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Chapter 1: INTRODUCTION

1. Evolution of Wireless Technologies

At the beginning of 2001, more than one out of 10 people in the world had a mobile

telephone. The end-user equipment size, weight, and costs have dropped over 20% per year over

the past 15 years. This incredible growth in the industry is due to the development of wireless

communication technologies.

The first generation wireless communication system was the analog advanced mobile

phone system (AMPS), developed primarily by AT & T. This system used a 30 kHz channelspacing while narrowband AMPS (N-AMPS), which was developed by Motorola, worked within a

10 kHz channel spacing thus increasing the AMPS capacity. The frequency division multiple

access (FDMA) systems divide a wide frequency band into smaller frequency bands that are

assigned to specific users allowing different users to communicate at the same time.

These first generation systems had capacity limitations since each spectral channel could be

allocated to only one user. Because of the capacity limitations of the FDMA based analog cellular

systems, the first digital cellular systems were based on time division multiple access (TDMA).

TDMA systems divide their signals into shorter time slots thus allowing several mobile telephones

to communicate on a single radio carrier frequency. The digital AMPS (D-AMPS) was developed

in the late 1980s which was followed by the first Groupe Special Mobile (GSM) deployments.

Today, it is estimated that there are over 800 million GSM subscribers across the 190 countries of

the world. These TDMA systems come under the second generation cellular systems. Figure shows

the evolution of wireless technologies in various stages.

Spread spectrum technology, which was initially used in military applications, is another

approach to achieve multiple access. In it, a narrowband signal is spread over a wide frequency

band for transmission using code division multiple access (CDMA); it is also called spread

spectrum multiple access (SSMA).

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Figure1.1 Evolution of Wireless Technologies

CDMA was pioneered and commercially developed by QUALCOMM in 1995. In it,

multiple users can share the radio channel at the same time. The frequency reuse limitations in

FDMA and TDMA are less in CDMA and so CDMA is an attractive alternative to GSM.

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Figure 1.2 Various Multiple Access Technologies

The international telecommunications union (ITU) undertook the international mobile

telephony-2000 (IMT-2000) project and developed the third generation systems. The primary third

generation technologies which were approved by ITU in 1998 were :

Wideband CDMA (W-CDMA), developed by the European telecommunication standardization

institute (ETSI).

Cdma2000, developed by the telecommunications industry association (TIA).

EDGE (Enhanced Data Rates for GSM Evolution) which was co-sponsored by ETSI and the

TIA.

As the wireless personal communications field has grown over the last few years, the

method of communication known as spread spectrum has gained a great deal of prominence.

Spread spectrum involves spreading the desired signal over a bandwidth much larger than the

minimum bandwidth necessary to send the signal. It was originally developed by the military as a

method of communications that is less sensitive to intentional interference or jamming by third

parties, but has become very popular in the realm of personal communications recently. Spread

spectrum methods can be combined with Code Division Multiple Access (CDMA) methods to

create multi-user communications systems with very good interference performance.

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Chapter 2: Spread Spectrum Communication

Systems

2.1 Introduction

Spread spectrum signals for digital communications were originally developed and used for

military communications either (l) to provide resistance to hostile jamming, (2) to hide the signal

by transmitting it at low power and, thus, making it difficult for an unintended listener to detect its

presence in noise, or (3) to make it possible for multiple users to communicate through the same

channel. Today, however, spread spectrum signals are being used to provide reliable

communications in a variety of commercial applications, including mobile vehicular

communications and interoffice wireless communications.

As stated before, spread spectrum systems afford protection against jamming (intentional

interference) and interference from other users in the same band as well as noise by spreading

the signal to be transmitted and performing the reverse de-spread operation on the received

signal at the receiver. This de-spreading operation in turn spreads those signals which are not

properly spread when transmitted, decreasing the effect that spurious signals will have on the

desired signal. Spread Spectrum systems can be thought of as having two general properties: first,

they spread the desired signal over a bandwidth much larger than the minimum bandwidth needed

to send the signal, and secondly, this spreading is carried out using a pseudorandom noise (PN)

sequence. In a general sense, we will see that the increase in bandwidth above the minimum

bandwidth in a spread spectrum system can be thought of as applying gain to the desired signal

with respect to the undesirable signals. We can now define the processing gain GPas

inf

RF

P

o

BWG

BW=

Where BWRF is the bandwidth that the signal has been increased, and BWinfo is the minimum

bandwidth necessary to transmit the information or data signal. Processing gain can be thought of

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as the improvement over conventional communication schemes due to the spreading done on the

signal. Often, a better measure of this gain is given by thejamming margin,

m i n( ) ( )J P M d B G d B=

Which indicates the amount of interference protection offered before the signal is corrupted.

The spreading function is achieved through the use of a pseudorandom noise sequence (PN

sequence). The data signal is combined with the PN sequence such that each data bit is encoded

with several if not all the bits in the PN sequence. In order to achieve the same data rate as was

desired before spreading, the new data must be sent at a rate equal to the original rate multiplied by

the number of PN sequence bits used to encode each bit of data. This increase in bandwidth is the

processing gain, which is a measure of the noise and interference immunity of this method of

transmission.

