UNIT-5 Spread Spectrum Communication.pdf

UNIT-V
SPREAD SPECTRUM COMMUNICATION
 Introduction and History
 Advantages of Spread Spectrum
 Generation and Characteristics of PN sequence
 Direct Sequence Spread Spectrum
 Frequency Hopping Spread Spectrum
 Applications of DSSS and FHSS
 Acquisition and Tracking in DSSS
 Acquisition and Tracking in FHSS

UNIT-5
SPREAD SPECTRUM COMMUNICATION
INTRODUCTION
In any digital communication system, the basic design factors are 1) efficient utilisation of
channel bandwidth and 2) minimizing the transmitted power. Some of the major problems
encountered in specific communication systems are
1. Combating or suppressing the detrimental effects of interference due to jamming,
interference arising from other users of the channel, and self-interference due to
multipath propagation.
2. Hiding a signal by transmitting it at low power and making it difficult for an unintended
listener to detect the signal.
3. Achieving message privacy in the presence of other listeners.
These problems can be successfully solved by using a technique called spread spectrum
modulation.
SPREAD SPECTRUM COMMUNICATION SYSTEM
A system is defined to be a spread spectrum communication system if it fulfils 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 done by the correlation of
the received spread signal with a synchronized replica of the spreading signal used to
spread the information.
4) In the transmitter of a digital communication system, such frequency spreading of
signal is achieved along with the Bandpass modulator circuit.
MODEL OF SPREAD SPECTRUM DIGITAL COMMUNICATION SYSTEM
The block diagram shown in Figure 5.1 illustrates the basic elements of a spread spectrum
digital communication system.
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 which
interfaces with the modulator at the transmitting end and the second which interfaces with the
demodulator at the receiving end. These two generators produce a pseudorandom or
pseudonoise (PN) binary-valued sequence, which is used to spread the transmitted signal at the
modulator and to dispread the received signal at the demodulator.

Figure 5.1 Model of Spread-Spectrum Digital Communication System.
Time synchronization of the PN sequence generated at the receiver with the PN
sequence contained in the received signal is required in order to properly dispread the received
spread-spectrum signal. In a practical system, synchronization is established prior to the
transmission of information by transmitting a fixed PN bit pattern which 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, the transmission 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. Interference is
introduced in the transmission of the spread-spectrum signal through the channel. The
characteristics of the interference depend to a large extent on its origin. The interference may
be generally categorized as being either broadband or narrowband (partial band) relative to the
bandwidth of the information-bearing signal, and either continuous in time or pulsed
(discontinuous) in time.
Two types of digital modulation are considered, namely, PSK and FSK. PSK
modulation is appropriate for applications where phase coherence between the transmitted
signal and the received signal can be maintained over a time interval that spans several symbol
(or bit) intervals. On the other hand, FSK modulation is appropriate in applications where phase
coherence of the carrier cannot be maintained due to time variations in the transmission
characteristics of the communications channel. The PN sequence generated at the modulator is
used in conjunction with the PSK modulation to shift the phase of the PSK signal
pseudorandomly, as described below at a rate that is an integer multiple of the bit rate. The
resulting modulated signal is called a direct-sequence (DS) spread-spectrum signal. When used
in conjunction with binary or M-ary (M > 2) FSK, the PN sequence is used to select the
frequency of the transmitted signal pseudorandomly. The resulting signal is called a frequency-
hopped (FH) spread-spectrum signal. Although other types of spread-spectrum signals can be
generated, our treatment will emphasize DS and FH spread-spectrum communication systems,
which are the ones generally used in practice.

