UNIVERSITY OF NAIROBI

TITLE:

SYNCHRONIZATION OF DIRECT SEQUENCE SPREAD

SPECTRUM SIGNALS Project Index: 086

Project Report By:

ONAYA OYOO JOSEPH

F17/2050/2004 Supervisor:

DR. V. K ODUOL

Examiner:

DR G.S.O ODHIAMBO.

A project presented in partial fulfillment of the requirement for the

award of the degree of

BACHELOR OF SCIENCE

In

ELECTRICAL & ELECTRONIC ENGINEERING Submission Date 20th June 2008

ii

DEDICATION

To my parents, their love, care and support

iii

ACKNOWLEDGEMENT

Throughout this project period I have leaned a lot in this area of telecommunications and

have appreciated the spirit of consultation from classmates and friends who have offered me

assistance and support.

My special appreciation goes to my project supervisor Dr. V .K Oduol for his support and

guidance throughout this period.

Great thanks, goes to my family members who have supported and encourage me throughout

my time in campus.

Special appreciation goes to my friends Julian, Ibrahim, and Moses for their encouragement

and support as I worked on this project. A special thanks goes to my girlfriend Arnoda for her

love and encouragement throughout this project. I recognize my classmates for their

encouragement and criticism on various areas as I worked on this project.

Finally I give thanks to the Almighty God for the strength and wisdom to remain focused

throughout my life and in the completion of this project.

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ABSTRACT

This write up starts by giving a brief introduction to spread spectrum communication systems

in general. It describes how in spread spectrum systems, the signal to be transmitted is spread

over a large bandwidth by use of a pseudo noise code generated by a P.N code generator at

the transmitter. At the receiver, the signal is despread using a synchronized replica of the

pseudo noise code. The signal is acquired at the receiver, using coarse acquisition and

tracking.

The second chapter goes on to describe direct sequence spread spectrum signals in detail

giving a brief description on pseudonoise sequences their properties and types.

The third chapter emphasizes code synchronization where acquisition of spreading sequences

using matched filter and serial search acquisition is described. It goes further to describe

tracking of the direct sequence spread spectrum signals using delay locked loop and Tau-

Dither loop.

The design of an acquisition system has been implemented using a matlab code given in the

appendix and a multiuser environment has been implemented to show how spread spectrum

signals can reject uncorrelated signals. Analysis of the results is carried out and conclusion

has been drawn. MATLAB results are shown in the various graphs.

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TABLE OF CONTENTS

1 Introduction………………………………………………………………………………….1

2 Direct Sequence Spread Spectrum Signals………………………………………………….2

2.1 Pseudonoise sequences…………………………………………………………………8

2.2 Randomness properties………………………………………………………………...8

2.3 Types of PN sequences………………………………………………………………...9

3 Code synchronization………………………………………………………………………13

3.1 Acquisition of spreading sequences………………………………………………......13

3.2 Matched filter acquisition……………………………………………………………..15

3.3 Serial search acquisition………………………………………………………………17

3.4 Code tracking………………………………………………………………………....20

4 Design of code acquisition and tracking……………………………………………….......28

4.1 Design………………………………………………………………………………....28

4.2 Results………………………………………………………………………………...33

4.3 Analysis……………………………………………………………………………….37

4.4Future work……………………………………………………………………………37

4.5 Conclusion……………………………………………………………………………

vi

LIST OF FIGURES

1.1 Model of spread spectrum digital communication system………………………………...2

2.1 Examples of (a) data modulation and (b) spreading waveform…………………………...4

2.2 Functional block diagram of direct-sequence system with PSK or DPSK

(a)transmitter and (b) receiver………………………………………………………………6

2.3 Spectra of desired signal and interference: (a) wideband-filter output and

(b) demodulator input………………………………………………………………………7

2.4 Autocorrelation of maximal sequence and random binary sequence…………………..….9

2.5 General feedback shift register with m stages……………………………………………10

2.6 (a) Three-stage linear feedback shift register and (b) contents after successive shifts…..11

3.1 Digital matched filter……………………………………………………………………..15

3.2 Configuration of a serial-search acquisition system enabled by a matched filter………..16

3.3: Serial-search acquisition system…………………………………………………………………….17

3.4 Flow graph of multiple-dwell system with consecutive-count strategy………………….19

3.5 Flow graph of multiple-dwell system with up-down strategy……………………………19

3.6 Trajectories of search positions: (a) uniform search and (b) broken-center Z search……20

3.7 Delay-locked loop………………………………………………………………………..21

3.8 Discriminator characteristic of delay-locked loop for � = 1 2⁄ …………………………24

3.9Tau-dither loop……………………………………………………………………………26

4.1 Generic acquisition block diagram……………………………………………………….28

4.2 Delay locked loop for tracking of direct sequence signals……………………………….29

1

CHAPTER 1

INTRODUCTION

A spread spectrum modulation scheme is any digital modulation technique that utilizes a

transmission bandwidth much greater than the modulating signal bandwidth, independently

of the bandwidth of the modulating signal.

There are several reasons why it might be desirable to employ a spread spectrum modulation

scheme. Among these are to provide resistance to unintentional interference and multipath

transmissions, to provide resistance to intentional interference (also known as jamming) [1],

to provide a signal with sufficiently low spectral level so that it is masked by the background

noise (i.e., to provide low probability of detection), and to provide a means for measuring

range between transmitter and receiver.

Spread spectrum systems were historically applied to military applications and still are. Much

of the literature on military applications of spread spectrum communications is classified. A

notable application of spread spectrum to civilian uses was to cellular radio in the 1990s with

the publication of interim standard IS-95 by the US Telecommunications Industry

Association (TIA) [2]. Another more recent application of spread spectrum to civilian uses is

to wireless local area networks (LANs), with standard IEEE 802.11 published under the

auspices of the Institute of Electrical and Electronics Engineers (IEEE) [3]. The original

legacy standard, released in July 1997, includes spread spectrum modem specifications for

operation at data rates of 1 and 2 Mbps, and the 802.11b standard, released in Oct. 1999, has

a maximum raw data rate of 11 Mbps with both operating in the 2.4 GHz band. Specifications

802.11a and 802.11g, released in Oct. 1999 and June 2003, respectively, use another

modulation scheme known as orthogonal frequency division multiplexing, with the former

operating in the 5 GHz band and the latter operating in the 2.4 GHz band.

Spread spectrum communication can be utilized using the following techniques;

Direct sequence spread spectrum (DS-SS)

A random or pseudo random code is used to spread the baseband signal. This will cause fast

phase transitions in the carrier frequency that contains the data.

Frequency hopping spread spectrum (FH-SS)

2

A random or a pseudo random code is used to shift the carrier frequency in a random manner.

This ends up modulating different portions of the data signal with different carrier

frequencies.

Hybrid system (DS/FH)

This is a combination of the two; DS and FH techniques. Where one data bit is divided over

frequency hop channels, and one complete PN code of length N is multiplied with the data

signal.

Figure 1.1 Model of spread spectrum digital communication system

Modulator

Pseudorandom pattern

generator

Channel Demodulator Channel

Decoder

Pseudorandom pattern

generator

Pseudorandom

pattern

3

CHAPTER 2

DIRECT SEQUENCE SPREAD SPECTRUM SIGNALS

A spread-spectrum signal is a signal that has an extra modulation that expands the signal

bandwidth beyond what is required by the underlying data modulation. Spread-spectrum

communication systems are useful for suppressing interference, making interception difficult,

accommodating fading and multipath channels, and providing a multiple-access capability.

The

most practical and dominant methods of spread-spectrum communications are direct-

sequence modulation and frequency hopping of digital communications.

At first it might seem that a spread-spectrum signal is counterproductive insofar as the

receive filter will require an increased bandwidth and, hence, will pass more noise power to

the demodulator. However, when any signal and white Gaussian noise are applied to a filter

matched to the signal, the sampled filter output has a signal-to-noise ratio (SNR) that is

inversely proportional to the noise-power spectral density [1]. The remarkable aspect of this

result is that the filter bandwidth and, hence, the output noise power are irrelevant. Thus, we

observe that there is no fundamental barrier to the use of spread-spectrum communications.

