Parallel Sequence Spread Spectrum-Orthogonal Frequency

Division Multiplexing (PSSS-OFDM) Scheme - a Novel

Physical Layer for Robust Wireless Communication Systems

Thesis by

Paulo Isagani M. Urriza

BS CoE

Submitted to the Graduate Division

College of Engineering

University of the Philippines

In Partial Fulfillment of the Requirements

For the Degree of Master of Science

in Electrical Engineering (C&C)

College of Engineering

University of the Philippines

Diliman, Quezon City

August 2009

This thesis, entitled “PARALLEL SEQUENCE SPREAD

SPECTRUM-ORTHOGONAL FREQUENCY DIVISION

MULTIPLEXING (PSSS-OFDM) SCHEME - A NOVEL

PHYSICAL LAYER FOR ROBUST WIRELESS

COMMUNICATION SYSTEMS”, prepared and submitted by

PAULO ISAGANI M. URRIZA, in partial fulfillment of the

requirements for the degree of MASTER OF SCIENCE IN

ELECTRICAL ENGINEERING (C&C) is hereby accepted.

JOEL JOSEPH S. MARCIANO JR.Thesis Adviser

Accepted as partial fulfillment of the requirements for the degree

of MASTER OF SCIENCE IN ELECTRICAL ENGINEERING

(C&C).

ROWENA CRISTINA L. GUEVARADean, College of Engineering

ii

Table of Contents

Table of Contents v

List of Tables vi

List of Figures vii

Abstract ix

Acknowledgements x

1 Introduction 1

1.1 Overview of Multicarrier Spread Spectrum . . . . . . . . . . . . . . . 2

1.2 Motivations for Integrating PSSS and OFDM . . . . . . . . . . . . . 3

1.3 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Multicarrier Spread Spectrum 7

2.1 Spread Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Spreading Spectrum in a Multicarrier Systems . . . . . . . . . . . . . 8

2.2.1 Multicarrier Direct-Sequence Spread Spectrum . . . . . . . . . 9

2.2.2 Multicarrier CDMA . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2.3 Multitone Spread Spectrum . . . . . . . . . . . . . . . . . . . 10

2.2.4 Frequency Diversity Spread Spectrum . . . . . . . . . . . . . . 10

2.3 Frequency Diversity in Multicarrier Spread Spectrum . . . . . . . . . 11

2.3.1 Diversity Combining . . . . . . . . . . . . . . . . . . . . . . . 12

2.3.2 Spreading Transforms for MC-SS . . . . . . . . . . . . . . . . 12

2.3.3 Rate Adaptation . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.4 Channel Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.5 Parallel Sequence Spread Spectrum . . . . . . . . . . . . . . . . . . . 14

iii

3 Problem Statement 15

3.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4 Development of the PSSS-OFDM Algorithm 17

4.1 General Design Parameters . . . . . . . . . . . . . . . . . . . . . . . . 17

4.1.1 System Block Diagram . . . . . . . . . . . . . . . . . . . . . . 17

4.1.2 Hybrid 802.11a . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.1.3 Scope of the Design Space . . . . . . . . . . . . . . . . . . . . 21

4.2 Design of the Spreading Block . . . . . . . . . . . . . . . . . . . . . . 21

4.2.1 Precoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.2.2 Dynamic Thresholding . . . . . . . . . . . . . . . . . . . . . . 24

4.3 Integration of PSSS with multicarrier techniques . . . . . . . . . . . . 26

4.3.1 Interleaving in the Frequency Domain . . . . . . . . . . . . . . 27

4.3.2 Fully Integrated PSSS-OFDM . . . . . . . . . . . . . . . . . . 28

4.4 Rate Adaptation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.4.1 Variable Spreading . . . . . . . . . . . . . . . . . . . . . . . . 29

4.4.2 Rate-Adaptive OFDM . . . . . . . . . . . . . . . . . . . . . . 30

4.5 Equalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.6 Final PSSS-OFDM Algorithm . . . . . . . . . . . . . . . . . . . . . . 33

5 Performance Measurements 36

5.1 PSSS, OFDM and PSSS-OFDM Transceiver Schemes for Simulations 36

5.1.1 Data Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.1.2 OFDM Subcarriers and Spreading Sequence . . . . . . . . . . 37

5.2 Performance in Additive White Gaussian Noise . . . . . . . . . . . . 38

5.2.1 Normalization of SNR . . . . . . . . . . . . . . . . . . . . . . 38

5.2.2 PSSS-OFDM without precoding . . . . . . . . . . . . . . . . . 39

5.2.3 PSSS-OFDM with precoding . . . . . . . . . . . . . . . . . . . 40

5.3 Performance in Frequency Selective Fading . . . . . . . . . . . . . . . 42

5.3.1 Channel Model . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.3.2 Comparison of PSSS and PSSS-OFDM . . . . . . . . . . . . . 43

5.3.3 Comparison of PSSS-OFDM and BPSK-OFDM . . . . . . . . 46

6 Hardware Architecture for the PSSS-OFDM Transceiver 53

6.1 PSSS-OFDM Design Parameters for Hardware Implementation . . . . 54

6.2 Rapid Prototyping Design Flow . . . . . . . . . . . . . . . . . . . . . 55

6.2.1 Software Design Flow . . . . . . . . . . . . . . . . . . . . . . . 55

6.2.2 Hardware Target . . . . . . . . . . . . . . . . . . . . . . . . . 55

6.3 Design of the PSSS-OFDM Encoder . . . . . . . . . . . . . . . . . . . 56

iv

6.3.1 Functional Block Diagram . . . . . . . . . . . . . . . . . . . . 57

6.3.2 PSSS Spreader . . . . . . . . . . . . . . . . . . . . . . . . . . 59

6.3.3 IFFT Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

6.4 Design of the PSSS-OFDM Decoder . . . . . . . . . . . . . . . . . . . 62

6.4.1 Functional Block Diagram . . . . . . . . . . . . . . . . . . . . 62

6.4.2 PSSS Despreader . . . . . . . . . . . . . . . . . . . . . . . . . 62

6.5 Testing and Characterization . . . . . . . . . . . . . . . . . . . . . . . 66

6.5.1 Test Vector Generation . . . . . . . . . . . . . . . . . . . . . . 66

6.5.2 Functional Verification . . . . . . . . . . . . . . . . . . . . . . 67

6.5.3 Logic Utilization . . . . . . . . . . . . . . . . . . . . . . . . . 68

7 Conclusions 69

7.1 Summary of Contributions . . . . . . . . . . . . . . . . . . . . . . . . 70

7.2 Future Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

A Spread Spectrum 73

A.1 Introduction to Spread Spectrum Systems . . . . . . . . . . . . . . . 73

A.2 Motivations for Spread Spectrum . . . . . . . . . . . . . . . . . . . . 74

A.3 Processing Gain and Jamming Margin . . . . . . . . . . . . . . . . . 75

B Orthogonal Frequency Division Multiplexing (OFDM) 77

B.1 Motivations for Multi-carrier vs. Single-carrier Systems . . . . . . . . 78

B.2 Introduction to OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . 78

B.3 Subcarrier Symbol Structure . . . . . . . . . . . . . . . . . . . . . . . 80

B.4 Cyclic Prefix (Guard Interval) . . . . . . . . . . . . . . . . . . . . . . 80

C Sample PSSS Encoding/Decoding 82

Bibliography 86

v

List of Tables

4.1 Relevant Parameters of the 802.11a OFDM PHY adapted for PSSS-

OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.2 PSSS-OFDM Interleaving Pattern (Pa, Pb, and Pc, are the 3 PSSS

sequences) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

6.1 Specifications of the Xilinx Virtex 4 XC4VFX12 FPGA [24] . . . . . 56

6.2 Logic Utilization of the PSSS-OFDM Transmitter . . . . . . . . . . . 68

6.3 Logic Utilization of the PSSS-OFDM Receiver . . . . . . . . . . . . . 68

vi

List of Figures

1.1 MC-SS transmission model [2] . . . . . . . . . . . . . . . . . . . . . . 3

1.2 PSSS-OFDM system block diagram . . . . . . . . . . . . . . . . . . . 4

1.3 PSSS encoder block diagram . . . . . . . . . . . . . . . . . . . . . . . 5

2.1 Generation of the frequency diversity spread spectrum waveform [3] . 11

2.2 SS-OFDM transmitter architecture [15] . . . . . . . . . . . . . . . . . 13

4.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.2 Sample 15-PSSS Encoded Data with and without Precoding . . . . . 23

4.3 Histogram of 15-PSSS without precoding . . . . . . . . . . . . . . . . 24

4.4 Histogram of 15-PSSS with precoding . . . . . . . . . . . . . . . . . . 25

4.5 BER of Precoded and Non-Precoded PSSS in AWGN . . . . . . . . . 26

4.6 Varying Decision Threshold as a Result of Precoding . . . . . . . . . 27

4.7 Histogram of PSSS-OFDM with varying amount of spreading . . . . . 31

5.1 63 symbol m-sequence used for PSSS and PSSS-OFDM simulations . 39

5.2 BER comparison of PSSS, PSSS-OFDM, and BPSK-OFDM under

AWGN (without precoding) . . . . . . . . . . . . . . . . . . . . . . . 41

5.3 BER comparison of PSSS-OFDM and BPSK-OFDM under AWGN

(with precoding) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.4 Envelope of the Frequency Selective Channel Impulse Response using

the Exponential Decay Model (τRMS = 50ns) . . . . . . . . . . . . . . 44

vii

5.5 BER vs. RMS Delay Spread comparison of plain PSSS and PSSS-

OFDM under Frequency Selective Fading (Eb/N0 = 10dB) . . . . . . 45

5.6 BER vs. Eb/N0 comparison of plain PSSS and PSSS-OFDM under

Frequency Selective Fading (τRMS = 50ns) . . . . . . . . . . . . . . . 46

5.7 BER vs. RMS Delay Spread comparison of PSSS-OFDM modes and

BPSK-OFDM under Frequency Selective Fading (Eb/N0 = 10dB) . . 47

5.8 BER vs. RMS Delay Spread comparison of PSSS-OFDM modes and

BPSK-OFDM under Frequency Selective Fading (Eb/N0 = 0dB) . . . 48

5.9 BER vs. RMS Delay Spread comparison of PSSS-OFDM modes and

BPSK-OFDM under Frequency Selective Fading (Eb/N0 = 20dB) . . 49

5.10 BER vs. Eb/N0 comparison of PSSS-OFDM modes and BPSK-OFDM

under Frequency Selective Fading (τRMS = 200ns) . . . . . . . . . . . 52

6.1 Xilinx Virtex 4 XC4VFX12 development board used as target platform 57

6.2 Top-level block diagram of the PSSS Spreader . . . . . . . . . . . . . 58

6.3 Block diagram of the PSSS spreader . . . . . . . . . . . . . . . . . . . 60

6.4 Block diagram of the accumulator block used in the PSSS spreader . 61

6.5 Top-level block diagram of the PSSS-OFDM Decoder . . . . . . . . . 63

6.6 Block diagram of the PSSS despreader . . . . . . . . . . . . . . . . . 64

6.7 Block diagram of the correlator used in the PSSS despreader . . . . . 65

6.8 Quantization error resulting from the fixed-point implementation of

the PSSS encoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

B.1 Multicarrier communication system . . . . . . . . . . . . . . . . . . . 79

B.2 Orthogonal Subcarriers . . . . . . . . . . . . . . . . . . . . . . . . . . 81

C.1 a(i) - 31-sample m-sequence (N = 5) . . . . . . . . . . . . . . . . . . 83

C.2 d(i) - Data bits expressed in bipolar format . . . . . . . . . . . . . . . 84

C.3 u(i) - Transmitted PSSS sequence . . . . . . . . . . . . . . . . . . . . 84

C.4 c(i) - Received data after correlation . . . . . . . . . . . . . . . . . . 85

viii

Abstract

Multi-carrier spread spectrum (MCSS) methods based on OFDM use a linear trans-

form to spread energy of transmitted symbols over statistically independent Rayleigh

fading subcarriers, in order to obtain diversity gain at the receiver. In this thesis, we

present and investigate a novel MCSS system which uses Parallel Sequence Spread

Spectrum (PSSS) as its spreading transform. This technique called PSSS-OFDM,

allows flexible control over the amount of spreading to provide a variable rate link

at minimal complexity gain over standard OFDM, requiring only a simple correlator

before the IFFT block. Using a single-tap phase correction equalizer, simulations

show a gain of 4dB in Eb/N0 at a BER of 0.1 over plain PSSS. With the additional

complexity due to the FFT block and the equalizer, it is able to achieve data rates

which are 9 to 10 times higher than PSSS giving it potential for use in wideband

applications such as WLANs. Simulations show that PSSS-OFDM provides diversity

gain over standard BPSK-OFDM by trading robustness for lower spectral efficiency.

PSSS-OFDM achieves comparable BER to standard OFDM at approximately 50%

of the spectral efficiency through the use of precoding. The scheme also performs

progressively better against OFDM as RMS delay spread is increased. Thus, PSSS-

OFDM could be used to provide OFDM with multipath robustness in channels with

high delay spread as a substitute for coded OFDM. Finally, to assess the feasibil-

ity of implementing PSSS-OFDM in hardware, the transceiver was developed and

implemented in a Xilinx Virtex 4 XC4VFX12 platform through a rapid prototyping

approach using Xilinx System Generator.

ix

Acknowledgements

First of all, I thank the Lord God. Without His blessing, none of these would have

ever been possible.

