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IMPERIAL COLLEGE LONDON

MIMO HSDPA Using System Value Approach

Hamdi Joudeh

Supervisor: DR. M.K. GURCAN

This report is submitted in partial fulfilment of the requirements for the Degree of

Master of Science (MSc) and the Diploma of Imperial College (DIC)

Department of Electrical and Electronic Engineering

Imperial College London

September 2011

Abstract

Multi-code transmission systems such as HSDPA suffer from severe throughput losses in

frequency selective channels. Energy-constrained rate optimization schemes e.g. the two-

group resource allocation algorithm, improve the performance of HSDPA in such conditions.

However, the computational complexity of such algorithms makes them unattractive solu-

tions. System value approach has been developed recently to reduce the computational

complexity required to perform energy-constrained rate optimization for multi-code trans-

mission systems. This report presents the work done on combining the two-group algorithm

improved by system value approach with MIMO HSDPA. A MIMO HSDPA model that can be

used with different MIMO pre-processing schemes and offers flexibility for resource alloca-

tion was developed. Simulations showed that system value approach significantly reduces

computational complexity. However, bit rates are slightly over-estimated due to approxi-

mation errors. This error was reduced by using optimum and suboptimal channel selec-

tion schemes which were developed to improve the throughput as well. Furthermore, the

developed channel selection schemes provided flexible selection between MIMO diversity

and spatial multiplexing and hence improved performance in MIMO channels with spa-

tial correlations. The improved MIMO HSDPA system gave up to 65% increase in average

throughput over the current standard for a typical urban channel model. Finally, the com-

putational complexity was further reduced using a combination of interference cancelation

and recursive matrix inversion calculations.

i

Contents

Abstract i

Contents ii

List of Figures v

List of Tables vi

Acknowledgement viii

Acronyms ix

Notation xi

1 Introduction 1

1.1 MIMO HSDPA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.1.1 Performance In Frequency Selective Channels . . . . . . . . . . . . . . 2

1.2 Problem Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.1 Computational Complexity . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.2 System Value Approach . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.3 This Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Report Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 MIMO HSDPA Model 6

2.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1.1 MIMO Signature Sequences . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1.2 MIMO Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

ii

CONTENTS iii

2.1.3 Received MIMO Signature Sequences . . . . . . . . . . . . . . . . . . . 8

2.1.4 Data Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.1.5 MIMO Despreading Filter . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2 MIMO Radio Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2.1 Statistical Channel Model . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2.2 Power Delay Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2.3 Spatial Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2.4 Generation of a Fading Correlated MIMO Channel . . . . . . . . . . . 16

2.3 Link Level Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3.1 Radio Channel Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.3.2 System Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.3.3 Generating Multiple MIMO Channels . . . . . . . . . . . . . . . . . . . 22

3 Resource Allocation 23

3.1 MIMO HSDPA Standard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.1.1 D-TxAA Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.1.2 Precoding Weights Selection . . . . . . . . . . . . . . . . . . . . . . . . 25

3.1.3 Single-Stream Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.1.4 Resource Allocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.1.5 Wasted SNIR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.2 Constrained Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.2.1 Equal-Rate Margin Adaptive Loading . . . . . . . . . . . . . . . . . . . 30

3.2.2 Residual Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.2.3 Two-Group Rate Adaptive Loading . . . . . . . . . . . . . . . . . . . . 32

3.2.4 Two-Group Loading with Single-Stream Mode . . . . . . . . . . . . . . 33


3.3 Simulation and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.3.1 Total Throughput . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.3.2 Number of Applied Channels . . . . . . . . . . . . . . . . . . . . . . . 35

3.3.3 Matrix Inversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

CONTENTS iv

4 System Values 39

4.1 Signature Sequence Design and Channel Selection . . . . . . . . . . . . . . . 39

4.1.1 Optimum MIMO Signature Sequences . . . . . . . . . . . . . . . . . . 39

4.1.2 Channel Selection using Water-Filling . . . . . . . . . . . . . . . . . . 41

4.2 System Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.2.1 Gurcan system values and upper bounds . . . . . . . . . . . . . . . . . 43

4.3 Resource Allocation With System Values . . . . . . . . . . . . . . . . . . . . . 44

4.3.1 Improved Two-Group Rate Adaptive Loading . . . . . . . . . . . . . . 46

4.3.2 Optimum Channel Selection For Two-Group Loading . . . . . . . . . . 47

4.3.3 Suboptimal Channel Selection For Two-Group Loading . . . . . . . . . 48


4.4 Successive Interference Cancelation . . . . . . . . . . . . . . . . . . . . . . . . 50

4.4.1 SIC implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.4.2 Iterative Energy and Covariance Matrix Inversion Calculations . . . . . 51

4.5 Simulation and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.5.1 Total System Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.5.2 Total Throughput . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.5.3 Matrix inversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.5.4 Spatial Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

4.5.5 Approximation Error and Energy Margin . . . . . . . . . . . . . . . . . 60

4.5.6 SIC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5 Conclusion 65

A I-METRA Channel Parameters 67

B Simulation Package 68

B.1 Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

B.2 Resource Allocation Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

B.3 Presentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

References 71

List of Figures

2.1 Ped-A and Ped-B power delay profiles. . . . . . . . . . . . . . . . . . . . . . . 20

2.2 Ped-A and Ped-B modified power delay profiles. . . . . . . . . . . . . . . . . . 20

3.1 TGmode and D-TxAA - Throughput - Ped-A. . . . . . . . . . . . . . . . . . . . . 35

3.2 TGmode and D-TxAA - Throughput - Ped-B. . . . . . . . . . . . . . . . . . . . . 36

3.3 TGmode and D-TxAA - Number of Channels Applied . . . . . . . . . . . . . . . 36

3.4 Total Two-Group throughput for different energy error values. . . . . . . . . . 38

3.5 Number of matrix inversions for different energy error values. . . . . . . . . . 38

4.1 Total system value for different energy allocation schemes. . . . . . . . . . . . 54

4.2 Upper bounds, D-TxAA and TGSV schemes - Throughput - Ped-A. . . . . . . . 55

4.3 Upper bounds, D-TxAA and TGSV schemes - Throughput - Ped-B. . . . . . . . . 56

4.4 Number of matrix inversions for different schemes for energy error 0% and

1%. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.5 Throughput and number of applied channels - Ped-A(corr). . . . . . . . . . . . 59

4.6 Throughput and number of applied channels - Ped-B(corr). . . . . . . . . . . . 59

4.7 Approximation error - Throughput and energy margin - Water-filling selection 61

4.8 Approximation error - Throughput and energy margin - Suboptimal selection 62

4.9 Approximation error - Throughput and energy margin - Optimum selection . . 63

4.10 Energy margin for system value two-group with SIC energy calculations . . . 63

B.1 General steps for resource allocation schemes programs. . . . . . . . . . . . . 69

v

List of Tables

2.1 Simulation Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.1 Average number of matrix inversions for different energy error values. . . . . 37

4.1 Maximum required matrix inversions for different resource allocation schemes. 50

4.2 Matrix inversion required for system value with SIC. . . . . . . . . . . . . . . 54

4.3 Average capacity increase for different two-group schemes compared to D-

TxAA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.4 Average number of matrix inversion for different schemes. . . . . . . . . . . . 58

4.5 Average number of matrix inversion - SIC energy calculation. . . . . . . . . . 61

A.1 I-METRA channel parameters for Ped-A(corr) and Ped-B(corr). . . . . . . . . . . 67

B.1 Resource allocation schemes MATLAB programs. . . . . . . . . . . . . . . . . 69

vi

To Yousef...

vii

Acknowledgement

My effort alone could not have produced this thesis. A number of individuals provided

invaluable support and guidance, which helped shape both the contents and process of

completing the work.

My first thanks go to my supervisor Dr. Mustafa K. Gurcan who kindly invested his time

to teach me how to think creatively and become a true researcher. His brilliant insights

have, undoubtedly, opened for me new horizons.

I would also like to thank all teaching staff in the department of Electrical and Electronic

Engineering who gave me support and from whom I learned during the MSc course at

Imperial College.

Many thanks to Hani Qaddumi Scholarship Foundation without whose help, it would

have been impossible for me to study in the UK.

Last but certainly not least, I wish to acknowledge the critical role my family has played

in helping me become the person I am.

viii

Acronyms

2G Second Generation

3G Third Generation

3GPP Third Generation Partnership Project

AMC Adaptive Modulation And Coding

AoA Angle Of Arrival

AS Angle Spread

CSI Channel State Information

DSL Digital Subscriber Line

D-TxAA Dual-Stream Transmit Antenna Array

FDD Frequency Division Duplex

GSM Global System for Mobile Communication

HSDPA High Speed Downlink Packet Access

HSPA High Speed Packet Access

HSUPA High Speed Uplink Packet Access

ICI Inter-Code Interference

i.i.d Independent and Identically Distributed

I-METRA Intelligent Multi-Element Transmit and Receive Antennas

ISI Inter-Symbol Interferences

ix

ACRONYMS x

LOS line of sight

MCS Modulation and Coding Scheme

MIMO Multiple-Input Multiple-Output

MMSE Minimum Mean Square Error

MSE Mean Square Error

NLOS No Line Of Sight

OVSF Orthogonal Variable Spread Factor

PAS Power Angular Spectrum

PCI Precoding Control Indicator

PDP Power Delay Profile

SIC Successive Interference Cancelation

SISO Single-Input Single-Output

SNIR Signal to Noise and Interference Ration

SNR Signal to Noise Ration

SVD Singular Value Decomposition

TTI Transmission Time Interval

TxAA Transmit Diversity Antenna Array

UE User Equipment

UMTS Universal Mobile Telephone System

WCDMA Wideband Code Division Multiple Access

Notation

A Matrix

~a, ~A Column vector

a, A Scalar

A (col : l) lth column of matrix A

|~a| Norm of vector ~a

|a| Absolute value of a

E [ . ] Expectation operator

(.)T Transpose

(.)H Complex conjugate transpose (Hermitian)

diag (~a) Diagonal matrix of vector ~a

diag (A) Vector of diagonal elements of matrix A

rank (A) Rank of matrix A

trace (A) Trace of matrix A (summation of diagonal elements)

⊗ Kronecker product

� Hadamard product

〈X,Y 〉 Cross correlation between X and Y

IN (N ×N) Identity matrix

~0N (N × 1) Vector of zeros

xi

Chapter 1

Introduction

The Global System for Mobile Communication (GSM) is probably the most successful second

generation (2G) mobile communication system. Introduced in the early 90s of the last

century to offer voice communication services and short text messaging, GSM was further

enhanced to include data transmission. However, GSM was never intended to be used as a

data network as it was based on circuit switched technology [14]. The increasing demand

for multimedia communication and data access fuelled the development of third generation

(3G) mobile communication systems. Universal Mobile Telephone System introduce by the

Third Generation Partnership Project (3GPP) in Release 99 was born with the new century

and it is considered the 3G legal inheritor of GSM. UMTS uses wideband code division

multiple access (WCDMA) as the air interface technology and provides internetworking

with deployed GSM networks [22].

The theoretical maximum throughput for UMTS Release 99 is 2 Mbps. However, the

peak data rate is limited to 384 kbps in practice. This enabled low-end data applications

but it was obvious that it would not withstand the increase in demand for mobile data

services. High Speed Downlink Packet Access (HSDPA) was one of the solutions introduced

to meet this demand. HSDPA was introduced as part of UMTS Release 5 to enable high speed

data access. HSDPA is based on multi-code transmission where several signature sequences

(spreading codes) are applied as parallel channels to provide users with a mobile service

similar to the one provided by fixed Digital Subscriber Lines (DSL). HSDPA uses techniques

including Adaptive Modulation and Coding (AMC), fast link adaption and fast physical layer

1

CHAPTER 1. INTRODUCTION 2

retransmission to realise a peak data rate of 14 Mbps. In UMTS Release 6, techniques used

with HSDPA were extended to be used in the uplink direction. This is known as High Speed

Uplink Packet Access (HSUPA) and together with HSDPA they form what is known as High

Speed Packet Access (HSPA) [22].

1.1 MIMO HSDPA

WCDMA UMTS and HSPA achieved remarkable global success and continuous increase in

mobile broadband drove further improvements [9]. To increase spectral efficiency and

throughput, Multiple-Input Multiple-Output (MIMO) techniques were applied to HSDPA

in Release 7 as part of evolved HSPA (HSPA+) achieving a peak downlink rate of 28 Mbps.

Later releases included more improvements that will be discussed in chapter 3.

Generally speaking, MIMO systems usually operates in one of two modes; spatial mul-

tiplexing mode or transmit diversity mode [10]. For spatial multiplexing, multiple data

streams are transmitted simultaneously over orthogonal beams using precoding and mul-

tiple transmit antennas. For transmit diversity, one data stream is transmitted where pre-

coding over the multiple transmit antennas is used to enhance the received signal quality

and hence increase data rate. MIMO HSDPA is no exception as precoding is used on top of

spreading either to reuse the set of signature sequences over multiple data streams (spatial

multiplexing) or to improve the detection of the same number of signature sequences used

for Single-Input Single-Output (SISO) HSDPA (transmit diversity).

1.1.1 Performance In Frequency Selective Channels

Peak rates estimated for HSDPA generally assume perfect channel conditions. However, dif-

ferent environments would give different channel conditions which are not always perfect.

Frequency selective channels are known to have a bad effect on multi-code transmission

systems. The transmitted signal arrives with different delays and a signature sequence is

generally non-orthogonal to delayed versions of itself or other sequences. For significant

delay spreads, orthogonality of sequences is destroyed [25] causing inter-code interference

(ICI). In addition to ICI, MIMO HSDPA also suffers from inter-stream interference [34] as

delay spread damages precoding orthogonality as well. Furthermore, measurement based


evaluations for MIMO HSDPA show that measured rates are far from achievable throughputs

for urban scenarios where delay spread can be significant [29].