BENEFICIAL ATTRIBUTES OF SPREAD SPECTRUM SYSTEMS
Spread spectrum modulation was originally developed for military applications where
resistance to jamming (interference) is of major concern. However there are civilian
applications that also benefit from the unique characteristics of spread spectrum modulation.
We hereby list the following beneficial attributes of spread spectrum systems.
1) Interference suppression benefits:
(i) In combating intentional interference (jamming), the transmitter introduces an element of
unpredictability or randomness (pseudo randomness) in each of the transmitted coded signal
waveforms. This is known to the intended receiver only, but not to the jammer. Thus
interference due to jamming is suppressed.
(ii) Resolvable multipath components resulting from time dispersive propagation
through a channel may be viewed as a form of self-interference. This type of
interference may also be suppressed by the introduction of pseudorandom
pattern in the transmitted signal.
2) Multiple Access: Spread spectrum methods can be used as a multiple access technique in
order to share a communication resource among numerous users in a coordinated
manner. Interference from the other users arises in multiple access communication
systems in which a number of users share a common channel bandwidth. The
transmitted signals in this common channel spectrum may be distinguished from one
another by superimposing a different pseudorandom pattern, also called a code, in
each transmitted signal. Thus, a particular receiver can recover the transmitted
information intended for it by knowing the code or key, used by the corresponding
transmitter. This type of communication technique, which allows multiple users to
simultaneously use a common channel for transmission of information, is called
Code Division Multiple Access (CDMA).
3) Energy Density Reduction
A message may be hidden in the background noise by spreading its bandwidth with
coding and transmitting the resultant signal at a low average power. Because of its low power
level, the transmitted signal is said to be “covert”. It has a
low probability of being intercepted (detected) by a casual listener. Hence, it is also called as a
Low-Probability of Intercept (LPI) signal. A Radiometer is a simple power measuring
instrument that can be used to detect the presence of spread spectrum signals within some
bandwidth, B.
4) Fine Time Resolution:
Spread spectrum signals are used to obtain accurate range (time delay) and range rate
(velocity) measurements in radar and navigation. Distance can be determined by measuring
the time delay of a pulse as it traverses the channel.

5) Message Privacy
Message privacy may be obtained by superimposing a pseudorandom pattern
on a transmitted message. The message can be demodulated by the intended receivers,
who know the pseudorandom pattern or key used at the transmitter, but not by any other
receivers, who do not know the key.
Thus the Spread Spectrum Communication Provides
(a) Protection against eavesdropping
(b) Resistance to intentional jamming
(c) Resistance to fading caused by multipath effects
(d) Multi-user facility over a given channel
(e) Ranging facility
SPREAD SPECTRUM APPROACHES (HISTORICAL BACKGROUND)
There are two spread-spectrum approaches called Transmitted Reference (TR) and Stored
Reference (SR).
(i) In a TR system, the transmitter send two versions of truly random spreading signal
(wideband carrier) – one modulated by data and the other unmodulated. The
receiver used the unmodulated carrier as the reference signal for despreading
(correlating) the data modulated carrier.
(ii) In a SR system, the spreading code signal is independently generated at both the
transmitter and the receiver. Since the same code must be generated independently
at two locations, the code sequence must be deterministic, even though it should
appear random to unauthorized listeners. Such random appearing deterministic
signals are called pseudonoise (PN), or pseudorandom signals.
Modern spread spectrum systems use Stored Reference (SR) approach which uses a
Pseudonoise (PN) or pseudorandom code signal.
PSEUDO-NOISE SEQUENCES (PN-SEQUENCES)
A pseudonoise (PN) sequence may be defined as a coded sequence of 1’s and 0’s with
certain autocorrelation properties. The PN sequence is a deterministic, periodic signal that is
known to both the transmitter and receiver. Even though the signal is deterministic it appears
to have the statistical properties of sampled white noise. Hence, it appears to be a truly random
signal, to an unauthorised listener.
PN sequences have many of the properties possessed by a truly random binary
sequence. A random binary sequence is a sequence in which the presence of a binary symbol
1 or 0 is equally probable. There are three basic properties that can be applied to any periodic
binary sequence as a test for the appearance of randomness. They are described as follows
1) Balance Property: In each period of the sequence, the number of 1’s is always one
more than the number of 0’s. This property is called the balance property.
For an ML sequence generated by n-stage shift register with linear feedback:
(i) Period = 2 1
m
 bits
(ii) Number of 1s =
1
2m

(iii) Number of 0s =
1
2 1
m

2) Run Property: Among the runs of 1’s and of 0’s in each period of the sequence, one-half
the runs of each kind are of length one, one-fourth are of length two, one-eighth are of length
three, and so on. This property is called the Run property. A run is defined as a sequence of a
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.
For an ML sequence generated by an n-stage linear feedback shift register, the total number of
runs is
 