A direct-sequence signal is a spread-spectrum signal generated by the direct mixing of the

data with a spreading waveform before the final carrier modulation. Ideally, a direct-sequence

signal with binary phase-shift keying (BPSK) or differential PSK (DPSK) data modulation

can be represented by

����= ���������cos�2����+ ��(2.1)

where A is the signal amplitude,�(�) is the data modulation, �(�)is the spreading waveform,

��is the carrier frequency, and � is the phase at �= 0. The data modulation is a sequence of

nonoverlapping rectangular pulses of duration �� each of which has an amplitude �� = + 1 if

the associated data symbol is a 1 and �� = − 1 if it is a 0 (alternatively, the mapping could be

1 → − 1And 0 → + 1) Equation (2-1) implies that ����= ���������2����+ � +

������which explicitly exhibits the phase-shift keying by the data modulation.

4

Figure 2.1: Examples of (a) data modulation and (b) spreading waveform.

The spreading wave form has the form

����= ∑ �������� ��− ����(2.2)

Where �� each equals +1 or –1 and represents one chip of the spreading sequence, the chip

waveform (t) is ideally confined to the interval �0, ��� to prevent interchip interference in the

receiver. A rectangular chip waveform has �(�) = � (�, ��) where

���, ��= �1,0 ≤ �≤ �0, ��ℎ������(2.3)

Figure 2.1 above depicts an example of �(�) and p(t) for a rectangular chip waveform.

Message privacy is provided by a direct-sequence system if a transmitted message cannot be

recovered without knowledge of the spreading sequence. To ensure message privacy, which

is assumed henceforth, the data-symbol transitions must coincide with the chip transitions.

Since the transitions coincide, the processing gain � = �� ∕ �� is an integer equal to the

(a)

(b)

�(�)

�(�) 1

-1

1

-1

5

number of chips in a symbol interval. If W is the bandwidth of �(�) and B is the bandwidth

of ����the spreading due to p(t) ensures that s(t) has a bandwidth W >> B.

Figure 2.2 is a functional or conceptual block diagram of the basic operation of a direct-

sequence

system with PSK. To provide message privacy, data symbols and chips, which are

represented by digital sequences of 0’s and 1’s, are synchronized by the same clock and then

modulo-2 added in the transmitter. The adder output is converted according to 0 → 1and1 →

+ 1 before the chip and carrier modulations. Assuming that chip and symbol synchronization

has been established, the received signal passes through the wideband filter and is multiplied

by a synchronized local replica of ����. If �(�) is rectangular, then �(�) = ± 1 and ��(�) = 1

Therefore, the multiplication yields the despread signal

�����= ��������= �����cos�2��� + �� (2.4)

at the input of the PSK demodulator. Since the despread signal is a PSK signal, a standard

coherent demodulator extracts the data symbols. Figure 2.3(a) is a qualitative depiction of the

relative spectra of the desired signal and narrowband interference at the output of the

wideband filter. Multiplication of the received signal by the spreading waveform, which is

called despreading, produces the spectra of Figure 2.3(b) at the demodulator input. The signal

bandwidth is reduced to B, while the interference energy is spread over a bandwidth

exceeding W. Since the filtering action of the demodulator then removes most of the

interference spectrum that does not overlap the signal spectrum, most of the original

interference energy is eliminated.

6

Figure 2.2: Functional block diagram of direct-sequence system with PSK or DPSK: (a)

transmitter and (b) receiver.

An approximate measure of the interference rejection capability is given by the ratio W/B.

Transmitted signal

Data symbols Wideband ���

�

Synchronization system Spreading

waveform

Chip

Waveform

Wideband

filter

Oscillator Spreading

sequence generator

PSK

Carrier

Symbol

(a)

(b)

Data symbols

7

Figure 2.3: Spectra of desired signal and interference: (a) wideband-filter output

and (b) demodulator input.

Whatever the precise definition of a bandwidth, W and B are proportional to 1 ��⁄ and 1 ��⁄ ,

respectively, with the same proportionality constant, therefore,

� =��

�� =

�� (2.5)

which links the processing gain with the interference rejection illustrated in figure 2.3. Since

its spectrum is unchanged by the despreading, white Gaussian noise is not suppressed by a

direct-sequence system. In practical systems, the wideband filter in the transmitter is used to

limit

the out-of-band radiation. This filter and the propagation channel disperse the chip waveform

so that it is no longer confined to �0, ���. To avoid interchip interference in the receiver, the

filter might be designed to generate a pulse that satisfies the Nyquist criterion for no

intersymbol interference [5]. A convenient representation of a direct-sequence signal when

the chip waveform may extend beyond �0, ��� is

� �����

�

����

�����− ����cos�2����+ ��(2.6)

Interference

Signal

Signal

Interference

Frequency Frequency

Spectral density Spectral density

(a) (b)

8

Where [�] denotes the integer part of � when the chip waveform is assumed to be confined

to[0, ��] then (2-6) can be expressed by (2-1) and (2-2).

2.1 Pseudonoise Sequences

The spread-spectrum approach called transmitted reference (TR) can utilize a truly random

code signal for spreading and despreading, since the code signal and the data modulated

signal are simultaneously transmitted over different regions of the spectrum. The stored

reference (SR) approach cannot use a truly random code signal since the code needs to be

stored or generated at the receiver. For SR system a pseudonoise or pseudorandom code

signal must be used [5]

The difference between a random signal and a pseudorandom signal is that a random signal

cannot be predicted; its future variations can only be described in a statistical sense.

However, a pseudorandom signal is not random at all; it is a deterministic, periodic signal

that is known to both transmitter and receiver. Its been given the name “pseudonoise” or

“pseudorandom” because even though the signal is deterministic, it appears to have the

statistical properties of sampled white noise. It appears to unauthorized listener, to be a truly

random signal.

2.2 Randomness Properties

There are three basic properties that can be applied to any periodic sequence as a test for the

appearance of randomness. The properties, called balance, run, and correlation, are described

for binary signals as follows:

• Balance Property:

Good balance require that in each period of the sequence, the number of binary one differs

from the number of binary zeros by at most one digit.[5]

• Run Property:

A run is defined as a sequence of single type of binary digit(s) the appearance of the alternate

digit in a sequence starts a new run. The length of the run is the number of digits in the run.

Among the runs of ones and zeros in each period, it is desirable that about one-half the runs

of each type are of length 1, about one-fourth are of length 2, one-eighth are of length 3 and

so on.[5]

• Correlation Property:

9

If a period of the sequence is compared term by term with any cyclic shift of itself, it is best if

the number of agreements differs from the number of disagreements by not more than one

count. [5].

2.3 Types of PN sequence

Maximal Length Sequences

Maximal length shift register sequence or m-sequences are so called due their property that

all possible shift register states except the all-zero state occur in a single, K length, cycle of

generated sequence [6]. Therefore for a shift register with n elements, the longest or

maximum (m) length sequence which can be generated is = 2� − 1 .

Due to the occurrence of all shift register states (except the all-zero state) each m-sequence

will consist of 2��� ones and (2��� − 1) zeros.

The correlation properties of the m-sequence family are interesting due to their flat periodic

autocorrelation side-lobes; figure 2.4 provides a good approximation to an impulsive

autocorrelation function.

Figure 2.4 Autocorrelation of maximal sequence and random binary sequence.

A shift-register sequence is a periodic binary sequence generated by combining the outputs of

feedback shift register. A feedback shift register, which is diagrammed in figure 2.5, consists

of consecutive two-state memory or storage and feedback logic. Binary sequences drawn

from the alphabet {0, 1} are shifted through the shift register in response to clock pulses. The

contents of the stages, which are identical to their outputs, are logically combined to produce

the input to the first stage. The initial contents of the stages and the feedback logic determine

the successive contents of the stages. If the feedback logic consists entirely of modulo-2

Random binary

��� ���

��

1

1��

Maximal

10

adders (exclusive-OR gates), a feedback shift register and its generated sequence are called

linear.