I would like to thank my advisor Prof. Joel Marciano whose guidance and support

throughout this entire endevour have been invaluable. Without his vision, technical

expertise and devotion to excellence, this entire project would have been impossible.

I owe to him in large part what I have learned both inside, and more importantly,

outside the classroom regarding the field of wireless communications, signal process-

ing, as well as teaching. It has been my great fortune and privelege to have worked

with him.

Thanks to Prof. Tata Alvarez and Prof. Franz de Leon for their patience in

answering all my questions (no matter how busy they are), ever since I started grad

school and also for being part of my thesis defense panel. They have both been

extremely supportive of me and my work and have always been there to point me in

the right direction whenever I lost my way.

I would also like to thank the Department of Science and Technology (DOST)

Accelerated Human Resource Development Program (AHRDP) for supporting this

work financially through my MS scholarship and thesis grant. I sincerely hope that

their institution might be able to support the research of more graduate students in

the future.

I am also grateful for the oppurtunity to have been part of the UP Diliman Electri-

cal and Electronics Engineering Institute’s (EEEI) vibrant and encouraging teaching

staff during my short stint as one of their teaching associates. The guidance of the

x

senior faculty as well as the other TA’s have been instrumental towards my growth as

an academic as well as honing my teaching skills. I wish to express my gratitude to

the entire EEEI faculty for all the guidance they gave and the camaraderie we shared.

Thanks to the other MS students, Wilson, Roma, Dean and Tanya, Menandro,

Lew, Allan and She, Snap, Rose, Fed, Dae and everyone else. Grad life would have

been extremely dull and monotonous without these people to cheer me up and help

with the load once in a while. I thank them for all the stimulating discussions and

interesting ideas they have shared with me.

Finally, and most importantly, I would like to express gratitude to my parents and

my sister. They have been with me through thick and thin. They have supported

me through the ups and downs. Their endless love and belief in me have inpired me

time and again and this thesis is dedicated to them.

xi

Chapter 1

Introduction

The development of next generation wireless networks depends upon suitable wireless

transmission and access schemes. These schemes need to provide the high data rates

needed to support multimedia services in mobile radio communications. They also

need to maintain a certain level of robustness against errors in order to guarantee the

integrity of the communications link.

The problem is that these two cannot be perfectly addressed by a single scheme

at the same time. A fundamental trade-off exists which requires a scheme to sacrifice

robustness in order to increase its data rate and vice versa. To increase the amount

of error protection provided by a particular scheme, it needs to introduce more re-

dundancy to the transmitted data. Thus, a lower data rate will be achieved given a

fixed bandwidth.

Another problem arises due to the dynamic nature of the channel impairments.

Depending on the current wireless environment, an optimum scheme might choose to

sacrifice data-rate for better error protection in a channel with high levels of inter-

ference. On the other hand, it might sense a clear channel and thus choose a high

data rate, opting for less error protection. The scheme must be able to adapt to the

1

dynamic channel in order to utilize the allotted spectrum efficiently.

In order to address these problems, various techniques which combine spread

spectrum and multi-carrier techniques have been developed. Multi-carrier techniques

such as orthogonal frequency division multiplexing (OFDM) are especially preferred

in high data rate applications because of its ability to transform a fading multipath

channel into flat fading subcarriers. This results in a very robust scheme aimed

particularly at multipath fading channels.

An issue with OFDM and other multicarrier techniques is the lack of built-in

diversity. Each data symbol is sent on a single subcarrier in a single OFDM symbol.

There is therefore no redundancy, neither in the time domain nor in the frequency

domain. A common approach used to introduce this needed redundancy is through

the use of coded OFDM [1]. An alternative method of introducing frequency diversity

is to use spread spectrum schemes to complement OFDM. These integrated schemes

are collectively known as multicarrier spread spectrum (MC-SS) schemes.

1.1 Overview of Multicarrier Spread Spectrum

Multicarrier spread spectrum or MC-SS is a form of spread spectrum transmission,

where the spreading is exclusively performed in the frequency domain [2]. The un-

derlying transmission scheme is OFDM, which is a special case of multicarrier trans-

mission. Fig. 1.1 illustrates a generalized vector/matrix based transmission model of

an MC-SS system.

The vector b represents the binary data to be transmitted. After mapping, the

resulting vector x is transformed by the N ×N matrix T often called the spreading

matrix. Subsequently, the vector s is transmitted over a multipath fading channel

2

b MAP T D +Detector/Decoder

x s z y b, x , s

n

Figure 1.1: MC-SS transmission model [2]

using OFDM with N parallel subchannels represented by D (α). Finally, after adding

some noise vector n, a detector is used to recover the transmitted data.

The addition of a spreading block before OFDM allows an MC-SS system to

introduce frequency diversity which can overcome the obstacle of severely faded sub-

channels and bandlimited Gaussian interference. Spreading is commonly achieved by

plain symbol repetition over multiple OFDM subcarriers [3].

This thesis focuses on an alternative spreading method called Parallel Sequence

Spread Spectrum or PSSS [4] which utilizes cyclically shifted PN sequences instead

of symbol repetition.

1.2 Motivations for Integrating PSSS and OFDM

A block diagram of the proposed MC-SS system discussed in this thesis is shown in

Fig. 1.2. The spreading matrix, T, is represented by the PSSS-spreader block, while

the multi-carrier portion is accomplished by the ASK-OFDM modulator. Amplitude

shift keying is used in this thesis as the main modulation technique for the PSSS

symbols which are inherently multivalent.

The primary motivation for integrating PSSS with OFDM is the low complexity

gain incurred in implementing PSSS. Both the PSSS encoder and decoder require a

simple cyclic correlator to be implemented in hardware. Another advantage is the

3

PSSSSpreader

ASK-OFDMmodulator

ChannelCompensation

ASK-OFDMdemodulator +

CHANNEL

Binary Generator

PSSSDe-spreader

Decision

Noise

Figure 1.2: PSSS-OFDM system block diagram

high flexibility in varying the amount of spreading at the cost of throughput. This can

be done by choosing only a subset of all the cyclically shifted PN sequences used in

transmitting the data. This corresponds to multiplying 0 to some of the M-sequences

in Fig. 1.3.

We claim that with a properly designed adaptation scheme, this technique could be

used to achieve efficient transmission by introducing the proper amount of spreading

required by a particular wireless environment. If the channel is clear, less spreading

is used and consequently data is transmitted faster. However, if the channel is noisy,

more spreading could be introduced.

1.3 Thesis Organization

This thesis attempts to develop and investigate a novel MC-SS system based upon

the integration of PSSS and OFDM. This scheme is referred to as PSSS-OFDM. The

work covers the various design aspects including theoretical analysis, simulations in

various channel environments, and the development of a hardware architecture for

4

S/P ●

●●

M-Seq-1 X

M-Seq-2 X

M-Seq-i X

●●●

Σ PSSSSeq

InfoBits

Figure 1.3: PSSS encoder block diagram

this scheme.

Chapter 2 discusses various existing multi-carrier spread spectrum systems and

their major contributions to the body of knowledge. It also presents a key parame-

ter in these systems called frequency diversity and how MC-SS systems might take

advantage of this property through the use of various combining schemes. Finally, it

briefly discusses the role of the PSSS algorithm in creating the new MC-SS system

which is the focus of this thesis. This chapter requires a working knowledge of two

digital communication techniques, namely spread spectrum and OFDM. Appendix

A (Spread Spectrum) and Appendix B (OFDM) are provided to discuss these two

topics in more detail.

Chapter 3 describes the specific problems that this thesis addresses. Building upon

the works presented in Chapter 2, the design parameters and goals in developing the

5

new scheme are introduced.

Chapter 4 provides a description of the PSSS-OFDM algorithm. It presents an

analysis of the various design choices made in developing the algorithm and the ra-

tionale behind them. It also presents a scheme which enables the variation of the

amount of spreading introduced through the PSSS-OFDM scheme.

Chapter 5 presents the results of simulations done with the PSSS-OFDM scheme.

It details how the scheme performs in various channel conditions based on BER

plots of the system. The robustness of the scheme in interference is also investigated.

These results are compared with other existing MC-SS systems and to the plain PSSS

scheme.

Chapter 6 describes the design and implementation of a particular hardware ar-

chitecture that employs the PSSS-OFDM algorithm. A Xilinx System Generator

model of this architecture is presented and investigated through various behavioral

simulations. This chapter also discusses the optimizations made in the architecture

in order to reduce the complexity of the system while maintaining its performance.

Chapter 7 concludes this work and proposes steps for future research.

6

Chapter 2

Multicarrier Spread Spectrum

This thesis focuses on the design and implementation of a novel physical layer scheme

which accomplishes spectral spreading entirely in the frequency domain. This tech-

nique belongs to a general class of algorithms referred to as multicarrier spread spec-

trum (MC-SS).

In this chapter we discuss various MC-SS techniques that have been proposed.

We then proceed to a discussion of frequency diversity which is a key parameter

of these systems. This involves analyzing how systems might exploit this property

through various combining schemes. We then discuss various channel models to which

these systems have been applied to, and how equalization can be used to aid such

systems. Finally, we introduce a relatively new temporal spread spectrum scheme

called Parallel Sequence Spread Spectrum. We emphasize its role in this work, placed

in the context of previous MC-SS systems.

2.1 Spread Spectrum

Spread spectrum modulation is defined as any technique that requires a transmission

bandwidth much greater than the modulating signal bandwidth [5]. The two basic

7

types of spread spectrum are frequency hopping (FHSS) and direct sequence (DSSS).

These two schemes perform very well in multipath fading channels but are vulnerable

in the presence of bandlimited Gaussian interference. This interference could be in

the form of intentional jamming, or due to narrowband communication links that

coexist with the signal1.

In order to alleviate the effect of bandlimited Gaussian interference, a cascade of

a noise-whitening filter with an adaptive Notch-filter is required. This results in a

very complicated receiver architecture.

One way of simplifying the receiver is to use spectral spreading in the frequency

domain. With the help of Fast Fourier Transform (FFT) algorithms, this could be

done very efficiently. An example of such a scheme is Orthogonal Frequency Division

Multiplex (OFDM) which is used in most wide-band communication systems due

to its ability to transform a frequency selective channel and make it appear like a

slow flat-fading channel. It also simplifies the equalization process into a simple

multiplication by a complex number2.

2.2 Spreading Spectrum in a Multicarrier Systems

Different methods of spreading spectrum in in the frequency domain have been pro-

posed. These schemes are based on OFDM and are referred to as multicarrier spread

spectrum or spread spectrum OFDM. The main difference between these schemes is

how the actual spreading is achieved, as well as the method of utilizing the resulting

frequency diversity at the receiver. An overview of most of these schemes is presented

in [6].

1Spread spectrum is discussed in more detail in Appendix A2OFDM fundamentals are presented in Appendix B

8

2.2.1 Multicarrier Direct-Sequence Spread Spectrum

The first method of creating an MC-SS system, is to multiply a data sequence by

a spreading sequence as is done in conventional DSSS, but allow it to modulate

M subcarriers instead of just one. We can clearly see that this introduces an Mth

order diversity. This system, first proposed in [7], is referred to as multicarrier direct-

sequence spread spectrum (MC-DSSS). The anti-jamming performance of this scheme

in the presence of joint pulse/partial-band noise jamming was further investigated in

[8].

The receiver for this system is comprised of one correlator for each subcarrier.

After parallel despreading of the subcarriers, their outputs are combined using a

maximal-ratio combiner (MRC). This is referred to as symbol-level combining (as

oppose to the chip-level combining used in other MC-SS systems). The use of MRC

gives this system a narrowband interference suppression effect. Also, the use of mul-

tiple correlators allows for a low-speed parallel processing architecture aimed at a low

power consumption device.

This scheme could easily be extended to serve as a multiple-access scheme by

giving different spreading codes to different users. This scheme is called multicarrier

direct-sequence code division multiple access (MC-DS-CDMA) [7].

2.2.2 Multicarrier CDMA

If instead of multiple copies of a DSSS stream being modulated into different subcarri-

ers, we use each chip of a single DSSS sequence to modulate the different subcarriers,

the scheme is referred to as multicarrier CDMA (MC-CDMA) [9]. This means that

9

DSSS is performed entirely in the frequency domain. At the receiver, a single correla-

tion is done on each OFDM frame. A similar scheme called spread spectrum OFDM

(SS-OFDM) was also proposed in [10]. The performance of this SS-OFDM system

when used with a convolutional channel code was investigated in [11] and [12].

2.2.3 Multitone Spread Spectrum

Another variation of MC-SS is to first generate a multicarrier signal through an FFT,

similar to conventional OFDM. This OFDM frame is then spread in the time domain

by multiplying it with a spreading sequence. In [13], this scheme is investigated and

referred to as multitone spread spectrum (MT-SS).

2.2.4 Frequency Diversity Spread Spectrum

Finally, in [3], a generalized scheme for spreading in the Fourier domain and the

derivation for its optimum detector is presented. This scheme is referred to as fre-

quency diversity spread spectrum, but is also called spread spectrum OFDM (SS-

OFDM) in the literature. When the term MC-SS is used in the literature, it is

generally understood that this is in reference to FD-SS, although it has been shown

in previous sections that MC-SS actually refers to a wider class of schemes. A block

diagram of this technique is shown in Fig. 2.1.