1.2 Problem Overview

The Resource allocation scheme used in MIMO HSDPA standards allocate equal energies

to all signature sequences in operation [6]. Bit rates are allocated equally to all signature

sequences that belong to the same precoded data stream. In frequency selective channels,

the system suffers from ICI and inter-stream interference as discussed earlier. Different

signature sequences will experience different signal to noise and interference ration (SNIR)

at the receiver. Hence, the bit rate of sequences in a given data stream will be limited to the

bit rate operational by the sequence with the least quality. Using equalization is common

for such conditions [25,28]. However, when the delay spread is significant, a receiver with

moderate complexity only reduces the channel effect and orthogonality is not restored.

This problem can be approached by combining equalization at the receiver with energy

control at the transmitter to achieve minimum possible ICI [33]. A constrained optimization

process based on equal-rate margin adaptive loading can be used to calculate energies and

bit rate to operate. This process includes a search for the maximum possible bit rate using

iterative energy calculations. The bit rate is chosen from a finite set provided by AMC which

possible results in quantization loss. Quantization loss can be reduced (and hence the bit

rate increased) using smaller bit granularities. However, it may be wise to avoid using very

small bit granularities as it would lengthen the iterative search operation. Quantization

loss can also be reduced using two-group rate adaptive loading where a higher bit rate is

assigned to a number of signature sequences known as the second group [20].

1.2.1 Computational Complexity

Originally developed for SISO HSDPA, two-group rate adaptive loading can be applied to

MIMO HSDPA with some modification. However, the main holdback is that constrained

optimization based algorithms are computationally heavy. This is due to the a large number

of matrix inversions required for iterative bit rate search and energy calculations. This

computational complexity may not be suitable for mobile applications with limited battery


life and signal processing capabilities

1.2.2 System Value Approach

System value approach [17] was developed to reduce the computational complexity re-

quired to perform rate optimization for multi-code transmission systems. System value ap-

proach significantly reduces the number of matrix inversions required to perform equal-rate

margin adaptive loading and two-group rate adaptive loading. Furthermore, system value

approach can be combined with interference cancelation and recursive matrix calculations

to reduce complexity to a level that can be practical for implementation.

1.2.3 This Project

The main focus of this project is the downlink single user throughput where all available

signature sequences are allocated to one User Equipment (UE). The throughput is improved

by combining system value approach and MIMO HSDPA. The accuracy of the new approach

is tested, limits are explored and performance is improved using channel selection. Further-

more, the system value improved MIMO HSDPA system is compared to the current HSDPA

system standardized by 3GPP. All results and plots provided in this project are based on

MATLAB simulations.

1.3 Report Organization

This report consists of five chapters. After this chapter, chapter 2 describes the MIMO HS-

DPA model used throughout this work. This includes MIMO channel model and the MIMO

receiver model. Furthermore, the method used to generate MIMO channels for simulation

and other simulation parameters are described.

The HSDPA model described in chapter 2 is used to model the MIMO HSDPA standard at

the beginning of chapter 3. The rest of chapter 3 deals with resource allocation beginning

with the scheme used in the current standard which is followed by a modified two-group

resource allocation algorithm for MIMO HSDPA. Simulation results associated with perfor-

mance evaluation and analysis are provided at the end of the chapter.


Chapter 4 starts by providing optimum signature sequence design and water-filing based

channel selection which are essential for the system value approach. Afterwards, system

value approach is presented followed by an improved two-group loading schemes using

system values. Furthermore, improved signature sequence selection schemes are presented.

Interference cancellation and energy calculations are provided before presenting simulation

results and analysis at the end of the chapter.

Finally, Chapter 5 concludes this report. The five chapters are followed by a couple of

Appendices including MIMO channel correlation parameters used and explanation for the

MATLAB simulation package developed as part of this project. The full MATLAB code is

provided in the associated CD.

Chapter 2

MIMO HSDPA Model

This chapter introduces the MIMO HSDPA model used throughout the report. This model

includes the MIMO receiver design and signal to noise and interference ratio (SNIR) cal-

culations. The MIMO channel model used throughout this report is also described in this

chapter including the method used to generate different MIMO channels. Finally, the link

level simulator parameters used in this work are discussed at the end of this chapter.

2.1 System Model

This section presents some of the MIMO system parameters and provides formulation for

the MIMO signature sequences used throughout this report.

We assume a MIMO multi-code CDMA system applying Nt transmit antennas, Nr receive

antennas and a spreading factor per transmit antenna equal to N . Ideally, a maximum of

min (Nt, Nr) independent data streams can be multiplexed given typical MIMO channel

conditions [31]. The total number of available channels 1 Ktotal can reach min (Nt, Nr)N .

However, the number of channels for the user data transmission K is usually less than

the total number of available channels K < Ktotal as one (or more) signature sequence is

preserved for common channels.

A common formulation is done by loading each of the data streams with N (or less)

channels where the set of N signature sequences is typically reused over all data streams.

1The term ”channel” is used in this report to refer to a code channel spread by a signature sequence. However,the term ”MIMO channel” refers to the radio channel response.

6

CHAPTER 2. MIMO HSDPA MODEL 7

This is usually followed by a MIMO pre-processing stage where each data stream is weighted

by Nt weights and transmitted over the Nt antennas [11].

2.1.1 MIMO Signature Sequences

The model given in this report integrates all MIMO pre-processing into the signature se-

quences and assumes that each channel is spread using Nt different signature sequences,

one for each transmit antenna. The set of Nt signature sequences used to spread a given

channel form what is defined as a MIMO signature sequence which is NNt chips long. For

the K channels used in data transmission, the NtN ×K MIMO signature sequence matrix

given as

S = [~s1, · · ·~sK−1, ~sK ]

=[ST1 , · · · ,STNt

]T(2.1)

where the vectors have the properties of unity norm |~sk|2 = 1 and the N ×K matrix Snt is

the ntht transmit antenna signature sequence matrix.

This formulation serves the purpose of looking at the MIMO multi-code system as a SISO

system extended to include more channels and helps applying existing theory. However,

even though the MIMO signature sequences have extended lengths, the same spreading

factor per antenna is used and there is no need to increase bandwidth or decrease symbol

rate.

2.1.2 MIMO Channel

A MIMO channel is generally viewed as a set of NrNt MIMO paths connecting each transmit

antenna to all receive antennas. When the radio channel is frequency selective, each of the

MIMO paths is formulated as a multipath fading channel on its own. However, these MIMO

paths can be correlated as we will see later.

Assuming that the number of resolvable paths at each antenna is L, the multipath chan-

nel impulse response vector for the MIMO path between the ntht transmit antenna and the


nthr receive antenna is given as

~h(nr,nt) =[h

(nr,nt)0 , h

(nr,nt)1 , · · · , h(nr,nt)

L−1

]T(2.2)

where the lth tap represents the channel response at delay lTc and with Tc being the chip

period. The (N + L− 1) ×N channel convolution matrix [20] of the MIMO path from the

ntht transmit antenna to the nthr receive antenna is formed as

H(nr,nt) =

h(nr,nt)0 0 · · · 0

... h(nr,nt)0

...

h(nr,nt)L−1

.... . . 0

0 h(nr,nt)L−1 h

(nr,nt)0

......

. . ....

0 0 · · · h(nr,nt)L−1

(2.3)

and the Nr (N + L− 1)×NtN MIMO channel convolution matrix can be formed as

H =

H(1,1) · · · H(1,Nt)

.... . .

...

H(Nr,1) · · · H(Nr,Nt)

(2.4)

When simulations are carried out, a fading radio channel would generally follow a stan-

dard power delay profile (PDP). This will be discussed in more depth alongside with corre-

lations between MIMO paths in section 2.2.

2.1.3 Received MIMO Signature Sequences

The MIMO channel convolution matrix convolves the MIMO signature sequence matrix S

and yields the Nr (N + L− 1)×K MIMO receiver signature sequence matrix given as

Q = HS

= [~q1, · · · ~qK−1, ~qK ]

=[QT

1 , · · · ,QTNr

]T(2.5)


where the (N+L−1)×K matrix Qnr is the nthr receive antenna receiver signature sequence

matrix. The same concept applied to S is applied here where the Nr (N + L− 1) chips long

received MIMO signature sequence for a given channel is formed by stacking Nr received

signature sequences, one from each receive antenna.

In the presence of more than one resolvable path (L > 1), signature sequences per re-

ceive antenna would be longer than signature sequences per transmit antennas. This causes

inter-symbol interference (ISI) that should be considered and dealt with at the receiver. The

Nr (N + L− 1) × 3K extended receiver signature sequence matrix - incorporating ISI - is

formulated as

Qe =[Q,Q(−1),Q(+1)

](2.6)

where Q(−1) = H(−1)S =[~q

(−1)1 , · · · , ~q(−1)

K

]is the MIMO receiver signature sequence matrix

for the previous symbol and Q(+1) = H(+1)S =[~q

(+1)1 , · · · , ~q(+1)

K

]is the MIMO receiver

signature sequence matrix for the next symbol. H(−1) is the channel convolution matrix for

the previous symbol period which given as

H(−1) =

(JT)N H(1,1) · · ·

(JT)N H(1,Nt)

.... . .

...(JT)N H(Nr,1) · · ·

(JT)N H(Nr,Nt)

(2.7)

and H(+1) is the channel convolution matrix for the next symbol period which is given as

H(+1) =

JNH(1,1) · · · JNH(1,Nt)

.... . .

...

JNH(Nr,1) · · · JNH(Nr,Nt)

(2.8)

where the (N + L− 1)× (N + L− 1) shift matrix J is given as [30]

J =

~0TN+L−2 0

IN+L−2~0N+L−2

(2.9)

When the matrix J(JT)

operates on a column vector, it downshift (upshift) the column

by N chips filling the top (bottom) of the column with N zeros.


2.1.4 Data Transmission

In HSDPA, bits are encapsulated in packets with lengths determined by the transmission

time interval (TTI). The number of symbols per channel transmitted over one TTI is constant

and given as

N (x) =TTINTc

(2.10)

Typically, the transmitter adapts the transmission rate by changing the modulation and

coding combination. This is done every TTI as information regarding channel estimation is

fed back from the receiver [14]. For simplicity, it is assumed that the radio channel is a block

fading channel [36] where the channel response is constant over a TTI. Hence, all symbols

in a block of N (x) symbols per channel would - hypothetically - experience the same channel

conditions. A block of normalized transmitted M-QAM symbols for K channels formulates a

N (x) ×K transmit symbol matrix given as

X = [~x1, · · · , ~xK ] (2.11)

where symbols for each channel have unity average energy. The average symbol energy

assigned to each channel is controlled by the K ×K amplitude matrix given as

A = diag(√

E1,√E2, · · · ,

√EK

)(2.12)

where Ek is the average symbol energy assigned to channel k. Energies satisfy∑K

k=1Ek ≤

ET where ET is the total available energy per symbol period at the transmitter. After as-

signing energies to the K channels, symbols are spread using S and then transmitted using

the Nt transmit antennas.

At the receiver, the received chips are formulated using the same concept used in 2.1.3

where chips received from theNr receive antennas and belonging to the same symbol period

are stacked to form a received symbol chip vector. The N (x) received symbols chip vectors


form the Nr (N + L− 1)×N (x) received symbols matrix which can be written as

R = QeAeX + N

= [~r1, · · · , ~rN(x) ]

=[RT1 , · · · ,RTNr

]T(2.13)

where Rnr is the (N + L− 1) × N (x) received symbols matrix at the nthr receiver antenna

and N is the Nr (N + L− 1) ×N (x) noise matrix assuming a white Gaussian radio channel

with sampled noise variance at the receiver N0 = 2σ2. ISI is incorporated in R by using the

3K × 3K extended amplitude matrix given as

Ae = diag(√

E1, · · · ,√EK ,

√E1, · · · ,

√EK ,

√E1, · · · ,

√EK

)= I3 ⊗ A (2.14)

and the 3K ×N (x) extended transmit symbol matrix is given as

X =[X,X(−1),X(+1)

]T(2.15)

where X(−1)(

X(+1))

contains symbols transmitted in the previous (next) symbol period and

can be obtained by shifting columns of X down (up) by one and filling the top (bottom) of

the X with K zeros.

The formulation of R makes it easy to apply the MIMO despreading filter provided in

the next subsection. However, if it is required to stack the received chips in the same way

in a practical system, intersection between adjacent symbol periods when L > 1 should be

considered.

2.1.5 MIMO Despreading Filter

Orthogonal signature sequences are generally used to spread channels in HSDPA. For fre-

quency selective channels (L > 1), the received signal suffers from ISI as shown in the R

model. ISI destroys orthogonality of signature sequences [25] producing inter-code inter-

ference (ICI) between the received signature sequences and degrading the performance of


the conventional matched filter RAKE receiver [26]. Alternatively, Minimum Mean Square

Error (MMSE) equalization partially restore orthogonality providing improved performance

over conventional RAKE [15], [27].

For SISO and SIMO multi-code systems, MMSE filter coefficients calculation at the re-

ceiver takes ICI in consideration. However, For a MIMO multi-code system, spatial inter-

ference between signals transmitted on different transmit antennas should be considered in

addition to ICI [28]. An MMSE filter is generally followed by a despreading stage where

data streams belonging to different channels are separated.