Figure 2.5: General feedback shift register with m stages.

Figure 2.5 (a) illustrates a linear feedback shift register with three stages and an output

sequence extracted from the final stage. The input to the first stage is the modulo-2 sum of

the contents of the second and third stages. After each clock pulse, the contents of the first

two stages are shifted to the right, and the input to the first stage becomes its content. If the

initial contents of the shift register are 0 0 1, the subsequent contents after successive shift are

listed in figure 2.6 (b). since the shift register returns to its initial state after 7 shifts, the

periodic output sequence extracted from the final stage has a period of 7 bits.

If a linear feedback register reached the zero state with all its contents equal to 0 at some

time, it would always remain in the zero state, and the output sequence would subsequently

be all 0’s. Since a linear � -stage feedback shift register has exactly 2� − 1 nonzero states,

the period of its output sequence cannot exceed2� − 1. A sequence of period 2� − 1

generated by a linear feedback shift register is called a maximal or maximal-length sequence.

(a)

1 2 3

Clock

Output

Feedback Logic

1 2 3 m

Clock

11

Shift Contents

Initial Stage 1 Stage 2 Stage 3 1 0 0 1 2 1 0 0 3 0 1 0 4 1 1 0 5 1 1 1 6 0 1 1 7 0 0 1

(b)

Figure 2.6: (a) Three-stage linear feedback shift register and (b) contents after successive

shifts.

A pseudonoise or pseudorandom sequence is a periodic binary sequence with a nearly even

balance of 0’s and 1’s and an autocorrelation that roughly resembles, over one period, the

autocorrelation of a random binary sequence [1]

Pseudonoise sequences, which include the maximal sequences, provide practical spreading

sequences because their autocorrelations facilitate code synchronization in the receiver. Other

sequences have peaks that hinder synchronization.

Gold and Kasami codes

Selected pairs of m-sequences exhibit a three-valued periodic cross-correlation function, with

a reduced upper bound on the correlation levels as compared with the rest of the m-sequence

set. This m-sequence family subset is referred to as the preferred pair and one such unique

subset exists for each sequence length. For the preferred pair of m-sequences of order n, the

periodic cross-correlation and an autocorrelation sidelobe levels are restricted to the values

given by �– ����, − 1, ����− 2� where:

����= �2���

� + 1,����

2���

� + 1,�����(2.7)

The enhanced correlation properties of the preferred pair can be passed on to the other

sequences derived from the original pair. By a process of modulo-2 addition of the preferred

pair the resulting derivative sequence shares the same features and can be grouped with the

preferred pair as a member of the newly created family members at each successive shift.

12

Gold codes are widely used in spread spectrum systems such as the international Navstar

global positioning system (GPS), which uses 1023 chip gold codes for the civilian clear

access (C/A) part of the positioning service [3]

Walsh sequences

Walsh sequences have the attractive property that all codes in a set are precisely orthogonal.

A series of codes �����, for � = 0,1,2, … . . , �are orthogonal with weight K over the

interval 0 ≤ �≤ �, when:

� ������� �����= ��,���� = �0,���� ≠ �

�

�

(2.8)

Where n and m have integer values and K is a non-negative constant which does not depend

on the indices m and n but only on the code length K. This means that, in a fully synchronized

communication system where each user is uniquely identified by a different Walsh sequence

from a set, the different users will not interfere with each other at the proper correlation

constant, when using the same channel.

Walsh sequence systems are limited to code lengths of � = 2� where n is an integer. When

Walsh sequences are used in communication systems the code length K enables K orthogonal

codes to be obtained. This means that communication system can serve many users per cell as

the length of the Walsh sequence.

13

CHAPTER 3

CODE SYNCHRONISATION A spread-spectrum receiver must generate a spreading sequence or frequency hopping pattern

that is synchronized with the received sequence or pattern; that is the corresponding chips or

dwell intervals must precisely or nearly coincide.

Any misalignment causes the signal amplitude at the demodulator output to fall in accordance

with the autocorrelation or partial autocorrelation function.

Although the use of precision clocks in both the transmitter and the receiver limit the timing

uncertainty in the receiver, clock drifts, range uncertainty, and the Doppler shift may cause

synchronization problems. Code synchronization, which is either sequence or pattern

synchronization, might be obtained from separately transmitted pilot or timing signals. It may

be aided or enabled by feedback signals from the receiver to the transmitter. However, to

reduce the

cost in power and overhead, most spread-spectrum receivers can acquire code

synchronization from the received signal.

Code acquisition is the operation by which the phase of the receiver-generated sequence is

brought to within a fraction of a chip of the phase of the received sequence [7]. After this

condition is detected and verified, the tracking system is activated. Code tracking is the

operation by which synchronization errors are further reduced or at least maintained within

certain bounds. Both the acquisition and tracking devices regulate the clock rate. Changes in

the clock rate adjust the phase or timing offset of the local sequence generated by the receiver

relative to the phase or timing offset of the received sequence.

3.1 Acquisition of spreading sequences

Acquisition provides coarse synchronization by limiting the choices of the estimated values

to a finite number of quantized candidates. Since the presence of the data modulation

impedes code synchronization, the transmitter is assumed to facilitate the synchronization by

transmitting the spreading sequence without any data modulation. In nearly all applications,

non-coherent code synchronization must precede carrier synchronization because the signal

energy is spread over a wide spectral band. Prior to despreading, which requires code

synchronization the signal-to-noise ratio (SNR) is unlikely to be sufficiently high for

successful carrier tracking by a phase-locked loop. The received signal is

14

����= ����+ ����(3.1)

Where s�t� is the desired signal and n(t) is the additive white Gaussian noise for a direct-

sequence system with PSK modulation, the desired signal is:

����= �2����− ��cos�2��� + 2����+ ��(3.2)

Where S is the average power, �(�)is the spreading waveform,�� is the carrier frequency, �

is the random carrier phase, and� and �� are the unknown code phase and frequency offset,

respectively, that must be estimated. The frequency offset may be due to a Doppler shift or to

a drift or instability in the transmitter oscillator.

One method of acquisition is to use a parallel array of processors, each matched to candidate

quantized values of the timing and frequency offsets [6]. The largest processor output then

indicates which candidates are selected as the estimates. An alternative method of acquisition,

which is much less complex, but significantly increases the time needed to make a decision,

is to serially search over the candidate offsets. Since the frequency offset is usually negligible

or requires only a few candidate values, I will analyze the code synchronization in which only

the timing offset � is estimated. Search methods rather than parallel processing are examined.

It must be noted that both the acquisition and tracking devices regulate the clock rate and so

changes in the clock rate adjust the phase or the timing offset of the local sequence generated

by the receiver relative to the phase or the timing offset of the received sequence.

In a benign environment, sequential estimation methods provide rapid acquisition [7].

Successive received chips are demodulated and then loaded into the receiver’s code generator

to establish its initial state. The tracking system then ensures that the code generator

maintains synchronization. However, because chip demodulation is required, the usual

despreading mechanism cannot be used to suppress interference during acquisition. Since an

acquisition failure completely disables a communication system, an acquisition system must

be capable of rejecting the anticipated level of interference. To meet this requirement,

matched-filter acquisition and serial-search acquisition are the most effective techniques in

general.