To see how the spreading process helps protect the signal from outside interference, let us

look at the types of interference that are possible. The three major types of interference that can

arise when using wireless networks are: (1) noise, (2) intentional interference from a jammer or

other source trying to disrupt communications, and (3) unintentional interference from other users

of the same frequency band. Noise can be considered as background white Gaussian noise (WGN),

and can be said to have power spectral density N0. Since the noise is white, the spreading of the

bandwidth does not have much of an effect here. The noise power is constant over the entire

bandwidth, so increasing the bandwidth actually lets more noise into the system, which might be

seen as detrimental. However, we will see that this is not really a problem.

Intentional interference comes from sources who are actively trying to corrupt the data

transmission by sending power transmissions in the same band as the intended transmission. The

big difference between intentional interference and noise is that intentional interference is, by its

very nature, a finite power signal, since it must be transmitted from a real source. Thus the

spreading performed on the data signal allows the signal to hide itself in a larger bandwidth,

forcing the jamming signal to distribute its power over this new much larger bandwidth, and thus

intuitively diminishing the effect that the jamming signal has on the data signal.

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The third major source of signal corruption comes from unintentional interference due to

other users using the same frequency band, and here, the system uses the PN sequence and the

technique of CDMA to combat this type of interference. In a wireless communications network, all

the signals propagate through the air by way of electromagnetic waves, thus there is no way to

ensure that one user will receive only the signal he or she desires; that user will receive all the

signals being sent in that band. By giving each of the signals to be transmitted in the frequency

band its own code (CDMA) which is orthogonal to the other codes used in that band, the effect of

these other signals will effectively be zero at the receiver (when the receiver correlates the input

signal it receives with the code of the transmission it wants to receive, only the desired signal will

Remain). The following sections will analyze and derive the specifics of the two major types of

spread spectrum systems, Direct Sequence and Frequency Hop. Since the mechanisms by which

the above advantages are achieved vary between the two methods, the analysis has been left until

those sections.

The basic elements of a spread spectrum digital communication system are illustrated in

Figure 2.1. We observe that the channel encoder and decoder and the modulator and demodulator

are the basic elements of a conventional digital communication system' In addition to these

elements, a spread spectrum system employs two identical pseudorandom sequence generators, one

of which interfaces with the modulator at the transmitting end and the second of which interfaces

with the demodulator at the receiving end' These two generators produce a pseudorandom or

pseudo noise(PN) binary-valued sequence that is used to spread the transmitted signal in frequency

at the Inoculators to dispread the received signal at the demodulator. Time synchronization of the

PN sequence generated at the receiver with the PN sequence Contained in the received signal is

required to properly dispread the received spreads spectrum signal. In a practical system,

synchronization is established prior to the transmission of information by transmitting a fixed PN

bit pattern that is designed so that the receiver will detect it with high probability in the presence of

interference. After time synchronization of the PN sequence generators is established, thetransmission of information commences. In the data mode, the communication system usually

tracks the timing of the incoming Received signal and keeps the PN sequence generator in

synchronism.

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Figure 2.1 spread spectrum digital communication system

There are two basic types of spread spectrum signals for digital communications namely direct

sequence (DS) spread spectrum and frequency_ hopped (FH) spread spectrum

2.2 Direct Sequence Spread Spectrum

In telecommunications, direct-sequence spread spectrum (DSSS) is a modulation

technique. As with other spread spectrum technologies, the transmitted signal takes up more

bandwidth than the information signal that is being modulated. The name 'spread spectrum' comes

from the fact that the carrier signals occur over the full bandwidth (spectrum) of a device's

transmitting frequency.

2.2.1 Features

It phase-modulates a sine wave pseudo randomly with a continuous string of pseudo noise

(PN) code symbols called "chips", each of which has a much shorter duration than an information

bit. That is, each information bit is modulated by a sequence of much faster chips. Therefore, the

chip rate is much higher than the information signal bit rate. It uses a signal structure in which the

sequence of chips produced by the transmitter is known a priori by the receiver. The receiver can

then use the same PN sequence to counteract the effect of the PN sequence on the received signal

in order to reconstruct the information signal.

2.2.2 Transmission method for DSSS

Direct-sequence spread-spectrum transmissions multiply the data being transmitted by a

"noise" signal. This noise signal is a pseudorandom sequence of 1 and 1 values, at a frequency

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much higher than that of the original signal, thereby spreading the energy of the original signal into

a much wider band as shown in figure 2.2. The resulting signal resembles white noise, like an

audio recording of "static". However, this noise-like signal can be used to exactly reconstruct the

original data at the receiving end, by multiplying it by the same pseudorandom sequence (because

1 1 = 1, and 1 1 = 1). This process, known as "de-spreading" as shown in figure 2.3,

mathematically constitutes a correlation of the transmitted PN sequence with the PN sequence that

the receiver believes the transmitter is using.

For de-spreading to work correctly, the transmit and receive sequences must be

synchronized. This requires the receiver to synchronize its sequence with the transmitter's

sequence via some sort of timing search process. However, this apparent drawback can be a

significant benefit: if the sequences of multiple transmitters are synchronized with each other, the

relative synchronizations the receiver must make between them can be used to determine relative

timing, which, in turn, can be used to calculate the receiver's position if the transmitters' positions

are known. This is the basis for many satellite navigation systems.

