- 1 -14

Communication Systems

Lecture 14

- 2 -14

Spread spectrum technique

The spread spectrum system (SSS) is one in which the transmitted

signal is spread over a wide frequency band, much wider, than the

minimum bandwidth required to transmit the information being

sent.

-A system is defined to be a speared spectrum system if it fulfills

the following requirements:

1-The signal occupies a bandwidth much in excess of the minimum

bandwidth necessary to send the information.

2-Spreading is accomplished by means of a spreading signal, often

called a code signal, which is independent of the data.

3-At the receiver, despreading (recovering the original data) is

accomplished by the correlation of the received spread signal with a

synchronized replica of the spreading signal used to spread the

information.

Note

Standard modulation such as FM and PCM also spread the

spectrum of an information signal, but they do not qualify as spread

spectrum systems since they do not satisfy all the conditions above.

- 3 -14

The advantages of spread spectrum systems

-Interference suppression.

-White Gaussian noise is a mathematical model has infinite power

spread uniformly over all frequencies. The communication is

possible with this interfering noise (white Gaussian noise) of

infinite power because only the finite power noise components that

are present within the signal bandwidth can interfere with the

signal.

-For a typical narrowband signal, this means that only the noise in

the signal bandwidth degrade performance.

The idea behind a spread spectrum anti-jam (AJ) system is as

follows:

a- consider that many orthogonal signal components are available to

a communication link and that only a small subset of these signal

coordinates are used at any time.

[Against white Gaussian noise, with infinite power, the use of

spreading offers no performance].

b-The noise from interferer (jammer) with a fixed finite power and

with uncertainty as to where in the signal space the signal

components (coordinates) are located, the jammer’s choices are

limited to the following:-

1-jam all the signal components (coordinates) of the system,

with equal amount of power in each one, with the result that a

little power is available for each component (coordinate).

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2-jam a few signal components (coordinates) with increased

power in each of the jammed coordinates.

Fig (14.1) compares the effect of spreading in the presence of white

noise with spreading in the presence of interferer (jammer). The

power spectral density of the signal is denoted G(F) before

spreading and Gss(f) after spreading.

Fig(14.1)

-Fig(14.1a) it can be seen that the single sided power spectral

density of white noise, is unchanged as a result of expanding the

signal bandwidth.

-Fig(14.1b) shows the case of received jammer power J, and power

spectral density where W is the unspread bandwidth.

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If interferer choice results in a reduction in interferer noise spectral

density by because

ssss W

WJ

W

JJ 00

broadband jammer noise spectral density (14.1)

If interferer choice 2 results in a reduction in the number of signal

coordinates, that the jammer can increase its noise spectral density

from where ρ is the portion of

interferer (jammer) bandwidth.

2-Energy density reduction.

Since in SSS, the signal is spread over many more signaling

components than conventional modulation schemes, the resulting

signal power is spread uniformly in the spread domain. Thus the

received signal is small, very difficult to detect by anyone except

the desired receiver (or intended receiver) systems designed for this

special task are known as low probability of detection (LPD) or low

probability of intercept (LPI).

3-Fine time resolution

Spread spectrum signals can be used for ranging or determination

of position location. Distance can be determined by measuring the

time delay between transmitted and received signal. Uncertainly in

the delay measurements is inversely proportion proportional to the

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bandwidth of the signal pulse as shown in fig (14.2). The

uncertainty of the measurement, t, is proportional to the rise time

of pulse, is given by

fig(14.1a)

Multiple access

-Multiple access refers to techniques that enable sharing a common

communication channel between multiple users.

-There is a difference between multiplexing and multiple access.

With multiplexing users requirements (or plans) are fixed, or at

most, slowly changing. The user allocation is assigned a priori and

the multiplexing (sharing) is usually a process that takes place

within the confines of a local site (e.g a circuit board). With

multiple access, usually involves the remote multiplexing (sharing)

- 7 -14

of a user and users requirements are changed (e.g satellite

communications).