3.1.1 Matched-Filter Acquisition.

Matched-filter acquisition provides potentially rapid acquisition when short programmable

sequences give adequate security. The matched filter in an acquisition system is matched to

15

one period of the spreading waveform, which is usually transmitted without modulation

during acquisition. The sequence length or integration time of the matched filter is limited by

frequency offsets and chip-rate errors. The output envelope, which ideally comprises

triangular autocorrelation spikes, is compared with one or more thresholds, one of which is

close to the peak value of the spikes. If the data-symbol boundaries coincide with the

beginning and end of a spreading sequence, the occurrence of a threshold crossing provides

timing information used for both symbol synchronization and acquisition. A major

application of matched-filter acquisition is for burst communications, which are short and

infrequent communications that do not require a long spreading sequence.

A digital matched filter that generates �(�, 0) for noncoherent acquisition of a binary

spreading waveform is illustrated in Figure 3.1.

Figure 3.1: Digital matched filter

The digital matched filter offers great flexibility, but is limited in the bandwidth it can

accommodate. The received spreading waveform is decomposed into in-phase and quadrature

baseband components, each of which is applied to a separate branch. The outputs of each

digitizer are applied to a transversal filter. Tapped outputs of each transversal filter are

multiplied by stored weights and summed. The two sums are squared and added together to

produce the final matched-filter output. A one-bit digitizer makes hard decisions on the

received chips by observing the polarities of the sample values. Each transversal filter is a

shift register, and the reference weights are sequence chips stored in shift-register stages. The

transversal filter contains G successive received spreading-sequence chips and a correlator

Oscillator

Filter

digitizer

Transversal

filter Square

∑ Reference

Weights

Filter,digitize

r

Transversal

filter Squarer

π/2

Output signal Input signal

16

that computes the number of received and stored chips that match. The correlator outputs are

applied to the squarers. Matched-filter acquisition for continuous communications is useful

when serial-search acquisition with a long sequence fails or takes too long. The transmission

of the short sequence may be concealed by embedding it within the long sequence. The short

sequence may be a subsequence of the long sequence that is presumed to be ahead of the

received sequence and is stored in the programmable matched filter.

Figure 3.2 depicts the configuration of a matched filter for short-sequence acquisition and a

serial-search system for long-sequence acquisition. The control signal provides the short

sequence that is stored or recirculated in the matched filter.

Figure 3.2: Configuration of a serial-search acquisition system enabled by a matched filter.

The control signal activates the matched filter when it is needed and deactivates it otherwise.

The short sequence is detected when the envelope of the matched-filter output crosses a

threshold. The threshold-detector output starts a long-sequence generator in the serial-search

system at a predetermined initial state. The long sequence is used for verifying the acquisition

and for despreading the received direct-sequence signal. To expedite the process several

matched filters in parallel may be used.

3.1.2 Serial-Search Acquisition

Serial-search acquisition consists of a search, usually in discrete steps, among candidate code

phases of a local sequence until it is determined that the local sequence is nearly

Matched Filter Envelope

Detector

Threshold

Detector

Serial-search

acquisition system Input

To tracking system

and demodulator

17

synchronized with the received spreading sequence. Conceptually, the timing uncertainty

covers a region that is quantized into a finite number of cells, which are search positions of

relative code phases or timing alignments. The cells are serially tested until it is determined

that a particular cell corresponds to the alignment of the two sequences to within a fraction of

a chip.

Input

To tracking system and demodulator

From tracking system

Figure 3.3: Serial-search acquisition system.

Figure 3.3 depicts the principal components of a serial-search acquisition system. The

received

direct-sequence signal and a local spreading sequence are applied to a noncoherent correlator.

If the received and local spreading sequences are not aligned, the sampled correlator output is

low. Therefore, the threshold is not exceeded, the cell under test is rejected, and the phase of

the local sequence is retarded or advanced, possibly by generating an extra clock pulse or by

blocking one. A new cell is then tested. If the sequences are nearly aligned, the sampled

correlator output is high, the threshold is exceeded, the search is stopped, and the two

sequences run in parallel at some fixed phase offset. Subsequent tests verify that the correct

cell has been identified. If a cell fails the verification tests, the search is resumed. If a cell

passes, the two sequences are assumed to be coarsely synchronized, demodulation begins,

and the tracking system is activated. The threshold-detector output continues to be monitored

so that any subsequent loss of synchronization activates the serial search.

Non-coherent

correlator

Threshold

Detector

Spreading

sequence

Voltage

controlled

Search Control

18

There may be several cells that potentially provide a valid acquisition. However, if none of

these cells corresponds to perfect synchronization, the detected energy is reduced below its

potential peak value. The step size is the separation between cells. If the step size is one-half

of a chip, then one of the cells corresponds to an alignment within one-fourth of a chip. On

the average, the

misalignment of this cell is one-eighth of a chip, which may cause a negligible degradation.

As the step size decreases, both the average detected energy during acquisition and the

number of cells to be searched increase.

The dwell time is the amount of time required for testing a cell and is approximately equal to

the length of the integration interval in the non-coherent correlator. An acquisition system is

called a single-dwell system if a single test determines whether a cell is accepted as the

correct one. If verification testing occurs before acceptance, the system is called a multiple-

dwell system. The dwell times either are fixed or are variable but bounded by some

maximum value. The dwell time for the initial test of a cell is usually designed to be much

shorter than the dwell times for the verification tests. This approach expedites the acquisition

by quickly eliminating the bulk of the incorrect cells.

In any serial-search system, the dwell time allotted to a test is limited by the Doppler shift,

which causes the received and local chip rates to differ. As a result, an initial close alignment

of the two sequences may disappear by the end of the test.

A multiple-dwell system may use a consecutive-count strategy, in which a failed test causes a

cell to be immediately rejected, or an up-down strategy, in which a failed test causes a

repetition of a previous test. Figures 3.4 and 3.5 depict the flow graphs of the consecutive-

count and up-down strategies, respectively, that require D tests to be passed before

acquisition is declared. If the threshold is not exceeded during test 1, the cell fails the test,

and the next cell is tested. If it is exceeded, the cell passes the test, the search is stopped, and

the system enters the verification mode.

19

Figure 3.4: Flow graph of multiple-dwell system with consecutive-count strategy.

The same cell is tested again, but the dwell time and the threshold may be changed. Once all

the verification tests have been passed, the code tracking is activated, and the system enters

the lock mode. In the lock mode, the lock detector continually verifies that code

synchronization is maintained. If the lock detector decides that synchronization has been lost,

reacquisition begins in the search mode.

Figure 3.5: Flow graph of multiple-dwell system with up-down strategy.

The order in which the cells are tested is determined by the general search strategy. Figure

3.6(a) depicts a uniform search over the cells of the timing uncertainty. The broken lines

Test 1

Reject

Test 2 Test D

Lock Mode

Pass Verification Mode

Pass

Pass Fail

Fail Fail Start

Test 1

Reject

Test 2 Test D

Lock Mode

Pass Pass

Fail

Verification Mode

Fail Fail Start

20

represent the discontinuous transitions of the search from the one part of the timing

uncertainty to another. The broken-center Z search, illustrated in Figure 3.6(b), is appropriate

when a priori information makes part of the timing uncertainty more likely to contain the

correct cell than the rest of the region. A priori information may be derived from the

detection of a short preamble.

Figure 3.6: Trajectories of search positions: (a) uniform search and (b) broken-center Z

search.

If the sequences are synchronized with the time of day, then the receiver’s estimate of the

transmitter range combined with the time of day provide the a priori information. 3.2 Code Tracking Coherent code-tracking loops operate at baseband following the coherent removal of the

carrier of the received signal. An impediment to their use is that the input SNR is usually too

low for carrier synchronization prior to code synchronization and the subsequent despreading

of the received signal. Furthermore, coherent loops cannot easily accommodate the effects of

data modulation. Non-coherent loops operate directly on the received signals and are

unaffected by the data modulation.

Uncertainty Uncertainty

Cell Time Time

Cell 1 2 . . . . . . . . . . . . . . . 1 2 . . . . . . . . . . . . . . .

21

Figure 3.7: Delay-locked loop.