Channel coding introduces redundancies in the data. The coded data is then serial-

to-parallel converted and multiplied to a secret chip value. Each chip is then used

to modulate a different subcarrier through an FFT. In [3], only a simple repetition

code was used for the channel encoder. A suboptimal detector was also proposed

which simply ignores subcarriers that have high interference. It was shown that

if the interference was sufficiently narrowband, this detector performed close to the

10

Cha

nnel

Enc

oder

i,0

i,1

i,N-1

0t

1t

N−1t

Σ

TransmittedSignal

ChipSymbols

InformationSymbols

ith block Mapper

Figure 2.1: Generation of the frequency diversity spread spectrum waveform [3]

optimal weighted detector. Another suboptimal detection for FD-SS, which eliminates

the need for channel estimation by using a constant envelope PSK modulation, is

presented in [14].

2.3 Frequency Diversity in Multicarrier Spread Spec-

trum

The main advantage of MC-SS is the frequency diversity it introduces. This protects

the transmitted signal from frequency selective fading, as well as bandlimited Gaus-

sian interference. Also, due to the use of OFDM, the interference suppression and

equalization at the receiver architecture is less complex, requiring only a single-tap

equalizer for each subcarrier [5]. The frequency diversity introduced can then be

11

efficiently utilized with the help of diversity combining.

2.3.1 Diversity Combining

Two major approaches used to exploit the frequency diversity in an MC-SS system

are employed. Maximal ratio combining (MRC) [7, 9, 15] provides optimal interfer-

ence suppression but destroys the orthogonality of the spreading sequence resulting

in multiple access interference (MAI) in CDMA systems or inter-symbol interference

in single user MC-SS systems. Another scheme which is less complex and preserves

orthogonality is equal gain combining (EGC) [9]. In [15], a comparison of various di-

versity combining schemes is presented. It uses minimum mean-square error (MMSE)

equalization [16] to partially restore the orthogonality of the spreading sequences.

2.3.2 Spreading Transforms for MC-SS

The choice of the spreading matrix also has a major impact in the robustness of an

MC-SS in the presence of interference. The effect of different spreading matrices in

the performance of the MC-SS system is investigated in [17]. In particular, this work

focused on the use of the Hadamard and Fourier matrices [2]. It was shown that the

Fourier matrices perform asymptotically better than the Hadamard matrix. However,

the use the Hadamard transform requires considerably less complexity because it uses

only two chip levels (+1 and -1).

2.3.3 Rate Adaptation

The MC-SS schemes discussed so far provided a fixed amount of spreading or pro-

cessing gain. Since MC-SS requires bandwidth expansion to achieve robustness to

interference, data rate is sacrificed for a given fixed bandwidth. In order to improve

12

the efficiency of the scheme, in terms of the trade-off between spreading and data

rate, the amount of spreading can be adapted based on the channel environment.

This idea was implemented for FD-SS in [18]. Instead of using all subcarriers to

transmit replicas of a single symbol, only a subset of the subcarriers is used. Along

with an adaptation strategy, this allows for the introduction of variable spreading.

However, this scheme only allowed for processing gains which were powers of two.

This idea of rate adaptation could also be applied to other MC-SS system such as

DS-CDMA which uses a spreading sequence instead of simple repetition. This idea

is illustrated in Fig. 2.2. Instead of using all possible spreading sequences cn, only

a subset can be selected. This is referred to as a partially-loaded spread spectrum

system. This is in contrast to a full-load system which makes use of all spreading

sequences. By using only some of the sequences and summing them together, we can

achieve a variable amount of spreading and data rate.

the channel with a variance of N0/2 per dimension.

Π

c0

cK-1

S

/

P

I F F

T

Cyclic prefix and

transmit

filter

s(t) Channel impulse

response

+AWGN

b0

bK-1

S

/

P

b0 ….bK-1

M-1 groups of

chip streams

Figure 2.2: SS-OFDM transmitter architecture [15]

2.4 Channel Models

Most of the work done with MC-SS systems are simulations of frequency selective

fading channels. In particular, a lot of work has been done which investigates the

13

performance of these schemes in the presence of bandlimited Gaussian interference

[3, 14, 8], since this is where frequency diversity becomes most advantageous. Fre-

quency selective Rayleigh fading is also of interest [18] because OFDM is robust in

these channel environments. In [13], a multipath Rician fading channel was also

investigated.

2.5 Parallel Sequence Spread Spectrum

This thesis focuses on a relatively new form of spread spectrum to make an MC-SS

system that has rate adaptation built-in to it. The spreading scheme used, called

parallel sequence spread spectrum (PSSS) [4], uses cyclically shifted versions of a

maximal-length sequence (m-sequence) as the spreading matrix. PSSS has been used

as one of the PHY layer schemes for the 802.15.4 WPAN standard [19]. Appendix C

presents a more thorough discussion of the scheme and a sample encoding/decoding

of PSSS.

The scheme presented in this thesis, also referred to as parallel sequence spread

spectrum OFDM (PSSS-OFDM), is a variant of DS-CDMA which makes use of the

PSSS algorithm to accomplish spreading in the frequency domain.

14

Chapter 3

Problem Statement

Spread-spectrum techniques are methods by which energy generated in a particular

bandwidth is deliberately spread in the frequency domain, resulting in a signal with

a wider bandwidth. This bandwidth expansion provides spread spectrum with in-

creased robustness to interference, jamming signals, as well as self-interference due to

multipath propagation. It also achieves message privacy because of the need to know

the exact spreading sequence used in order to demodulate the signal.

A recent development in spread spectrum technology is Parallel Sequence Spread

Spectrum (PSSS). It allows for increased bit rates by using a multivalent signal instead

of just binary signaling used by Direct Sequence Spread Spectrum (DSSS). This gain

in bit rate is achieved through minimal complexity increase. The trade-off however is

less resistance to frequency selective impairments because of relatively less bandwidth

spreading.

Another popular technique used for wideband systems is Orthogonal Frequency

Division Multiplexing (OFDM). This technique is very spectrally efficient because it

makes use of overlapping subcarriers in the frequency domain. It provides high bit

rates with the benefits of very simple equalization and excellent robustness against

15

frequency selective channel effects such as inter-symbol interference (ISI).

The integration of OFDM with PSSS will provide it with increased robustness

in frequency selective channels as well as a means of low complexity equalization.

However, for this technique to be viable for use in practical communication systems,

an integrated scheme must first be developed and investigated

Parameters of the new system such as modulation scheme, bandwidth usage, and

OFDM parameters also need to be designed and optimized with the goal of developing

an integration of the two schemes to provide the performance gains already identified

but at acceptable complexity increase.

3.1 Objectives

In this thesis, a scheme based on incorporating Parallel Sequence Spread Spectrum

with OFDM (PSSS-OFDM) will be developed and implemented in a practical system.

This scheme will then be tested under varying channel conditions to determine its

performance gain against plain PSSS as well as plain OFDM.

The main objectives of this thesis are as follows:

1. Design an integrated PSSS-OFDM scheme.

2. Perform a series of tests that will verify the performance gains that the system

provides.

3. Develop a hardware architecture for the PSSS-OFDM scheme.

4. Identify the system performance parameters such as achievable bit rate and

hardware complexity in terms of logic utilization.

16

Chapter 4

Development of the PSSS-OFDMAlgorithm

In this chapter we present the various design issues encountered in the development

of the PSSS-OFDM algorithm. We begin by describing the system in terms of its

basic building blocks and their corresponding functions, taking care to carefully define

the scope of the design space investigated in this thesis. This is done by designating

the core design parameters based on an existing OFDM scheme which is modified to

achieve the final PSSS-OFDM scheme.

The latter part of this chapter discusses and investigates the effect of different

design configurations for PSSS-OFDM. We present various design parameters and

analyze the effects of each. The aim being the creation of a final PSSS-OFDM algo-

rithm design to be implemented in a hardware architecture.

4.1 General Design Parameters

4.1.1 System Block Diagram

The PSSS-OFDM algorithm is composed of transmit and receive blocks whose block

diagrams are illustrated in Fig. 4.1. For the most part, the components of these two

17

blocks are simply inverse operations of each other (i.e. DFT and IDFT). However,

they are fundamentally different in their functionality and complexity. To simplify the

discussion, blocks responsible for synchronization and packetization are not included

in the model.

S/P

S/P

IDF

T

●●●

M-Seq-1 X

M-Seq-2 X

M-Seq-i X

●●●

Σ

PSSSSeq

P/SInfo

Bits

PSSS OFDM

Pre

codi

ng

Cyc

lic P

refix

Inse

rtio

n

SentData

(a) Transmitter

S/P

DF

T

CyclicalCorrelator

M-Seq

Sin

gle-Tap Eq

ualization

Decision &Thresholding

Cyclic P

refixR

em

oval

DecodedBits

ReceivedData

(b) Receiver

Figure 4.1: System Block Diagram of the PSSS-OFDM Tranceiver

18

Transmitter

The first part of the transmitter block performs the PSSS algorithm as described in

[4] and demonstrated in Appendix C. The result of this process is a multivalent PSSS

chip sequence which is then processed by a precoding block to efficiently utilize the

dynamic range. Each chip in this PSSS sequence will modulate a specific subcarrier

in the OFDM symbol.

The transformation of the PSSS chips corresponding to the available OFDM sub-

carriers is done through the Inverse Discrete Fourier Transform (IDFT) block. This

produces the time-domain OFDM symbol. After this, a cyclic prefix composed of the

first N samples of the OFDM sysmbol is appended. This is done to eliminate any

intersymbol interference which may result from frequency selective fading channels.

Receiver

After removing the cyclic prefix from the received OFDM symbol, the OFDM sub-

carriers are recovered through a Dicrete Fourier Tranform (DFT). The resulting sub-

carrier symbols are basically the PSSS chips that have been exposed to channel im-

pairments resulting in the loss of orthogonality between the spreading sequences and

addition of noise and interference. To compensate for the frequency selective fading,

an equalization process is performed. In particular, the minimum mean-square error

(MMSE) algorithm is applied. Since the DFT produces frequency-disjoint subcarriers

this becomes a very simple single-tap equalization.

Once the channel impairments have been compensated, the PSSS chips are cycli-

cally correlated with the original M-sequence. The output of the correlation are soft

bits in bipolar form. These can then be translated into bits by proper thresholding.

19

4.1.2 Hybrid 802.11a

In an effort to reduce the scope of the design space, and simplify the overall design

process, we choose an existing OFDM scheme to act as a baseline for the design of the

PSSS-OFDM scheme. In particular, the physical layer scheme of the 802.11a WLAN

Standard [20] was chosen. The resulting scheme could be thought of as a hybrid

between the 802.11a OFDM PHY and the PSSS algorithm.

The PHY specification for 802.11a uses OFDM at the 5 GHz band. It pro-

vides variable data payload capabilites by varying the modulation scheme used. This

OFDM scheme uses 52 subcarriers, 4 of which are pilot symbols, that can be modu-

lated using BPSK, QPSK, 16-QAM, or 64-QAM. This is achieved through a 64-point

FFT. Convolutional coding for forward error correction is also used but is not inves-

tigated in this thesis. The chosen 802.11a specifications relevant to the PSSS-OFDM

are summarized in Table 4.1.

Parameter Value

Channel Bandwidth 20 MHzNSD: Number of data subcarriers 48NSP : Number of pilot subcarriers 4NST : Number of subcarriers (total) 52 (NSD +NSP )∆F : Subcarrier frequency spacing 0.3125 MHz (=20 MHz/64)TFFT : Inverse Fast Fourier Transform 3.2µs (1/∆F )(IFFT) / Fast Fourier Transform (FFT)periodCylclic Prefix 16 samples

Table 4.1: Relevant Parameters of the 802.11a OFDM PHY adapted for PSSS-OFDM

20

4.1.3 Scope of the Design Space

This thesis focuses on integrating PSSS and OFDM to create a multicarrier spread

spectrum (MC-SS) system. We further limit the parameters to be investigated in

our development by explicitly defining here the aspects of the digital communication

system which will be excluded.

• OFDM parameters such as subcarrier spacing, channelization, and others are

retained from their 802.11a values. We focus mainly on the formation of the

OFDM subcarriers before the Fourier transformation.

• Only the baseband signal is investigated and perfect symbol synchronization is

assumed.

• No form of channel estimation is included since perfect channel knowledge is

also assumed.

• No channel coding is employed before the PSSS-OFDM algorithm in order to

ensure that all gains due to diversity result from the spreading done in frequency

by the PSSS scheme.

The succeeding sections detail the various design parameters investigated in cre-

ating the final PSSS-OFDM scheme.

4.2 Design of the Spreading Block

The length of an m-sequence is limited to 2N − 1 where N is an integer. Thus, the

length of a given PSSS sequence is also constrained to 2N − 1. Since we have 48 data

subcarriers available, the maximum PSSS sequence length that could be used is 15 or

21

N = 4. This assumes that a single PSSS sequence is not allowed to span more than one

OFDM symbol. We initially choose PSSS-15 (15-chip PSSS sequence) with a single

chip cyclic extension similar to the IEEE 802.15.4-2006 [19] PSSS proposal. This

results to a sequence length of 16. By concatenating or interleaving (See Sec. 4.3.1),

three of these PSSS sequences could be used to form the 48 data subcarriers we need.

Additional frequency diversity could be made available by using longer PSSS se-

quences, those that span more than one OFDM symbol (N > 4). This however comes

at the sacrifice of more complexity at the receiver. This technique will not only con-

tribute frequency diversity but instead provides some time diversity too. If more

frequency diversity is desired, a wider FFT should be used with its corresponding

complexity increase. The choice of the width of the FFT determines the subcarrier

spacing which is chosen based on the channel coherence bandwidth.