-Spread spectrum methods can be used a multiple access technique,

in order to multiplex (share) a communication resource among

numerous users. The technique, termed code division multiple

access (CDMA), since each simultaneous user employ a unique

spread spectrum signaling code. One of the by products of this type

of multiple access is the ability to provide communication privacy

between users with different spreading signals. An unauthorized

user cannot easily monitor the communications of the authorized

users.

The basis of spread spectrum technology

-The basis of spread spectrum technology is expressed by Shannon

theorem in the form of channel capacity

)3.14.....(..........1log2

NS

WC

where

C=capacity in bit/sec, N=noise power

W=bandwidth in Hz, S=Signal power

This equation shows the relationship between the ability of a

channel to transfer error–free information, compared with the signal

to noise ratio existing in the channel and the bandwidth used to

transmit the information.

- 8 -14

Letting C be the desired system information rate and changing

bases, we find

a)4.14(1log44.12

NS

W

C

Note

114

1

3

1

2

11log

32

N

Sfor

N

S

N

S

N

S

N

S

N

Se

and for S / N small, say 0.1,

)5.14(44.1

44.1

b)4.14(44.1

S

CNW

CW

SN

N

S

W

C

Eq (14.5) shows that for any given noise to signal ratio we can have

a low information error rate by increasing the bandwidth used to

transfer the information. For example if we want a system to

operate in a link in which the interfering noise is 100 time greater

than the signal and if C=3k bit/s

MHzW 244.1

103100 3

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Spread spectrum techniques

The following techniques are used in spread spectrum systems:-

1-Direct sequence (DS)

2-Frequency hopping (FH)

3-Pulsed frequency modulation (chirp)

4-Time hopping (TH)

5-Hybrid forms [DS/FH, FH/TH and DS/FH/TH]

All the techniques mentioned above require a pseudo random noise

(PN) code generator for bandwidth spreading. A (PN) generator

produces a binary sequence which is apparently random but can be

reproduced deterministically by the intended recipients.

Pseudonoise sequences

-A random signal cannot be predicted, its future variations can only

be described in a statistical sense. However, pseudorandom signal is

not random at all, it is deterministic, periodic signal that is known

to both transmitter and receiver.

Why the name Pseudonoise or pseudorandom? Even though the

signal is deterministic, it appears to have the statistical properties of

sampled white noise. It appears, to an unauthorized listener, to be a

truly random signal.

Randomness properties of a pseudorandom signal

-There are three basic properties that can be applied to any periodic

binary sequence as a test for appearance of randomness:-

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1-Balance property. Good balance requires as a sequence, the

number of binary ones differs from the binary zeros by at most one

digit

2-Run property. A run is defined as a sequence of a single type of

binary digit (or digits). The appearance of the alternate digit in a

sequence starts a new run. Among the runs of ones and zeros in

each period, it is desirable that about one half the runs of each type

are length 1, about one fourth are of length 2, one eight are of

length 3 and so on.

3-Correlation property. 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.

Let us consider the output sequence of PN generator is

0001001101011111

1)No. of zeros =7, No. of ones =8

2)Consider the zero runs, there are four of them.

one half are of length 1 and

one fourth are length 2

one fourth are length 3

Consider the linear shift register illustrated in fig(14.2). It is made

up of a four stage register for storage and shifting, a modulo-2

adder, and a feedback path from the adder to the input of the

register. The shift register operation is controlled by a sequence of

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clock pulses. At each clock pulse the contents of each state in the

register is shifted one stage to the right. The shift register sequence

is defined to the output of the last stage in this example.