Figure 2.2 Generation of Spreading Sequences

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The resulting effect of enhancing signal to noise ratio on the channel is called process gain.

This effect can be made larger by employing a longer PN sequence and more chips per bit, but

physical devices used to generate the PN sequence impose practical limits on attainable processing

gain.

Figure 2.3 Generation of De-spreading Sequences

If an undesired transmitter transmits on the same channel but with a different PN sequence

(or no sequence at all), the de-spreading process results in no processing gain for that signal. This

effect is the basis for the code division multiple access (CDMA) property of DSSS, which allows

multiple transmitters to share the same channel within the limits of the cross-correlation properties

of their PN sequences.

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Systems using DS-SS require more bandwidth and this contradicts the concept of

bandwidth conservation. However, many advantages exist to using such a system. The

development of DS-SS was conducted for the military, so the most advantageous facet is the

inherent security of the system. The PN sequence encodes the data making it difficult to intercept

and decode the signal without knowing the coded sequence used. The spreading process also

makes jamming the signal difficult because the jamming signal is spread during the despreading

process. Thus reducing its effect on the transmitted signal.

Because each signal is encoded with a unique PN sequence, multiple signals can be

transmitted within the same frequency band. Code Division Multiple Access (CDMA) uses spread

spectrum technology and each transmitter uses a different spreading code to allow for multiple

transmissions over the same channel. This property of the CDMA method of transmission has

increased the popularity of this type of wireless communication. The CDMA method is widely

used in current wireless systems and its use in next generation systems is anticipated. In GPS, each

satellite transmits data that has been spread by a PN sequence. All satellites transmit independently

using different spreading codes in the same frequency band so the system is classified as CDMA.

2.3 Frequency Hopped Spread Spectrum

Frequency hopping is one of two basic modulation techniques used in spread spectrum

signal transmission. In frequency hopped spread spectrum the available channel bandwidth W is

subdivided into a large number of non-overlapping frequency slots. In any signaling interval the

transmitted signal occupies one or more of the available frequency slots. The selection of the

frequency slot in each signal interval is made pseudo randomly according to the output from a PN

generator. It is the repeated switching of frequencies during radio transmission, often to minimize

the effectiveness of "electronic warfare" - that is, the unauthorized interception or jamming of

telecommunications. It also is known as frequency- hopping code division multiple access ( FH-

CDMA). Spread spectrum modulation techniques have become more common in recent years.

Spread spectrum enables a signal to be transmitted across a frequencyband that is much wider than

the minimumbandwidth required by the information signal. The transmitter "spreads" the energy,

originally concentrated in narrowband, across a number of frequency band channels on a wider

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electromagnetic spectrum. Benefits include improved privacy, decreased narrowband interference,

and increased signal capacity.

In an FH-CDMA system, a transmitter "hops" between available frequencies according to a

specified algorithm, which can be either random or preplanned. The transmitter operates in

synchronization with a receiver, which remains tuned to the same center frequency as the

transmitter. A short burst of data is transmitted on a narrowband. Then, the transmitter tunes to

another frequency and transmits again. The receiver thus is capable of hopping its frequency over a

given bandwidth several times a second, transmitting on one frequency for a certain period of time,

then hopping to another frequency and transmitting again. Frequency hopping requires a much

wider bandwidth than is needed to transmit the same information using only one carrier frequency.

The spread spectrum approach that is an alternative to FH-CDMA is direct sequence code divisionmultiple access (DS-CDMA), which chops the data into small pieces and spreads them across the

frequency domain. FH-CDMA devices use less power and are generally cheaper, but the

performance of DS-CDMA systems is usually better and more reliable. The biggest advantage of

frequency hopping lies in the coexistence of several access points in the same area, something not

possible with direct sequence.

Certain rules govern how frequency-hopping devices are used. In North America, the Industrial,

Scientific, and Medial (ISM) waveband is divided into 75 hopping channels, with power

transmission not to exceed 1 watt on each channel. These restrictions ensure that a single device

does not consume too much bandwidth or linger too long on a single frequency.

2.3.1 Features

FHSS is one of two types of spread spectrum radio, the other being direct-sequence spread

spectrum. FHSS is a transmission technology used in wireless transmissions where the data signal

is modulated with a narrowband carrier signal that "hops" in a random but predictable sequence

from frequency to frequency as a function of time over a wide band of frequencies. The signal

energy is spread in time domain rather than chopping each bit into small pieces in the frequency

domain. This technique reduces interference because a signal from a narrowband system will only

affect the spread spectrum signal if both are transmitting at the same frequency at the same time. If

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synchronized properly, a single logical channel is maintained. The transmission frequencies are

determined by a spreading, or hopping, code. The receiver must be set to the same hopping code

and must listen to the incoming signal at the right time and correct frequency in order to properly

receive the signal. Current FCC regulations require manufacturers to use 75 or more frequencies

per transmission channel with a maximum dwell time (the time spent at a particular frequency

during any single hop) of 400 ms.