4.2.1 Precoding

An issue which arises when data is encoded in PSSS is the fact that the amplitude

distribution of each PSSS sequence will vary from one set of data to another. As a

result, a particular set of data bits might have a DC offset or a range that is less than

the maximum dynamic range at the transmitter. In order to alleviate this problem

and efficiently utilize the dynamic range, a precoding process based on Eqn. 4.2.1 and

Eqn. 4.2.2 must be used.

p′ (m) = p (m)− (Max+Min)

2(4.2.1)

p′′ (m) =p′ (m)

p′max(4.2.2)

22

The original PSSS sequence here is p (m). The first step removes the DC offset

while the second one ensures a range of -1 to 1. The effect of this precoding operation

on 8 consecutive PSSS sequences is shown in Fig. 4.2. We see that the transmitted

waveform after precoding has a uniform range and is centered at zero.

0 20 40 60 80 100 120

−10

−5

0

5

10

Without Precoding

Index i

Am

plitu

de

0 20 40 60 80 100 120−1

−0.5

0

0.5

1With Precoding

Index i

Am

plitu

de

Figure 4.2: Sample 15-PSSS Encoded Data with and without Precoding

Before precoding, the amplitude distribution of 15-PSSS (Fig. 4.3) approximates a

normal distribution. However, after precoding (Fig. 4.4), the amplitude takes on fewer

23

levels and have relatively larger intervals between levels resulting in better detection.

In Fig. 4.5, we see that precoding provides a noticeable gain for PSSS in the presence

of additive white gaussian noise (AWGN). Based on this result, some a similar form

of precoding should be incorporated to PSSS-OFDM to efficiently utilize the dynamic

range available at the transmitter.

−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 10

1

2

3

4

5

6x 104 15−PSSS Amplitude Distribution

Figure 4.3: Histogram of 15-PSSS without precoding

4.2.2 Dynamic Thresholding

Removing the DC offset from the original PSSS sequence involves subtracting a con-

stant value from every PSSS chip. As a consequence, the soft bits after correlation at

the receiver are no longer centered at zero. This means that the decision threshold

varies depending on the particular data transmitted. In Fig. 4.6, we see the result

of the correlation process on 4 different PSSS sequence. The dashed lines indicate

24

−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 104 15−PSSS Amplitude Distribution with Precoding

Figure 4.4: Histogram of 15-PSSS with precoding

where the decision thresholds should be.

One way of addressing this dynamic threshold problem is by interleaving zeros in

between data bits. Since the data bits are bipolar (-1 or +1), the interleaved zeros,

halfway between -1 and +1 can be used to determine the dynamic threshold. A

particular way of doing this could be to average out all the symbols known to carry

a zero and use the resulting value to decide whether a data symbol is -1 or +1. This

removes the possibility of using the full-load (L = K) mode of PSSS with precoding.

Data bits are interleaved with zeroes in such a way as to spread the bits as far away

from each other to lessen the effect of loss of orthogonality between the spreading

sequences.

At the receiver, the threshold level can be calculated by taking the average of all

bit positions loaded with zeroes. Since these bit positions were loaded with zeroes,

25

−5 0 5 1010

−3

10−2

10−1

100

Eb/No

BE

R

BER Comparison of PSSS in AWGN with and without precoding

15PSSS (w/ precoding)15PSSS (w/o preoding)

Figure 4.5: BER of Precoded and Non-Precoded PSSS in AWGN

they will be placed halfway between the minimum and maximum values even with a

DC offset. This also means that when higher data rates are used, less bit positions

can be averaged to form the dynamic threshold. This consequently results in a poorer

performance when precoding is used.

4.3 Integration of PSSS with multicarrier techniques

Once the particular method of spreading has been established, the next step in the

development of the PSSS-OFDM is integration with OFDM. For our particular im-

plementation, the OFDM parameters are based on the 802.11a OFDM PHY. In this

scheme we have 48 subcarriers available for data plus an additional 4 subcarriers for

26

0 10 20 30 40 50 60−5

−4

−3

−2

−1

0

1

2

3

4

5Varying Decision Threshold w/ Precoding

Index i

Sof

t Bit

Leve

l

Figure 4.6: Varying Decision Threshold as a Result of Precoding

pilot symbols.

4.3.1 Interleaving in the Frequency Domain

The frequency diversity of the scheme could be improved by making sure that each

chip belonging to a particular PSSS sequence experiences independent fading. This

can be done by interleaving multiple PSSS sequence into one OFDM symbol. In the

case of the scheme we are developing, a total of three 15-PSSS sequences (with an

additional cyclical extension) can be interleaved to form the 48 data subcarriers that

comprise one OFDM symbol.

27

4.3.2 Fully Integrated PSSS-OFDM

There is also a possibility of integrating PSSS and OFDM into a single step process.

The idea stems from the fact that the process of producing an OFDM symbol (i.e.

use of IFFT) has a very similar form as the process of encoding PSSS sequences.

The PSSS algorithm is basically a set of parallel multiplications followed by a

summation. Shown in Eqn. 4.3.1 is the standard formula for the Discrete Fourier

Transform or equivalently the FFT.

X (k) =N−1∑n=0

x(n)W nkN k = 0, 1, ..., N − 1 (4.3.1)

Where W nkN = e−

2πNkn, which are also called twiddle factors. Based on this formula

and by considering the process of encoding PSSS, there is a possibility of incorporating

both processes (composed of multiplication and then summation) into a single step

process. This can be done by either integrating the spreading into the process of

calculating the twiddle factors or possibly including it within each FFT butterfly

calculation.

One promising approach is to view the spreading operation as a convolution be-

tween the information symbols and the spreading code. This convolution process can

be done entirely in the frequency domain where it simplifies into a term by term

multiplication of the FFT of the two sequences.

However, there are still issues that need to be solved before this approach can

be fully utilized. First of all, all FFT algorithms are optimized to work with block

lengths that are powers of two. PSSS sequences on the other hand have block lengths

that are one less than a power of two1.

1A direct result of the construction of m-sequences (length = 2M − 1)

28

Another issue is the need to include the precoding process into this integrated

scheme. One way this can be done, is to remove the DC component from the FFT by

simply forcing the first sample to zero. Dynamic range can then be adjusted using a

similar process as with standard PSSS precoding but using the FFT of the signal.

Once these issues are addressed a more efficient and less complex PSSS-OFDM

can be created. This will potentially make PSSS-OFDM an alternative physical layer

scheme in applications where area and power are top priority. These include mobile

applications such as wireless personal area networks (WPANs).

4.4 Rate Adaptation

4.4.1 Variable Spreading

Throughput can be sacrificed for more spreading if the channel is very hostile. As

mentioned earlier, this could be achieved by not using all possible shifted sequences.

If a number of bits less than K is used as input to the PSSS algorithm, these unused

bits are set to 0 instead of -1 or +1. These 0’s will be interleaved over the entire

sequence and will also act as a dynamic threshold that will be used for the decision

at the receiver. This technique effectively increases multipath fading resistance and

adds additional spreading gain to the system. Thus, a trade-off between interference

resistance and data rate is possible.

To ensure that the dynamic threshold samples are distributed evenly over the

entire OFDM bandwidth, an equal number of cyclic shifts are used to generate the

set of spreading sequences used. By increasing the number of shifts in between two

successive spreading sequences we can reduce K and improve robustness against in-

terference.

29

The result of varying the spreading of PSSS-OFDM can be seen through an am-

plitude distribution plot as shown in Fig. 4.7. In this figure, we focus only on the

PSSS-OFDM modes that are a power of 2. The term ”mode” is used here to indicate

the number of bits that are loaded into 1 OFDM symbol. For example, PSSS-OFDM

2 or mode 2 is able to transmit 2 bits for every OFDM symbol.

We can see from the histograms that the amplitude distribution of PSSS-OFDM

becomes increasingly complex as the mode is increased. In the extreme case of PSSS-

OFDM mode 32, we get an amplitude distribution with 43 distinct levels. The closer

the levels, the less robust it will be to impairments in the channel such as noise, fading

and interference. This result is in line with our earlier analysis that higher data rates

will have less robustness to fading.

Varying the amount of spreading can be done by simpling inserting more and more

zeros in between data symbols. The actuall transmitter and receiver architecture does

not need to be modified in order to do this.

4.4.2 Rate-Adaptive OFDM

As discussed in Chapter 2, a similar MC-SS scheme which incorporated variable

spreading was proposed in [18]. However, this scheme used only a simple repetition

code to introduce spreading. As a result, it could only vary the amount of spreading

in powers of two. For PSSS-OFDM we could use spreading factors which are not

powers of two just by adding more zeros in between data symbols.

30

−1.5 −1 −0.5 0 0.5 1 1.50

50

100Histogram of PSSS−OFDM 2

−1.5 −1 −0.5 0 0.5 1 1.50

200

400Histogram of PSSS−OFDM 4

−1.5 −1 −0.5 0 0.5 1 1.50

2000

4000Histogram of PSSS−OFDM 8

−1.5 −1 −0.5 0 0.5 1 1.50

2

4x 105 Histogram of PSSS−OFDM 16

−1.5 −1 −0.5 0 0.5 1 1.50

2

4

x 105 Histogram of PSSS−OFDM 32 (Monte Carlo)

Figure 4.7: Histogram of PSSS-OFDM with varying amount of spreading

4.5 Equalization

An advantage of using OFDM is the simplification of the equalization block. Since the

data is sent in individual subcarriers and not as a single carrier, we can independently31

equalize each data symbol through a gain and phase adjustment. This is referred to

as single-tap equalization. It involves multiplying each subcarrier with a particular

complex number. This is in contrast to an adaptive filtering approach used in single

carrier systems.

At the receiver, the signal is sampled and then demapped from the subcarriers via

an FFT. Due to the frequency selectiveness of the channel, the orthogonal m-sequences

used for spreading lose their orthogonality, creating inter-code or self-interference [15].

The simplest method of equalizing the subcarriers is to apply phase correction. This

entails tracking the phase error of each subcarrier and then correcting these phase

errors through a one-tap phase correction equalizer. This means that the amplitude of

each subcarrier is not modified. This method of equalization is referred to as Equal

Gain Combining (EGC). However, EGC is not able to compensate for the loss of

orthogonality.

One way to partially restore orthogonality is through the use minimum mean-

square error (MMSE) equalization. Applying MMSE to the subcarriers was shown to

be optimal for full-load systems. It could also be used for partial loaded systems but

results in sub-optimal detection [16].

The application of MMSE for PSSS-OFDM is particularly advantageous because

it leads to narrowband interference suppression effect. Plain PSSS is prone to narrow-

band jamming and its suppression requires the use of an adaptive notch filter which

leads to higher complexity.

MMSE could be accomplished in OFDM by using a single-tap adaptive equalizer

for each subcarrier. The equalization coefficient is given by Eqn. 4.5.1, where hl is the

32

complex channel gain of the lth subcarrier and 1/λ = Es/N0 (the subcarrier signal-

to-noise ratio). Since we assumed perfect channel knowledge, the values of hl and N0

are provided for the receiver.

gl =h∗l

|hl|2 + λ(4.5.1)

4.6 Final PSSS-OFDM Algorithm

Based on the ideas presented in this chapter we arrive at a final PSSS-OFDM algo-

rithm whose performance we will be evaluating in Chapter 5 and translating into a

hardware architecture in Chapter 6. This algorithm is described in the following set

of steps:

1. The data bits to be transmitted, after suitable channel coding (in our case, we

do not perform any coding), is represented bipolarly (-1 or +1) and divided into

three streams using a serial to parallel conversion.

2. PSSS is applied to each of the three serial streams using a 15-chip m-sequence.

3. Precoding is applied to each PSSS sequence to remove the DC offset and max-

imize the dynamic range.

4. The three PSSS sequences are interleaved with each other and an IFFT opera-

tion is applied to generate the OFDM symbol. Table 4.2 shows the interleaving

pattern used to reorder the data into the OFDM subcarriers.

5. A 16-symbol cyclic prefix extension is added in order to protect the OFDM

symbol from ISI and simplify the equalization process at the receiver.

33

6. At the receiver, we remove the cyclic prefix extension and apply an FFT oper-

ation to extract the data from the subcarriers.

7. MMSE equalisation is applied (perfect channel knowledge is assumed). The

equalisation process is a simple multiplication of each subcarrier to a complex

number to correct the phase error as well as the amplitude distortion.

8. The three PSSS sequences are extracted from the subcarriers and correlated

with the same m-sequence used at the transmitter.

9. Finally, dynamic thresholding is applied to decide whether a given symbol is a

1 or a 0.

In the following chapter we analyze the performance of this algorithm under var-

ious channel conditions. We also investigate a possible hardware architecture that

could be used to implement it in an actual prototyping platform.