The filter used throughout this report operates on signals received from the Nr antennas

[11] and performs equalization and despreading simultaneously. The formulation of Q and

R makes it possible to use the same approach used in [19] for SISO to design a MIMO

MMSE despreading filter. The filter coefficients for channel k can be found by minimizing

the mean square error (MSE) given as

ξ2k = E

[(xk − ~wHk ~r

)2], k = 1, · · · ,K (2.16)

where xk is a symbol transmitted over channel k with unity average energy and ~r is the

Nr (N + L− 1)× 1 MIMO received chip vector formulated by stacking the chip vectors cor-

responding to the same symbol period of xk and obtained from theNr receive antennas. The

Nr (N + L− 1)×1 vector of MIMO despreading filter coefficients obtained from minimizing

ξ2k is given as

~wk =√EkC−1~qk , k = 1, · · · ,K (2.17)

where C is the Nr (N + L− 1)×Nr (N + L− 1) covariance matrix at the receiver given as

C = E[~r~rH

]= QeA

2eQ

He + 2σ2INr(N+L−1) (2.18)

A normalized vector that compensates for the path and filtering losses is given as

~wn,k =C−1~qk

~qHk C−1~qk(2.19)


where ~wHn,k~qk = 1 is satisfied. The received symbols vector for the kth channel can be

obtained as

~χTk = ~wHn,kR (2.20)

The MSE for the kth channel after using ~wn,k can be written as ξ2k = 1−Ek~qHk C−1~qk from

which the SNIR at the output of the filter for the kth channel γk can be obtained as

γk =1− ξ2

k

ξ2k

=Ek~q

Hk C−1~qk

1− Ek~qHk C−1~qk(2.21)

SNIR calculation inherits the covariance matrix inversion process required to obtain the

filter coefficients. This can create a computational problem when energy optimization is

performed as with will see in the next chapter.

2.2 MIMO Radio Channel

A radio channel can experience two types of fading; large scale fading and small scale fading

(referred to as multipath fading). Large scale fading affects the mean power of the received

signal. It is mainly caused by path loss and shadowing and occurs over relatively large

distances. On the other hand, small scale fading affects the instantaneous amplitude and

phase of the received signal. It is mainly caused by constructive and destructive additions

of multipath signals and varies over very short distances [35].

For simplification, it is assumed that there is no inter-cell interference. It is also assumed

that the channel is normalized and hence average received power is not attenuated. As a

result, large scale fading is not considered in the model. However, the potential capacity

of a MIMO system strongly depends on the multipath richness that creates decorrelations

between MIMO paths [32]. Hence small scale fading plays a main role in modelling a MIMO

channel.


2.2.1 Statistical Channel Model

A multipath fading channel can be statistically characterized by its Power Delay Profile

(PDP) and Doppler Power Spectrum. The PDP mainly defines delay spread where the

Doppler power spectrum defines the coherent time [16]. It is assumed that the radio chan-

nel is a block fading channel and the channel is re-estimated for each block of data, therefore

the Doppler power spectrum is not considered in the channel model. On the other hand,

the power delay profile specifies the time dispersion and frequency selectivity of the channel

which plays a vital role in this work.

For a MIMO channel, the mean angle of arrival (AoA) and the Power Angular Spectrum

(PAS)- which defines the angule spread (AS) - characterize the correlations between MIMO

paths. These correlations have significant impact of the number sub-channels a MIMO chan-

nel can offer and hence its capacity. The statistical MIMO channel model given in [32] maps

any given PDP and integrates spatial correlations as well. In the following subsections, the

model will be adjusted to match the formulation given in this report.

2.2.2 Power Delay Profile

For a radio channel with L resolvable paths, the discrete PDP sampled at periods of Tc is

given as

P (n) =

L−1∑l=0

Plδ (n− l) (2.22)

where Pl is the power at the lth tap (delay lTc). It is assumed that the different NrNt MIMO

paths have the same PDP and hence the average power of channel taps for a given delay is

constants and given as

Pl = E[∣∣∣h(nr,nt)

l

∣∣∣2] (2.23)

for all l ∈ [1, · · · , L− 1], nt ∈ [1, · · · , Nt] and nr ∈ [1, · · · , Nr].


2.2.3 Spatial Correlation

The spatial correlation between a pair of antennas mainly depends on the mean angle of

arrival (AoA) and the PAS. If the PAS has a small AS, most sub-rays forming resolvable paths

arrive at each antenna from the same angle creating high spatial correlation.

When the distance between the transmitter and receiver is sufficiently larger than their

antennas spacing (which is generally the case), the MIMO paths correlations can be obtained

from the spatial correlations between the receiving antennas and the spatial correlations

between the transmitting antennas. The spatial correlation between two receive antennas

is given as

ρr (nr1, nr2) =⟨h

(nr1,nt)l , h

(nr2,nt)l

⟩(2.24)

for all nr1 and nr2 ∈ [1, · · · , Nr] and nt ∈ [1, · · · , Nt] and

〈X,Y 〉 =E [XY ]− E [X] E [Y ]√(

E [X2]− E [X]2)(

E [Y 2]− E [Y ]2) (2.25)

In the same manner, correlation between transmit antennas can be written as

ρt (nt1, nt2) =⟨h

(nr,nt1)l , h

(nr,nt2)l

⟩(2.26)

for nt1 and nt2 ∈ [1, · · · , Nt] and nr ∈ [1, · · · , Nr]. It is assumed that the correlation between

two receive (transmit) antennas is independent of the transmit (receive) antenna [32].

The correlation between a given pair of antennas is independent of l and channel taps

are uncorrelated from one delay to another regardless of the transmitting and receiving

antennas

⟨h

(nr,nt)l1

, h(nr,nt)l2

⟩= 0 ,for l1 6= l2 (2.27)

The Nr × Nr receiver correlation matrix can be formed from the spatial correlation


coefficients as follows

Rr =

ρr (1, 1) · · · ρr (1, Nr)

.... . .

...

ρr (Nr, 1) · · · ρr (Nr, Nr)

(2.28)

In the same manner, the Nt ×Nt transmitter correlation matrix can be formed as follows

Rt =

ρt (1, 1) · · · ρt (1, Nt)

.... . .

...

ρt (Nt, 1) · · · ρt (Nt, Nt)

(2.29)

The correlation between the MIMO path connecting ntht1 transmit antenna to the nthr1

receive antenna and the MIMO path connecting the ntht2 transmitting antenna to the nthr2 re-

ceiving antenna can be calculated from the spatial correlation coefficients at the transmitter

and receiver as

ρ (nr1nt1, nr2nt2) =⟨h

(nr1,nt1)l , h

(nr2,nt2)l

⟩= ρr (nr1, nr2) ρt (nt1, nt2) (2.30)

The NrNt × NrNt MIMO paths correlation matrix can be formulated using the transmitter

correlation matrix and the receiver correlation matrix as follows

RMIMO = Rr ⊗ Rt (2.31)

2.2.4 Generation of a Fading Correlated MIMO Channel

When simulation is carried out, it is required to generate NrNt vectors each with L taps.

Each of the vectors corresponds to a MIMO path and correlations should be reflected in

them. For a given MIMO path with no line-of-sight (NLOS), taps are usually modelled

as random variables with Rayleigh-distributed amplitudes and uniformly-distribute phases.

However, in the presence of a dominating line-of-sight (LOS), the first tap (arriving at delay

zero) has Ricean-distributed amplitude and uniformly-distribute phase where the rest of the

taps follow the same NLOS distribution.


The tap vectors to be generated for all MIMO paths form the NrNt × L MIMO channel

taps matrix given as

Htap =[~h(1,1), · · · ,~h(1,Nt), · · · ,~h(Nr,1), · · · ,~h(Nr,Nr)

]T(2.32)

Given the PDP of the channel, the MIMO paths correlation matrix RMIMO and the Ricean

factor KRic, Htap is generated as follows.

Generating Correlated Random Variables:

The NrNt × L random matrix V is generated with elements of independent and identically

distributed (i.i.d) circularly symmetric complex Gaussian random variables with zero mean

and unity variance 2 CN (0, 1). Elements of V have Rayleigh-distributed amplitudes and

uniformly-distribute phases. To create correlations between the elements of each column of

V, the NrNt ×NrNt mapping matrix CR is used as

VCorr = CRV (2.33)

assuming that each element in a given column of VCorr is a linear combination of the ele-

ments in the corresponding column in V [24]. Given that elements of V have zero mean and

unity variance and assuming that applying CR does not change the mean and variance, the

MIMO paths correlation matrix can be written as

RMIMO = E[VCorr (col : l) VCorr (col : l)H

]= E

[CRV (col : l) V (col : l)H CHR

](2.34)

where X (col : l) refers to the lth column of a matrix X. As E[V (col : l) V (col : l)H

]= INrNt

We conclude that the mapping matrix should satisfy

RMIMO = CRCHR (2.35)

To calculate CR from RMIMO, square-root decomposition can be used if correlations are real

or lower-Cholsky decomposition if correlations are complex [12].

2CN(0, σ2

)can be generated as Z = X + jY where X and Y are i.i.d N

(0, σ

2

2

).


Power Shaping and Rician Fading:

Having the correlations between MIMO paths mapped, taps need to be power shaped to

follow a given PDP and Rician fading of zero delay taps should be adjusted in the presence

of a dominating LOS. The L× L power shaping matrix AP is given as

AP = diag

(√P0

KRic + 1,√P1, · · · ,

√PL−1

)(2.36)

and the NrNt × L LOS matrix HLOS is given as

HLOS =

√KRicP0

KRic + 1

1 0 · · · 0

......

. . ....

1 0 · · · 0

(2.37)

the MIMO channel taps matrix can be generated as

Htap = HLOS + VCorrAP (2.38)

When there is NLOS (KRic = 0), the mean matrix will be all zeros. However, when a LOS

is present (KRic 6= 0), the first column of the mean matrix will be non-zero where a fraction

of first taps power will be a assigned to the fixed LOS components.

AoA Adjustment:

When a signal arrives at the receive antennas with AoA 6= 0, different receive antennas will

receive the signal with different phase shifts due to the difference in distance travelled. It

is important to map this in the channel especially in the presence of non-zero correlations

between MIMO paths. However, this is not as important in the case of zero spatial correla-

tions as paths experience random phase variations between different antennas due to large

AS [12].

For a uniform linear array of antennas, the mean phase shift at each antenna relative to

the first antenna form the receive array steering vector given as

~c (φ) = [c1 (φ) , · · · , cNr (φ)]T (2.39)


where φ is the mean AoA of the signal. Elements of the array steering vector are given as

cnr (φ) = fnr (φ) e−j2π(nr−1)(d/λ)sin(φ) , nr = 1, · · · , Nr (2.40)

where d is the spacing between the antennas, λ is the wavelength and fnr (φ) is the complex

radiation pattern of the nthr receive antenna. It is assumed that all antennas have isotropic

radiation patterns and hence fnr (φ) = 1 for nr = 1, · · · , Nr. This way, all elements of the

steering vector will have unity magnitudes and the c1 (φ) will be the reference with zero

phase for all φ. For a given delay, it is assumed that all MIMO paths arrive with the same

mean AoA defined as φl , l = 0, · · · , L− 1. The array steering vectors for the L paths form

the NrNt × L angle adjustment matrix as follows

Wc = [~c (φ0) , · · · ,~c (φL−1)]⊗~1Nt (2.41)

from which Htap can be modified as

Htap,c = Wc �Htap (2.42)

where MIMO paths for a given delay and corresponding to the same receive antenna are

multiplied by the same steering coefficient.

2.3 Link Level Simulation

Simulations are widely used to evaluate the performance of mobile communication net-

works and systems. This is generally carried out over two levels; link level simulation and

system level simulation [7]. Link level simulation considers a single transmitter (Node B)

and a single receiver (UE). However, system level simulation considers multiple transmitters

and receivers to model the network performance in general.

Throughout this report, it is assumed that all resources in a given cell are dedicated

to a single user. The main comparison parameter between different schemes is the single

user average throughput for a given MIMO channel. Therefore, link level simulation is

mainly considered throughout this work. This section provides description for the link level


simulator and the simulation parameters.

2.3.1 Radio Channel Model

Two channel models are used throughout this report; ITU Pedestrian-A (Ped-A) and ITU

Pedestrian-B (Ped-B) [23]. The PDPs of both channels are shown in figure 2.1. The two

PDPs are modified to suit the HSDPA system with chip period Tc = 260.4 n sec. The modified

PDPs are shown in figure 2.2 where delays are rounded to the closest chip period and the

first two samples of Ped-A are combined in the process.

0 500 1000 1500 2000 2500 3000 3500 4000−30

−20

−10

0

n sec

dB

PED − A

0 500 1000 1500 2000 2500 3000 3500 4000−30

−20

−10

0

n sec

dB

PED − B

Figure 2.1: Ped-A and Ped-B power delay profiles.

0 2 4 6 8 10 12 14−30

−20

−10

0

Tc

dB

PED − A

0 2 4 6 8 10 12 14−30

−20

−10

0

Tc

dB

PED − B

Figure 2.2: Ped-A and Ped-B modified power delay profiles.

Using the modified PDPs, the channel coefficients are generated as mentioned in section


2.2 where spatial correlations are assumed to be zero if not mentioned otherwise. The

background noise at the receiver is modelled as additive white Gaussian noise with fixed

single sided power spectral density N0 = 0.02.

2.3.2 System Parameters

The MIMO configuration throughout this work is set to 2 × 2 MIMO where Nr = Nt = 2.

This is the most common configuration for MIMO HSDPA and it is well defined in standards.

The spreading factor per transmit antenna is set to N = 16 and the maximum number

of channels available for user data transmission is limited to K = 30. The chip rate is

given as fc = 1Tc

= 3.84Mchip/sec. Scrambling codes are not considered in the model

or implemented in the simulations as a single user is only considered without inter-cell

interference.

It is assumed that information bits transmitted over one symbol period in a single chan-

nel can be selected from a range defined as {0, 0.25, · · · , 5.75, 6}. The bit granularity is 0.25

and the maximum realizable rate is 6 bits per symbol per channel when 64-QAM is applied.