1
2
N 
, where 2 1
m
N  
3) Correlation Property The autocorrelation function of a sequence is periodic and binary
valued. This property is called the correlation property.
Let
 
0 1 2 1
, , , N
C C C C 
be an ML sequence of period, 2 1
m
N   generated by an n-stage
LFSR. The normalized circular or cyclic autocorrelation function of the sequence is defined as
follows:
1
(i )modN
0
1
( ) , 0,1, , 1
N
c i
i
R C C N
N

 



  

Where τ is the shift and the suffix i 
 is modulo-N (remainder obtained after dividing i+τ
by N).
If symbol 1 and symbol 0 are represented by +1 volt and -1 volt, then ACR function has only
two values. Thus
1 for =kN, k=0,1,2.....
( ) 1
for kN, k=0,1,2...
c
R
N





 




Pseudo Noise (PN) sequence generator
The class of sequences used in spread spectrum communications is usually periodic in
that a sequence of 1s and 0s repeats itself exactly with a known period. The maximum length
sequence, a type of cyclic code represents a commonly used periodic PN sequence. The
maximum length sequences or PN sequences can be generated easily using shift register
circuits with feedback from one or more stages.
A PN sequence generator using a 3-stage shift register is shown in Figure 5.2.

Figure 5.2 PN Sequence or Maximum length Generator
The 3-stage shift register consists of 3 flip-flops regulated by a single timing clock. At each
pulse of the clock, the state of each flip-flop is shifted to the next one. The feedback function
is obtained by using modulo-2 addition of the outputs of flip-flops x2 and x3. The feedback term
is applied to the input of the first flip-flop x1. The maximum length sequence output is obtained
by noting the contents of flip-flop x3 at each clock pulse. The maximum-length sequence so
generated is always periodic with a period of
2 1
m
N   ... (5.1)
Where m is the length of the shift register. Here m=3 and so N=23
-- 1=7.
For the PN sequence generator of Figure 5.2, if we assume that the shift
register contents are initially 111, then with each clocking pulse, the contents will
change as shown in the following table 5.1
Table 5.1 Operation of PN sequence generator

Hence for one period, the output PN sequence is 1 1 1 0 0 1 0, with a sequence length of 7.
Thereafter, the sequence will be repeated.
Important Observations
 The length of the PN sequence is N = 2 1
m
 , where m is the number of shift register
stages.
 The PN sequence repeats itself after every ‘N’ clock cycles.
 The PN sequence is an NRZ type pulse signal with logic ‘l’ represented by + 1 and
logic’0’ represented by -1, as shown in Figure 5.3.
Figure 5.3 PN Sequence waveform
 The duration of every bit is known as the chip duration c
T . The chip rate c
R is defined
as the number of bits (chips) per second and inverse of Tc is called chip frequency.
1
c
c
T
R
 …. (5.2)
 The period of the PN sequence is b c
T NT

 The autocorrelation function R() is a periodic function of time and it is a two valued
function is given by
2
2
1
( ) ( ) ( )
c
c
T
T
c
R c t c t d
T
  

 
 …. (5.3)
Figure 5.4 PN Sequence Autocorrelation

Example 5.1
A four stage shift register with feedback connections taken from the outputs of stages 4 and 1
through a modulo – 2 adder, is used for PN sequence generation. Assuming the initial contents
of the shift register to be 0100, determine the output sequence. What is the length of the
sequence?
Sol. The PN sequence generator is shown in Figure 5.5
Figure 5.5 PN Sequence Generator
If the initial contents of the shift register are 0100, then with each clocking pulse, the contents
will change as shown in the following table 5.2.
The output PN sequence is 0 0 1 0 0 0 1 1 1 1 0 1 0 1 1. After 15 shifting’s, the initial contents
of the shift registers are once again obtained. For further shifting’s, the same cycle of events
will repeat. Thus, the length of one period of the PN sequence is, N = 2m
– 1 = 24
– 1 = 15. Hence
the sequence is a maximal length sequence.
Testing of PN sequence for Randomness Properties
Let us consider example 5.1 for testing of PN sequence, for Randomness properties.
1) Balance Property: The output PN sequence is given by 0 0 1 0 0 0 1 1 1 1 0 1 0 1 1. There
are seven 0s and eight 1s in the sequence. Hence balance property is satisfied.
2) Run Property: Consider the zero runs - there are four of them. One-half are of length 1,
one fourth are of length 2. The same is true for the one runs. Hence run property is satisfied.
3) As shown in Figure 5.4, the autocorrelation function R () will be a periodic function of time
and will be a two valued function. Hence the correlation property is also satisfied.
4) For an m-stage linear feedback shift register the sequence repetition period in clock pulses
is N = 2m
– 1. Thus it can be seen that the sequence generated by the shift register generator of
Figure 5.5 is an example of maximum length sequence.