34

Subcarrier No. Data Subcarrier No. Data

0 Null 32 Null1 Pa(1) 33 Null2 Pb(1) 34 Null3 Pc(1) 35 Null4 Pa(2) 36 Null5 Pb(2) 37 Null6 Pc(2) 38 Null7 Pa(3) 39 Null8 Pb(3) 40 Pa(9)9 Pc(3) 41 Pb(9)10 Pa(4) 42 Pc(9)11 Pb(4) 43 Pa(10)12 Pc(4) 44 Pb(10)13 Pa(5) 45 Pc(10)14 Pb(5) 46 Pa(11)15 Pc(5) 47 Pb(11)16 Pa(6) 48 Pc(11)17 Pb(6) 49 Pa(12)18 Pc(6) 50 Pb(12)19 Pa(7) 51 Pc(12)20 Pb(7) 52 Pa(13)21 Pc(7) 53 Pb(13)22 Pa(8) 54 Pc(13)23 Pb(8) 55 Pa(14)24 Pc(8) 56 Pb(14)25 Null 57 Pc(14)26 Null 58 Pa(15)27 Null 59 Pb(15)28 Null 60 Pc(15)29 Null 61 Pa(1)30 Null 62 Pb(1)31 Null 63 Pc(1)

Table 4.2: PSSS-OFDM Interleaving Pattern (Pa, Pb, and Pc, are the 3 PSSS se-quences)

35

Chapter 5

Performance Measurements

In order to evaluate the performance of PSSS-OFDM in comparison to plain PSSS,

and BPSK-OFDM, various MATLAB simulations were used to test the scheme in

different channel environments. This chapter discusses the results of these simulations

and highlights the advantages and disadvantages of using PSSS-OFDM as a physical

layer scheme for digital communications in wideband applications.

We begin by defining the different schemes under test and the parameters used

for each. This is followed by a description of the various channel environments used

in the simulations. Finally, we proceed with the results of the different simulations

and analysis of these results.

5.1 PSSS, OFDM and PSSS-OFDM Transceiver

Schemes for Simulations

For the performance comparisons to be a fair representation of the abilities of each

scheme, we need to keep as many design parameters constant over the different tran-

ceiver schemes. The following subsections discuss each of these parameters and how

they were chosen.

36

5.1.1 Data Rate

Various parameters affect the data rate of a digital communication system. These

parameters include:

• Modulation Scheme (BPSK, QAM, etc.)

• Transmission Bandwidth

• Subcarrier Spacing (for multicarrier schemes)

• Symbol Period (for single-carrier schemes)

• Length of Cyclic Prefix

For our simulations, we need to keep the data rate constant when comparing

PSSS, OFDM and PSSS-OFDM. To do this, we limit our discussion with binary

signaling (BPSK modulation) and use a constant bandwidth of 20 MHz (as defind in

the 802.11a standard). We also use the same amount of cyclic prefix (16 symbols) for

all of the schemes under test.

However, when dealing with diversity gain comparisons, there is a need to compare

different data rates. This is because higher diversity schemes result in lower data

rates because of the redundancy. In these cases, we keep the schemes in equal footing

by using the same amount of AWGN noise for every data bit transmitted. This is

equivalent to using normalized SNR per bit or Eb/N0.

5.1.2 OFDM Subcarriers and Spreading Sequence

In practical OFDM implementations, some subcarriers are unused in order to create

a guard band and ensure that the signal bandwidth does not exceed the allowed

37

transmission bandwidth (20 Mhz). However, in our tests, we apply a simplifying

assumption of using all available subcarriers except the first one (DC component).

This assumption ensures that the single-carrier scheme (PSSS) will use the same

bandwidth as the proposed multi-carrier scheme (PSSS-OFDM). It also ensures that

no particular scheme will have an unfair advantage in the presense of multipath fading

since all of them use exactly the same bandwidth and cyclic prefix extension.

Thus, we have 63 available data subcarriers with a frequency spacing of 0.3125

MHz (∆F=20 MHz/64). Given these 63 subcarriers, we can utilize an m-sequence

with length of 63 as shown in Fig. 5.1. With these parameters set, the only difference

between the PSSS and PSSS-OFDM schemes being compared is the application of a

Fourier transform and MMSE equalisation.

5.2 Performance in Additive White Gaussian Noise

5.2.1 Normalization of SNR

To ensure that any gains we observe are due to the introduction of frequency diversity,

which is the focus of these simulations, we must normalize the amount of AWGN noise

added to each bit. We do this by scaling the amount of noise based on the number

of subcarriers used and the number of m-sequence cyclic shifts loaded with data (i.e.

L). Equation 5.2.1 gives us the normalized noise variance used for a given value of

Eb/N0.

σ2N =

1

2

K

L

NSD

NST

10Eb/N0/10 (5.2.1)

Where K is the length of the m-sequence used (63 in our simulations), L is the

number of m-sequence cyclic shifts loaded with data, NSD is the total number of data

38

0 10 20 30 40 50 60−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Index i

M−sequence of length 63

Figure 5.1: 63 symbol m-sequence used for PSSS and PSSS-OFDM simulations

subcarriers (63 in our simulations) and NST is the total number of subcarriers (64

based 802.11a).

5.2.2 PSSS-OFDM without precoding

We first analyze the schemes under additive white gaussian noise (AWGN). The

channel model for this is given in Equation 5.2.2 [5]. The noise (n(t)) is complex and

Gaussian distributed. This results in a channel where symbol errors are independent

from each other. In the presence of AWGN we do not expect any advantage in

using PSSS-OFDM over PSSS, because the frequency diversity and multipath fading

resistance is not utilized. In Fig. 5.2, we see that this is indeed the case. PSSS and

PSSS-OFDM perform equally well under the same Eb/N0.

s′ (t) = s (t) + n (t) (5.2.2)

39

We also note from the BER plot that using L < K (i.e. not loading all the

cyclically shifted m-sequences) also result in similar performance. This means that

lower data rates with more spreading and therefore more frequency diversity do not

offer any gains when the channel is pure AWGN. Given the same amount of corrupting

noise per bit, PSSS and PSSS-OFDM perform equally well.

However, OFDM under BPSK modulation performs better than any of the PSSS

schemes. This result agrees with the original PSSS paper [4], wherein a gain of 6dB

is possible with simple BPSK modulation when compared to PSSS. This results from

the inefficient use of the transmit dynamic range and the introduction of a DC offset

when using PSSS. This effect could be alleviated through the use of precoding as

discussed in Section 4.2.1.

5.2.3 PSSS-OFDM with precoding

The precoding process removes the DC offset inherent to PSSS encoding. It also

maximizes the use of the transmit dynamic range by scaling the PSSS chips in one

sequence so that the maximum and minimum are at +1 and -1 respectively. In

Fig. 5.3, we can see that the effect of precoding is to bring down the PSSS-OFDM

bit error rate level. This results in a BER performance that is very close but only

slightly poorer than BPSK-OFDM, at a deviation of 0.26 dB in Eb/N0.

Precoding does come at the cost of additional complexity because an averaging

operation should be performed for all unused PSSS sequences to calculate for the

dynamic threshold. It also renders the full-load (L = K) mode of PSSS-OFDM

unusable. Some of the sequences must be loaded with a 0, instead of actual data, to

form the dynamic threshold used in this precoding technique.

40

−10 −5 0 5 1010−7

10−6

10−5

10−4

10−3

10−2

10−1

100

Eb/N

0

BE

R

BER Comparison in AWNG (w/o precoding)

PSSS, L=63PSSS−OFDM, L=63PSSS−OFDM, L=31BPSK−OFDM

Figure 5.2: BER comparison of PSSS, PSSS-OFDM, and BPSK-OFDM underAWGN (without precoding)

This does not pose a serious drawback however, since the main purpose of PSSS-

OFDM is to introduce frequency diversity. At its full-load or highest data rate mode,

PSSS-OFDM does not offer any diversity in frequency. In these cases, it is not an

advisable scheme to be used. Instead of using PSSS-OFDM with all sequences loaded,

a more efficient technique would be to switch off PSSS encoding all together when

the maximum data rate is desired and multipath fading is at a minimum. This gives

us plain BPSK-OFDM modulation which performs better in those cases.

Based on these results, succeeding simulations will focus on the precoded mode

of PSSS-OFDM. This also means that the full-load PSSS-OFDM-63 mode will no

41

−10 −5 0 5 1010−7

10−6

10−5

10−4

10−3

10−2

10−1

100

Eb/N

0

BE

R

BER Comparison in AWGN (w/precoding)

BPSK−OFDMPSSS−OFDM, L=31 (w/o precoding)PSSS−OFDM, L=31 (precoded)

Figure 5.3: BER comparison of PSSS-OFDM and BPSK-OFDM under AWGN (withprecoding)

longer be used in comparisons. Instead, plain BPSK-OFDM will be the baseline

when comparing the schemes in terms of diversity gain.

5.3 Performance in Frequency Selective Fading

As we have seen in the previous section, PSSS-OFDM does not offer any gains in

non-fading AWGN channels due to the lack of diversity to exploit. The real benefits

of PSSS-OFDM can be observed in multipath fading environments where the multi-

ple replicas arriving at the receiver can be taken advantage of. In particular, with

proper equalisation and diversity combining, multicarrier spread spectrum systems

42

are expected to perform better in the presence of frequency selective fading com-

pared to simple AWGN. In the following subsections we investigate the performance

of PSSS-OFDM in frequency selective fading and compare this to plain PSSS and

BPSK-OFDM.

5.3.1 Channel Model

The mathematical model used for frequency selective fading is based on the exponen-

tial decay model from [21]. The channel impulse response is described by Equation

5.3.1 where Bn and θn represent the magnitude and phase of the nth component, tn

the corresponding time delay and L the total number of samples in the impulse re-

sponse. The envelope of Bn is an exponential decay whose samples follow a Rayleigh

distribution as shown in Equation 5.3.2, where Are and Aim are Gaussian distributed.

h (t) =L∑n=1

Bnejθnδ (t− tn) (5.3.1)

Bn = (Are + jAim)e−n/τRMS (5.3.2)

Fig. 5.4 shows the envelope of several realizations of this channel model given

τRMS = 50ns.

5.3.2 Comparison of PSSS and PSSS-OFDM

PSSS is designed to be a low complexity transmission scheme for use in Wireless

Personal Area Networks. As a result of this, the PSSS included in the scheme utilizes

a correlator approach for detection instead of equalisation. The received PSSS signal

is correlated with the m-sequence and the peaks in the correlated signal is used for

43

0 20 40 60 80 100 120 140 160 180 200 2200

0.5

1

1.5

t (ns)

ampl

itude

Envelope of the Channel Impulse Response

Figure 5.4: Envelope of the Frequency Selective Channel Impulse Response usingthe Exponential Decay Model (τRMS = 50ns)

thresholding. This offers some degree of robustness to multipath fading given that

only a subset of all sequences are used.

If equalisation is to be applied for PSSS, it will require an adaptive filtering ap-

proach whose order should be comparable to the length of the channel impulse re-

sponse.

Since PSSS-OFDM is a multicarrier tranmission scheme, the process of equalisa-

tion is greatly simplified into a single-tap phase tracking and correction. This allows

PSSS-OFDM to achieve better performance in channel environments with high delay

spread compared to PSSS. We can see in Fig. 5.5 that all modes of PSSS-OFDM

44

perform better than PSSS.

0 100 200 300 400 500 600 700 800 900 100010

−2

10−1

100

τRMS

BE

R

PSSS vs. PSSS−OFDM in Frequency Selective Fading Channel

PSSS−OFDM, L=31PSSS−OFDM, L=40PSSS−OFDM, L=48PSSS, L=31PSSS, L=15PSSS, L=7PSSS, L=3PSSS−OFDM, L=60

Figure 5.5: BER vs. RMS Delay Spread comparison of plain PSSS and PSSS-OFDMunder Frequency Selective Fading (Eb/N0 = 10dB)

At a delay spread of 100ns, which is typical in 802.11a and other indoor applica-

tions, the performance of PSSS-OFDM-60 is comparable to that of PSSS-7. PSSS-

OFDM also performs much better at higher delay spread. We also see in Fig. 5.6

that PSSS-OFDM performs better compared to PSSS as Eb/N0 is varied. In this

figure, we can see a gain of 4dB in Eb/N0 at a fixed BER of 0.1. This suggests that

PSSS-OFDM has good potential for use in high-data rate applications wherein the

additional complexity gain due to IFFT and single-tap equalisation is acceptable in

order to achieve better multipath performance.

45

−15 −10 −5 0 5 10 1510

−3

10−2

10−1

100

Eb/N0

BE

R

Comparison of PSSS vs. PSSS−OFDM with varying Eb/N0in Frequency Selective Channel (τRMS = 50ns)

PSSS−31PSSS−OFDM−31

Figure 5.6: BER vs. Eb/N0 comparison of plain PSSS and PSSS-OFDM underFrequency Selective Fading (τRMS = 50ns)

5.3.3 Comparison of PSSS-OFDM and BPSK-OFDM

Based on the results discussed in the previous subsection, we can conclude that PSSS-

OFDM is no longer in the same performance class as plain PSSS. By this we mean

that PSSS-OFDM can achieve data rates which are 9 to 10 times faster than PSSS

at a typical delay spread of 100ns and still offer some level of robustness to multipath

fading. This is a direct result of the inclusion of an equalisation block. It is therefore

46

0 100 200 300 400 500 600 700 800 900 100010

−3

10−2

10−1

τRMS (ns)

BE

R

PSSS−OFDM in Frequency Selective Fading Channel

BPSK−OFDMPSSS−OFDM, L=48PSSS−OFDM, L=40PSSS−OFDM, L=31PSSS−OFDM, L=23PSSS−OFDM, L=15PSSS−OFDM, L=7

Figure 5.7: BER vs. RMS Delay Spread comparison of PSSS-OFDM modes andBPSK-OFDM under Frequency Selective Fading (Eb/N0 = 10dB)

more appropriate to offer PSSS-OFDM as an alternative to BPSK-OFDM which also

requires an equalisation.