The overall bandwidth required for frequency hopping is much wider than that required to

transmit the same information using only one carrier frequency. However, because transmission

occurs only on a small portion of this bandwidth at any given time, the effective interference

bandwidth is really the same. Whilst providing no extra protection against wideband thermal noise,

the frequency-hopping approach does reduce the degradation caused by narrowband interferers.One of the challenges of frequency-hopping systems is to synchronize the transmitter and receiver.

One approach is to have a guarantee that the transmitter will use all the channels in a fixed period

of time. The receiver can then find the transmitter by picking a random channel and listening for

valid data on that channel. The transmitter's data is identified by a special sequence of data that is

unlikely to occur over the segment of data for this channel and the segment can have a checksum

for integrity and further identification.

2.3.2 Transmission method for FHSS

A block diagram of the transmitter and receiver for a FH spread spectrum system is shown in

Figure 2.4 The modulation is either binary or M-ary FSK. For example if binary FSK is employed,

the modulator selects one of two frequencies, f0 or f1 corresponding to the transmission of a0 for

a1. The resulting binary FSK signal is translated in frequency by an amount that is determined by

the output sequence from PN generator which is used to select a frequency fc that is synthesized by

the frequency synthesizer. This frequency-translated signal is transmitted over the channel. For

example, by taking m bit form the PN generator, we may specify possible carrier frequencies.

At the receiver, there is an identical PN sequence generator, synchronized with the received

signal, which is used to control the output of the frequency synthesizer. Thus the pseudorandom

frequency translation introduced at the transmitter is removed at the demodulator by mixing the

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synthesizer output with the received signal. The resultant signal is then demodulated by means of

an FSK demodulator, a signal for maintaining synchronism of the PN sequence generator with the

FH received signal is usually extractor form the received signal.

Figure 2.4 frequency hopped spread spectrum system

Although binary PSK modulation generally yield better performance than FSK , it is

difficult to maintain phase coherence in the synthesis of the frequencies used in the hopping pattern

and, also, in the propagation of the signal over the channel as the signal is hopped from one

frequency to another over a wide bandwidth. Consequently, FSK modulation with non-coherent

demodulation is usually employed in FH spread spectrum systems. The frequency hopping rate,

denoted as Rh, may be selected to be either equal to the symbol rate, lower than the symbol rate, or

higher than the symbol rate. If Rh is equal to lower part at the symbol rate, the FH system is called

a slow hopping system. If Rh is higher that symbol rate, the FH system is called a fast hopping

system

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2.4 CDMA

Time division multiple access (TDMA) and frequency division multiple access (FDMA)

are commonly used multiple access communications systems. TDMA communications use theentire bandwidth to which it is assigned and separates each user by assigning a repetitive time

interval. The user can only communicate in the assigned time slots. This TDMA approach is

inefficient because, during idle times, communications do not use that portion of the fixed timeslot

for operation. In FDMA communications, each user is assigned a frequency slot in the

communication bandwidth in which to communicate. This FDMA approach is inefficient because,

during idle times, communications do not require that portion of the bandwidth for operation.

TDMA also requires synchronization overhead to maintain the operational performance of the

system. In the FDMA system, imperfect band-pass filters exist, requiring frequency slots to be

separated by guard bands to prevent interference from adjacent frequency slots.

The enhancement in performance obtained from a DS spread spectrum signal through the

processing gain and the coding gain can be used to enable many DS spread spectrum signals to

occupy the same channel bandwidth, provided that each signal has its own pseudorandom

sequence, thus it is possible to have several users transmit message simultaneously over the same

channel bandwidth. This type of digital communication, in which each transmitter/receiver user

pair has its own distinct signature code for transmitting over a common channel bandwidth, is

called code division multiple access.

In digital cellular communications, a base station transmits signal to number of mobile

receivers using orthogonal PN sequence, one for each intended receiver, these signals are perfectly

synchronized at transmission, so that they arrive at each mobile receiver in synchronism.

Consequently, due to the orthogonality of the number of PN sequence, each intended receiver can

demodulate its own signal without interference from the other transmitted signals that share the

same bandwidth. However, this type of synchronism cannot be maintained in the signals

transmitted from the mobile transmitters to the base station. In the demodulation of each DS spread

spectrum signal at the base station, the signals from the other simultaneous users of the channel

appear as additive interference. Let us determine the number of simultaneous signals that can be

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accommodated in a CDMA system. We assume that all signals have identical average powers at

the base station. In many practical system the received signals power level from each user is

monitored at the base station, and power control is exercised over all simultaneous users by use of

a a control channel that instructs the users on whether to increase or decrease their power levels.