Table 5.2 Operation of PN sequence generator
Demerits of Spread Spectrum System
The use of a spreading code in the transmitter produces a wideband transmitted signal that
appears noise like to a receiver that has no knowledge of the spreading code. Naturally, this
technique provides improved protection against interference. But there are also some demerits
involved in this method. They are
 Increased transmission bandwidth
 System complexity
 Processing delay
Hence, spread spectrum systems are employed only for those applications where security of
transmission is our primary concern.
CLASSIFICATION OF SPREAD SPECTRUM MODULATION TECHNIQUES
The SS modulation techniques are broadly classified into two categories namely, the
averaging type systems and the avoidance type systems. The averaging systems reduce the
interference by averaging it over a long period. The Direct Sequence Spread Spectrum (DS-
SS) system is an averaging system. The avoidance type systems reduce the interference by
making the signal avoid the interference over a large fraction of time. Some of the avoidance

type systems are Frequency Hopping (FH) system, Time hopping (TH) system, Chirp and
hybrid modulation system.
Figure 5.6 Classification of Spread Spectrum Communication
DIRECT SEQUENCE SPREAD SPECTRUM SYSTEMS
The most important advantage of spread spectrum modulation is that it provides
protection against externally generated interfering signals such as jamming signals. The Direct
Sequence Spread Spectrum (DS-SS) technique can be used in practice for such interference
suppression. For this transmission of information signal is carried over a band pass channel
(eg. Satellite channel). For such an application, the coherent Binary Phase Shift Keying (BPSK)
is used in the communication system.
In the Direct sequence spread spectrum (DS-SS) systems, the use of a PN sequence to
modulate a phase shift keyed signal achieves instantaneous spreading of the transmission
bandwidth.
DS-BPSK Transmitter
The Figure 5.7 shows the transmitter section of the Direct Sequence Spread Spectrum
with coherent BPSK. The transmitter section uses two stages of modulation. In the first stage
the input data sequence is first converted into an NRZ sequence b(t) by the NRZ encoder. This
sequence b(t) is used to modulate a wide band pseudo-noise sequence c(t) by applying these
two sequences to the product modulator or multiplier. Both sequences are in polar form. The
product sequence m(t) = b(t)*c(t) will have a spectrum which will be same as that of c(t). The
modulated signal m(t) is used to modulate the local carrier for BPSK modulation at the second
stage. We can also use QPSK modulation.

Figure 5.7 DSSS-BPSK Transmitter
The second stage modulated output s(t) is thus a Direct Sequence Spread binary phase shift
keyed (DS | BPSK) signal. The phase modulation (t) of S (t) has one of the two values, 0
and, depending on the polarities of the data sequence and PN sequence, as shown in the Table
5.3.
Table 5.3 Truth table for phase modulation (t), Radians
Performance Analysis of DSSS
Inorder to discuss the effect of multiplying the data sequence by the PN sequence, we shall
consider only the baseband DS spread-spectrum i.e without initial carrier modulation by the
data sequence.
Let the NRZ bipolar waveform of the data sequence be denoted as by b (t) and the NRZ of PN
sequence is denoted by C (t). Let the digit duration be Tb seconds and the PN sequence digit
duration be Tc seconds. It is always arranged that Tc<<Tb. Figure 5.8 illustrates the wave forms
for the first stage of modulation.