Fig. 5.7 shows us a BER comparison of different PSSS-OFDM modes and BPSK-

OFDM when RMS delay spread is varied and Eb/N0 is fixed at 10dB. Similar com-

parisons at 0dB and 20dB Eb/N0 are also shown in Fig. 5.8 and Fig. 5.9. We

can clearly see that more diversity gain is achieved as lower PSSS-OFDM modes are

used. In particular, BPSK-OFDM performs somewhere in between PSSS-OFDM-48

and PSSS-OFDM-40. Lower modes offer even better performance at the cost of slower

data rates.

47

0 100 200 300 400 500 600 700 800 900 1000

10−0.8

10−0.7

τRMS(ns)

BE

R

PSSS−OFDM in Frequency Selective Channel (Eb/N0=0dB)

PSSS−OFDM, L=48PSSS−OFDM, L=40PSSS−OFDM, L=31PSSS−OFDM, L=23PSSS−OFDM, L=15PSSS−OFDM, L=7BPSK−OFDM

Figure 5.8: BER vs. RMS Delay Spread comparison of PSSS-OFDM modes andBPSK-OFDM under Frequency Selective Fading (Eb/N0 = 0dB)

48

0 100 200 300 400 500 600 700 800 900 100010

−6

10−5

10−4

10−3

10−2

10−1

PSSS−OFDM in Frequency Selective Channel (Eb/N0=20dB)

τRMS(ns)

BE

R

BPSK−OFDMPSSS−OFDM, L=48PSSS−OFDM, L=40PSSS−OFDM, L=31PSSS−OFDM, L=23PSSS−OFDM, L=15PSSS−OFDM, L=7

Figure 5.9: BER vs. RMS Delay Spread comparison of PSSS-OFDM modes andBPSK-OFDM under Frequency Selective Fading (Eb/N0 = 20dB)

49

We also see a basic trend in the BER of all the PSSS modes. At zero delay spread,

all schemes perform at the same BER. This BER is equivalent to the one we observed

for AWGN channels in the previous section. Looking closer at the plot at zero delay

spread, we can verify that BPSK-OFDM performs slightly better than all the PSSS-

OFDM. This is consistent with the results for AWGN channels wherein BPSK-OFDM

performed about 0.26dB better even with precoding applied. PSSS-OFDM however,

does not offer any advantages if only one copy of the signal is present, as is the case

with τRMS = 0.

Once we start to increase the RMS delay spread we observe that the PSSS-OFDM

modes performs progressively better than plain OFDM. This is because more replicas

of the signal is present and the receiver is able to exploit that. In fact, lower PSSS-

OFDM modes (those with higher transmit diversity) can be observed to follow this

improving trend until a higher delay spread compared to higher modes. We can

verify this by looking at the minimum BER point of each of the plots. PSSS-OFDM-

40 performs best at approximately τRMS = 50ns while the lowest data rate shown,

PSSS-OFDM-7 performs best at approximately τRMS = 300ns.

This movement of the minimum BER point towards higher τRMS is a direct result

of the amount of diversity inherent to the multipath channel. In a channel with low

delay spread, all the energy of each symbol arrives over a relatively small interval

of time. Here we have very minimal diversity in the multipath environment. Corre-

spondingly, lower PSSS-OFDM modes do not have that much diversity to exploit.

However, in a channel with high delay spread, replicas of the signal arrive over a

larger time interval. This rich multipath environment could be better utilized by a

scheme designed for higher diversity, such as the lower PSSS-OFDM modes.

50

An alternative way of looking at this result is seen at the frequency domain.

Channels with higher delay spread have a narrower coherence bandwith. Coherence

bandwith is defined as the range of frequencies in which frequency selective fading can

be considered flat. In a channel with low coherence bandwidth, OFDM subcarriers

tend to fade more indepently from each other. Consequently, more spreading is ad-

vantageous because if a particular OFDM subcarrier fades there is higher probability

that a replica of it will not, leading to diversity gain after correlation.

Based on this plot, we can choose a particular PSSS-OFDM mode which will give

the best tradeoff between spectral efficiency and BER depending on the multipath

environment.

If we fix the value of τRMS and vary Eb/N0 we get the BER plot in Fig. 5.10. A

value of τRMS = 200ns was chosen since this is a typical value of delay spread in indoor

applications. We can see that BPSK-OFDM performance is close to PSSS-OFDM-40

at Eb/N0 < 10dB. However, BPSK-OFDM performs progressively better at higher

Eb/N0 finally reaching a noise floor in between PSSS-OFDM-15 and PSSS-OFDM-7.

51

Figure 5.10: BER vs. Eb/N0 comparison of PSSS-OFDM modes and BPSK-OFDMunder Frequency Selective Fading (τRMS = 200ns)

52

Chapter 6

Hardware Architecture for thePSSS-OFDM Transceiver

In the previous chapters, we have described the design of the PSSS-OFDM algorithm

and analyzed its performance in various channel conditions. In this chapter, we

proceed in discussing a particular hardware implementation of the scheme using a

rapid prototyping design flow based on the Xilinx System Generator [22] software.

The motivations for implementing PSSS-OFDM in actual hardware include:

1. Demonstrating the feasibility of the approach for actual hardware deployment.

2. Investigating the implementation-specific issues in translating the algorithm

into hardware. These include:

(a) Fixed-point representation and quantization errors

(b) Timing

(c) Area and Memory constraints

We start the chapter with a discussion of the specific design parameters chosen

for the PSSS-OFDM algorithm implemented. We then proceed with describing the

53

design flow used in developing the hardware implementation. The rest of the chapter

deals with the actual design and testing of the PSSS-OFDM transceiver.

6.1 PSSS-OFDM Design Parameters for Hardware

Implementation

The PSSS-OFDM hardware implementation design is based upon the algorithm de-

scribed in Section 4.6, but with some modifications. The deviations from the final

PSSS-OFDM algorithm were done in the interest of reducing the complexity of the

design process and allowing this thesis to focus on the core design issues of the al-

gorithm. In particular, the deviations/simplifications to the PSSS-OFDM algorithm

are as follows:

1. Precoding and Dynamic Thresholding were not implemented -

although precoding was shown to provide gains to PSSS-OFDM (Section 5.2.3),

the hardware implementation for dynamic thresholding adds substantial com-

plexity to the design and was not implemented.

2. No equalization - the implementation was only tested in perfect, noiseless

channel conditions. As such, equalization is not included in the hardware de-

sign. Actual hardware implementation of this block would require a channel

estimation block as well as a preamble and packetization structure.

3. Full-Load mode only - only the highest data rate mode (L = K) of PSSS-

OFDM has been implemented. Implementing the variable data rate mode re-

quires a preamble and packetization structure which was not included for this

work.

54

However, even this simplified PSSS-OFDM algorithm provides us with signifi-

cant insights regarding the merits and issues of designing the complete PSSS-OFDM

algorithm as described in Section 4.6. Future work can build upon this simplified

architecture by designing a preamble and packetization format for PSSS-OFDM as

well as the MMSE and precoding modules.

6.2 Rapid Prototyping Design Flow

6.2.1 Software Design Flow

In order to develop the hardware implementation, a design flow based on Mat-

lab/Simulink from Mathworks [23] coupled with the Xilinx System Generator [22] was

used to map high-level block diagrams and timing specifications to an FPGA con-

figuration. This graphical design environment supports simultaneous development of

signal processing algorithms and digital design descriptions for their hardware real-

ization. Therefore, no translation is required and allows signal processing researchers

to realize hardware implementation of developed algorithms.

The design flow also allows Matlab scripts, such as those created for the simula-

tions in Chapter 5, to be easily integrated into the hardware verification phase. Using

this methodology, test vectors could be generated using the high-level scripts already

developed and later compared to the actual outputs from the hardware implementa-

tion in a single design/test environment.

6.2.2 Hardware Target

Designs created with Xilinx System Generator are device independent given that a

supported Xilinx FPGA is used and the synthesizer is able to satisfy the area and

55

timing constraints. However, to facilitate the testing phase, as well as resource estima-

tion, a particular FPGA development board (Xilinx Virtex 4 XC4VFX12) is chosen

for this thesis. The board is shown in Fig. 6.1 and has the following specifications:

• Xilinx XC4VFX12-10FF668 FPGA (See Table 6.1)

• 64 MB of DDR SDRAM

• 4 MB of Flash (for FPGA configuration data, etc.)

• 10/100/1000 Ethernet PHY

• On-board 100MHz LVTTL Oscillator

Parameter Value

CLB Array 64 x 24Number of Slices 5,472Number of LUTs 10,944Maximum Distributed RAM or Shift-registers 86Number of Flip-Flops 10,944

Table 6.1: Specifications of the Xilinx Virtex 4 XC4VFX12 FPGA [24]

6.3 Design of the PSSS-OFDM Encoder

The aim of the encoder block is to translate information to be transmitted from

its raw form (bits) into PSSS-OFDM frames (complex valued symbols). Since the

transmitter deals with a digital source for its input, the design must prioritize low

complexity instead of accuracy. This is in contrast to the receiver block which accepts

noisy signals from an analog to digital converter (ADC). At the receiver, the priority

56

Figure 6.1: Xilinx Virtex 4 XC4VFX12 development board used as target platform

becomes accurate representation of the received data in order to reduce detection

errors.

6.3.1 Functional Block Diagram

The encoder block is basically a two-step process composed of a PSSS spreading step

followed by an OFDM block (IFFT). Based on the algorithm described in Section

4.6 we first need to apply the PSSS-15 algorithm to three parallel data streams.

57

out_valid

2

psss_seq

1

register3

In1In2In3In4In5In7In8In9In10In11In12In13In14In15In16en

Out1Out2Out3Out4Out5Out6Out7Out8Out9

Out10Out11Out12Out13Out14Out15

register2

In1In2In3In4In5In7In8In9In10In11In12In13In14In15In16en

Out1Out2Out3Out4Out5Out6Out7Out8Out9

Out10Out11Out12Out13Out14Out15

register1

In1In2In3In4In5In7In8In9In10In11In12In13In14In15In16en

Out1Out2Out3Out4Out5Out6Out7Out8Out9

Out10Out11Out12Out13Out14Out15

psss2

In1

en

Out1Out2Out3Out4Out5Out6Out7Out8Out9

Out10Out11Out12Out13Out14Out15valid

psss1

In1

en

Out1Out2Out3Out4Out5Out6Out7Out8Out9

Out10Out11Out12Out13Out14Out15valid

psss

In1

en

Out1Out2Out3Out4Out5Out6Out7Out8Out9

Out10Out11Out12Out13Out14Out15valid

Slice4

[a:b]

Slice3

[a:b]

Slice2

[a:b]

Slice1

[a:b]

Slice

[a:b]

Serial to Parallel

s

enpz

-1

Mux2

sel

d0

d1

Mux1

seld0d1d2d3d4d5d6d7d8d9d10d11d12d13d14d15d16d17d18d19d20d21d22d23d24d25d26d27d28d29d30d31

Mux

seld0d1d2d3d4d5d6d7d8d9d10d11d12d13d14d15d16d17d18d19d20d21d22d23d24d25d26d27d28d29d30d31

Delay1

z-1

Counter

rst out

Constant

0

System

Generator

s_valid

3

bs_valid

2

data

1

Spreader In 2

Spreader In 1

Bit Stream

Spreader In 3

PSSS Valid

Figure 6.2: Top-level block diagram of the PSSS Spreader

This results in three PSSS sequences which are then interleaved and loaded into the

OFDM subcarriers through an IFFT operation. The top-level block diagram1 for the

hardware architecture is shown in Fig. 6.2.

The input bits are fed to this block in a serial/bitstream format which is then

1All block diagrams with the Xilinx System Generator “X” logo were directly captured fromthe actual Matlab/Simulink design environment and are the actual hardware descriptions used indevelopment.

58

split into three parallel bitstreams which are the inputs to the PSSS spreading blocks.

PSSS sequences for each 15-bit frames are then generated and stored in a pipeline

register. An interleaver, implemented as a 64-to-1 multiplexer is used to converth the

parallel PSSS sequences into the serial input required by the IFFT block. Unfortu-

nately, Xilinx System Generator mux blocks only allow up to 32 inputs. Two 32-to-1

multiplexers are used to solve this limitation.

The outputs of the pipeline registers are connected to the multiplexers in the order

they should appear in one OFDM frame (see Table 4.2). A counter is used to generate

the “select” input for the multiplexers.

An alternative architecture for the interleaver, would be to store the inputs in

RAM and read the data in the order required by the interleaver as described in

Section 4.6. However, this introduces additional latency because the data can only

be written to RAM one at a time2.

6.3.2 PSSS Spreader

The PSSS spreading operation (see Equation 6.3.1) consists of a summation of cycli-

cally shifted m-sequences, b ((i+ k)modL), multiplied by the unipolarly represented

data, d (i). This operation does not require actual multipliers because the m-sequence

can only take on values of +1 or -1 while the data can only be 0 or 1. Thus, the

spreading operation simplifies into either adding an m-sequence when d(i) = 1, or

ignoring an m-sequence when d(i) = 0.

u (i) =K∑k=1

b ((i+ k)modL) d (i) (6.3.1)

2Dual-port RAM is an exception. However this is still not enough for our implementation.