Assume that stage is initially filed with one and the remaining

stages are filled with zeros, that is the initial state of the register is

1000. The shift register states will be as follows:-

1X 2X 3

X4

X

fig(14.2)

a-Since the last state, 1000 corresponds to the initial state 1000, we

see that the register repeats the forgoing sequence after 15 clock

pulse.

b-The o/p sequence is obtained by noting the contents of stage at

each clock pulse.

c-The output sequence: 00100110101111

-The shift register generator produces sequences that depend on the

number of stages, the feedback tap connections and initial

conditions. The output sequences can be classified as:-

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1-Maximal length, have the property that for an n stage linear

feedback shift register the sequence repetition period in clock pulse

P is

2-Nonmaximal length, if the sequence length is less than ( )

PN autocorrelation function

-The autocorrelation function of a periodic waveform χ(t), with

period is given by

And the average power of a periodic signal χ(t) is given by

-The autocorrelation function of a periodic waveform χ(t),

with period in normalized from

Where χ(t) is a periodic pulse waveform representing a PN code,

we refer to each fundamental pulse as a PN code symbol or a chip.

-For a PN waveform of a unit chip duration and period P chips, the

normalized autocorrelation function may be expressed as

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(14.7)

The normalized autocorrelation function for a maximal sequence ,

is shown plotted in fig(14.3), for three stages if reference sequence

1110010

Shift Sequence Agreement Disagreement1 0111001 3 42 1011100 3 43 0101110 3 44 0010111 3 45 1001011 3 46 1100101 3 40 1110010 7 0 +1

1110010daadadd

d=differencea=agreement

fig(14.3)

Direct sequence spread spectrum systems

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-The block diagram in fig(14.4a) shows a direct sequence (DS)

modulator. Direct sequence is the name given to the spectrum

spreading technique whereby a carrier wave is modulated with a

data signal. χ(t), then the data modulated signal is again modulated

with a high speed (wideband) spreading signal g(t).

The ideal suppressed carrier binary phase shift keying BPSK

modulation results in instantaneous changes either 0 or π radians

according to the data. Thus, the data phase modulated can be

expressed by

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fig(14.4)

Where P is the amplitude of the carrier . The transmitted

waveform can be expressed by

Where g(t) is an antipodal spreading code (signal) with +1or -1.

The modulator based on eq(14.8b) is shown in fig (14.4b).

-If the data input pulse χ(t) is binary value (either +1 or -1), then the

initial step in the DS/BPSK modulation can be accomplished by the

modulo-2 addition of the binary data sequence with the binary

spreading sequence.

-Demodulation of the DS/BPSK is accomplished by correlating or

remodulating the received signal with a synchronized replica of the

spreading signal g(t- d), where d is the receiver estimate of the

propagation delay from the transmitter to the receiver. In the

absence of noise and interference, the output signal from the

correlator can be written as

- 16 -14

Where the constant A is a system gain parameter and φ is a random

phase angle in the range (0,2π). Since g(t)=±1, the product

will be unity if , that is, if the code signal

at the receiver is exactly synchronized with the code signal at the

transmitter. When it is synchronized, the output of the receiver

correlator is the despread data modulated signal. The despreading

correlator is then followed by a conventional demodulator for

recovering the data.

Let us consider an example of DS/BPSK modulation and

demodulation as a shown in fig(14.5) following the block diagrams

of fig(14.4b and d). The demodulation is a two steps:-

a-Despreading is accomplished by correlating the received signal

with a synchronized replica of the code.

b-Data demodulation, is accomplished by a conventional BPSK.

-In the example of fig(14.5) we see the code replica in

fig(14.5e) as the phase shift (either o or π) that is produced at the

receiver by despreading code.

Fig(14.5f) shows the resulting estimate of the carrier phase

after despreading or after has been added to . At this

point the original data pattern can be recognized. The final step

shown in fig(14.5) can be obtained after BPSK demodulator.

- 17 -14

)(tx

)(tg

)()( tgtx

)()( ttxg

)(ˆ tg

)(ˆ tx

)(tx

fig(14.5)

Processing gain and jamming margin

A fundamental subject in spread spectrum systems is how much

protection spreading can provide against interfering signals with

finite power. The process gain of a processor is defined as the

difference between the output (S/N) ratio of the processor and the

input (S/N) of the processor.

-Spread spectrum develops its process gain in a sequential signal

bandwidth spreading and despreading operation. The process gain

of a spread spectrum processor can be defined as

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Where is the spread spectrum bandwidth (the total bandwidth

used by the spreading technique) R is the data rate.