Furthermore, the modulation gap Γ is assumed to be 0 dB. More about bit rates is available

in the following chapter. The simulation parameters are summarized in table 2.1.

Parameter Value

PDP Ped-A, Ped-B

MIMO config. 2× 2

SF/antenna (N) 16

Noise PSD (N0) 0.02

Bit Granularity 0.25

Mod. gap (Γ) 0 dB

Max Num. of Ch. (K) 30

Chip rate (fc) 3.84 Mchip/sec

Table 2.1: Simulation Parameters


2.3.3 Generating Multiple MIMO Channels

The channel coefficients are generated using Rayleigh (or Ricean) random variables. There-

fore, their instantaneous values can vary even if the PDP and spatial correlation matrix were

constant. It is assumed that the MIMO channel stays constant during the transmission of one

packet. However, to evaluate the overall performance for a given PDP and spatial correla-

tion matrix, the MIMO channel is generated multiple times and parameters to be observed

as total throughput or allocated energies are averaged over the generated channels. The

number of channels generated is set to 20 where averages of observed parameters usually

converge to constant values.

Chapter 3

Resource Allocation

In mobile radio communications systems, resources such as bandwidth and energy are lim-

ited. This fact makes utilizing available resources very important. In this work we assume

that bandwidth is fully utilized and we try to tackle the problem of energy utilization. This

can be done by optimizing the energy allocation scheme which has a significant impact on

the throughput of HSDPA systems especially in frequency selective channels.

This chapter starts by describing the current MIMO HSDPA standard highlighting the

energy allocation scheme used. Other resource allocation schemes are then discussed before

presenting simulation results.

3.1 MIMO HSDPA Standard

MIMO HSDPA was standardized by 3GPP in Release 7 in order to increase HSDPA through-

put. The Dual-Stream Transmit Antenna Array (D-TxAA) scheme was chosen as the MIMO

extension for the frequency division duplex (FDD) mode of HSDPA. D-TxAA has two modes

of operation; dual-stream mode and singe-stream mode [1].

In dual-stream mode, two independent data streams are transmitted; a primary stream

and a secondary stream. The two streams are spatially multiplexed using precoding weights

and transmitted simultaneously using both transmit antennas. Each data stream can carry

up to N − 1 channels and both streams use the same set of signature sequences achieving

code reuse. If the SNIR at the receiver is not sufficient to decode a second data stream, the

secondary data stream will be switched off and the system will operate under single-stream

23

CHAPTER 3. RESOURCE ALLOCATION 24

mode where one data stream is precoded and transmitted over both antennas [22].

In Release 8, the peak throughput was further increased by introducing higher-order

modulation for MIMO HSDPA [4]. Dual-Cell HSDPA (DC-HSDPA) introduced for SISO in

Release 8 was extended to include MIMO in Release 9 [5]. In DC-HSDPA, one HSDPA re-

ceiver will receive two different carriers each from a different cell. This improves the achiev-

able throughput especially for receivers near the edge of a cell. The concept of DC-HSDPA

was further extended to include more cells (carriers) in Four-Carrier HSDPA introduced in

Release 10 [2] and Eight-Carrier HSDPA introduced in Release 11 [3].

This work is mainly concerned about single user throughput when operating using one

carrier. Hence, Multi-Carrier HSDPA are not considered in this work.

3.1.1 D-TxAA Model

In this subsection, a model for D-TxAA will be given. Modelling will be limited to 2 × 2

MIMO configuration which is most common for MIMO HSDPA.

D-TxAA uses a fixed spreading factor per transmit antenna N = 16 and a set of 15

OVSF (orthogonal variable spread factor) signature sequences for data transmission. The

15 orthonormal signature sequences form the 16×15 OVSF signature sequence matrix given

as

SOVSF16 = [~sOVSF16,1, · · ·~sOVSF16,14, ~sOVSF16,15] (3.1)

where each vector represents a signature sequence. Assuming that the system is operating

in dual-stream mode, the maximum number of channels that can be used for data transmis-

sion is K = 30. The channels are divided into two data streams, a primary stream and a

secondary stream. The same matrix SOVSF16 is used to spread channels in both data streams.

After spreading, each of the data streams is weighted using a pair of precoding weights and

then transmitted over both transmit antennas. Precoding weights for both streams form the

2× 2 precoding matrix [11] given as

WD =

w(1)p w

(1)s

w(2)p w

(2)s

= [~wp, ~ws] (3.2)


where w(nt)p is the ntht transmit antenna precoding weight for the primary data stream and

w(nt)s is the ntht transmit antenna precoding weight for the secondary data stream. By inte-

grating signature sequences and precoding, the 32× 30 MIMO signature sequence matrix S

can be obtained as

S = WD ⊗ SOVSF16 =

w(1)p SOVSF16 w

(1)s SOVSF16

w(2)p SOVSF16 w

(2)s SOVSF16

(3.3)

Given that vectors of SOVSF16 are orthonormal, if ~wp and ~ws are orthonormal, then the

system can be viewed as if it uses 30 orthonormal signature sequences each having the

length of 32.

3.1.2 Precoding Weights Selection

The precoding weights are drawn from a closed-loop transmit diversity code book where

w(1)p and w(1)

s are equal and have a constant real value given as

w(1)p = w(1)

s =1√2

and w(2)p and w(2)

s have variable complex values defined as

w(2)p ∈

{1 + j

2,1− j

2,−1 + j

2,−1− j

2

}

w(2)s = −w(2)

p

The primary precoding vector and secondary precoding vector are orthonormal regardless

of the values drawn. Therefore, the two data streams are transmitted on orthogonal beams

[22] where the same set of signature sequences is reused.

The precoding weights are selected to maximize the SNIR at the receiver and hence

achive the highest throughput for a given channel. This process is carried out by the receiver

and a precoding control indicator (PCI) - carrying information about the preferred weights

- is fed back to the transmitter [1]. The selection can be performed by choosing w(2)p that


maximizes the following expression [8]

w(2)p : max

(~wHp Gh ~wp

)(3.4)

where Gh is the 2L× 2 Grammian matrix of the channel response vectors given as

Gh =

~h(1,1) ~h(1,2)

~h(2,1) ~h(2,2)

H ~h(1,1) ~h(1,2)

~h(2,1) ~h(2,2)

(3.5)

Once the transmitter receives the PCI which refers to the value of w(2)p , both precoding

vectors can be calculated and used for beamforming.

3.1.3 Single-Stream Mode

The SNIR at the receiver may be insufficient to transmit two data streams. In this case, the

secondary stream is switched off and the system will operate in a single-stream mode which

is backwards compatible with the transmit diversity antenna array (TxAA) mode. The same

precoding applies but the precoding matrix will be reduced to the primary precoding vector

WS =

w(1)p

w(2)p

= ~wp (3.6)

the number of channels available for data transmission reduces to 15 and the MIMO signa-

ture sequence matrix is formulated as

S = WS ⊗ SOVSF16 =

w(1)p SOVSF16

w(2)p SOVSF16

(3.7)

Although the number of channels used with TxAA is same as SISO, TxAA generally

performs better than SISO as it exploits the diversity gain of the radio channel. For receivers

with one antenna, TxAA can also be used in a MISO configuration [5].


3.1.4 Resource Allocation

HSDPA uses AMC to control the transmission bit rates over channels [22]. The bit rate in

bits per symbol period for a single channel is defined as

b (p) , p = 1, · · · , P (3.8)

which is chosen from a finite set of P discrete bit rates achieved by changing the Modulation

and Coding Scheme (MCS).

For dual-stream mode, all channels belonging to the same data stream operate on the

same bit rate. However, bit rates for the two data streams are not necessarily the same. The

bit rate for primary channels is defined as b (pp) where the bit rate for secondary channels

is defined as b (ps). If the system operates in single-stream mode, only b (pp) needs to be

assigned. The values of b (pp) and b (ps) depend on the SNIR at the output of the despreading

filter for all channels in operation. Assuming that the signals are despread at the receiver

using a MIMO MMSE despreading filter, the total throughput of the system is given next.

Dual-Stream mode

All HSDPA standards (including MIMO HSDPA) allocate equal energies to channel used in

data transmission [6]. Assuming that the system uses the K data transmission channels,

energy used to transmit one symbol over the kth channel is given as

Ek =ETK

, k = 1, · · · ,K (3.9)

and SNIR at the output of the MIMO MMSE despreading filter for the kth channel is calcu-

lated as

γk =ETK ~qHk C−1~qk

1− ETK ~qHk C−1~qk

, k = 1, · · · ,K (3.10)

Assuming that channels 1, · · · , K2 belong to the primary data stream and channels(K2 + 1

), · · · ,K


belong to the secondary data stream, bpp and bps are chosen to satisfy

γ(bpp)≤ γk , k = 1, · · · , K

2(3.11)

γ (bps) ≤ γk , k =

(K

2+ 1

), · · · ,K (3.12)

where γ (bp) is the minimum SNIR at the output of the receiver a channel should have to be

able to transmit bp bits per symbol period. For M-QAM and modulation gap value Γ, γ(bpp)

and γ (bps) are given as

γ(bpp)

= Γ(

2bpp − 1)

(3.13)

γ (bps) = Γ(

2bps − 1)

(3.14)

The total achievable bit rate in bits per symbol period is given as

RT =K

2

(bpp + bps

)(3.15)

Single-Stream mode

When the secondary stream is switched off, the number of available data transmission chan-

nels reduces to K2 . Energy used to transmit one symbol over the kth channel is given as

Ek =2ETK

, k = 1, · · · , K2

(3.16)

and SNIR at the output of the MIMO MMSE despreading filter for the kth channel is calcu-

lated as

γk =2ETK ~qHk C−1~qk

1− 2ETK ~qHk C−1~qk

, k = 1, · · · , K2

(3.17)

It is important to note that C used in (3.10) is not the same as C used in (3.17). The

former uses all MIMO signature sequences and energies calculated from (3.9). However,

the later uses half the number of MIMO signature sequences and energies calculated from

(3.16). All channels belong to one data stream and bp is chosen satisfy

γ (bp) ≤ γk , k = 1, · · · , K2

(3.18)


where

γ (bp) = Γ(

2bp − 1)

(3.19)

The total achievable bit rate in bits per symbol period is given as

RT =K

2bp (3.20)

Mode Selection

After choosing the precoding vector, the receiver carries out received SNIR calculations

for both single and double stream modes which require two covariance matrix inversions.

The rates for double-stream mode bpp and bps and the single stream-mode rate bp are then

calculated. The receiver would report that double-stream mode is preferred if

(bpp + bps

)> bp

otherwise the receiver would report that using on stream is preferred.

3.1.5 Wasted SNIR

For a given data stream, the bit rate used for channels is bounded to the bit rate achievable

by the channel with the worst condition. This produces wasted SNIR which comes from

channels with better conditions. The total wasted SNIR for double-stream mode is given as

Wasted SNIR =

K∑k=1

ETK ~qHk C−1~qk

1− ETK ~qHk C−1~qk

− K

2

(Γ(

2bpp − 1)

+ Γ(

2bps − 1))

(3.21)

For single-stream mode, the wasted SNIR is given as

Wasted SNIR =

K2∑

k=1

2ETK ~qHk C−1~qk

1− 2ETK ~qHk C−1~qk

− K

2Γ(

2bp − 1)

(3.22)

In frequency selective radio channels, the wasted SNIR can be significant as different chan-

nels would have different conditions due to ISI and ICI. The next section will demonstrate


how to utilize the wasted SNIR to transmit higher bit rates.

3.2 Constrained Optimization

The wasted SNIR produced by equal-energy loading can be utilized by energy-constrained

rate optimization (constrained optimization) which uses iterative calculations to find the

bit rate and the transmission energies. This will be applied to both single-stream and

dual-stream modes. However, in dual-stream mode data streams are not separated and

all channels are considered in the same bit assignment process. Optimizing bit rates for

the two streams separately may offer higher throughput, but the complexity is significantly

increased as well.

The optimization methods are first presented assuming that all channels are applied,

then single-stream mode and mode selection are discussed afterwards.

3.2.1 Equal-Rate Margin Adaptive Loading

In a multi-code transmission system where the same bit rate is used over all channels, equal-

rate margin adaptive loading is used to maximize the sum capacity especially when different

signature sequences experience different SNIRs at the receiver. Equal-rate margin adaptive

loading makes sure that each channel produces minimum possible interference by allocating

just enough energy to satisfy a target SNIR [33]. The target SNIR corresponding to a bit

rate bp is given as γ∗ (bp) = Γ(2bp − 1

)where the bit rate index p is selected to maximize

the total achievable bit rate such as

p : max RT = Kb (p) (3.23)

subject to the energy constraint given as

K∑k=1

Ek (bp) ≤ ET <K∑k=1

Ek (bp+1) (3.24)

For an MMSE despreading filter, the maximum p that satisfies (3.23) and (3.24) and the

energies for different channels can be calculated iteratively as follows:


1. The bit rate index is initialized as p = 1.

2. The energies are initialized as Ek(0) = ETK , k = 1, · · · ,K and the iterations index is

initialized as i = 1.

3. Ae(i) is calculated by plugging Ek(i−1), k = 1, · · · ,K into equation (2.14).

4. C(i) is calculated by plugging Ae(i) into equation (2.18).

5. The inverse of the covariance matrix in calculated and the new set of energies is

calculated as

Ek(i) =Γ(2bp − 1

)(1 + Γ

(2bp − 1

))~qHk C−1

(i) ~qk, k = 1, · · · ,K

6. If Ek(i) ≈ Ek(i−1) for k = 1, · · · ,K or i = Imax1 go to the next step. Otherwise,

i = i+ 1 and steps are repeated starting from step 3.