59

valid

16

Out15

15Out14

14Out13

13Out12

12Out11

11Out10

10Out9

9Out8

8Out7

7Out6

6Out5

5Out4

4Out3

3Out2

2Out1

1

Sequence

Accumulator

data

rst

mseq

en

psss 14

psss 13

psss 12

psss 11

psss 10

psss 9

psss 8

psss 7

psss 6

psss 5

psss 4

psss 3

psss 2

psss 1

psss 0

Relational 2

a

b

a=b

z-0

Relational 1

a

b

a=b

z-0

LFSR

rst

en

dout

Counter 3

rst

en

out

Counter 2

rst

en

out

Constant2

2

Constant1

15

BitBasher

b a

System

Generator

en

2

data _in

1

M-Sequence

Enable Accumulate

Figure 6.3: Block diagram of the PSSS spreader

Implementing this behavior in hardware involves first generating the m-sequences

using the LFSR block provided by Xilinx System Generator as shown in Fig. 6.3.

The LFSR block allows instantiation of all registers. This loading capability is used

to initialize the m-sequence into the LFSR block. It then outputs an m-sequence that

is one cyclic shift from the previous LFSR output.

Since the m-sequence is stored in the LFSR as bits and not in bipolar format (+1

or -1), we need a block that will translate the m-sequence bits into either an increment

(+1) or decrement (-1) operation. This can be implemented using up-down counters

with enable pins as shown in Fig. 6.4. This accumulator block is composed of 15 up-

down counters which are cleared at the start of a PSSS frame and either increments,

decrements, or retains the value based on the input data as well as the m-sequence

coming from the LFSR block.

60

.

.

.

.

.

.

.

.

.

only a section of the entire block diagram is shown

psss11

4

psss12

3

psss13

2

psss14

1

Slice 3

[a:b]

Slice 2

[a:b]

Slice 1

[a:b]

Slice

[a:b]

Logical 3

and

z-0

Logical 2

and

z-0

Logical 1

and

z-0

Logical

and

z-0

Counter 14

up

rst

en

out

Counter 13

up

rst

en

out

Counter 12

up

rst

en

out

Counter 11

up

rst

en

out

System

Generator

en

4

mseq

3

rst

2

data

1

Figure 6.4: Block diagram of the accumulator block used in the PSSS spreader

6.3.3 IFFT Block

An IFFT block, available as an IP-core in Xilinx System Generator was used in this

design. The IFFT block was configured to perform a 64-point IFFT as well as add

a 16-sample cyclic prefix. The output of the PSSS spreader is used as the real part

of the input to this block while the imaginary part is always zero. The output of the

IFFT block has both real and imaginary components.

61

6.4 Design of the PSSS-OFDM Decoder

The decoder performs a similar but inverse process as the encoder. The main dif-

ferences are the use of an FFT instead of an IFFT block and the use of an actual

fixed-point correlator for despreading. Up-down counters can no longer be used at

the receiver since the received signals can take on arbitrary fixed-point values and are

corrupted with noise.

6.4.1 Functional Block Diagram

After the FFT extracts the information from the subcarriers, the decoder performs

a simlar parallel processing of PSSS-15 frames as the encoder. The FFT block used

is the same as the IP-core used in the IFFT block in the encoder but configured

to perform the forward transform. Additional timing logic was designed in order to

ignore the 16-sample cyclic prefix at the start of each OFDM frame.

Fig. 6.5 shows the top-level block diagram of the encoder. Here, a ROM is used to

store the deinterleaving pattern used to extract the three PSSS-15 sequences from one

OFDM frame with the aid of three multiplexers. Once the three PSSS-15 sequences

are completely stored within a shift-register architecture, the PSSS decoder can start

the correlation process.

6.4.2 PSSS Despreader

As shown in Fig. 6.6, three despreaders working in parallel were created in order

to extract the binary data from the received PSSS sequences. The output of these

despreaders are stored in a pipeline register which captures all the binary data con-

tained in one OFDM frame. Similar to the encoder block, a set of multiplexers are

62

Out3

3

rx_data

2

valid

1

shiftreg2

d

enOut

shiftreg1

d

enOut

shiftreg

d

enOut

psss_despreader

psss 1

psss 2

psss 3

fft _index

valid

rxdata

lfsr _on

ROM

addrz-1

Mux 2

sel

d0

d1

Mux 1

sel

d0

d1

Mux

sel

d0

d1

Logical

xor

z-0

FFT

rx_re

rx_im

en

real

valid

Delay 2 z-1

Delay 1 z-1

Delay

z-1

Counter

en out

Convert3

cast

Convert

cast

Constant3

1

System

Generator

tx_bits

4

rx_valid

3

rx_imag

2

rx_real

1

psss 2

psss 3

psss 1

diff

Figure 6.5: Top-level block diagram of the PSSS-OFDM Decoder

used to deinterleave the data and convert them into a serial/bitstream format. At

this point, a decision can be made using a comparator with a threshold of 0. All

values greater than 0 produce an output of 1, otherwise the ouput is 0.

63

lfsr_on

3

rxdata

2

rx_valid

1

register 3

In 1

In 2

In 3

In 4

In 5

In 7

In 8

In 9

In 10

In 11

In 12

In 13

In 14

In 15

In 16

en

Out 1

Out 2

Out 3

Out 4

Out 5

Out 6

Out 7

Out 8

Out 9

Out 10

Out 11

Out 12

Out 13

Out 14

Out 15

register 2

In 1

In 2

In 3

In 4

In 5

In 7

In 8

In 9

In 10

In 11

In 12

In 13

In 14

In 15

In 16

en

Out 1

Out 2

Out 3

Out 4

Out 5

Out 6

Out 7

Out 8

Out 9

Out 10

Out 11

Out 12

Out 13

Out 14

Out 15

register 1

In 1

In 2

In 3

In 4

In 5

In 7

In 8

In 9

In 10

In 11

In 12

In 13

In 14

In 15

In 16

en

Out 1

Out 2

Out 3

Out 4

Out 5

Out 6

Out 7

Out 8

Out 9

Out 10

Out 11

Out 12

Out 13

Out 14

Out 15

interleaver _control

en

tx _valid

mux _sel

mux _sel 2

decision

a

b

a>b

z-0

correlator _control

fft _ index

lfsr _rst

Out 2

lfsr _out

preg _we

correlator 3

psss

mseq

rst

Out 1

Out 2

Out 3

Out 4

Out 5

Out 6

Out 7

Out 8

Out 9

Out 10

Out 11

Out 12

Out 13

Out 14

Out 15

correlator 2

psss

mseq

rst

Out 1

Out 2

Out 3

Out 4

Out 5

Out 6

Out 7

Out 8

Out 9

Out 10

Out 11

Out 12

Out 13

Out 14

Out 15

correlator

psss

mseq

rst

Out 1

Out 2

Out 3

Out 4

Out 5

Out 6

Out 7

Out 8

Out 9

Out 10

Out 11

Out 12

Out 13

Out 14

Out 15

Mux 5

sel

d0

d1

Mux 4

seld0d1d2d3d4d5d6d7d8d9d10d11d12d13d14d15d16d17d18d19d20d21d22d23d24d25d26d27d28d29d30d31

Mux 3

seld0d1d2d3d4d5d6d7d8d9d10d11d12d13d14d15d16d17d18d19d20d21d22d23d24d25d26d27d28d29d30d31

Constant 5

0

System

Generator

fft_index

4

psss3

3

psss2

2

psss1

1

RxData

Figure 6.6: Block diagram of the PSSS despreader

64

.

.

.

.

.

.

.

.

.only a section of the entire block diagram is shown

Out4

4

Out3

3

Out2

2

Out1

1

Slice 3

[a:b]

Slice 2

[a:b]

Slice 1

[a:b]

Slice

[a:b]

Negate

x(-1)

Mux3

seld0d1

Mux2

seld0d1

Mux1

seld0d1

Mux

seld0d1

Accumulator 3

b

rstq

Accumulator 2

b

rstq

Accumulator 1

b

rstq

Accumulator

b

rstq

System

Generator

rst

3

mseq

2

psss

1

Figure 6.7: Block diagram of the correlator used in the PSSS despreader

The PSSS despreading operation given in Equation 6.4.1, can be efficiently accom-

plished through the correlator architecture shown in Fig. 6.7. The correlator works

by performing the computation of all c(i) in parallel, while each data symbol u(k)

is accumulated in serial fashion. A 2-to-1 multiplexer is then used to select either

the positive or the negative of the particular u(k) depending on the chip value of the

m-sequence at index i. After 15 cycles, the accumulators will contain the binary data

ready for thresholding.

c (i) =L∑k=1

u (k) a ((k + i)modL) (6.4.1)

65

6.5 Testing and Characterization

After each block has been tested separately for functionality, we proceed to system

level testing. The testing methodology involves transmitting a fixed set of data and

verifying the output before the receiver and after the decision. This was accomplished

by producing the expected output using the Matlab scripts used in Chapter 5. Since

the transmission is noiseless, we expect to get the transmitted bits perfectly after

decision. However, the complex numbers before the receiver are expected to have

some deviation due to precision and quantization errors.

6.5.1 Test Vector Generation

The test data is adapted from the example encoding used in the 802.11 Annex G [20]

which uses an ASCII encoded message of the characters of the well-known “Ode to

Joy” by F. Schiller:

Joy, bright spark of divinity,

Daughter of Elysium,

Fire-insired we tread

Thy sanctuary.

Thy magic power re-unites

All that custom has divided,

All men become brothers

Under the sway of thy gentle wings...

The characters are converted to binary representation using ASCII encoding and

loaded into a ROM which is then read by the PSSS-OFDM encoder for processing.

66

6.5.2 Functional Verification

In order to verify if the blocks are working correctly, the output generated by the

system generator model is subtracted from the expected output generated using the

Matlab scripts. In Fig. 6.8 we see this difference for the real and imaginary part of

the output of the encoder. We can see that the actual ouput has some deviation from

the simulated output (ranging from -0.15 to 0). This is a result of the quantization

errors due to fixed point representation. In this particular implementation, 15 bits

are used for the encoder ouput. However, this value can be easily changed using a

Matlab initialization script

0 50 100 150 200 250 300 350 400 450 500−0.2

−0.15

−0.1

−0.05

0

0.05

index

erro

r

Quantization Error of Real Part

0 50 100 150 200 250 300 350 400 450 500−0.2

−0.15

−0.1

−0.05

0

0.05

index

erro

r

Quantization Error of Imaginary Part

Figure 6.8: Quantization error resulting from the fixed-point implementation of thePSSS encoder

If we wanted to reduce the amount of deviation, we simply need to increase the

number of bits at the encoder output. In this implementation 15-bits were used at

67

the transmitter because this is the lowest allowable number of bits when the IFFT

IP-block is used. In practical implementations, this word length would be influenced

by both the area constraints and the word length of the available digital to analog

converter (DAC).

Finally, the receiver was verified to be working by counting the number of bit

errors. There are no bit errors in the working receiver since transmission is noiseless

and perfectly synchronized.

6.5.3 Logic Utilization

Shown in Table 6.2 and Table 6.3 is the logic utilization for the transmitter and the

receiver block respectively.

Parameter Value Max Percent

Slice Flip Flops 2,174 10,944 19%4 input LUTs 1,886 10,944 17%Occupied Slices 1,612 5,472 29%FIFO16/RAMB16s 3 36 8%DSP48s 6 32 18%

Table 6.2: Logic Utilization of the PSSS-OFDM Transmitter

Parameter Value Max Percent

Slice Flip Flops 2,815 10,944 25%4 input LUTs 2,450 10,944 22%Occupied Slices 2,111 5,472 38%FIFO16/RAMB16s 3 36 8%DSP48s 6 32 18%

Table 6.3: Logic Utilization of the PSSS-OFDM Receiver

68

Chapter 7

Conclusions

This thesis developed a novel multi-carrier spread spectrum (MCSS) scheme based

on the incorporation of parallel sequence spread spectrum (PSSS) and orthogonal

frequency division multiplexing (OFDM). An algorithm for this new scheme, called

PSSS-OFDM, was designed and its performance in various channel conditions were

investigated. This technique allows flexible control over the amount of spreading

to provide a variable rate link at minimal complexity gain over standard OFDM,

requiring only a simple correlator before the IFFT block. Using a single-tap phase

correction equalizer, simulations show a gain of 4dB in Eb/N0 at a BER of 0.1.

The PSSS-OFDM algorithm was shown to provide frequency diversity to plain

OFDM whenever the RMS delay spread is high and exploiting diversity is possible.

However, this diversity gain can be achieved with minimal complexity gain since

the PSSS algorithm only requires a simple correlator for its receiver. The scheme

also allows for the variation of the amount of spreading using the same hardware

architecture but with lower data rates. With the additional complexity due to the

FFT block and the equalizer, it is able to achieve data rates which are 9 to 10 times

higher than PSSS giving it potential for use in wideband applications such as WLANs.

69

PSSS-OFDM achieves comparable BER to standard OFDM at approximately

50% of the spectral efficiency through the use of precoding. The scheme also per-

forms progressively better against OFDM as RMS delay spread is increased. Thus,

PSSS-OFDM could be used to provide OFDM with multipath robustness in channels

with high delay spread as a substitute for coded OFDM. Finally, the transceiver was

developed and implemented in a Xilinx Virtex 4 XC4VFX12 platform through a rapid

prototyping approach using Xilinx System Generator.

7.1 Summary of Contributions

This work was able to completely develop the PSSS-OFDM scheme from algorithm

design, up to hardware implementation. Using this approach, the various issues in

both the theoretical domain as well as the practical domain have been addressed.