-For direct sequence systems, is approximately the code chip

rate and the processing gain can be expressed as

This process gain does not mean that the processor can perform

satisfactorily when faced with an interfering signal having a power

level larger than the desired signal by the amount of the available

process gain. For this reason, jamming Margin ( ) is used to

express the capability of the spread spectrum system under

interference conditions. can be expressed as

Frequency Hopping system (FH)

-In a frequency hopping system spread spectrum, the frequency of

the modulating signal shift by a PN code. The frequency shifting is

performed by a frequency mixer (converter).

-The modulation most commonly used with this technique is M-ary

frequency shift keying (MFSK), where information bits

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are used to determine which one of M frequencies is to be

transmitted. The position of the M-ary signal set is shifted

pseudorandomly by the frequency synthesizer over a hopping

bandwidth . A typical FH/MFSK system block diagram is

shown in fig(14.6). In a conventional MFSK system, the data

symbol modulates a fixed frequency carrier, in an FH/MFSK the

data symbol modulates a carrier whose frequency is

pseudorandomly determined. In either case, a single tone is

transmitted:-

-The FH system in fig(14.6) contains two step modulation process-

data modulation and frequency hopping modulation.

-Also FH system can be implemented as a single step whereby the

frequency synthesizer produces a transmission tone based on the

simultaneous the desired PN code and the data.

-At each frequency hop time, a PN generator feeds the frequency

synthesizer a frequency word (as a sequence of chips), which

selects one of symbol–set positions.

The frequency hopping bandwidth , and the minimum

frequency spacing between hop positions ∆f, determine the

minimum of chips necessary in the frequency word. Thus

Number of tones contained in (14.11a)

- 20 -14

-Note

-The receiver for FH system reverses the signal processing steps of

the transmitter. The received signal is first FH demodulated

(dehopping) by mixing it with the same sequence of

pseudorandomly selected frequency tones that was used for

hopping. Then the dehopped signal is applied to a conventional

bank of M noncoherent energy detectors to select the most likely

symbol.

fig(14.6)

-The processing gain in FH is larger than DS because the SS

technology permits FH bandwidth larger than implementable DS

bandwidth ( ).

-Since FH techniques operate over such wide bandwidths, it is

difficult to maintain phase coherence from hop to hop. Therefore,

noncoherent demodulation is used for HF.

-Let us consider the FH example illustrated in fig(14.7). The input

data consist of a binary sequence with data rate R=150 bit/s. The

modulation is 8-ary FSK.

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The symbol rate is

The symbol duration (T)= =20 msec

The frequency is hopped once per symbol

The hopping rate=50 hop/sec

Fig(14.7) shows the time-bandwidth plane of the communication

resource.

The tone separation

Which corresponds to the minimum required tone spacing for the

orthogonal signaling.

fig(14.7)

-In a conventional 8-ary MFSK scheme, a single tone (offset from

, the fixed center frequency of the data band). The only difference

in this FH/MFSK example is that the center frequency of the data

band is not fixed, the center frequency is changed according PN

code as indicated in the dashed line.

- 22 -14

Robustness of FH

Robustness characterizes a signals ability to withstand

impairments from the channel, such as noise, jamming, fading and

so on. A signal configured with multiple replicate copies, each

transmitted on a different frequency, has a greater likelihood of

survival than does a single such signal with equal total power and

frequency (i.e one single frequency). The greater the diversity

(multiple transmissions, at different frequencies, spread in time),

the more robust the signal against random interference. The

following example should clarify the concept. Consider a message

consisting of three symbols: . If a diversity technique is used

with repeating the message N times. Let us choose N=4. Then, the

repeated symbols called chips can be written

Each chip is transmitted at a different hopping frequency (the center

of the data bandwidth is changed for each chip). The resulting

transmissions at frequencies yield a more robust signal

than without such diversity as shown in fig(14.8).