To motivate the design of the non-coherent loop, one may adapt the statistic in appendix B. If

the maximum-likelihood estimate is assumed to be within the interior of its timing

uncertainty region and �(�, ��) is a differentiable function of �,then the estimate �̂ that

maximizes �(�, ��) may be found by setting

����, ���

�� = 0����

= �̂(3.3)

A major problem with this approach is that �(�, ��) given by statistics [1] is not

differentiable if the chip waveform is rectangular. This problem is circumvented by using a

difference equation as an approximation of the derivative. Thus, for a positive ���, we set

��(�, ��)

�� ≈���+ ���, ���− �(�− ���, ��)

2���(3.4)

This equation implies that the solution of (3-3) may be approximately obtained by a device

that finds the �̂ such that

���̂+ ���, ���− ���̂− ���, ���= 0(3.5)

Bandpass Square

Spreading

Sequence

Voltage

controlled Loop filter

Bandpass

filter

Square

Law

∑

Reference/Precise

Advanced Delayed

Error

Received

22

To derive an alternative to this equation, we assume that no noise is present, �� = 0 and that

the correct timing offset of the received signal is �= 0 doing necessary substitution and

using trigonometry, we obtain

���̂, 0�=�2 �� �������− �̂���

�

��

�

(3.6)

If �(�) is modeled as the spreading waveform for a random binary sequence and the interval

[0,T] includes many chips, then the integral is reasonably approximated by its expected value,

which is proportional to the autocorrelation

�����= ⋀ ����

�(3.7)

where the triangular function is defined by

⋀���= �1 − |�|,|�| ≤ 10,|�| > 1(3.8)

Substituting this result into (3-5), we find that the maximum-likelihood estimate is

approximately obtained by a device that finds the�̂ such that

�����̂+ ����− ��

���̂− ����= 0(3.9)

The non-coherent delay-locked loop [9], which is diagrammed in Figure 3.7, implements an

approximate computation of the difference on the left-hand side of (3.9) and then continually

adjusts so that this difference remains near zero. The estimate is used to produce the

synchronized local spreading sequence that is used for despreading the received direct-

sequence signal. The code generator produces three sequences, one of which is the reference

sequence used for acquisition and demodulation. The other two sequences are advanced and

delayed, respectively, relative to the reference sequence. The product is usually equal to the

acquisition step size, usually but other values are plausible. The advanced and delayed

sequences are multiplied by the received direct-sequence signal in separate branches. For the

received direct-sequence signal (3.2), the signal portion of the upperbranch mixer output is

������= ������������+ ��� − ����cos�2��� + �� �3.10�

Where � = √2� and ��� is the delay of the reference sequence relative to the received

sequence. Although � is a function of time because of the loop dynamics, the time

dependence is suppressed for notational convenience. Since each bandpass filter has a

bandwidth on the order of 1 ��⁄ where �� is the duration of each symbol, is not significantly

23

distorted by the filtering. Nearly all spectral components except the slowly varying expected

value of �����(�+ ��� − ���) are blocked by the upper-branch bandpass filter. Since this

expected value is the autocorrelation of the spreading sequence, the filter output is

������≈ ����������� − ����cos�2��� + ��(3.11)

Any double-frequency component produced by the square-law device is ultimately

suppressed by the loop filter and is therefore ignored. Since �����= 1, the data modulation is

removed and the upper branch output is

������≈��

2 ������� − ����(3.12)

Similarly, the output of the lower branch is

������≈��

2 ����− ��� − ����(3.13)

The difference between the output of the two branches is the error signal:

�����≈��

2 �������� − ����− ��

��− ��� − �����(3.14�)

Since is an even function, the error signal is proportional to the left-handside of (3.9).

When necessary substitutions are made [1] we find the following equation.

�����≈��

2 ���, ��(3.14�)

Where �(�, �) is the discriminator characteristic or S-curve of the tracking loop

For 0 ≤ � ≤ 1 2⁄ ,

���, ��= �

4��1 − ��,0 ≤ �≤ �4��1 − ��,� ≤ �≤ 1 − �1 + ��− ����− � − 2�,1 − � ≤ � ≤ 1 + �0,1 + � ≤ �

(3.15)

For 1 2⁄ ≤ � ≤ 1,

���, ��= �

4��1 − ��,0 ≤ � ≤ 1 − �1 + ��− ����− � + 2�,1 − � ≤ � ≤ �(3.16)1 + ��− ����− � − 2�,� ≤ �≤ 1 + �

01 + � ≤ �

In both cases, ��− �, ��= − ���, ��

24

Figure 3.8 illustrates the discriminator characteristic for � = 1 2⁄ .The filtered error signal is

applied to the voltage-controlled clock. Changes in the clock frequency cause the reference

sequence to converge toward alignment with the received spreading sequence. When

0 < ����< 1 + �, the reference sequence is delayed relative to the received sequence. As

shown in Figure 3.8, �(�, �) is positive, so the clock rate is increased, and �(�) decreases.

The figure indicates that ��(�) → 0 as �(�) → 0 similarly, when �(�) < 0, we find that

�� → 0 as �(�) → 0.

Thus, the delay-locked loop tracks the received code timing once the acquisition system has

finished the coarse alignment. The discriminator characteristic of code-tracking loops differs

from that of phase-locked loops in that it is nonzero only within a finite range of �.

Figure 3.8: Discriminator characteristic of delay-locked loop for � = 1 2⁄

Outside that range, code tracking cannot be sustained, the synchronization system loses lock,

and a reacquisition search is initiated by the lock detector. Tracking resumes once the

acquisition system reduces to within the range for which the discriminator characteristic is

nonzero.

When short spreading sequences are used in a synchronous direct-sequence network, the

reduced randomness in the multiple-access interference may cause increased tracking jitter or

even an offset in the discriminator characteristic [10]. For orthogonal sequences, the

interference is zero when synchronization exists, but becomes large when there is a code-

phase error in the local spreading sequence. In the presence of a tracking error, the delay-

locked- loop arm with the larger offset relative to the correct code phase receives relatively

S (ε,d)

1

-1

1.5 -1.5 0.5 -0.5

ε

25

more noise power than the other arm. This disparity reduces the slope of the discriminator

characteristic and, hence, degrades the tracking performance. Moreover, because of the non-

symmetric character of the cross-correlations among the spreading sequences, the

discriminator characteristic may be biased in one direction, which will cause a tracking

offset. The non-coherent tau-dither loop, which is depicted in Figure 4.17, is a lower

complexity alternative to the non-coherent delay-locked loop. The dither generator produces

the dither signal a square wave that alternates between +1 and –1. This signal controls a

switch that alternately passes an advanced or delayed version of the spreading sequence. In

the absence of noise, the output of the switch can be represented by

�� = �1 + ����

2 ����+ ��� − ����+ �1 − ����

2 ����− ��� − �����3.17�

where the two factors within brackets are orthogonal functions of time and alternate between

+1 and 0. Only one of the factors is nonzero at any instant. The received direct-sequence

signal is multiplied by s��t�, filtered, and then applied to a square-law device. If the bandpass

filter has a sufficiently narrow bandwidth, then a derivation similar to that of (3-12) indicates

that the device output is

�� ≈ ��

��������

����

����� − ����+ ��

��������

����

��− ��� − ����(3.18)

Figure 3.9: Tau-dither loop.

Spreading

sequence

Switch

Bandpass

filter

Square-law

device

Dither

Generator

Loop Filter Voltage

Controlled

Delayed Advanced

Input

Reference

26

Since �����1 + �����= 1 + ���� and �����1 − �����= − �1 + �����, the input to the loop

filter is

�����

≈��

2 �1 + ����

2 �������� − ����−

��

2 �1 − ����

2 �����− ��� − ����(3.19)

which is a rectangular wave if the time variation of is ignored. Since the loop filter has a

narrow bandwidth relative to that of ����, its output is approximately the direct-current

component of �����, which is the average value of �����. Averaging the two terms of (3-19),

we obtain the filter output:

�����≈��

4���

����� − ����− ������� − �����(3.20)

The substitution of (4-99) yields the input clock signal input:

�����≈��

4 ���, ��(3.21)

where the discriminator characteristic is given by (3-15) to (3-16). Thus, the tau-dither loop

can track the code timing in a manner similar to that of the delay-locked loop. A detailed

analysis indicates that the tau-dither loop provides less accurate code tracking [6]. However,

the tau-dither loop requires less hardware than the delay-locked loop and avoids the need to

balance the

gains and delays in the two branches of the delay-locked loop.