7. If∑K

k=1Ek(i) > ET , then p = p− 1 and search is complete. Otherwise, p = p+ 1 and

steps are repeated starting from step 2.

After finding the bit rate index p and the transmission energies, the MIMO MMSE despread-

ing filter coefficients are calculated using equation (2.19). It is assumed that there is a

perfect feedback link between the receiver and transmitter used to report the transmission

energies and rate to be used by the transmitter.

3.2.2 Residual Energy

Assuming an infinite set of bit rates where bit granularity goes to zero, bp will be selected

such as∑K

k=1Ek (bp) = ET . However, zero bit granularity is not practically achievable as bp

is selected from a finite set to satisfy (3.24) where equality is not necessarily satisfied. This

produces residual energy given as

ER = ET −K∑k=1

Ek (bp) (3.25)

The residual energy is not used to transmit any useful data and produces a gap between the

achievable capacity curves for continuous and discrete rates.1Imax is the maximum number of iterations required to calculate a set of energies.


3.2.3 Two-Group Rate Adaptive Loading

In order to utilize the residual energy produced by using discrete bit rates with equal-rate

margin adaptive loading, a two-group rate adaptive loading scheme was implemented in

[20,21]. Two-group loading algorithm assigns an adjacent higher bit rate bp+1 tom channels

known as the second group. Assuming that channels are ordered in a way such that

Ej (bp+1)− Ej (bp) < Ek (bp+1)− Ek (bp) , j > k and j, k = 1, · · · ,K (3.26)

then the number of channels in the second group m is chosen to maximize the total achiev-

able bit rate such as

m : max RT = (K −m) b (p) +mb (p+ 1) (3.27)

subject to the energy constraint given as

K−m∑k=1

Ek (bp) +

K∑k=K−m+1

Ek (bp+1) ≤ ET <K−m+1∑k=1

Ek (bp) +

K∑k=K−m+2

Ek (bp+1) (3.28)

Iterative calculation is used to calculate the maximum m that satisfies (3.27) and (3.28) as

follows:

1. Equal-rate margin adaptive loading is carried out to find p.

2. The number of channels in the second group is initialized as m = 1.

3. The energies are initialized as Ek(0) = ETK , k = 1, · · · ,K and the iterations index is

initialized as i = 1.

4. Ae(i) is calculated by plugging Ek(i−1), k = 1, · · · ,K into equation (2.14) and C(i) is

calculated by plugging Ae(i) into equation (2.18).

5. The inverse of the covariance matrix in calculated and the new set of energies is


calculated as

Ek(i) =Γ(2bp − 1

)(1 + Γ

(2bp − 1

))~qHk C−1

(i) ~qk, k = 1, · · · ,K −m

Ek(i) =Γ(2bp+1 − 1

)(1 + Γ

(2bp+1 − 1

))~qHk C−1

(i) ~qk, k = (K −m+ 1) , · · · ,K

6. If Ek(i) ≈ Ek(i−1) for k = 1, · · · ,K or i = Imax go to the next step. Otherwise, i = i+1

and steps are repeated starting from step 4.

7. If∑K

k=1Ek(i) > ET , then m = m − 1 and search is complete. Otherwise, m = m + 1

and steps are repeated starting from step 3.

Using two-group rate adaptive loading, the same total rate realised by equal-rate margin

adaptive loading with zero bit granularity is roughly achieved using two discrete bit rates

and without a significant increase in complexity.

3.2.4 Two-Group Loading with Single-Stream Mode

Switching off the second stream may improve performance in some MIMO channel condi-

tions. The same two-group algorithm explained in the previous subsection can be applied

to a single data stream by using the K2 signature sequences given in (3.7).

To select the best mode of operation, the two-group loading algorithm should be per-

formed twice and the mode with the higher total rate will be chosen. However, performing

two-group loading algorithm is computationally heavy for most mobile application which

will be discussed in the following subsection.


The main holdback of using constrained optimization is the computational complexity of

the algorithms. This is due to the high number of covariance matrix inversions required

when performing equal-rate margin adaptive and two-group rate adaptive loading.

When equal-rate margin adaptive loading is performed, the search for p requires up to

P energy calculation processes as the allocated bit rate can be the last one in the group

of available rates. Each energy calculation process requires up to Imax iterations. Each


iteration would require a covariance matrix inversion to calculate the new set of energies

and the total number of matrix inversions can reach PImax. If two-group loading algorithm

is to be performed as well, this would add up to (K − 1) Imax covariance matrix inversions

required to find m. The total number of matrix inversions required to perform two-group

loading algorithm can go up to (P +K − 1) Imax.

Furthermore, selecting the mode of operation weather it is single-stream or double-

stream would require up to(P + K

2 − 1)Imax matrix inversions to perform two-group load-

ing algorithm for half the number of channels. Hence, the maximum total number of matrix

inversions required to perform two-group loading with best mode selection is(2P + 3K

2 − 2)Imax.

3.3 Simulation and Analysis

The values of the simulation parameters are given in section 2.3. Performance comparison

is carried out between D-TxAA MIMO HSDPA standard and the one improved using con-

strained optimization. An evaluation of the computational complexity required to run the

two-group loading algorithm is also provided in this section.

3.3.1 Total Throughput

The total achievable rates in bits per symbol RT is plotted against the average SNR per

receive antenna ETN0

for D-TxAA and two-group loading with best mode selection (TGmode)

resource allocation schemes. Both single-stream and double-stream modes are considered

where calculations are carried out for both and the best mode of operation is selected for

each SNR value. The comparison is carried out for Ped-A and Ped-B channel models and

spatial correlation is assumed to be zero. For Ped-A, the delay spread is not significant

and the orthogonality of MIMO signature sequences can be restored easily by the equalizer.

Therefore the difference in performance between D-TxAA and TGmode is not significant as

shown in figure 3.1. In contrast, the Ped-B channel has a large delay spread and it is difficult

for the equalizer to restore orthogonality. Hence, the difference in performance is significant

where TGmode provides around 4.5 dB of average gain as shown in figure 3.2.

The average increase in total throughput can be calculated as a percentage from the


average rate of D-TxAA as follows:

Rinc =E[RT,TGmode

]− E [RT,D-TxAA]

E [RT,D-TxAA](3.29)

Where average rates are obtained from averaging over the SNR range. TGmode provides

around 7% increase over D-TxAA for Ped-A. This is not significant as expected for Ped-A

channel mode. However, for Ped-B channel mode the increase is around 40%.

0 5 10 15 20 25 30 350

20

40

60

80

100

120

140

160

180

ET/N0 dB

RT

bits

/sym

bol

TG

mode

D−TxAA

Figure 3.1: TGmode and D-TxAA - Throughput - Ped-A.

3.3.2 Number of Applied Channels

Figure 3.3 shows the number of applied channels against SNR. For Ped-A, D-TxAA start ap-

plying the second stream at high SNR values where sufficient decoding of the second stream

is possible. However, the second stream is not used for Ped-B channel and D-TxAA operates

as a diversity system over the whole SNR range. On the other hand, TGmode operates the

second stream at high SNRs for both Ped-A and Ped-B channels. Choosing between 15 and

30 channels to operate leaves the system with few options. In the next chapter, channel se-

lection will be applied where the system would choose the number of channels to maximize

the total throughput.


0 5 10 15 20 25 30 350

10

20

30

40

50

60

70

80

90

100

ET/N0 dB

RT

bits

/sym

bol

TG

mode

D−TxAA

Figure 3.2: TGmode and D-TxAA - Throughput - Ped-B.

5 10 15 20 25 30 350

5

10

15

20

25

30

35

ET/N0 dB

Cha

nnel

s U

sed

Ped−A

TG

mode

D−TxAA

5 10 15 20 25 30 350

5

10

15

20

25

30

35

ET/N0 dB

Cha

nnel

s U

sed

Ped−B

TG

mode

D−TxAA

Figure 3.3: TGmode and D-TxAA - Number of Channels Applied


3.3.3 Matrix Inversions

For P = 24, K = 30 and Imax = 50, the maximum number of matrix inversions required

to run TGmode is 3400. However, this upper bound is not necessarily reached. The actual

number of matrix inversions required can be controlled by allowing an error rate in the

energy calculation process. The energy error is calculated as a percentage of the total

available energy as follows

errorE =

∑Kk=1

(Ek(i) − Ek(i−1)

)ET

(3.30)

Figure 3.4 shows the RT curves for TGmode over the Ped-B channel for different values

of errorE . The difference in the RT is barely noticed. However, the drop in the number

of matrix inversions is significant as errorE increases as shown in figure 3.5. Generally,

the number of matrix inversions would rise for higher SNRs as p would normally be larger

and the search starts from p = 1. To compare the values of required matrix inversions for

different energy errors, the average required matrix inversions over the whole SNR range is

obtained and given in 3.1.

errorE Av. Matrix Inv.

0 2142

0.001 570

0.01 239

0.05 100

0.1 70

Table 3.1: Average number of matrix inversions for different energy error values.

The average is relatively close to the maximum for zero error. For higher errorE values,

the average is significantly smaller than the maximum. However, it is important to keep

in mind that the energies calculated do not completely converge as errorE increases and

the expected RT would go down. Assuming that an energy error between 5% and 10% is

acceptable. An average number of required matrix inversions around 100 is still high for

mobile applications. This number will be significantly reduced in the next chapter.


0 5 10 15 20 25 30 350

10

20

30

40

50

60

70

80

90

100

ET/N0 dB

RT

bits

/sym

bol

Error 0Error 0.1%Error 1%Error 5%Error 10%

Figure 3.4: Total Two-Group throughput for different energy error values.

0 5 10 15 20 25 30 350

500

1000

1500

2000

2500

3000

3500

ET/N0 dB

Mat

rix In

vers

ions

Error 0Error 0.1%Error 1%Error 5%Error 10%

Figure 3.5: Number of matrix inversions for different energy error values.

Chapter 4

System Values

In the previous chapter, performance of MIMO HSDPA in frequency selective channels was

improved in terms of total throughput by using two-group resource allocation. However, the

process is computationally heavy as it requires a significant number of covariance matrix in-

versions and may be impractical for applications with limited signal processing capabilities.

In this chapter, system value approach is used to reduce the number of matrix inver-

sions required to implement two-group loading. System value approach is optimized using

channel selection schemes that replace mode selection used in the previous chapter. Fur-

thermore, interference cancelation with recursive matrix inversion calculations are used to

eliminate the remaining matrix inversions after using system value approach. System value

approach works best with optimum MIMO signature sequences. Hence, the chapter starts

by presenting the optimum sequence design.

4.1 Signature Sequence Design and Channel Selection

4.1.1 Optimum MIMO Signature Sequences

In frequency selective radio channels, the multipath nature destroys orthogonality between

the MIMO signature sequences used earlier. This creates cross-correlations between re-

ceived MIMO signature sequences causing ICI. Assuming perfect channel state information

(CSI) where the multipath radio channel is known to the transmitter, the MIMO signature

sequences can be adapted to consider the multipath channel effect and produce orthogonal

39

CHAPTER 4. SYSTEM VALUES 40

received MIMO signature sequences with zero cross-correlations such as

〈~qi, ~qj〉 = ~qHi ~qj = 0 , i, j = 1, · · · ,K and i 6= j (4.1)

MIMO signature sequences that satisfy (4.1) can be obtained by combining singular

value decomposition (SVD) with the MIMO channel convolution matrix H. The MIMO sig-

nature sequences are given as the Eigen vectors of theNtN×NtN channel Grammian matrix

defined as

GH = HHH (4.2)

Eigen vectors of GH can be obtained from the eigen decomposition given as

GH = VHDHVHH (4.3)

where DH = diag (~µH) is the diagonal matrix of the eigen values which are defined in a

vector as ~µH = [µH,1, µH,2, · · · , µH,NtN ]. VH is the eigen vectors matrix defined as VH =

[~vH,1, ~vH,2, · · · , ~vH,NtN ]. Using VH as the MIMO signature sequences matrix, the correlations

between the received MIMO signature sequences are obtained from the Grammian matrix

of the received MIMO signature sequences as

(HVH)H HVH = VHH VHDHVHH VH

= DH (4.4)

with zero cross-correlations and channels power gains given by the diagonal terms (eigen

values). The channel Grammian matrix produces NtN eigen vectors and corresponding

eigen values. However, the number of non-zeros eigen values is determined by the rank of

the channel Grammian matrix which is conditioned by

rank(HHH

)≤ min (Nt, Nr)N (4.5)

and hence the maximum number of channels that can be used is limited to Ktotal ≤

min (Nt, Nr)N and the MIMO signature sequences are chosen as the eigen vectors in VH


corresponding to non-zero eigen values. If K channels are used in data transmission where

K < Ktotal, the optimum MIMO signature sequence matrix is given as

S = [~vH,1, ~vH,2, · · · , ~vH,K ] , µH,1, · · · , µH,K 6= 0 (4.6)

and the MIMO receiver signature sequence matrix Q is obtained using (2.5). The diagonal

terms of the received MIMO signature sequences Grammian matrix represent channels gains

given as

|hH,k|2 =[QHQ

]k,k

= µH,k , k = 1, · · ·K (4.7)

When optimum MIMO signature sequences are used, received MIMO signature sequences

have zero-cross correlations and channel gains provide a good indicator for the quality of

channels. Channels gains can be used to order the channels instead of incremental ener-

gies when two-group loading is performed. The channel ordering may not be the same as

the one with incremental energies as ISI is still present and shifted parts of the sequences

are not orthogonal. However, the two ordering schemes will give very close results as the

equalizer minimizes the effect of ISI.