- 23 -14

fig(14.8)

Fast hopping versus slow hopping

-For frequency hopping systems, the term chip is used to

characterize the shortest continuous waveform in the system. FH

system is classified as:-

1-Slow frequency hopping (SFH), in which the symbol rate is

an integer multiple of the hop rate. That is several symbols are

transmitted on each frequency hop.

2-Fast frequency hopping (FFH), in which the hop rate . That is,

the carrier frequency will change or hop several times during the

transmission of one symbol.

fig(14.9) shows FFH and SFH.

- 24 -14

1f

2f

3f

4f

1f

fig(14.9)

Processing gain for FH

The processing gain for FH can be expressed by the general

equation for processing gain as

Time hopping(TH)

Time hopping is pulse modulation with PN code sequence is used

to key the transmitter on and off as shown in fig(14.10). Transmitter

on and off times are there for pseudorandom, like the code, which

give an average transmit duty cycle of as much as 50%.

12 nPT

- 25 -14

fig(14.10)

-TH has found major application in combination with frequency

hopping. The fine difference separating time frequency and plain

frequency hopping is that in FH systems the transmitted frequency

is changed at each code bit time, whereas a TH/FH system may

change frequency only at one/zero transitions in the PN code (or

change both frequency and time of transitions). Fig(14.11) shows a

time hopping system.

fig(14.11)

-TH is used for ranging and multiple access applications.

Pulsed FM (chirp) systems

-One type of spread spectrum modulation that does not necessarily

employ coding but does use a wider bandwidth than that absolutely

required so that it can realize processing gain is chirp modulation.

- 26 -14

-Chirp modulation has found its main application in radar but it also

applicable to data communications.

-Chirp transmission are characterized by pulse RF signals whose

frequency varies in some known way during each pulse period. The

advantage of these transmission for radar is that significant power

reduction is possible.

-The receiver used for chirp signals is a matched filter, matched to

the angular rate of change of the transmitter frequency-swept

signal.

-The transmitted signal can be generated by using VCO and

matched filter used in the receiver as dispersive delay line (DDL).

Fig(14. 12) shows typical waveform and block diagram for chirp

system.

t

tB

B/2

where

fig(14.12)

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-The chirp matched filter compresses a frequency sweep, usually

linear, which provides an improvement in output signal (voltage) to

noise ratio equal to , Where the compression ratio

Where transmitted pulse duration

For example in radar system

- 28 -14

t

tB

fig(14.12a)

Synchronization for SSS

For both DS and FH spread spectrum systems, a receiver must

employ a synchronized replica of the spreading or code signal to

demodulate the received signal successfully. The process of

synchronizing the locally generated spreading signal with the

received SS signal is usually accomplished in two steps:-

a-Acquistion, consists of bringing the two spreading signals into

coarse alignment with one another.

b-Tracking, takes over and continuously maintains the best possible

waveform fine alignment by means of a feedback loop.

Acquisition

- 29 -14

-The acquisition problem is one of searching a limited region of

time and frequency uncertainty in order to synchronize the received

spread spectrum signal with the locally generated spreading signal.

Acquisition process can be classified as:-

a)coherent. B)noncoherent.

-Since the dispreading process typically takes place before carrier

synchronization, and therefore the carrier phase is unknown at this

point, most acquisition process utilized noncoherent detection.

-When determining the limits of the uncertainty in time and

frequency, the following items must be considered:-

1-uncertainty in the distance between the transmitter and receiver

translates into uncertainty in the amount of propagation delay.

2-Uncertainty of the receiver relative velocity with respect to the

transmitter translates into uncertainty in the value of Doppler

frequency offset of the incoming signal.

3-Relative oscillator instabilities between the transmitter and the

receiver result in frequency offset between the two signals.

Correlator structures method for acquisition

-A common feature of all acquisition methods is that the receiver

signal and the locally generated signal are first correlated to

produce a measure of similarity between the two. This measure is

then compared with a threshold to decide if the two signals are in

synchronism. If they are in synchronism, the tracking loop takes

over. If they are not in synchronism, the acquisition procedure

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provides for a phase or frequency change in the locally generated

uncertainty region, and another correlation process is started again.