Figure 5.8 waveforms of first stage of modulation
The spectrum of m(t), the baseband DS-spread spectrum signal is almost the spectrum of c(t)
itself(since product of b(t) and c(t) in time domain is convolution of spectra). Figure 5.9
illustrates the waveforms for the second stage of modulation for one period of the PN sequence.
Figure 5.9 waveforms of second stage of modulation
Inorder to illustrate how the spread spectrum modulation enables us to reject deterministic
interfering signals added to the transmitted signal S (t) during the course of passage through
the channel, we are adding the interfering signal i (t) to the DS spread spectrum signal S(t).
r(t) = s(t)+i(t)=b(t)*c(t)+i(t) …(5.4)
The first operation to be performed at the receiver is to de-spread the received signal. Let it is
multiplied by the PN sequence waveform c(t), which is assumed to be perfect
synchronization with the c(t) used at the transmitting end.

Z(t)=r(t)*c(t)=b(t)*c(t)2
+i(t)*c(t) …(5.5)
But c(t) is either -1 or +1 at any time, hence
Z(t)=b(t)+i(t)*c(t) …(5.6)
From above equation we find that when we de-spread the message or data, the interference
signal gets spread over a wide bandwidth by getting multiplied by the PN sequence waveform
c (t). The z (t) is integrated over period of Tb acting as LPF and removes the wide-band
component i (t)*c (t), thus achieving the suppression of interfering signal.
DS-BPSK Receiver
The receiver section consists of two stages of demodulation. In the first stage the
received signal r(t) is subjected to coherent detection using the locally generated carrier signal.
This carrier signal is arranged to be in phase and frequency synchronism with the carrier used
at the transmitter. In the second stage, the output of the coherent detector is subjected to
despreading. It is multiplied with a locally generated PN sequence, which is in synchronism
with the one at the transmitter. After despreading, it is integrated over a bit duration to get the
observed random signal V. This is used for decision making, which provides an estimate of the
original data sequence. The figure 5.10 shows the Receiver section of DS-BPSK system.
Figure 5.10 DSSS-BPSK Receiver
Important Observation
 In practice, the transmitter and receiver of Figures 5.7 and 5.10 are followed. In the
transmitter spectrum spreading is performed prior to phase modulation. Also phase
demodulation is done first and then despreading is done second, in the receiver.
 In the model of DS spread spectrum BPSK system used for analysis, the order of these
two operations are interchanged. In the transmitter, BPSK is done first and spectrum
spreading is done subsequently. Similarly, at the receiver also, spectrum despreading is
done first and then phase demodulation is done second.
 This is possible, because the spectrum spreading and BPSK are both linear operations.

MODEL for DS spread-spectrum BPSK communication system:
Let the carrier signal at the transmitter have a power of P0 and a frequency fc so that the
carrier signal may be represented as √2𝑃0cosω0t. Let the jamming signal be of normalized
power Pj and frequency fc so that it is J (t) = √2𝑃
𝑗cos (ω0t+θ). The jammer signal phase will
not have any relationship with the phase of the carrier used for BPSK modulation. θ, in general
is uniformly distributed over [0,2π] and assuming perfect synchronization of PN sequence at
transmitter and receiver. Assuming that the locally generated carrier signal has a normal power
of unity and it is in frequency and phase synchronism with the carrier used at the transmitter.
Figure5.11 Model of DS spread spectrum BPSK system
With the data d(t) in polar NRZ, the BPSK modulator is just a product device. Hence,
0 0
(t) 2 (t)cos
s P d t

 …(5.7)
And 0 0
(t) s(t)*c(t) 2 (t)cos * (t)
x P d t c

  …(5.8)
0 0 0
y(t) 2 (t)cos * (t) 2 cos( )
j
P d t c P t
  
   …(5.9)
And 2
0 0 0
(t) 2 (t)cos * (t) 2 cos( )*c(t)
j
z P d t c P t
  
   …(5.10)
But 2
(t)
c is equal to 1 for all t.
Therefore, 0 0 0
z(t) 2 (t)cos 2 cos( )*c(t)
j
P d t P t
  
   …(5.11)
The coherent detector is a gain a product device followed by a LPF. Hence the input, w(t) to
the LPF in the coherent detector is given by
0
w(t) z(t)* 2 cos t