The advantage of the CDMA method over the other methods is that instead of isolating

each user, all users share the channel resources. Each user is assigned a unique PN sequence with

which to encode and decode the data. They all transmit on the same carrier frequency with

approximately the same power level that is below the background noise level. The PN sequences

used in the system have low cross-correlations with each other, and therefore, interference with

other signals is low. GPS uses a PN sequence called Gold Sequences, which are a class of low

cross-correlation codes. This approach makes each user seem as though they are operating alone

within a channel of high background noise. This allows systems using CDMA to accommodate a

large number of users within the same bandwidth and no part of the system is reserved for idling

users. The receiver will synchronize with the desired signal bringing the power of that data signal

above the background noise. This process works despite the fact that the signals all transmit on the

same bandwidth and at approximately the same power level. GPS signals utilize CDMA

communications using direct sequence bi-phase modulation of the carrier frequency. From any

location on the surface of the earth, five to twelve GPS satellites are typically visible at any given

time. Demodulation of the CDMA signals transmitted provides a spreading gain that renders the

power level of the signal above that of the background noise level.

Chapter 3: PN-sequences

3.1 Generation of PN sequences

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On the basis of what has been said of the DS spread-spectrum system that is the core of the

CDMA system, we can state that CDMA is an MA technique that uses spread-spectrum

modulation by each accessing party with its own unique spreading code, with all accessing parties

sharing the same spectrum. It is also clear now that spread-spectrum modulation is accomplished

by means of PN codes. The narrowband information signal or information sequence is modulated

(multiplied) by the wideband spreading signal (sequence), thereby spreading the information signal

spectrum to a substantially greater bandwidth prior to transmission. It is important to recognize

that CDMA can only be accomplished by spread-spectrum modulation, while spread-spectrum

modulation does not mean CDMA.

Pseudorandom or pseudonoise (PN) sequences are used in data scrambling in the IS-95

system as well as for spread-spectrum modulation. Data scrambling is achieved by changing the

data sequence "randomly" or in a noise-like fashion before transmission. At the receiver, the

scrambled sequence is "changed back" to the original data sequence. The two concepts,

"randomness" and "changing back," are the key ideas involved in understanding the CDMA

system. If the generated sequence were completely random, the receiver would have no way to

change back. On the other hand, if the receiver knows how to change back, the sequence cannot be

completely random.Consider the following sequences:

Data sequence 1 1 0 0 1 0 1 0 0 1 0 1 0 1...

Random sequence 1 0 1 0 0 0 0 1 0 1 1 0 1 0...

Transmitted sequence 0 1 1 0 1 0 1 1 0 0 1 1 1 1...

The transmitted sequence is a scrambled version of the data sequence obtained by the bit-

by-bit modulo-2 addition of the data sequence and a random sequence. At the receiver, an identical

"random" sequence is added to the received sequence, which in the absence of noise is the

transmitted sequence:

Transmitted sequence 0 1 1 0 1 0 1 1 0 0 1 1 1 I...

Random sequence 1 0 1 0 0 0 0 1 0 1 1 0 1 0.. .

Data sequence 1 1 0 0 1 0 1 0 0 1 0 1 0 1.. .

This illustration reveals two fundamental requirements on the random sequence:

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It must be reproducible at the receiver;

It must be reproduced in synchronism with the scrambling sequence at the transmitter.

These two requirements make it virtually impossible to use a completely random sequence and

hence, in practice, we use a sequence that has sufficient randomness to be unrecognizable to

unintended receivers and yet is deterministic to make it relatively easy to generate and to

synchronize at the receiver.

The most important method of generating such binary sequences is by means of a linear

feedback shift register (LFSR). For an LFSR sequence generator with n stages, the output sequence

will always be periodic because, whatever the initial conditions of the shift register, after a finite

number of clock pulses, the initial conditions must eventually be reproduced. Because the

maximum number of different combinations of n binary digits is 2n , the period cannot exceed 2n .

Because the all-zero condition, if reached, remains in the same state forever, it cannot appear in the

shift register if the initial condition (initial loading or state) is not all zeros. Therefore, the

maximum number of possible states is 2 1n .

A shift register output sequence with the period 2 1n is called a "maximal length

sequence" or "m-sequence" for short. M-sequences are also referred to as "pseudorandom

sequences" or PN sequences. When PN sequences clocked at very high rates are modulated

(multiplied) with data sequences in a communications system, such as the IS-95 system, it is a

spread spectrum system that provides 10 log (RN/Rb ) dB of "processing gain," where RN is the

PN sequence rate and Rb is the data rate.

The generation of PN sequences is accomplished using a linear feedback shift register

(LFSR)as shown in figure 2.5. In either case, the shift register generator is a finite-state machine

mechanized by a polynomial given in the form of

1 2 1

1 2 1( ) 1n n

ng D D s D s D s D

= + + + + + (1.1)

The polynomial (1.1) is a special type of polynomial, well tabulated in the literature, called

an generator polynomial, which specifies a set of nonzero coefficients {si), where si = 1 denotes a

connection and = 0 denotes the lack of a connection in the mechanization of the LFSR

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configuration. The sequences generated by such an LFSR with an initial loading of nonzero n-

tuples in the n stages, are periodic sequences with length N = 2 1n , and there are P different

sequences of length P that are shifted versions of the given initial sequence of length P. The

sequences generated in this way are the ones used. There are three most important properties

associated with a PN sequence, aside from the basic property that it has the maximal length of

2 1n , where n is the number of stages of the LFSR. Two of the three remaining properties have to

do with the randomness of the sequence, but the one we wish to mention here is the correlation

property. What it means is that if a complete sequence of length 2 1n is compared, bit by bit, with

any shift of itself (one of 2 1n remaining sequences), the number of agreements differs from the

number of disagreements by at most 1. This means that when two identical sequences are

compared, bit by bit, the number of agreements minus the number of disagreements is equal to the

number of agreements, which is 2 1n .