4.1.2 Channel Selection using Water-Filling

In the previous chapter, the maximum rate was obtained by using either half the number of

channels or the full number of channels where each half formed a data stream. This may

lead to include bad channels sometimes which may limit the rate or exclude good channels

from switching off the second stream. Channel selection can be used to identify and exclude

bad channels giving the transmitter more control over the signature sequences to achieve

higher throughput.

Water-filling optimization is generally used For parallel channels with different gains to

provide optimum channel selection and energy distribution in order to maximize the sum

capacity [13]. When optimum MIMO signature sequences are used and ISI effect is ignored,

water-filling can be used to identify and exclude weak channels as follows:

1. The matrix S is re-ordered in a way such that the channel gains corresponding to

signature sequences are in a descending order.


2. The matched filter receiver channel-SNR gk is calculated for the K channels as

gk =|hH,k|2

2σ2, k = 1, . . .K (4.8)

3. The number of channels to be used K∗ is initialized as K∗ = K.

4. The water-filling constant is calculated as

KWF =1

K∗

(ET +

1

Γ

K∗∑k=1

1

gk

)(4.9)

5. Energies for K∗ channels are calculated as

Ek,WF = KWF −1

Γgk, k = 1, . . .K∗ (4.10)

6. If EK∗,WF < 0, The number of channels to be used is set to K∗ = K∗−1 and steps are

repeated starting from step 4. Otherwise the number of codes to be used is set to K∗

by removing the last K −K∗ columns from S and Q can be calculated using equation

(2.5).

Using the resulting energies and the K∗ selected optimum codes, the water-filling ca-

pacity that gives a performance upper bound for a given MIMO channel can be calculated

as

CWF =

K∗∑k=1

log2

(1 +

Ek,WF ~qHk C−1~qk

Γ(1− Ek,WF ~q

Hk C−1~qk

)) (4.11)

where C is calculated using the optimum MIMO signature sequences and the water-filling

allocated energies.

4.2 System Values

System values are new parameters that play a key role in reducing the computational com-

plexity required to perform equal-rate margin adaptive loading and two-group rate adaptive


loading algorithms [17]. The system value for the kth channel is defined as

λk = Ek~qHk C−1~qk

=[A2QHC−1Q

]k,k

, k = 1, . . .K (4.12)

System values for the K channels form a K × 1 system value vector as

~λ = [λ1, λ2, · · · , λK ]T

= diag(A2QHC−1Q

)(4.13)

The kth channel SNIR at the output of the MIMO MMSE despreading filter can be written in

terms of the system value as

γk =λk

1− λk, k = 1, . . .K (4.14)

4.2.1 Gurcan system values and upper bounds

The system values obtained from distributing energy equally over the K∗ signature se-

quences selected by water-filling are referred to as Gurcan’s system values which can be

written in a vector as

~λG = diag

(ETK∗QH

(ETK∗QeQ

He + 2σ2INr(N+L−1)

)−1

Q

)(4.15)

The summation of Gurcan’s system values is given as

λT,G = trace

(ETK∗QH

(ETK∗QeQ


)−1

Q

)(4.16)

For a given channel, the summation of system values corresponding to unequal energy

loading are upper bounded by the summation of system values corresponding to equal

energy loading if the same energy constraint is satisfied [17]. Hence, λT,G gives an upper

bound referred to as Gurcan’s upper bound for total system values. Assuming that channels

can be loaded with non-equal rates and optimum signature sequences are used, the capacity


corresponding to Gurcan’s system values is referred to as Gurcan capacity and it is given as

CG =K∗∑k=1

log2

1 +

[ETK∗ QH

(ETK∗ QeQ


)−1Q]k,k

Γ

(1−

[ETK∗ QH

(ETK∗ QeQ


)−1Q]k,k

) (4.17)

The Gurcan capacity is found to approach the water-filling capacity and can be used as

an upper bound to compare the performance of different resource allocation schemes and

different signature sequences.

4.3 Resource Allocation With System Values

When equal-rate margin adaptive loading is performed, energy is allocated in a way such

that all channels meet a target SNIR. This is the same as performing inverse channel loading

where the channel seems to be the same for all signature sequences. Assuming that optimum

signature sequences are used where ICI is minimized and ignoring ISI for a while, a channel

gain given by |hH,k|2 would be the only factor determining the channel quality. Therefore,

energies for inverse channel loading can be calculated as

Ek,Inv =ET

|hH,k|2∑K

i=11

|hH,i|2, k = 1, · · · ,K (4.18)

Inverse channel energies can be used to produce the inverse channel system values given in

the vector ~λInv where all elements have very close values. The sum of the channel inversion

system values is found to be close in value to the total system value corresponding to equal

energy loading [17]. Hence, the following approximation holds

λk,Inv ≈ λmean =1

Ktrace

(ETK

QH

(ETK

QeQHe + 2σ2INr(N+L−1)

)−1

Q

), k = 1, · · · ,K

(4.19)

This approximation can be used to find the target system value and hence the target SNIR

for equal-rate margin adaptive loading with zero bit granularity. However, energy calcula-

tion given in equation (4.18) would not be accurate especially if non optimum signature

sequences are used. Energies can be calculated iteratively to meet a target SNIR that corre-


sponds to a target system value given as

λ∗ = λmean (4.20)

which is derived from the relation given in equation (4.19). An approximation for the total

capacity for equal-rate margin adaptive loading with zero bit granularity is given as

CMA = Klog2

(1 +

λmeanΓ (1− λmean)

)(4.21)

In practice, zero bit granularity is not achievable as discussed earlier. However, the same

concept can be applied for equal-rate margin adaptive loading with discrete bit rates. For

a set of P discrete bit rates, the target system value is chosen to maximize the rate p as

follows

max p : λ∗ (bp) ≤ λmean , p ∈ {1, · · · , P} (4.22)

where the target system value for a given bit rate is calculated as

λ∗ (bp) =Γ(2bp − 1

)1 + Γ

(2bp − 1

) , p = 1, · · · , P (4.23)

Furthermore, the total system value upper bound given by equal energy loading can be

used to determine the number of channels in the second group m if two-group loading is to

be used. The value of m is selected to satisfy

max m : (K −m)λ∗ (bp) +mλ∗ (bp+1) ≤ Kλmean , m ∈ {1, · · · ,K − 1} (4.24)

where K −m channels would have a target system value of λ∗ (bp) and m channels would

have the target system value of λ∗ (bp+1). Energies for the K channels that satisfy the

SNIRs corresponding to the target system values can be calculated iteratively as described

in the previous chapter. The main benefit from using system values is the elimination of the

iterative search for p and m and hence reducing the number of covariance matrix inversions

required to run two-group loading algorithm. This will be discussed more thoroughly in

subsection 4.3.4.


4.3.1 Improved Two-Group Rate Adaptive Loading

Optimum MIMO signature sequences and channel selection can be used to improve the

performance of two-group loading. Applying channel selection excludes weak channels

and removes the confusion around using single-stream or double-streams as the number

of channels will be pre-determined. The steps to perform two-group loading simplified by

system value approach and improved by optimum MIMO signature sequences and channel

selection are given as follows:

1. Water-filling is used to determine K∗.


signature sequences are in an ascending order and Q and Qe are calculated using

equations (2.5) and (2.6) respectively.

3. Energies are initialized as Ek(i=0) = ETK∗ , k = 1, . . .K∗ and the iteration index is set

to i = 1.

4. The extended amplitude matrix Ae(i=1) is formulated using Ek(i=0) and the covariance

matrix C(i=1) is calculated by plugging Ae(i=1) into equation (2.18).

5. The mean of the Gurcan system values is calculated as

λmean =1

K∗ trace(ETK∗QHC−1

(i=1)Q)

6. Two target system values for the first and second group are selected such as

λ∗ (bp) ≤ λmean < λ∗ (bp+1) , p ∈ 1, · · · , P

where λ∗ (bp) =Γ(2bp−1)

1+Γ(2bp−1)and λ∗ (bp+1) =

Γ(2bp+1−1)1+Γ(2bp+1−1)

and bp and bp+1 are the bit

rates for the first and second group respectively.

7. The number of channels in the second group is determined by calculating the largest

m that satisfies

(K∗ −m)λ∗ (bp) +mλ∗ (bp+1) < λT,G , m ∈ 1, · · · ,K∗ − 1


8. Energies to be allocated are then calculated iteratively as

Ek(i) (bp) =λ∗ (bp)

~qHk C−1(i) ~qk

, k = 1, . . .K∗ −m

Ek(i) (bp+1) =λ∗ (bp+1)

~qHk C−1(i) ~qk

, k = (K∗ −m+ 1) , . . .K∗

where C(i) which is used to calculate Ek(i) is calculated using Ek(i−1). The iterations

are repeated until Ek(i) ≈ Ek(i−1) for k = 1, . . .K∗, or i reaches Imax.

4.3.2 Optimum Channel Selection For Two-Group Loading

The channel selection scheme used earlier is based on water-filling. This gives optimum se-

lection when water-filling loading is used where different channels are assigned distinct bit

rates. However, for two-group loading which is based on equal-rate margin adaptive load-

ing, the SNIR for channels is brought up to meet a target SNIR. Therefore, some channels

which are assigned smaller amount of energy in water-filling would require more energy for

two-group loading. Excluding those channels may improve the total achievable rate.

Two-group loading was originally introduced to realise the total rate of equal-rate mar-

gin adaptive loading with zero bit granularity using non zero bit granularity. Hence, op-

timization is carried out with respect to equal-rate margin adaptive loading with zero bit

granularity and it applies for two-group loading. The optimization steps are given as follows



2. The optimum number of channels to be used K∗Opt is initialized as K∗

Opt = 1.

3. The signature sequence matrix of theK∗Opt sequences is found as SK∗

Opt=[~s1, · · · , ~sK∗

Opt

]from which QK∗

Optand Qe,K∗

Optcan be calculated using equations (2.5) and (2.6) respec-

tively.

4. The mean of the total system value upper bound over the K∗Opt channels is calculates

as

λmean,K∗Opt

=1

K∗Opt

trace

ETK∗

OptQHK∗

Opt

(ETK∗

OptQe,K∗

OptQHe,K∗

Opt+ 2σ2INr(N+L−1)

)−1

QK∗Opt


5. The total capacity for equal-rate margin adaptive loading with zero bit granularity

when using K∗Opt channels is calculates as

CK∗Opt

= K∗Optlog2

1 +λmean,K∗

Opt

Γ(

1− λmean,K∗Opt

)

6. If CK∗Opt≥ CK∗

Opt−1, K∗ = K∗Opt + 1 and steps are repeated starting from step 3.

However, if CK∗Opt< CK∗

Opt−1, the optimum number of channels to be used is given as

K∗Opt − 1.

The optimum channel selection gives improved performance over water-filling based se-

lection especially for MIMO channels with non-zero spatial correlations where water-filling

fails to identify some weak channels as shown in simulation results in section 4.5. However,

using optimum channel selection adds extra matrix inversions which are meant to be min-

imized. The number of matrix inversions required to perform optimum channels selection

is discussed in subsection 4.3.4. A suboptimal channel selection scheme which does not

require any matrix inversions in presented in the next subsection.

4.3.3 Suboptimal Channel Selection For Two-Group Loading

If optimum MIMO signature sequences are used, suboptimal channel selection for two-

group loading can be obtained using inverse channel energy loading. The general idea is

the same idea used with optimum channel selection where the number of applied channels is

changed and total capacity is tested. However, to avoid matrix inversions ISI is ignored and

hence a matched filter SNR is used instead of MMSE SNIR. The steps with full explanation

are given as follows



2. The optimum number of channels to be used K∗Sub is initialized as K∗

Sub = 1.

3. The signature sequence matrix of signature sequences SK∗Sub

is found from which QK∗Sub

is calculated


4. The K∗Sub channels gains are obtained as

[|hH,1|2 , · · · ,

∣∣∣hH,K∗Sub

∣∣∣2] = diag(

QHK∗

SubQK∗

Sub

)

5. Inverse channel energies for the K∗Sub channels are calculated as

Ek,Inv =ET

|hH,k|2∑K∗

Subi=1

1

|hH,i|2, k = 1, · · · ,K∗

Sub

6. The inverse channel capacity for matched filter receiver is calculated as

CK∗Sub

=

K∗Sub∑

k=1

log2

(1 +

Ek,Inv |hH,k|2

2σ2

)

7. If CK∗Sub≥ CK∗

Sub−1, K∗ = K∗Sub + 1 and steps are repeated starting from step 3.

However, if CK∗Sub

< CK∗Sub−1, the optimum number of channels to be used is given as

K∗Sub − 1.


The main motivation behind finding the system value approach is to eliminate the itera-

tive search for p and m and reduce the number of covariance matrix inversions. Assuming

that optimum MIMO signature sequences are used, one covariance matrix inversion is re-

quired to calculate the total system value for equal energy loading from which p and m

are obtained. Furthermore, this covariance matrix inversion can be used to perform the

first iteration when energies are calculated iteratively and the rest of the iterations would

require up to Imax− 1 matrix inversions depending on the energy error allowed. Hence, the

maximum number of matrix inversions required to perform two-group loading with system

value approach is Imax compared to (P +K−1)Imax when constrained optimization is used.

Furthermore, if optimum channel selection is implemented, up to K matrix inversions

are required to determine the optimum number of channels. Hence the total number of

matrix inversions required to perform two-group loading with optimum channels selection

using system value approach can reach Imax + K − 1 compared to (KP +∑K−1

k=1 k)Imax if


constrained optimization is used. A summery for the maximum required covariance matrix

Max. Matrix InversionsScheme

Const. Opt. System Value

Two-Group with water-filling ch. sel. (P +K − 1)Imax Imax

Two-Group with optimum ch. sel. (KP +∑K−1

k=1 k)Imax Imax +K − 1

Two-Group with suboptimal ch. sel. (P +K − 1)Imax Imax

Table 4.1: Maximum required matrix inversions for different resource allocation schemes.

inversions for the different two-group loading schemes discussed so far is provided in table

4.1. The same values may not apply for signature sequences with non zero cross-correlations

where an alternative channel ordering scheme may be necessary.

