.

Analysis of 2x2 is performed owing to the fact of reduced complexity and optimal transmit

power compared to other multibeam configurations.

6.6 Conclusion and Contribution

The dualbeam MIMO is the first of its kind proposed for MMW band with simple

modulation scheme i.e BPSK is chosen. As attenuation and human blockages reduce the

signal strength, either high gain antenna or adaptive antenna array were used to improve the

signal reception. High gain antenna is suitable if LOS condition is guaranteed while adaptive

antenna array has propagation delay issue which was of major concern in high definition

video streaming (Yong, S.K. and Chong, C-C. 2007). Hence as a solution to the above

problems, transmit beamformer based antenna array was proposed with equal power

allocation for the antenna elements. In indoor environment, with the influence of strong LOS

and reflected paths using directive antenna is preferred. But since the obstacles indoor

provide rich scattering environment, use of MIMO system with transmit beamforming is

considered.

The transmit diversity for 2x2 system is exploited with respect to STBC and dualbeam

generated using antenna array with two elements per array with out of phase feed

156

configuration. The dualbeam with transmit beamforming and STBC has given diversity gain

of 8 as against the diversity gain of 4 achieved using classical MIMO. The performance of

dualbeam 2x2 MIMO has a power gain of 1.6 dB compared to classical MIMO. The

performance study of dualbeam MIMO using TSV and Rayleigh was also carried out. In low

Eb/N0 range, with only receiver having the knowledge of CSI, the dualbeam performance

using TSV is better compared to Rayleigh with a power gain of 2dB. This is attributed to the

fact, that TSV being cluster based model, considers wide angle spread clusters that generates

almost full rank channel matrix, reducing correlation between the channel elements. Also,

with design criteria of beams satisfying out-of phase condition, the receiver decouples the

transmitted streams and better estimate of the transmitted signal is obtained. This work finds

application in fixed wireless access (FWA). The analysis and the results indicate a low

complex receiver with dualbeam transmit antenna achieves considerable improvement in

performance when the indoor channel is modeled using TSV.