1-Direct sequence parallel search acquisitions.

Fig(14.12) shows DS parallel search acquisitions. The locally

generated code g(t) is available with delays that are spaced

one-half chip ( ) apart. If the time uncertainty between the

local code and the received code is chips, and a complete

parallel search of the entire time uncertainty region is to be

accomplished in a single search time, 2 correlators are

used. Each carrelator simultaneously examines a sequence of

λ chips, after which the 2 correlator outputs are compared.

The locally generated code, corresponding to the correlator

with the largest output is chosen.

fig(14.12)

2-Frequency hopping parallel search acquisition.

- 31 -14

Fig(14.13) shows a simple parallel search acquisition. Assume

that a sequence of N frequencies from the hop sequence is

chosen as a synchronization pattern (without data

modulation). The N noncoherent matched filters each consists

of a mixer followed by a bandpass filter (BPF) and a square

law envelope detector(an envelope detector followed by a

square law device). If the frequency hopping sequence is

delays are inserted into the matched filters so

that when the correct frequency hopping sequence appear, the

system produces a large out, indicating detection of the

synchronization. Acquisition can be accomplished rapidly

because all possible code offsets are examined

simultaneously.

fig(14.13)

- 32 -14

Since the required number of correlator or matched filters are

large, fully acquisition techniques are not usually used.

Serial search acquisition techniques are used instead of

parallel acquisition technique.

3-Direct sequence serial search acquisition.

-A popular technique for the acquisition of spread spectrum

signals is to use a single correlator or matched filter to serially

search for the correct phase of the DS code signal or the

correct hopping pattern of the FH signal.

-In a stepped serial acquisition scheme for a DS systems, the

timing of the local PN code is set, and the locally generated

PN signal is correlated with the incoming PN signal. At fixed

examination intervals of , where. , the output signal

is compared to a preset threshold. If the output is below the

threshold, the phase of the locally generated code signal is

incremented by a fraction(usually one half) of a chip and the

correlation is reexamined. When the threshold is exceeded,

the PN code is assumed to have been acquired, the phase

incrementing process of the local code is stopped, and the

code tracking procedure will be initiated.

- 33 -14

fig(14.14)

4-FH serial search acquisition.

Fig(14.15) shows, the PN code generator controls the

frequency hopper. Acquisition is accomplished when the local

hopping is aligned with that of the received signal, in a similar

procedure to DS.

fig(14.15)

Tracking

-Once acquisition or coarse synchronization is completed, tracking

or fine synchronization takes place.

Tracking code loops can be classified as:-

- 34 -14

1. Coherent tracking loops: The carrier frequency and phase are

known exactly so that the loop can operate on a baseband

signal.

2. Noncoherent tracking loops: 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 noncoherent code loop is used to tract the

received PN code.

1)Full time early–late tracking loop [often referred to as a delay

locked loop (DLL)].

-A basic noncoherent DLL loops for a direct sequence spread

spectrum system using binary phase shift keying (BPSK) is shown

in fig(14.16). The data and the code g(t) each modulate the

carrier using BPSK, and as before in the absence of noise and

interference, the received waveform can expressed as

(14.14)

Where A is a system gain parameter and is a random phase angle

in the range (.0.2π). The locally generated code of the tracking loop

is offset in phase from the incoming g(t) by a time , where

[ is the chip duration of PN code]. The loop provides

fine synchronization by first generating two PN code sequences

delayed from each other by one chip. Two bandpass

- 35 -14

filters are designed to pass the data and to average the product of

g(t) and the two PN sequences .

fig(14.14)

-The square law envelop detector eliminates the data since

. The output of each envelope detector is given by

Where is the autocorrelation of the PN waveform.

-The feedback signal instructs the VCO either to increase or

decrease its frequency, then forcing τ to either increase or decrease.

-When τ, is a small number, , yielding the

despread signal Z(t), which is applied to the input of a conventional

data demodulator.

-The main problem with the DDL is that the early and late arms

must be precisely gain balanced or else the feedback signal

will be offset and will not zero signal when the error is zero. This

- 36 -14

problem is solved by using a time shared tracking loop in place of

the full time locked loop.