In the presence of frequency-selective fading, the discriminator characteristics of tracking

loops are severely distorted. Much better performance is potentially available from a non-

coherent tracking loop with diversity and multipath-interference cancellation [11], but a large

increase in implementation complexity is required.

27

CHAPTER 4

DESIGN OF CODE ACQUSITION AND TRACKING MECHANISM

4.1 Design

In the design of an acquisition mechanism, the following was put into consideration. Long

PN codes this ensures a good bit error rate performance and increases the data throughput

Large processing gain this reduces narrow band interference The following are some of the

design assumptions that were made during the design of this mechanism The additive white

Gaussian noise was band limited this ensured that it was possible to eliminate the noise from

the system. The filter used was ideal with a linear phase.

Figure 4.1 Generic acquisition block diagram

The proposed acquisition process was as shown in figure 4.1. The received signal was

multiplied by a locally generated code and after processing N chips, where N was the length

of the code, despreading took place. The value obtained from the despreader was the

compared to a threshold to establish weather or not lock had been established. A non coherent

loop is one in which the carrier frequency is not known exactly (due to Doppler effects, for

example), nor is the phase. In most instances, since the carrier frequency and phase are not

known exactly a priori, a non-coherent code loop is used to track the received PN sequence.

BPF

Reference

Spreading

Energy

Detector

Decision

Device

Control

Logic

Received

Hypothesized phase

28

In this design full-time early late tracking loop, often referred to as a delay-locked loop

(DLL), is implemented

Figure 4.2 Delay locked loop for tracking of direct sequence signals

Received Signal

To generate the received signal to be used in my design a random data generator was used

and the probability of generating ones and zeros was equal. The next stage was to encode the

random signal using a differential encoder

Differential Encoder

The polarity of data is presented in the phase change between the consecutive bits. The

differential decoder can correctly recover the original data as long as the phase difference

between successive symbols is maintained after the transmission. The absolute phase of each

symbol is not required for correct decoding

BPSK Modulator

The BPSK was a fully digital modulator which translates the spread signal into a digitized

inter-mediate frequency (IF) modulated signal by multiplying it with a digitized sine or

cosine wave from a numerically controlled oscillator (NCO).

Bandpass Square

Spreading

Sequence

Voltage

controlled Loop filter

Bandpass

filter

Square

Law

∑

Advanced

Signal � ��+

+ ��

Delayed � ��− ���

+ ��

Error

Received

Reference/Precise

���+ ��

29

After modulation, additive white Gaussian noise (AWGN) was added to the signal which

formed the input to the matched filter.

Matched filter

A matched filter is chosen for the despreading as it has a short acquisition time compared to

the active correlator.

Threshold detector

The threshold detector was used to determine weather the PN sequence was synchronized or

not this was determined by the autocorrelation function. The threshold value was set to an

average value of 6 to ensure that peaks whose heights have been reduced by Gaussian noise is

taken care of.

I have also simulated an environment where three users are present to further show how

spread spectrum communication is applied in a multiuser environment.

Values are initially assigned to the shift register these values are later used to generate the

three chipping sequences cseq1, cseq2 and cseq3 the program are as shown in appendix.

Generation of narrowband data signal

To generate user’s data we generate 10,000 polar data of 1’s and -1’s which are equi-probable

and my sampling rate equals to the chip rate with rectangular pulse shaping, each 1 will be

represented by 31 1’s and each -1 will be represented by 31 -1’s this is plotted in matlab

using the command psd function which shows only the positive part of the plot.

Spreading the narrowband Signal

Now the data sequence that has been generated is now spread by multiplying it with the first

chipping sequence. The psd function is used to display the graph which this time is a

wideband signal as it is spread by the chipping sequence.

This actually first makes the row to column rule satisfied for matrix multiplication that is first

used to spread the signal by spreading the original 10,000 user bits by first multiplying x-

numbered (31 used primarily) values of 1. This is actually the same matrix only repeating it x

times. This later reshaped to only one row of all the values that I got from initial

multiplication. Later this is multiplied and ready chipping sequence cseq and finally spread

according to the x length of PN-sequence. RESHAPE(X,M,N) function returns the M-by-N

matrix whose elements are taken column wise from X, an error will results if X does not

contain M*N elements. RESHAPE(X,…., [],….) calculates the length of the dimensions

represented by [], such that the product of the dimensions equals

PROD(SIZE(X)).PROD(SIZE(X)) must be evenly divisible by the product of the known

dimensions, only one occurrence of [] can be used. The essence behind the interference

30

rejection capability of a spread spectrum system is that the useful signal (data) gets multiplied

twice by the PN sequence, but the interference gets multiplied only once. Multiplication of

the received signal with the PN sequence of the receiver gives a selective de-spread of the

data signal with smaller bandwidth and high power density the interference signal is

uncorrelated with the PN sequence and is spread. Wideband noise can be due to multiple

spread spectrum users, multiple access mechanism and Gaussian Noise.

Wideband Interference

The other wideband signals are also generated using the other chipping sequences I used this

as the wideband interference to the first data sequence. At the receiver end the chip sequence

of user 1 will retrieve the original data and ignore the other two wideband signals as the chip

sequence doesn’t correlate with them.

Despreading Process

At the receiver the opposite of spreading was done here I tried to show that if the transmitted

data is multiplied with the same chipping of user 1 data then we get back to the original

signal sent. Reshaping is first done to the chipping sequence and it is multiplied by the

received signal then we turn the x0000 bit long received user into a 10000 bit long user data

size becomes same as the original data. The chipping sequences are being multiplied with

each other resulting into an autocorrelation value of 1and thus wideband signal become

narrow band. The interference signal due the other two wideband signals remain spread as it

is uncorrelated with user 1 PN sequence. All these are implemented in a MATLAB

environment using a code which is attached to this document.

31

4.2 Results

0 5 10 15 20-0.5

0

0.5

1

1.5

Ampl

itude

original data signal

0 5 10 15 20-2

-1

0

1

2

Ampl

itude

Spread Spectrum Signal

0 5 10 15 20-2

-1

0

1

2

Ampl

itude

BPSK modulated signal

0 20 40 60 80-5

0

5

Ampl

itude

BPSK modulated signal with noise

0 20 40 60 80

-10

0

10

Time

Ampl

itude

Matched filter output signal

0 20 40 60 80

-10

0

10

Time

Ampl

itude

power detector output signal

32

Results

0 20 40 60 80-20

0

20

Frequency

Ampl

itude

output signal at threshold detector

0 5 10 15 20-0.5

0

0.5

1

1.5

Ampl

itude

output signal at differential demodulator

0 5 10 15 20-0.5

0

0.5

1

1.5

Time

Ampl

itude

Original data signal

0 5 10 15 20-0.5

0

0.5

1

1.5

Time

Ampl

itudeoutput signal at differential demodulator

33

Results

0 0.2 0.4 0.6 0.8 1-40

-20

0

20

FrequencyPowe

r Spe

ctrum

Mag

nitud

e (d

B)

Narrow band signal for user2

0 0.2 0.4 0.6 0.8 1-40

-20

0

20

FrequencyPowe

r Spe

ctrum

Mag

nitud

e (d

B)

Narrow band signal for user3

0 0.2 0.4 0.6 0.8 1-40

-20

0

20

FrequencyPowe

r Spe

ctrum

Mag

nitud

e (d

B)