It is obvious that system value approach does a remarkable job in cutting off the num-

ber of required matrix inversions. However, matrix inversions are still required for energy

calculations. In the next section, interference cancelation and matrix inversion lemma will

be used to eliminate matrix inversions required for energy calculations.

4.4 Successive Interference Cancelation

Performing channel ordering at the receiver using channel gains or any other method en-

ables successive interference cancelation (SIC) to be implemented successfully. SIC has

many benefits including improved received SNIR for a given total transmit energy and us-

ing less transmit energy to achieve a given bit rate. However, the main objective behind

using SIC here is to eliminate covariance matrix inversions required for iterative energy

calculations.

4.4.1 SIC implementation

Ideally, the receiver should start by despreading and cancelling the channel with the best

quality when SIC is carried out. For the kth channel, the receiver performs despreading

using the MIMO MMSE despreading filter followed by nearest symbol approximation. The

stream of detected symbols is then spread, passed through a virtual radio channel and


subtracted from the received signal. Assuming that vectors of S are ordered in a way such

that the channel gains corresponding to signature sequences are in an ascending order

where channels are despread starting from the last channel and SIC is implemented, then

channel k will have to deal with k − 1 interfering channels instead of K − 1.

The number of interfering channels and the receiver covariance matrix used to calculate

the MIMO despreading filter coefficients change depending on the channel number k. The

receiver covariance matrix Ck used to design the receiver for channel k can be calculated

recursively from

Ck= Ck−1 + Ek ~qk ~qHk + Ek~q

(−1)k ~q

(−1)Hk + Ek ~q

(+1)k ~q

(+1)Hk (4.25)

where the covariance matrix when all channels are cancelled is given as

C0=2σ2INr(N+L−1) (4.26)

The MIMO MMSE despreading filter coefficients vector is calculated as

~wSIC,k =C−1k ~qk

~qHk C−1k ~qk

(4.27)

Even though the recursive construction of the covariance matrix and despreading coeffi-

cients starts from k = 1 up to k = K, the despreading and interference cancelling is carried

out starting from k = K and goes down as mentioned earlier.

4.4.2 Iterative Energy and Covariance Matrix Inversion Calculations

When SIC is implemented at the receiver, the transmission energy can be calculated us-

ing the recursive property of the covariance matrix and the matrix inversion lemma. The

knowledge of C−1k−1 is sufficient to calculate the energy value Ek. Then C−1

k can be obtained

recursively from C−1k−1 and Ek. In the same manner, C−1

k is used to calculate Ek+1 and so on.

This does not require any matrix inversion processes as the only matrix inversion required

is C−10 which is calculated as

C−10 =

(2σ2)−1

INr(N+L−1) (4.28)


The detailed steps and equations required to carry out this process are given as follows

1. The channel index is initialized k = 1 and the first inverse covariance matrix obtained

from equation (4.28).

2. The previous symbol vector and the next symbol vector are defined as

~qk,1 = ~q(−1)k = H(−1)~sk (4.29)

~qk,2 = ~q(+1)k = H(+1)~sk (4.30)

3. The distance vectors are defined as

~d = C−1k−1~qk (4.31)

~d1 = C−1k−1~qk,1 (4.32)

~d2 = C−1k−1~qk,2 (4.33)

4. The weighting functions are defined as

ξ = ~dH ~qk (4.34)

ξ1 = ~dH1 ~qk,1 (4.35)

ξ2 = ~dH2 ~qk,2 (4.36)

ξ3 = ~dH ~qk,1 (4.37)

ξ4 = ~dH ~qk,2 (4.38)

5. Having found the two-group algorithm parameters p andm previously, the target SNIR

is defined as

γ∗k = Γ(

2bp − 1), k ∈ [1, · · · , (K −m)] (4.39)

γ∗k = Γ(

2bp+1 − 1), k ∈ [(K −m+ 1) , · · · ,K] (4.40)


6. The energy is calculated iteratively using

Ek(i) =γ∗k

ξ − Ek(i−1)

(|ξ3|2

1 + Ek(i−1) ξ1+

|ξ4|2

1 + Ek(i−1) ξ2

) , i = 1, · · · , Imax,SIC (4.41)

for an arbitrary initial value Ek(i) for i = 0. The iterations are repeated until Ek(i) ≈

Ek(i−1) for k = 1, . . .K, or i reaches Imax,SIC.

7. After Ek(i) converges to a value Ek, the matrix weighting functions are calculated as

follows

ζ =Ekγ∗k

(4.42)

ζ1 =Ek

1 + Ek ξ1(4.43)

ζ2 =Ek

1 + Ek ξ2(4.44)

8. The inverse of the covariance matrix is calculated from

C−1k = C−1

k−1 −ζ ~d ~dH −(ζ1 + ζ ζ2

1 |ξ3|2)~d1~dH1 −

(ζ2 + ζ ζ2

2 |ξ4|2)~d2~dH2

+ζ ζ1

(ξ3~d ~dH1 + ξ∗3

(~d ~dH1

)H)+ ζ ζ2

(ξ4~d ~dH2 + ξ∗4

(~d ~dH2

)H)−ζ ζ1ζ2

(ξ3ξ

∗4~d2~dH1 + (ξ3ξ

∗4)∗(~d2~dH1

)H)(4.45)

9. If k < K, k = k+ 1 and steps are repeated starting from step 2. Otherwise, the energy

calculation is done.

Proofs for equations are given in [18]. In step 6, energy is calculated iteratively. How-

ever, iterations do not include any matrix inversions and hence the process is not computa-

tionally heavy. Combining this method with the system value approach eliminates the ma-

trix inversions required for iterative energy calculations. The remaining matrix inversions

are those required by system value approach and optimum channel selection. Table 4.2

shows the number of matrix inversions required to perform the resource allocation schemes

described earlier when system value approach is used with SIC.


Scheme Mat. Inv.

Two-Group with water-filling ch. sel. 1

Two-Group with optimum ch. sel. ≤ K

Two-Group with suboptimal ch. sel. 1

Table 4.2: Matrix inversion required for system value with SIC.

4.5 Simulation and Analysis

4.5.1 Total System Value

The system value approach is based on the relationship between the total system value

upper bound and the total system value for equal-rate margin adaptive loading with zero

bit granularity. This relationship will be verified where Ped-B channel model is used with

optimum MIMO signature sequences and water-filling channel selection to calculate the

total system value for different energy allocation schemes over different SNRs.

0 5 10 15 20 25 30 350

5

10

15

20

25

30

ET/N0 dB

Tot

al S

yste

m V

alue

GurcanMA 0.001Random Energy Loading

Figure 4.1: Total system value for different energy allocation schemes.

The curve corresponding to Gurcan total system value gives an upper bound as expected.

Furthermore, equal-rate margin adaptive with 0.001 bit granularity (MA0.001) is used as

an approximation for zero bit granularity margin adaptive loading. Energies for MA0.001

are realised using constrained optimization from where the total system value is obtained.

The fact that total system value of MA0.001 is close to the upperbound proves the validity


of the system value approximation. The third curve corresponds to randomly allocated

energies that follow the same total energy constraint. As expected, the total system value

corresponding to non-equal energy loading would not exceed the upper bound.

4.5.2 Total Throughput

In this subsection, the achievable rates for different resource allocation schemes are com-

pared to the upper bounds given by the water-filling capacity CWF and the Gurcan capacity

CG for Ped-A and Ped-B channel models with zero spatial correlations. The resource al-

location schemes considered are the MIMO HSDPA standard (D-TxAA), two-group loading

with system values and water-filling channel selection (TGSV,WF), optimum channel selec-

tion (TGSV,Opt) and suboptimal channel selection (TGSV,Sub). All schemes that use system

values use optimum MIMO signature sequences as well.

0 5 10 15 20 25 30 350

20

40

60

80

100

120

140

160

180

200

ET/N0 dB

RT

bits

/sym

bol

WFGurcanTG

SV,WFTG

SV,OptTG

SV,Sub

D−TxAA

Figure 4.2: Upper bounds, D-TxAA and TGSV schemes - Throughput - Ped-A.

For channel Ped-A (figure 4.2), throughputs of different schemes are close to each other

as the delay spread is very small to show the differences in performance. The average

gap between D-TxAA and the upper bounds is less than 2.5 dB. This gap is acceptable

considering that current standard does not apply optimum MIMO signature sequences or

channel selection. However, the average gap between D-TxAA and the upper bounds for

Ped-B is higher than 7.5 dB as shown in figure 4.3. This gap is relatively large and it


0 5 10 15 20 25 30 350

20

40

60

80

100

120

140

ET/N0 dB

RT

bits

/sym

bol

WFGurcanTG

SV,WFTG

SV,OptTG

SV,Sub

D−TxAA

Figure 4.3: Upper bounds, D-TxAA and TGSV schemes - Throughput - Ped-B.

reflects significant inefficiency in resource allocation. On the other hand, TGSV,WF reduces

the average gap to around 2.5 dB where TGSV,Sub reduces it to around 1.5 dB and TGSV,Opt

gives the better performance with an average gap around 1 dB. The main reason behind the

general improvement is using two-group loading and optimum MIMO signature sequences.

However, the gaps between the different schemes using two-group loading and the same

sequences are due to different channel selection schemes.

Av. C IncreaseScheme

Ped-A Ped-B

TGSV,WF 8% 48%

TGSV,Sub 11% 59%

TGSV,Opt 11% 65%

Table 4.3: Average capacity increase for different two-group schemes compared to D-TxAA.

Table 4.3 shows the increase in average throughput as a percentage of the D-TxAA av-

erage rate obtained using equation (3.29). The improvement is not significant for Ped-A as

expected. However, the proposed schemes provide significant improvement for Ped-B.


0 5 10 15 20 25 30 350

20

40

60

80

ET/N0 dB

Mat

rix In

vers

ions

errorE = 0%

TGSV,WF

TGSV,Opt

TGSV,Opt−II

TGSV,Sub

0 5 10 15 20 25 30 350

20

40

60

80

ET/N0 dB

Mat

rix In

vers

ions

errorE = 1%

TG

SV,WF

TGSV,Opt

TGSV,Opt−II

TGSV,Sub

Figure 4.4: Number of matrix inversions for different schemes for energy error 0% and 1%.

4.5.3 Matrix inversions

The main objective of using system value approach is to reduce the number of matrix inver-

sions required to run two-group loading algorithm. Figure 4.4 shows the number of matrix

inversions required by the different system value two-group loading schemes discussed ear-

lier for errorE = 0 and errorE = 0.01. The scheme referred to as TGSV,Opt-II is the same

as TGSV,Opt with modifying the optimum channel selection scheme in order to reduce the

number of matrix inversions. This is done by initializing the number channels as K∗Opt = K

2

at the beginning of the channel selection search process. If the capacity for(K∗

Opt + 1)

is

larger than the one for K∗Opt, the search continues by increasing K∗

Opt. Otherwise, K∗Opt is

decreased. This way the maximum number of matrix inversions for the search would not

exceed(K2 + 1

). Figure 4.4 shows that the modification added in TGSV,Opt-II is very effective

as the matrix inversions required for optimum channels selection are reduced.

The matrix inversions averaged over the SNR range for the different schemes and the

two energy error values are given in table 4.4. Compared to values given in the previous

chapter, system value approach seems to be doing an outstanding job. For 0% energy error,

TGSV,WF and TGSV,Sub require Imax = 50 matrix inversions where TGSV,Opt and TGSV,Opt-II


Matrix InversionserrorE TGSV,WF TGSV,Sub TGSV,Opt TGSV,Opt-II

0 50 50 64 54

0.01 12 12 22 11

Table 4.4: Average number of matrix inversion for different schemes.

require more matrix inversions for the channel selection scheme. Furthermore, allowing an

a small energy error of 1% reduces the number of matrix inversions significantly reaching

11 for TGSV,Opt-II.

4.5.4 Spatial Correlation

All simulations so far assume MIMO channels with zero cross correlations between MIMO

paths. However, spatial correlations between antennas at the transmitter and the receiver

usually yield partial correlations between MIMO paths in practice [32]. The model de-

scribed in chapter 2 is used to generate the correlated MIMO channels for simulations. The

main correlation-parameters required to implement the correlations are: the MIMO paths

correlation matrix RMIMO, the Ricean factorKRic and the mean AoA for different path delays.

Correlation-parameters for Ped-A and Ped-B channel models are taken from the Intelligent

Multi-Element Transmit and Receive Antennas (I-METRA) MIMO channel model proposed

by 3GPP [12] and they are used to produce Ped-A(corr) and Ped-B(corr). The values of the

correlation-parameters for Ped-A(corr) and Ped-B(corr) are given in Appendix A.

The throughputs for the different resource allocation schemes and the number of chan-

nels applied are plotted for Ped-A(corr) and Ped-B(corr) in figures 4.5 and 4.6 respectively. For

Ped-A(corr), the performances for different schemes are close to each other for reasons men-

tioned earlier. However, it is important to note that D-TxAA performs better than TGSV,WF

at high SNR values. The number of channels applied by TGSV,Opt, TGSV,Sub and D-TxAA

schemes prove that the extra channels allocated by water-filling channel selection are the

reason behind the throughput drop of TGSV,WF at high SNRs. For Ped-B(corr), two-group

schemes in general perform better than D-TxAA for reasons mentioned earlier. However,

TGSV,WF fails to keep up with TGSV,Opt and TGSV,Sub at high SNRs and it performs close to

D-TxAA. The reason again is the channel selection scheme.