The main research contributions of this research are:

1. The incorporation of the PSSS algorithm with OFDM in order to introduce

frequency diversity gain which can easily be varied depending on the channel

conditions. This new scheme was shown to provide substantial improvement

compared to PSSS and is comparable in performance to OFDM at 50% spectral

efficiency. Better multipath performance can also be achieved by using lower

spectral efficiency modes.

2. This thesis also investigated the performance of PSSS-OFDM in AWGN and

frequency selective channels with varying delay spread. These results have been

compared to plain PSSS and plain OFDM. It was shown that with proper

precoding and a simple equalization scheme which only tracks the phase offset

of each subcarrier, we can achieve data rates comparable to 802.11a. This result

70

suggests that PSSS-OFDM can be used as an alternative wideband, high-data

rate transmission scheme such as those used in WLANs.

3. We were also able to develop a hardware implementation for PSSS-OFDM using

a rapid prototyping approach which allowed us to completely develop the scheme

from algorithm to FPGA impelementation.

7.2 Future Research

1. The performance of the PSSS-OFDM algorithm can be compared to other tech-

niques designed to introduce frequency diversity in digital communication sys-

tems. An example of this would be coded OFDM which uses convolutional

coding techniques on the OFDM subcarriers to introduce diversity. A combina-

tion of coding and spreading could also be of potential value if its capabilities

and trade-offs can be investigated.

2. The complete hardware implementation of the PSSS-OFDM algorithm will re-

quire a channel estimation block as well as a dynamic thresholding block. It

will also require a synchronization block. This thesis only focused on the core

blocks required for PSSS-OFDM such as spreading, interleaving, and frequency

transformation. Future work can design the other blocks in order to create the

full PSSS-OFDM algorithm and investigate its hardware complexity trade-offs.

3. Designing a packetization and preamble format for the PSSS-OFDM frame will

also be a primary concern if PSSS-OFDM is to be implemented in actual wide-

band systems. The work done in this thesis regarding the performance of PSSS-

OFDM would be helpful in designing such a scheme.

71

4. Finally, actual field testing of a PSSS-OFDM transceiver would be instrumental

to verifying the observations made from simulations in this work.

72

Appendix A

Spread Spectrum

In this appendix1, we give a brief introduction to spread spectrum techniques. In re-

cent years, spread spectrum has produced advances in digital communications which

are not possible with standard signaling formats. We focus first on defining what con-

stitutes a spread spectrum system. We then discuss the advantages and disadvantages

of these systems.

A.1 Introduction to Spread Spectrum Systems

A spread spectrum system is one in which the transmitted signal is spread over a much

wider bandwidth than the minimum required to transmit the information being sent.

This is accomplished by modulating with the information to be sent together with a

wideband encoding signal.

The basis of spread spectrum technology is expressed by C.E. Shannon in the form

of channel capacity, given in Eqn. A.1.1. Here, C is the capacity in bits per second,

W is bandwidth in hertz, N is noise power and S is signal power. This equation shows

the relationship between the ability of a channel to transfer error-free information,

1Adapted from [25]

73

compared with the signal-to-noise ratio existing in the channel, and the bandwidth

used to transmit the information.

C = W log2

(1 +

S

N

)(A.1.1)

We see that for any given noise-to-signal ratio, we can have higher channel capacity

by increasing the bandwidth used to transfer information.

A spread spectrum system must meet two criteria: (1) the transmitted bandwidth

is much greater than the bandwidth or rate of the information being sent, and (2)

some function other than the information being sent is employed to determine the

resulting modulated RF bandwidth.

A.2 Motivations for Spread Spectrum

The following are some advantages to using spread spectrum techniques:

• Selective addressing capability.

• Code division multiplexing is possible for multiple access.

• Low-density power spectra for signal hiding.

• Message screening from eavesdroppers.

• Interference rejection.

The properties come about as a result of the coded signal format and the wider

signal bandwidth that results. A single receiver or group of receivers may be addressed

by assigning a given reference code to them, whereas others are given a different code.

74

Selective addressing can then be as simple as transmitting the proper code sequence

as modulation.

Receivers can also use codes with low cross correlation to provide minimum inter-

ference between users. Thus, more than one signal can be unambiguously transmitted

at the same frequency and at the same time.

Because of the wideband signal spectra generated by code modulation, the power

transmitted is low in any narrow region. Thus the density of spread spectrum sig-

nals is far less than that of more conventional signals in which all the transmitted

power is sent in a band of frequencies commensurate with the baseband infromation

bandwidth.

Again, because coded signals are employed, an eavesdroper cannot casually listen

to messages being sent.

A.3 Processing Gain and Jamming Margin

The most commonly used quantity in describing or specifying spread spectrum sys-

tems is that of processing gain or jamming margin.

Processing gain is equivalent to the bandwidth ratio between the information and

the RF bandwidth used to send it. This is gain is developed through the sequence

of signal bandwidth spreading and despreading operation. The transmit part of the

process may be accomplished with any one of the band-spreading modulation meth-

ods. Despreading is accomplished by correlating the received spread spectrum signal

with a similar local reference signal. When the tow signals are matched, the desired

signal collapses to its original bandwidth before spreading, whereas unmatched input

is spread by the local refernece to the local reference bandwidth or more.

75

A filter then rejects all but the desired, narrowband signal; that is, given a de-

sired signal and its interference, a spread spectrum receiver enhances the signal while

suppressing the effects of all other inputs.

The difference in output and input singal-to-noise ratios is its processing gain.

However this does not guarantee that a receiver can perform when faced with an

interfering signal having a power level larger than the desired signal by the amount

of available processing gain. The capability of a system to perform in such hostile

environments is called jamming margin.

Jamming margin is always less than the processing gain available from a system.

It takes into account the requirement for a useful system output singal-to-noise ratio

and allows for internal losses. As a result jamming margin is harder to compute than

processing gain.

76

Appendix B

Orthogonal Frequency DivisionMultiplexing (OFDM)

Multiple carrier transmission is a form of multichannel communications where the

frequency band of the channel is subdivided into a number of subchannels and in-

formation is transmitted on each of the subchannels [5]. This mode of transmission

is used primarily in situations where there is a high probability that one or more

subchannels will be unreliable from time to time. This type of channel is referred to

as a frequency selective channel and is commonly encountered in wideband multipath

transmission.

In this chapter we discuss a special case of multicarrier transmission called orthog-

onal frequency division multiplexing or OFDM. This technique, along with parallel

sequence spread spectrum (PSSS), forms the basis of the PSSS-OFDM scheme pro-

posed and investigated in this thesis.

77

B.1 Motivations for Multi-carrier vs. Single-carrier

Systems

High data-rate communication is desired in many applications. However, as the

symbol duration reduces with the increase of data-rate, systems that use single carrier

modulation suffer from more severe intersymbol interference (ISI) caused by dispersive

fading of wireless channels. This results in the need for complex equalization at the

receiver.

OFDM modulation divides the entire frequency selective fading channel into many

narrow band flat fading subchannels1 in which high bit-rate data are transmitted in

parallel and do not undergo ISI due to the long symbol duration [26].

In single-carrier systems, the highest data rate is limited by dispersive Rayleigh

fading. To reduce the effect of ISI in unequalized systems, the symbol duration must

be much larger than the delay spread of wireless channels. In OFDM, each subcarrier

is transmitted in parallel, thereby increasing the symbol duration and reducing ISI.

Therefore, OFDM is an effective technique for combating multipath fading and for

high-bit-rate transmission over mobile wireless channels.

B.2 Introduction to OFDM

Fig. B.1 illustrates a block diagram of a multicarrier communication system. A serial-

to-parallel buffer segments the information sequence into frames of Nf bits. The Nf

bits in each frame are parsed into N groups, where the ith group is assigned ni bits.

It is convenient to view the multicarrier modulation as consisting ofN independent

QAM channels, each operating at the same symbol rate 1/T , but each channel having

1Subchannel is sometimes also called subcarrier or tone

78

Serial-to-parallelbuffer

InputData

.

.

.

MulticarrierModulator

(inverse DFT)...

Add cyclicprefix, andparallel-to-

serial convert

D/Aconverter

Output totransmitter

Parallel-to-

serialconverter

.

.

.

.

.

.

Detector

.

.

.

.

.

.

Multicarrierdemodulator

(DFT)

.

.

.

.

.

.

Removecyclic

prefix andserial-to-parallelconvert

A/Dconverter

OutputBits

Figure B.1: Multicarrier communication system

a distinct QAM constellation, i.e., the ith channel will employ Mi = 2ni signal points.

We denote the complex-valued signal points corresponding to the information symbols

on the subchannels by Xk, k = 0, 1, ..., N − 1. In order to modulate N subcarriers by

the information symbols Xk, we employ the inverse DFT (IDFT).

Given these complex information symbols, the OFDM (modulated) signal can be

expressed as Eqn. B.2.1, where fk = f0 + k∆f , k = 0, 1, ..., N − 1. Ts and ∆f are

called the symbol duration and subcarrier spacing of OFDM, respectively. In order

for the receiver to demodulate the OFDM signal, the symbol duration must be long

enough such that Ts∆f = 1, which is called the orthogonality condition.

If this condition is satisfied, the OFDM signal can be demodulated using Eqn.

B.2.2, which can be accomplished using the discrete Fourier transform (DFT). Both

the DFT and the IDFT can be efficiently implemented using fast Fourier transform

(FFT) algorithms.

x (t) =N−1∑k=0

Xkej2πfkt, for 0 < T < Ts (B.2.1)

79

1

Ts

Ts∫0

x (t) e−j2πfktdt (B.2.2)

B.3 Subcarrier Symbol Structure

Each symbol in an OFDM frame modulates a particular subcarrier frequency. We can

visualize this through Fig. B.2. Each plot corresponds to one subcarrier. We can see

that the subcarriers overlap with each other resulting in efficient use of bandwidth.

However, at the peak of each subcarrier, all other subcarriers have nulls. This is a

consequence of the orthogonality condition. This means that given perfect frequency

syncronization, each information symbol can be perfectly recovered after the DFT.

B.4 Cyclic Prefix (Guard Interval)

The parallel transmission in OFDM results in a longer symbol period for each sub-

carrier. This virtually eliminates the effect of dispersive channels. However, this does

not eliminate inter-symbol interference (ISI) between OFDM frames.

One way of avoiding this ISI is to append a cyclic prefix to each OFDM block.

The cyclic prefix consists of the last v samples of an OFDM block appended to the

beginning of the block. Note that the addition of the cyclic prefix to the block of

data increases the length of the block to N + v samples.

If the channel impulse response is shorter than the appended cyclic prefix, the

convolution of the transmitted OFDM frame and the channel impulse response pro-

duces the received sequence. We are interested in the last N samples of this sequence

since it contains the actual data. The first v samples are simply discarded.

80

0−1/T−2/T−3/T−4/T−5/T−6/T 1/T 2/T 3/T 4/T 5/T 6/T−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

1.2

frequency

ampl

itude

Overlapping OFDM Subcarriers

Figure B.2: Orthogonal Subcarriers

Because of the cylclic prefix, succesive blocks (frames) of the transmitted infor-

mation sequence do not interfere with each other. After discarding the cyclic prefix,

there is virtually no ISI between OFDM frames.

81

Appendix C

Sample PSSS Encoding/Decoding

Presented here is an example of the encoding and decoding process of the PSSS

algorithm, upon which the scheme proposed in this thesis is based. This scheme was

originally presented in [4] to provide a physical layer for RF communications with

low complexity, and subsequently included in the 802.15.4 WPAN standard [19]. It

is based on an overlap of cyclically shifted binary spreading sequences.

In particular, it uses binary M-sequences whose autocorrelation properties allow

it to yield a discrete delta function when cyclically correlated with itself. This M-

sequences could easily be generated using a linear-feedback shift register architecture

(LFSR) and have length L = 2N − 1 [27]. An example of such a sequence, a(i), is

shown in Fig. C.1.

At the transmitter, the m-sequence a(i), of length K, is first expressed in unipolar

format (0 or 1) using Eqn. C.0.1 to create the signal b(i). On the other hand, the data

sequence is expressed in bipolar format (-1 or +1) to form the signal d(i) (Fig. C.2).

The cyclical shifts of b(i) are taken and each of these is multiplied to one data sample

from d(i). The resulting sequences are then added to form the transmitted signal u(i)

(Fig. C.3). This signal is now multivalent and is referred to as the PSSS-sequence.

82

The creation of the PSSS-sequence is summarized in Eqn. C.0.2.

b (i) =a (i) + 1

2=

1

0(C.0.1)

u (i) =K∑k=1

b ((i+ k)modL) d (i) (C.0.2)

At the receiver, a cyclical correlation (Eqn. C.0.3) of the received signal with the

original m-sequence a(i) is taken. This results in the recovery of the original data

signal but with a scaling value (Fig. C.4).

c (i) =L∑k=1

u (k) a ((k + i)modL) (C.0.3)

0 5 10 15 20 25 30−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Index i

a(i)

Spreading Sequence

Figure C.1: a(i) - 31-sample m-sequence (N = 5)

83

0 5 10 15 20 25 30−1

−0.5

0

0.5

1

Index i

d(i)

Data Signal

Figure C.2: d(i) - Data bits expressed in bipolar format

0 5 10 15 20 25 30−4

−2

0

2

4

6Transmitted Signal

Index i

u(i)

Figure C.3: u(i) - Transmitted PSSS sequence

84

0 5 10 15 20 25 30

−15

−10

−5

0

5

10

15

Received Signal

Index i

c(i)

Figure C.4: c(i) - Received data after correlation

85

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