Narrow band signal for user 1

0 0.2 0.4 0.6 0.8 1-20

-10

0

10

FrequencyPowe

r Spe

ctrum

Mag

nitud

e (d

B)Wide band signal for user 1 the spread signal

0 0.2 0.4 0.6 0.8 1-20

-10

0

10

FrequencyPowe

r Spe

ctrum

Mag

nitud

e (d

B)

Wide band signal for user 2 the spread signal

0 0.2 0.4 0.6 0.8 1-20

-10

0

10

FrequencyPowe

r Spe

ctrum

Mag

nitud

e (d

B)

Wide band signal for user 3 the spread signal

34

Results

0 0.2 0.4 0.6 0.8 1-20

-10

0

10

FrequencyPowe

r Spe

ctru

m M

agni

tude

(dB) The wideband inteference with the users desired data

0 0.2 0.4 0.6 0.8 1-40

-20

0

20

FrequencyPowe

r Spe

ctru

m M

agni

tude

(dB) Narrow band signal for user 1 after despreading

0 0.2 0.4 0.6 0.8 1-10

0

10

FrequencyPowe

r Spe

ctru

m M

agni

tude

(dB) interference remain wideband after despreading

0 0.2 0.4 0.6 0.8 1-40

-20

0

20

FrequencyPowe

r Spe

ctru

m M

agni

tude

(dB) Uncorrelated data 2 signal with user 1 PN sequence

0 0.2 0.4 0.6 0.8 1-20

-10

0

10

FrequencyPowe

r Spe

ctru

m M

agni

tude

(dB) Uncorrelated data 3 signal with user 1 PN sequence

0 0.2 0.4 0.6 0.8 1-40

-20

0

20

FrequencyPowe

r Spe

ctru

m M

agni

tude

(dB) Narrow band signal for user 2 after despreading

35

4.3 Analysis of Results

The acquisition results achieved through Matlab simulation showed how coarse

synchronization can be achieved using the designed circuit. The matched filter output was the

complete correlation function, with peaks depicting that the PN code in the received signal

and that in the receiver were in synchronism which enabled timing information to be acquired

for initial synchronization

The length of the code used in the design was 11 and since the matched filter was advanced at

a half chip rate, the peaks occur periodically at twice the length of the PN code observation

can be made from the matched filter output that the first correct detection occurs at twice the

length of the code.

It was observed that the acquisition time is dependent on the length of the PN sequence used

as longer PN sequences gave longer time to achieve initial synchronization.

In a multiuser environment the receiver will only correctly correlate the chipping sequence

that is similar to its own; this will ensure that only the desired signal is received. It is clear

from the graphs that the detection scheme for DSSS systems at the receiver end is based on

the mechanism of separating narrowband signals from a wideband pool. Therefore the more

the difference in bandwidth between our data and the spread signal, the easier it is to detect.

An initial seed of greater length gives us a longer usable chipping sequence. Every bit of the

user is multiplied with the entire chipping sequence; as a result, we get spread signal of

higher bandwidth if the chipping sequence is longer. Thus, for a longer seed, the difference in

bandwidth between the narrowband and wideband is greater, making detection easier and

more accurate.

4.4 Future Work

I recommend that a similar project should be undertaken with emphasis on how various types

of PN sequences can be used to achieve direct sequence spread spectrum communication and

their response in the presence of noise. I want to suggest that a further study may be done in

detail which PN codes best suit a multiuser environment

36

4.5 Conclusion

This report has demonstrated the principles of direct sequence spread spectrum signals it has

shown how acquisition is achieved and how PN sequences are unique and will only correlate

with the ones that are matched to them. A thorough discussion has been given on acquisition

and tracking and the various methods used to achieve the same have been expounded on. A

multiuser environment has been simulated and the results show how various codes will only

synchronize with the ones that match.

It can also be shown that the noise or interference signal will remain wide band after

multiplication by the PN sequence at the receiver. Showing how interference is rejected in

spread spectrum communication.

37

RFERENCES.

[1] Don Torrieri Principles of spread spectrum communication systems Springer 2005

[2] S.Haykin communication systems John Wiley and sons, third edition 1994

[3] R.L Peterson, R.E Ziemer and D.E Borth, introduction to spread spectrum

communications, Prentice hall Inc, 1995.

[4] J.G. Proakis, Digital Communications, New York: Mc Graw Hill, 1995

[5] Bernard Sklar Digital Communication Fundamentals and Applications Prentice Hall

[6] R. B. Ward and K. P. Y. Yiu, “Acquisition of Pseudonoise Signals by Recursion-Aided

Sequential Estimation,” IEEE Trans. Commun., vol. 25, pp. 784–794, August 1977.

[7] W. R. Braun, “PN Acquisition and Tracking Performance in DS/CDMA Systems with

Symbol-Length Spreading Sequence,” IEEE Trans. Commun., vol. 45, pp. 1595–1601,

December 1997.

[8] R. A. Dillard and G.M. Dillard, Detectability of Spread Spectrum Signals, Norwood, MA:

Artech House, 1989.

[9] TIA/EIA Interim Standard-95, “Mobile Station—Base Station Compatibility Standard

for Dual-Mode Wideband Spread Spectrum Cellular System,” July 1993.

[10] J. Geier, Wireless LANs, 2nd edition, Indianapolis, IN: Sams Publishing, 2001.

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APPENDIX A %this program first generates the spread signal; %the noise is added to the spread spectrum signal; %the signal then forms the input to the matched filter and acquisition is carried out. clear;%clear the memory space. Iter_No=2; %repeat the simulation data_No=1000; for EBNO_ITER=1:1, EbNo_dB=8; EbNo=10^(EbNo_dB/10); barker_11=[1 1 1 0 0 0 1 0 0 1 0];%PN code SampleNoPerChip=2;%2 samples per chip chip=barker_11*2-1;%PN code in polar format chip_rate=length(chip);%PN code length t=(0:1:200); Noi_var=SampleNoPerChip/2*chip_rate/EbNo;%calculate channel noise variance for Iter=1:2, %begin simulation %ORIGINAL DATA GENERATOR rand('seed',sum(100*clock));%set the seed of uniform generator to different value each time data_in=rand(1,data_No+2)>.5;%1 and 0 are generated with the same probabilty 0.5 figure(1); subplot(321); plot(t(1:20),data_in(1:20)); axis([0,20,-0.5,1.5]); ylabel('Amplitude'); title ('original data signal'); grid on; %INPUT PROCESSOR (INPSR) inpsr_out=data_in; %DIFFERENTIAL ENCODER(DENCO) N=length(inpsr_out);%the first axis is xor with 1 denco=zeros(1,N); denco(1)=xor(inpsr_out(1),1);%'xor' operation for i=2:N, denco(i)=xor(inpsr_out(i),denco(i-1)); end denco_out=[1 denco];%the 1 is also transmitted denco_out=2*denco_out-1;%change to polar format clear denco inpsr_out; %PN SPREAD CODER N=length(denco_out); pncod_out=zeros(1,N*chip_rate); for i=1:N, pncod_out(chip_rate*(i-1)+1:chip_rate*i)=denco_out(i)*chip; end subplot(322); plot(t(1:20),pncod_out(1:20)); axis([0,20,-2,2]); ylabel('Amplitude'); title('Spread Spectrum Signal');