We generate the m-sequence using a Linear Feedback Shift Register (LFSR). The LFSR is

implemented in the modular format as shown below in Figure 3.1.

Figure3.1 Linear Feedback Shift Register

The modular format is suited for efficient hardware implementation and is faster compared to a

simple format. The initial load of the register, 1 2 3 1 0[ , , , , , ]n n nr r r r r r = cannot be in the all zero

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state and the generator polynomial taps , 1 2 3 1 0[ , , , , , ]n n n ng g g g g g g = should be such that 0g

and ng are non zero. If the initial load is the all-zero state, the registerr cannot update to any other

state and will result in zero output all the time. The elements of g and r are from the binary set

{0,1}. In Figure 1, the tap 0g =1 and represents the connection from the LSB 0r of the register to all

other generator taps. During a clock tick, the value in 0r is clocked out as the first output bit d. In

hardware implementation, the binary value in g determines the presence or absence of a modulo 2

multiplier. In MATLAB implementation, we AND (modulo 2 multiply) 0r with ng through 1g to

obtain , 1 2 3 1[ , , , , ]n n n ns s s s s s = as shown in Figure 3.1. Next we update the register r. We XOR

(modulo 2 addition) the vectors 1, 2 3 1[ , , , ]n n ns s s s and 1, 2 3 1[ , , , ]n n nr r r r and store the result in

2, 3 4 0[ , , , ]

n n nr r r r

. Finally, the MSB of the registerr, 1nr , is updated with the value of ns . The

register r is now next state and during the next clock cycle, the LSB 0r is clocked out as next

output of the m-sequence and the process continues. Here, n denotes the size of the linear feedback

shift register. The length of generated m-sequence is N= 2 1n and it repeats with period N.

3.2 Properties of Maximal Length PN Sequences

The maximal length PN sequences or m-sequences generated have many of the same

properties of a truly random sequence. A truly random sequence has an equal probability of a 1 or

a 0 occurring and the PN sequences come close to that property.

The properties of m-sequences are:

1. The Balance Property: The number of 1s in the sequence is always one greater than the number

of 0s.

2. The Shift and Add Property: The Modulo-2 addition of an m-sequence with a time-shiftedversion of the same m-sequence yields a second time-shifted version of the same m-sequence.

3. The Correlation Property: When a full period of an m-sequence is compared with a time-shifted

version of itself, the number of mismatched chips will exceed the number of matched chips by one.

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3.3 The Cross-Correlation Problem

The cross-correlation function between two distinct pseudorandom sequences is a very

important consideration in MA communications systems where each user terminal (access

terminal) is assigned a PN generator whose polynomial is distinct from all other user terminals. In

fact, this is the type of CDMA spread-spectrum system used by the military. A distinction between

the military type of CDMA system and the nonmilitary type such as IS-95 is that, in the former, the

communications channel condition does not permit a phase coherent PN code MA system, as

opposed to the more controllable channel conditions of cellular or PCS applications in which

mobilility is not a panicular concern. In a military or high-mobility environment, where the carrier

phase tracking is of insurmountable difficulty, a CDMA system based on a single PN code

generator, such as the IS-95 system, is not possible. The problem of assigning code generators with

low cross-correlation peaks is an important consideration.

For CDMA applications, m-sequences are not optimal. The m-sequences have excellent

autocorrelation properties but their cross-correlation properties do not follow any particular rules

and typically exhibit undesirably high values. For CDMA, we need to construct a family of

spreading sequences, one for each which, in which the codes have well-defined cross-correlation

properties. In general, m-sequences do not satisfy the criterion. One popular set of sequences thatdoes are the Gold sequences. Gold sequences are attractive because only simple circuitry is needed

to generate a large number of unique codes. A Gold sequence is constructed by the XOR of two m-

sequences with the same clocking. Gold sequences are generated from two equal length m-

sequences that form a so called preferred pair. To achieve increased capacity, at an expense of

altering the correlation properties slightly, a pair of m-sequences may be used to generate a set of

Gold sequence.

To overcome the cross-correlation problem, Gold considers the bit-by- bit modulo-2 sum

of two pseudorandom sequences of the same length but generated by two distinct primitive

polynomials. If the length of the two PN sequences is P = 2 1n , then the resultant sequence also

repeats itself after P bits. Further, if one sequence is kept fixed and the second sequence is shifted

in time, a different resultant sequence is generated. In this way, P different sequences can be

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generated, one for each different time shift of the second sequence. Joining the two original PN

sequences, altogether 2 1n + different sequences can be generated with one pair of primitive

polynomials. These sequences are referred to as Gold sequences or Gold codes; they are not

maximal except for the two original PN sequences.