-The main advantages are that only one correlator need be used in

the design of the loop.

2)Tua–dither tracking loop.

-A problem with some control loops is that if things are going well

and the loop is tracking accurately, the control signal is essentially

zero. When the control signal is zero, the loop can get confused and

do mistakable things. One type of time shared tracking loop, called

the tau-dither loop (TDL), shown in fig(14.17).

-Intentionally injecting a small error in the tracking correction, so

that the loop kind vibrates around the correct answer. This vibration

is typically small, so that the loss in performance is minimal. This

design has the advantage that only one correlator is needed to

provide the code tracking function and the despreading function.

-As Shown in fig (14.17), the PN code generator is driven by a

clock signal whose phase is dithered back and forth with a square

wave switching function, this eliminates the necessity of ensuring

identical transfer functions of the early and late paths. The S/N

performance of the TDL is only about 1.1dB worse than that of the

DLL.

- 37 -14

fig(14.17)

SS Commercial applications

1-Code division multiple access

-Fig(14.18) shows the communication resource(CR) plane being

partitioned by the use of a hybrid combination of FDMA and

TDMA known as code division multiple access (DMA).

CDMA is an application of spread spectrum (SS) techniques. Since

SS techniques can be classified into two major categories, direct

sequence SS and frequency hopping FHSS, thus CDMA can be also

classified into two major parts.

- 38 -14

Code division multiplexing

fig(14.18)

a-FH-CDMA

At each time slot whose duration is usually short, the frequency

band are divided (i.e band assignments) in FH-CDMA as shown in

the fig(14.18). In fig(14.18), during time slot 1, signal 1, occupies

band 1, signal 2 occupies band 2 and the signal 3 occupies band 3.

During time slot 2, signal 1 hops to band 3, signal 2 hops to band 1,

and so on. The CR can thus fully utilized, but the participants,

having their frequency bands reassigned at each time slot. Each user

employs a specific pseudnoise (PN) code orthogonal control their

frequency bands and time slot.

-The block diagram in fig(14.19) shows CDMA frequency hopping.

At each frequency hop time the PN generaor feeds a code sequence

to a device called frequency hopper. The frequency synthesizer is

used to generate one of the allowable hop frequencies according PN

code. MFSK modulation is used with FH, the data symbol

modulates a carrier wave that hops across the total CR bandwidth.

- 39 -14

AtA cos]cos[ ttnA

hopsfrequency

lfundamenta

stepfrequencyMFSK

k2

fig(14.19)

b-DS-CDMA

In DS-CDMA, each of N user groups is given its own code,

wherei=1,2,3,…N. The user codes are approximately orthogonal, so

that the cross correlation of two different codes is near zero.

Fig(14.20) shows a DS/CDMA. The first lock shows the data

modulation of a carrier . The output of the data modulator

belonging to a user from group 1 is

(this is a general form independent modulation)

The next block, the data modulated signal is multiplied by the

spreading signal belonging to user group 1, and the resulting

signal is transmitted over the channel. Simultaneously,

users from group 2 through N multiply their signals by their own

code functions. Frequently, each ode function is kept secret, and its

use is restricted to the community of authorized users. The signal

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present at the receiver is the linear combination of the received

signals from N users

The first stage of the receiver multiples the incoming signals by

[for user 1]. The output of the multiplier will yield the signal

-If the code functions are chosen with orthogonal properties,

the desired signals can be extracted perfectly in the absence of noise

since and the undesired signals are easily rejected,

since

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fig(14.20)

Multipath channels

-fig (14.21) shows a communication link with two discrete paths.

The multipath wave is delayed by some time τ, compared with the

direct wave.