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grid on; clear denco-out; %BPSK MODULATOR with samplimg process (BPSPL) %The signal is generated in complex format N=fix(length(pncod_out)*SampleNoPerChip); bpspl_out=exp(j*(pncod_out(fix((0:N-1)/SampleNoPerChip)+1)<0)*pi); subplot(323); plot(t(1:20),bpspl_out(1:20)); axis([0,20,-2,2]); ylabel('Amplitude'); title('BPSK modulated signal'); grid on; clear pncod_out; %CHANNEL NOISE ADDER, AGC (CNAAA) %The noise also is in complex form %variance calculated from Eb/No N=length(bpspl_out); cnaaa_out=bpspl_out+(randn(1,N))+j*sqrt(Noi_var); subplot(324); plot(t(1:80),cnaaa_out(1:80)); ylabel('Amplitude'); title('BPSK modulated signal with noise'); grid on; %MATCHED FILTER(MAFLT) match_in=cnaaa_out; BitNo_Matchin=3; Quanlevel_Matchin=2^BitNo_Matchin; match_in=round(match_in*Quanlevel_Matchin)/Quanlevel_Matchin; BitNo_Matchout=10; Quanlevel_Matchout=2^BitNo_Matchout; tap=fliplr(chip);%reverse the chip N=length(match_in); fep_out=zeros(1,N);%preallocate the memory space fep_out(1)=match_in(1); fep_out(2:N)=(match_in(2:N)+match_in(1:(N-1)))/2; match=zeros(1,N); for i=1:N, k=fix((i-1)/2)+1; if k>chip_rate k=chip_rate; end match(i)=sum(tap(1:k).*fep_out(i:-2:(i-2*k+2))); end match_out=fix(match*Quanlevel_Matchout)/Quanlevel_Matchout; subplot(325); plot(t(1:80),match_out(1:80)); axis([0,80,-15,15]); xlabel('Time'); ylabel('Amplitude'); title('Matched filter output signal');

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grid on; clear match match_in fep_out cnaa_out dncov_out bpsl_out; %POWER DETECTOR BitNo_Viewport=8; Quanlevel_VP=2^BitNo_Viewport; BitNo_Magnitude=10; Quanlevel_Magnitude=2^BitNo_Magnitude; VP_CTRL=0; maflt_8=fix(match_out/2^VP_CTRL)*Quanlevel_VP/Quanlevel_VP; powde=real(match_out); powde_10=fix(powde*Quanlevel_Magnitude)/Quanlevel_Magnitude; subplot(326); plot(t(1:80),powde_10(1:80)); axis([0,80,-15,15]); xlabel('Time'); ylabel('Amplitude'); title('power detector output signal'); grid on; clear match_out; %THRESHOLD DETECTOR THRESHOLD=5;%define the threshold N=round(length(powde_10)/2/chip_rate)-2; thrshd_out=zeros(1,N);%preallocate the memory space flywheel=zeros(1,N); flywheel(1)=22;%first one is correctly detected Ha_win=1; for i=2:N, flywheel(i)=flywheel(i-1)+2*chip_rate; A=powde_10((flywheel(i)-Ha_win):(flywheel(i)+Ha_win)); max_A=max(A); B=find(A==max_A); if max_A>=THRESHOLD, flywheel(i)=flywheel(i)+B(1)-2; end end thrshd_out=maflt_8(flywheel); figure(2); subplot(321); plot(t(1:80),thrshd_out(1:80)); ylabel('Amplitude'); title('output signal at threshold detector'); grid on; clear powde_10 maflt_8; %DIFFERENTIAL DEMODULATOR (DDEMO) N=length(thrshd_out); test=zeros(1,N-1);%preallocate memory space test=thrshd_out(1:N-1).*conj(thrshd_out(2:N));%calculate the dot product for decision cicuirt data_out=test<0;%differential decoder's decision end end

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subplot(322); plot(t(1:20),data_out(1:20)); axis([0,20,-0.5,1.5]); ylabel('Amplitude'); title('output signal at differential demodulator'); grid on; %COMPARISON BETWEEN INPUT AND OUTPUT SIGNALS. subplot(323); plot(t(1:20),data_in(1:20)); axis([0,20,-0.5,1.5]); xlabel('Time'); ylabel('Amplitude'); title('Original data signal'); grid on; subplot(324); plot(t(1:20),data_out(1:20)); axis([0,20,-0.5,1.5]); xlabel('Time'); ylabel('Amplitude'); title('output signal at differential demodulator'); grid on; %PN SEQUENCE GENERATOR FOR USER 1 sreg=[1,0,1,0,1]; for i=1:31 n=sreg(1)+sreg(4); if mod(n,2)==1 s=1; else s=0; end if sreg(1)==1 cseq1(i)=1; else cseq1(i)=-1; end for k=1:4 sreg(k)=sreg(k+1); end sreg(5)=s; end %PN SEQUENCE GENEROTOR FOR USER 2 for i=1:31 n=sreg(1)+sreg(2)+sreg(3)+sreg(4); if mod(n,2)==1 s=1; else s=0; end if sreg(1)==1

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cseq2(i)=1; else cseq2(i)=-1; end for k=1:4 sreg(k)=sreg(k+1); end sreg(5)=s; end %PN SEQUENCE GENERATOR FOR USER 3 for i=1:31 n=sreg(1)+sreg(2)+sreg(4)+sreg(5); if mod(n,2)==1 s=1; else s=0; end if sreg(1)==1 cseq3(i)=1; else cseq3(i)=-1; end for k=1:4 sreg(k)=sreg(k+1); end sreg(5)=s; end %CODE FOR GENERATING USER 2 DATA for i=1:10000 ot=randint; if ot==0 data2(i)=-1; else data2(i)=1; end end for i=1:31 c(i)=1; end arr=data2'*c; arr=arr'; arr2=reshape(arr,1,[]); figure(1); subplot(322); psd(arr2); title('Narrow band signal for user2'); %CODE FOR GENERATING USER 3 DATA for i=1:10000 ot=randint; if ot==0

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data3(i)=-1; else data3(i)=1; end end for i=1:3 c(i)=1; end arr=data3'*c; arr=arr'; arr3=reshape(arr,1,[]); subplot(323); psd(arr3); title('Narrow band signal for user3'); %CODE FOR GENERATING USER 1 DATA for i=1:10000 ot=randint; if ot==0 data1(i)=-1; else data1(i)=1; end end for i=1:31 c(i)=1; end arr=data1'*c; arr=arr'; arr1=reshape(arr,1,[]); subplot(321); psd(arr1); title('Narrow band signal for user 1'); %SPREADING USER 1 NARROWBAND DATA j=1; for i=1:310000 arr1(i)=arr1(i)*cseq1(j); j=j+1; if (j==32) j=1; end end subplot(324); psd(arr1); title('Wide band signal for user 1 the spread signal'); %SPREADING OF USER 2 NARROWBAND DATA j=1; for i=1:310000 arr2(i)=arr2(i)*cseq2(j); j=j+1;

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if (j==32) j=1; end end subplot(325); psd(arr2); title('Wide band signal for user 2 the spread signal'); %SPREADING OF USER 3 NARROWBAND DATA j=1; for i=1:310000 arr3(i)=arr3(i)*cseq3(j); j=j+1; if (j==32) j=1; end end subplot(326); psd(arr3); title('Wide band signal for user 3 the spread signal'); %INTERFERENCE CODE arr=arr2 + arr3; figure(2); subplot(321); psd(arr1); hold on; [p,f]=psd(arr); plot(f,10*log10(p),'g'); title('The wideband inteference with the users desired data'); %DESPREAD SIGNAL WITH USER 1 DATA for i=1:10000 d(i)=1; end b=d'*cseq1; b=b'; cs=reshape(b,1,[]); ar1=arr1.*cs; subplot(322); psd(ar1); title('Narrow band signal for user 1 after despreading'); %DESPREAD OF INTERFERENCE AT THE RECEIVER ar=arr.*cs; subplot(323); psd(ar); title('interference remain wideband after despreading'); grid on; ar2=arr2.*cs; subplot(324); psd(ar2); title('Uncorrelated data 2 signal with user 1 PN sequence')

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ar3=arr3.*cs; subplot(325); psd(ar3); title('Uncorrelated data 3 signal with user 1 PN sequence'); %DESPREAD OF USER 2 DATA for i=1:10000 d(i)=1; end b=d'*cseq2; b=b'; cs=reshape(b,1,[]); ar2=arr2.*cs; subplot(326); psd(ar2); title('Narrow band signal for user 2 after despreading');

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