Chapter 4: Gold Code Sequences

4.1Gold Code Generation

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The usefulness of the pseudorandom sequences in a spread-spectrum system depends in

large part on their ideal autocorrelation properties. One of the randomness properties of the

pseudorandom sequence is the correlation property; that is, if a complete sequence is compared, bit

by bit, with any shift of itself, the number of agreements differs from the number of disagreements

by at most one. The cross-correlation function between two different pseudorandom sequences of

the same length is, however, an entirely different matter. It can have high peaks; and to make the

matter worse, there is no simple method available to calculate the cross-correlation function

between two pseudorandom sequences except by brute force calculation and simulation. For long

sequences, this is not possible even with the fastest computers.

The cross correlation properties are as important in communication systems as

autocorrelation properties. Cross correlation is a measure of agreement between the two different

codes. The periodic cross correlation between any pair of m-sequences is very high. Such high

values of cross correlation are undesirable in CDMA communications. For CDMA applications,

m-sequences are not optimal. For CDMA, we need to construct a family of spreading sequences,

one for each which, in which the codes have well-defined cross-correlation properties. In general,

m-sequences do not satisfy the criterion. One popular set of sequences that does are the Gold

sequences. Gold sequences are attractive because only simple circuitry is needed to generate a

large number of unique codes.Gold sequences have been proposed by Gold in 1967 and 1968.

These are constructed by EXOR-ing two PN sequences of the same length with each other. Gold

developed new sequences with better cross correlation properties called Gold sequences. Gold

sequences are defined using a pair of preferred sequences. Gold sequences of length N can be

constructed from a preferred-pair of PN-sequences. This two PN sequences are XORed (modulo-2

addition) together to generate Gold code sequences. The result is a new period sequences with the

period N = 2 1n . To achieve increased capacity, at an expense of altering the correlation

properties slightly, a pair of m-sequences may be used to generate a set of Gold sequence, which

have the property that the cross-correlation is always equal to 1, when the phase offset is zero.

Non-zero phase offset produces a correlation value from one of the three possible values. In this

work a pair of specially selected m-sequences (where m = 5) is taken, and performing the modulo-

2 sum of the two sequences for each of the L=2n-1 cyclically shifted version of one sequence

relative to the other sequence.

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The Configuration for the generation of the Gold code sequences from the modulo 2

addition of two same length PN sequences as shown in figure 4.1.

Figure.4.1 Generation of the Gold Code sequences

Chapter 5: Simulation Results

5.1 Simulation results for PN sequences

Suppose the generator taps are 0 1 2 3 4[ , , , , ]g g g g g g = =[1 0 1 0 1] and the corresponding

generator polynomial is,2 4

( ) 1g D D D= + + then the result will be displayed as given bellow:

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Enter the size of the Linear Feedback Shift Register (LFSR) = 4

Initial State of the LFSR =

0 0 0 0

The generator (gm) =

1 0 1 0 1

Status of Register after the 1 clock is : 1 0 1 0















The number of bits in PN-sequence = 15

Generated PN-sequence is : 1 0 1 0 0 0 1 0 1 0 0 0 1 0 1

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0 5 10 150

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 5.1 PN sequences(m-sequences) for N=4

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 00

0. 1

0. 2

0. 3

0. 4

0. 5

0. 6

0. 7

0. 8

0. 9

1

Figure 5.2 PN sequences(m-sequences) for N=10

The number of bits in PN-sequence = 1023

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5.2 Simulation Results for Gold Code Sequences

Suppose the first generator taps are 0 1 2 3 4[ , , , , ]g g g g g g = =[1 0 1 0 1] and the

corresponding generator polynomial is,2 4

( ) 1g D D D= + + . And second generator taps are

0 1 2 3 4[ , , , , ]g g g g g g = =[1 1 0 0 1] and the corresponding generator polynomial is,

1 4( ) 1g D D D= + + then the result will be displayed as given bellow:

Enter the size of the Linear Feedback Shift Register (LFSR)1 = 4

Enter the size of the Linear Feedback Shift Register (LFSR)2 = 4

Enter the first Generator polynomial = [1 0 1 0 1]Enter the second Generator polynomial = [1 1 0 0 1]
















The number of bits in PN1-sequence = 15

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The number of bits in PN2-sequence = 15

Generated PN1-sequence is :

1 0 1 0 0 0 1 0 1 0 0 0 1 0 1

Generated PN2-sequence is :

1 0 0 1 1 0 1 0 1 1 1 1 0 0 0

Generated gold-sequence is :

0 0 1 1 1 0 0 0 0 1 1 1 1 0 1

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The simulation results for N=4

The first generator polynomial for PN sequence 1 is [1 0 0 1 0 1 1 0 0 0 1 ]

The first generator polynomial for PN sequence 2 is [1 1 0 0 0 0 1 0 1 0 1 ]

As shown in figure 5.3,the generated PN sequences 1 for N=4,the total number of bits in these

sequences are N= 2 1n =15 bits


sequences are N= 2 1n =15 bits.

As shown in figure 5.5,the generated Gold Code sequences for N=4,the total number of bits in

these sequences are N= 2 1n

=15 bits.These Gold code sequences aer generated by XORing thePN sequences 1 and PN sequences 2.