In a DS, if we assume that the receiver is synchronized to the time

delay and RF phase of the direct path, the received signal can be

expressed as

Where x(t) is the data signal, g(t) is the code signal, n(t) is a zero

mean Gaussian noise process, and τ is the differential time delay

between the two paths. The angle is a random phase and α is the

attenuation of the multipath signal relative to the direct path. The

output of the correlator can be written as

Where =1. Also for , g(t)g( )≈0. Therefore, if is

less than the differential time delay between the multipath and

direct path signals, we can write

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Where is a zero mean Gaussian noise. We see that the SSS

effectively eliminates the multipath interference by virtue of its

code correlation receiver.

fig(14.21)

Note

If FH is used against the multipath problem, using another

mechanism to the improvement by rapid frequency change.

Advantages of CDMA

1-Privacy, When the code for a particular user group is only

distributed among authorized users, the CDMA process provides

privacy, since the transmission cannot easily be intercepted by

unauthorized users without the code.

2-Fading channels: If A particular portions of the spectrum is

characterized by fading signals in that frequency rage are

attenuated. In a FH/CDMA, only during the time a user hops into

the affected portion of the spectrum will user experience

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degradation. However, in a DS/CDMA only a part from the

spreaded bandwidth is affected.

3-Jam resistance according the processing gain .

4-Flexibility: All users can share the full spectrum of the resources

(frequency and time) asynchronously, that is the transition times of

the different users symbols do not have to coincide.

Ex14.1

A hopping bandwidth of 400 MHz and a frequency step size of 100

Hz are specified. What is the minimum number of PN chips that are

required for each frequency word?

Slution

Number of tones contained in

Minimum number of chips

Ex14.2

Consider the DS BPSK spread spectrum transmitter. Let the input

sequence 100110001, arriving at a rate of 75 bit/s, where the

leftmost bit is the earliest bit. Let g(t) be generated by the shift

register with initial state of 1111 and a cock rate of 225Hz.

a-Sketch the final transmitted sequence x(t)g(t).

b-What is the bandwidth of the transmitted (spread) signal.

c-What is the processing gain?

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d-Suppose that the estimated delay is too large by one chip time.

Sketch the despread chip sequence?

solution

x(t)=100110001 with data rate=75 bits

g(t) =111100010011010 with clock rate=225 Hz

Let

b-Bandwidth of

c-processing gain

d-x(t)g(t) 000100010100101111100010100

g(t) advanced by 1chip 01110001001101011110001001

O/P sum 01101001110100010001001110

Ex14.3

A total of 24 equal power terminals are to share a frequency band

through a code division multiple access (CDMA) system. Each

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terminals information at 9.6 kbit/s with a direct sequence spread

spectrum BPSK modulated signal. Calculate the minimum chip rate

of the PN code in order to maintain a bit error probability of

solution

from table of error function x=3.09

4.77=

W=4.77x23x9.6 kbit/s=1.05 MHz

minimum chip rate

where bit energy, bit duration

S=received signal power, R=data rate

where =averages signal power to average noise power

=Noise power spectral density

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W=bandwidth of the system

Ex14.4

Consider an FH/MFSK system .Let the PN generator be defined by

a 20 stage linear feedback shift register with a maximal length

sequence. Each state of the register dictates a new center frequency

within the hopping band. The minimum step size between center

frequencies is 200Hz. The register clock rate is 2KHz. Assume that

8-ary FSK modulation is used and that the data rate is 1.2kbit/s.

a-What is the hopping bandwidth.

b-What is the chip rate.

c-How many chips are there in each data symbol.

d-What is the processing gain.

solution

Hopping bandwidth=

Wss=number of states×minimum step between frequencies

b-chip rate =hop rate=2000chip/s

c-chip/symbol:

d-processing gain:

Ex14.5

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A feedback shift register PN generator produces a 31 bit PN

sequence at a clock rate of 10MHz. What are the equation and

graphical form of the autocorrelation function and power spectral

density of the sequence? Assume that pulses have values of ±1v.

Solution

The 31 bit sequence has autocorrelation function with a maximum

value at

Decreasing linearly to -1/31 at for T equal to a chip

interval

[total agreements –total disagreements in one full period of

the sequence with a τ position cyclic shift]

)12( 31P

R(τ) repeates for offset times= for

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