0 5 10 15 20 25 30 350

50

100

150

200

ET/N0 dB

RT

bits

/sym

bol

WFGurcanTG

SV,WF

TGSV,Opt

TGSV,Sub

D−TxAA

0 5 10 15 20 25 30 350

5

10

15

20

25

30

ET/N0 dB

Cha

nnel

s U

sed

TGSV,WF

TGSV,Opt

TGSV,Sub

D−TxAA

Figure 4.5: Throughput and number of applied channels - Ped-A(corr).

0 5 10 15 20 25 30 350

20

40

60

80

100

120

140

ET/N0 dB

RT

bits

/sym

bol

WFGurcanTG

SV,WF

TGSV,Opt

TGSV,Sub

D−TxAA

0 5 10 15 20 25 30 350

5

10

15

20

25

30

ET/N0 dB

Cha

nnel

s U

sed

TG

SV,WF

TGSV,Opt

TGSV,Sub

D−TxAA

Figure 4.6: Throughput and number of applied channels - Ped-B(corr).


Spatial correlations reduce the optimum number of channels where the MIMO system is

supposed to exploit the diversity gain. Optimum and suboptimal channel selection schemes

map this successfully and provide balance between spatial multiplexing and transmit di-

versity in different MIMO channel conditions where water-filling channel selection fails to

do the same. This shows the importance of channel selection in practical MIMO channel

conditions.

4.5.5 Approximation Error and Energy Margin

System value approach eliminates the iterative search for p and m. However, the approx-

imations given in equations (4.20), (4.22) and (4.24) assume that the total system value

can be equal to the upper bound which is not always the case as seen from figure 4.1. This

yields an approximation error where the estimated p andm using system value approach are

sometimes higher than those found using constrained optimization. To test the significance

of the approximation error, the total energy margin is defined as

marginE = 10log10

(ET∑Kchk=1Ek

)dB , Kch ∈

{K∗,K∗

Opt,K∗Sub

}(4.46)

Using constrained optimization guarantees that marginE is non negative. However, system

value approach may yield a negative margin where total energy required for transmission

would exceed the total available energy at the transmitter.

The approximation error is investigated for the three two-group channels selection schemes

over the Ped-B channel model. Figure 4.7 has two sub-figures; the first one plots the total

throughput for two-group loading with water-filling channel selection using constrained op-

timization (TGCO,WF) and system value approach (TGSV,WF) to calculate p and m. The other

sub-figure plots the energy margin for. The same description of figure 4.7 applies to figures

4.8 and 4.9 but for suboptimal channel selection scheme and optimum channel selection

scheme respectively. The energy margin for water-filling channel selection reaches −1 dB

and has an average of −0.5 dB over the whole SNR range. Suboptimal channel selection

seems to be reducing the approximation error as the margin is always greater than -0.5 dB

with an average around −0.1 dB. Furthermore, optimum channel selection gives the least

approximation error as the energy margin does not drop below -0.07 dB and has an average


around 0 dB.

0 5 10 15 20 25 30 350

20

40

60

80

100

120

ET/N0 dB

RT

bits

/sym

bol

TG

SV,WF

TGCO,WF

0 5 10 15 20 25 30 35

−1

−0.5

0

0.5

1

ET/N0 dB

Mar

gin E

dB

TG

SV,WF

Zero dB Margin

Figure 4.7: Approximation error - Throughput and energy margin - Water-filling selection

4.5.6 SIC

The main objective behind using SIC is to eliminate matrix inversions required for iterative

energy calculation. For Ped-B channel model and with SIC energy calculation and system

value approach implemented, only one matrix inversion is required to run TGSV,WF and

TGSV,Sub. More matrix inversions are required to perform optimum channel selection and

an average of 15 matrix inversions are required by TGSV,Opt. The improvement introduced

in TGSV,Opt-II reduces the average number of required matrix inversions to around 5.

Matrix Inversions

TGSV,WF TGSV,Sub TGSV,Opt TGSV,Opt-II

1 1 15 5

Table 4.5: Average number of matrix inversion - SIC energy calculation.


0 5 10 15 20 25 30 350

20

40

60

80

100

120

ET/N0 dB

RT

bits

/sym

bol

TG

SV,Sub

TGCO,Sub

0 5 10 15 20 25 30 35

−1

−0.5

0

0.5

1

ET/N0 dB

Mar

gin E

dB

TG

SV,Sub

Zero dB Margin

Figure 4.8: Approximation error - Throughput and energy margin - Suboptimal selection


0 5 10 15 20 25 30 350

20

40

60

80

100

120

ET/N0 dB

RT

bits

/sym

bol

TG

SV,Opt

TGCO,Opt

0 5 10 15 20 25 30 35

−1

−0.5

0

0.5

1

ET/N0 dB

Mar

gin E

dB

TG

SV,Opt

Zero dB Margin

Figure 4.9: Approximation error - Throughput and energy margin - Optimum selection

0 5 10 15 20 25 30 35−1

0

1

2

3

4

5

6

ET/N0 dB

Mar

gin E

dB

TG

SV,Sub

TGSV,Opt

TGSV,Sub

Zero dB Margin

Figure 4.10: Energy margin for system value two-group with SIC energy calculations


Another interesting thing to look at when SIC is implemented, is the energy margin.

Figure 4.10 plots the energy margins for the different schemes over Ped-B channel mode.

SIC has eliminated the negative margins of TGSV,Sub and TGSV,Opt where a negative margin

still appears for TGSV,WF. However, this negative margin is not significant as in the worst

case it does not drop below -0.1 dB. At high SNR values, the energy margins for different

schemes grow positively exceeding 5 dB for TGSV,WF and TGSV,Sub. This is expected as SIC

reduces interference and hence increases the potential capacity of channels. However, SIC

was mainly considered to simplify calculations and increasing the assigned rates was not

considered.

Chapter 5

Conclusion

Currently deployed MIMO HSDPA systems suffer from severe throughput losses in frequency

selective channels with significant delay spread. Such radio channel conditions are typical

for urban environments. Throughput losses are caused by inefficient resource allocation,

particularly the manner in which energy is distributed among different code channels. The

resource allocation scheme adapted by MIMO HSDPA distributes energy among all available

channels and rates are controlled per data stream where all channels belonging to the same

data stream are assigned the same bit rate. Furthermore, the system can choose to operate

in single-stream mode (transmit diversity) or dual-stream mode (spatial multiplexing).

It was found that using energy-constrained rate optimization, particularly two-group

loading algorithm, provides around 40% increase in average throughput for ITU Ped-B chan-

nel model. However, the computational complexity required to run the algorithm is high for

the majority of mobile applications due to the large number of covariance matrix inversions

required. System value approach and optimum signature sequence design were applied

to MIMO HSDPA in order to reduce computational complexity and improve performance.

The approach was found to work well and the number of matrix inversions was reduced

from the order of hundreds to the order of tens. However, system value approach produced

approximation error which results in a small negative energy margin. The main contribu-

tion of this work is the optimum and suboptimal channel selection schemes developed to

be used with system value approach. Optimum channel selection scheme improves average

throughput, reduces approximation error and reduces throughput loss in the presence of

65

CHAPTER 5. CONCLUSION 66

spatial correlations. Furthermore, channel selection provides automatic transition between

transmit diversity and spatial multiplexing and hence eliminates the confusion associated

with using single-stream mode or double-stream mode. However, optimum channel selec-

tion requires a few extra matrix inversion operations. Suboptimal channel selection provides

improvements very close to those provided by optimum channel selection without requiring

the extra matrix inversions. For ITU Ped-B channel mode, two-group loading improved by

system value approach, optimum signature sequences and channel selection provides up to

65% and 60% increase in average throughput for optimum channel selection and subopti-

mal channel selection respectively.

Finally, interference cancelation with recursive matrix inversions was tested with the sys-

tem value approach. This brought down the number of matrix inversions to one and elimi-

nated the negative energy margin for optimum and suboptimal channel selection schemes.

Interference cancelation produces a significant positive energy margin at high SNRs which

can be used to transmit extra data. However, interference cancelation was used mainly to

eliminate matrix inversions required by iterative energy calculation. Considering interfer-

ence cancelation to increase throughput is one of the points that can be considered in a

future work based on this project. Other suggested points that need to be explored include:

1. Combining the improved recourse allocation schemes with recently proposed 3GPP

improvements such as multiple-carrier MIMO HSDPA.

2. Considering system level modelling and simulation to test the overall system perfor-

mance and combining it with the link level model provided in this project.

3. Considering the multi-user problem where channels are allocated to multiple users in

the same cell.

4. Developing practical solutions for implementation problems such as the perfect CSI

assumed for energy allocation feedback and optimum signature sequences.

5. Implementing the system practically using software defined radio and testing it in a

proper environment to see if it performs as the theory states.

Appendix A

I-METRA Channel Parameters

The I-METRA correlation parameters for the spatially correlated channels are given in table

A.1 [12] where d is the antenna spacing at the receiver used to calculate the steering vector.

Parameter Ped-A(corr) Ped-B(corr)

ρr −0.3043 0.0819 + j0.4267

ρt 0.4640 + j0.8499 0.7544 + j0.0829

KRic 6 dB −∞ dB (NLOS)

22.5 (odd paths)AoA 22.5 (all paths)

-67.5 (even paths)

d 0.5λ 0.5λ

Table A.1: I-METRA channel parameters for Ped-A(corr) and Ped-B(corr).

The correlation matrices are formulated as

Rr =

ρr 1

1 ρ∗r

Rt =

ρt 1

1 ρ∗r

67

Appendix B

Simulation Package

This Appendix provides general explanation for the simulation package created as part of

this project. The programs and functions are all written using MATLAB and the full codes

are available in the associated CD. The programs can be divided into three categories; ini-

tialization, resource allocation schemes and presentation. Programs falling in each category

will be discussed alongside with functions used for each program.

B.1 Initialization

The first initialization program is Initialize Parameters.m. This program initializes the pa-

rameters given in table 2.1 except the channel model. The parameters are saved in a .mat

file which is loaded when running programs that need those parameters. The second ini-

tialization program is PDP.m. This program modifies the PDPs given by ITU to match the

HSDPA system. The function PDP conv.m is used in the process to re-sample the original

PDP at appropriate periods.

The las initialization program is Create MIMO ch.m This program creates MIMO chan-

nels required for the simulations and saves them in .mat files so that simulations for dif-

ferent schemes use exactly the same channels. This program uses the functions h gen.m,

MIMO PedA.m and MIMO PedB.m to create the four MIMO paths vectors for customized

PDP and correlations, I-METRA Ped-A and I-METRA Ped-B respectively.

68

APPENDIX B. SIMULATION PACKAGE 69

B.2 Resource Allocation Schemes

There are eight programs that estimate the total throughput, transmission energies and

number of matrix inversions for different resource allocations schemes. Those programs are

given in table B.1. For a given radio channel model, each program calculates the output

parameters (throughput, energies or number of matrix inversions) for 20 different MIMO

channels. The resulting output parameters are averaged over the 20 different MIMO chan-

nels to obtain the values that appear in the plots. A diagram that shows the general steps

performed by the programs is given in figure B.1.

Program Scheme

MIMO DTxAA iter.m D-TxAA

MIMO Constopt Mode Selc.m TGmode

MIMO SV WF Selc Iter.m TGSV,WF

MIMO SV SubOpt Selc Iter.m TGSV,Sub

MIMO SV Opt Selc Iter.m TGSV,Opt

MIMO Constopt WF Selc.m TGCO,WF

MIMO Constopt SubOpt Selc.m TGCO,Sub

MIMO Constopt Opt Selc.m TGCO,Opt

Table B.1: Resource allocation schemes MATLAB programs.

Read system parameters

Read first MIMO

channels

Prepare MIMO Signature

Sequences

Resource allocation for

SNR range

Calculated parameters

Last MIMO channel ?

Read next MIMO

channel

YesNo Average calculated

parameters

Export to .mat file

Figure B.1: General steps for resource allocation schemes programs.

All programs use the function H MIMO.m that takes the MIMO paths response vectors as

input and creates the MIMO channel convolution matrix. For MIMO signature sequences,

APPENDIX B. SIMULATION PACKAGE 70

the function OVSF Pre.m is used by the first two programs in table B.1 to create OVSF signa-

ture sequences with precoding where precoding changes according to the MIMO channel.

The rest of the programs use the function Opt Sig.m to create optimum MIMO signature

sequences. MIMO DTxAA iter.m uses the functions TxAA.m and DTxAA.m to perform single-

stream loading and double-stream loading respectively where MIMO Constopt Mode Selc.m

uses TG Original.m to do both single-stream and double-stream constrained optimization

two-group loading.

For two-group with system value approach, all programs have the same structure but dif-

fer in the channel selection scheme. MIMO SV WF Selc Iter.m uses the function C WF.m to

perform water-filling channel selection and calculate the water-filling capacity. The function

Gurcan.m is used to find the total system value upper bound and calculate Gurcan’s capacity

where the function TG p m.m uses system value approach to calculate p and m. Further-

more, the functions E TG iter.m and E TG SIC.m calculate energies iteratively and using SIC

respectively. Following the same structure, the only change in MIMO SV SubOpt Selc Iter.m

and MIMO SV Opt Selc Iter.m is in the channel selection scheme. The functions SubOpt Selec.m

and Opt Selec.m are used for suboptimal and optimum channel selection schemes respec-

tively. Finally, the last three programs in B.1 apply optimum sequences and channel selec-

tion with the function TG p m const opt.m to calculate p, m and energies using constrained

optimization.

The values that result from the programs described in this section are stored in different

.mat files. The same program may have more than one .mat destination for different channel

models.

B.3 Presentation

The presentation program plot results.mat uses the .mat files produced from running all

previous programs and produces the figures used in this report. Some calculations related

to different observations are carried out using the same program as well.

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