2 4 6 8 10 12 14-0.2

0

0.2

0.4

0.6

0.8

1

Generated m-sequence1 of length 2n1-1

Chip Index (k1)

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Figure 5.3 First PN Sequences for N=4

2 4 6 8 10 12 14-0.2

0

0.2

0.4

0.6

0.8

1

Generatedm-sequence2of length2 n2-1

ChipIndex(k2)

Figure 5.4 Second PN Sequences for N=4

2 4 6 8 10 12 14-0.2

0

0.2

0.4

0.6

0.8

1

Generatedgold-sequenceof length2 n2-1

ChipIndex (k)

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Figure 5.5 Generated Gold Code Sequences for N=4

The simulation results for N=10

The first generator polynomial for PN sequence 1 is [1 0 0 1 0 1 1 0 0 0 1 ]The first generator polynomial for PN sequence 2 is [1 1 0 0 0 0 1 0 1 0 1 ]


sequences are N= 2 1n =1023 bits


sequences are N= 2 1n =1023 bits.

As shown in figure 5.8,the generated Gold Code sequences for N=10,the total number of bits in

these sequences are N=2 1

n =1023 bits.These Gold code sequences aer generated by XORing the

PN sequences 1 and PN sequences 2.

100 200 300 400 500 600 700 800 900 1000-0.2

0

0.2

0.4

0.6

0.8

1

Generated m-sequence1 of length 2 n1-1

Chip Index (k1)

Figure 5.6 Generated PN Code 1 Sequences for N=10

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100 200 300 400 500 600 700 800 900 1000-0.2

0

0.2

0.4

0.6

0.8

1

Generatedm-sequence2of length2 n2-1

ChipIndex (k2)

Figure 5.7 Generated PN Code 2 Sequences for N=10

100 200 300 400 500 600 700 800 900 1000-0.2

0

0.2

0.4

0.6

0.8

1

Generated gold-sequence of length 2 n2-1

Chip Index (k)

Figure 5.8 Generated Gold Code Sequences for N=10

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5.3 Conclusion

From the above results and Graphs we can safely conclude the following :

1) I have successfully generated a PN sequences and Gold Code sequences. We can generate PN

sequences and Gold Code sequences of any bit length and modulate a message signal. This signal

is called spreaded signal. We have also successfully demodulate the spreaded signal using the same

Gold Code sequence to produce the original message signal.

2) Better Auto correlation of the Gold Codes over the PN sequences, thus proving that Gold Code

is more suitable for modulation and spreading of a message signal than the Pseudo Noise

sequences.

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REFERENCES

[1] Raymond L. Pickholtz, Donald L. Schilling, Laurence B. Milstein. Theory of Spread

Spectrum Communications -- A Tutorial, IEEE Transactions on Communications, Vol. COM-

30, May 1982, pp. 855-884.

[2] Robert C. Dixon. Spread Spectrum Communications, Second Edition, John Wiley and Sons,

New York, 1984.

[3] Edward A. Lee, David G. Messerchmitt, Digital Communications, Second Edition, Kluwer

Academic Publishers, USA, 1994.

[4] Marcus C. Wlden, Roger D. Pollard. On the Processing Gain and Pulse Compression Ratio of

Frequency Hopping Spread Spectrum Waveforms, IEEE National Telesystems Conference

Proceedings, 1993, pp. 215-219.

[5] T.S.D. Tsui, T.G. Clarkson. Spread Spectrum Communication Techniques, Electronics and

Communication Engineering Journal, Februaru 1994.

[6] Laurence B. Milstein, Donal L. Schilling. The Effect of Frequency-Selective Fading on a

Noncoherent FH-FSK System Operating with partial Band Tone Interference, IEEE

Transactions on Communications, Vol. COM-30, May 1982, pp. 904-912.

[7] G. Mandyam and J. Lai, Third- Generation cdma systems for enhanced data services,

Academic Press, 2002.

[8] B. Lee, B. Kim, Scrambling Techniques for CDMA Communications, New York Kluwer

Academic Publishers, 2002.

[9] http://en.wikipedia.org/wiki/Pseudorandom_binary_sequencehttp://

micromouse.cannock.ac.uk

[10] http://en.wikipedia.org/wiki/DSSS

[11] www.mathworks.com/

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APPENDIX

Abbreviations:

AMPS analog advanced mobile phone system

N-AMPS narrowband AMPS

D-AMPS digital AMPS

EDGE Enhanced Data Rates for GSM Evolution

TIA telecommunications industry association

CDMA code division multiple access

DS direct sequence

ERBF radial basis function with Euclidean distance measure

ETSI European Telecommunications Standards Institute

FDMA frequency division multiple access

FECC forward error correction coding

FH frequency hopping

GSM Global System for Mobile

IMT 2000 International Mobile Telecommunications 2000

ICI inter chip interference

ISI inter symbol interference

IS-95 interim standard-95

ITU International Telecommunication Union

MSC mobile switching centre

MUD multiuser detector

PG processing gain

PN pseudo-noise or pseudo-random

SS spread spectrum

TDMA time division multiple access

TH time hopping

UMTS Universal Mobile Telecommunication Standard

WCDMA wideband CDMA

Documents

Gold Sequences