 …(5.12)
2 2
0 0 0 0 0
2 (t)cos 2 c(t)[cos cos sin cos sin ]
j
P d t P t t t
     
   …(5.13)
0 0 0 0
(t)[1 cos2 ] (t)[1 cos2 ]cos (t)[1 sin 2 ]sin
j j
P d t P c t P c t
    
      …(5.14)
When w(t) is fed to the LPF , the output from it is given by,
0
(t) (t) c(t)cos
j
v P d P 
  …(5.15)
Hence C’
(t) represents the time signal corresponding to the part of the spectrum of c(t) which
passes through the LPF. The power spectrum of c(t)cos
j
P  is given by
2
2
[cos ] sin
(f)
2
j c c
c
PT E T f
S
T f
 

 
  
 
…(5.16)
Fc the chip frequency is very much greater than fb , the value of S(f) will be a constant equal to
the peak value of sinc2
function.
The PSD of the output term caused by the sinusoidal jamming signal is given by

2
[cos ]
(f)
2
j c
PT E
S

 …(5.17)
But  is a r.v which is uniformly distributed over [0,2π]. Hence,
2
[cos ]
E  =1/2
0
1
(f) ;
4
j c
b
b
PT
S f f
T
   …(5.18)
If the interfering signal were random channel noise ot two-sided PSD equal to
2

, then
1
2
b
e
E
P erfc

 …(5.19)
When we have the sinusoidal jamming instead of white noise
2

is replaced by S0(f), we get
2
1
2
b
e
j c
E
P erfc
PT
 …(5.20)
But 0
b b
E bitenergy PT
 
0
1
2 ( / 2)(f / )
e
j c b
P
P erfc
P f
 …(5.21)
The effective jammer power, [( / 2)(f / )]
jeff j c b
P P f

0
1
2
e
jeff
P
P erfc
P
 …(5.22)
The quantity (fc/fb) the ratio of the chip frequency to the bit frequency which is always very
much larger than 1, is called the processing gain and denoted by Gp
Processing gain=Gp= (fc/fb) …(5.23)
The processing gain is a measure of the extent to which the jamming
signal power is reduced due to the use of spread spectrum. So, higher the ratio of chip frequency
to bit frequency, better will be the resistance to a narrow band jamming signal.
Note: The Jammer is also another source of noise. If Pj is the jammers power at the receiver,
then
2 b
e
j
E
P Q
N
 , where /
j j c
N P w
 …(5.24)
wc the transmission bandwidth of DSSS system.
10 10
(indB)
10log 10log ( / )
p b j
JM G E N
  …(5.25)

Ranging using DS-Spread Spectrum Signals.
Let us know how DS spread signal is used for ranging, consider a DS spread spectrum signal
0 0
(t) 2 c(t)cos
s P t

 …(5.26)
For ranging s(t) is transmitted. After it impinges on the target, a part of the reflected signal is
received. The received signal r(t) is given by
0 0
(t) s(t 2T) 2 c(t 2T)cos ( 2 )
r P t T
  
     …(5.27)
The signal is now correlated with the chip signal c(t), delayed by an adjustable and accurately
known delay of τ seconds. The output of the correlator is
0
( ) ( 2 ) (t )
NT
R c t T c dt
 
  
 …(5.28)
Where NT is the total length of PN sequence c(t).
 is adjusted till R( ) takes a maximum value. When  =2T it is maximum. If v is the velocity
of electromagnetic waves
Range of the target= 5
1
( 3 10 )
2 2
v
d km
 
    …(5.28)
The accuracy of the measurement depends on Tc, smaller better is the accuracy.
DSSS-Code Division Multiple Accesses (CDMA): CDMA using Direct Sequence Spread
Spectrum (DSSS), in which each user is provided with a unique PN code and the PN codes
given to different users are almost uncorrelated.
There are n users, each one transmitting data using a DS spread spectrum BPSK system and all
of them use the same carrier frequency f0. Since all the DSSS signals will be present at the
input of each of the receivers, multiple access interference (MAI) exists at each of the receivers,
i.e., at the output of any given receiver, there will be some interference caused by the remaining
(n – 1) users. Let us analyze and see how this interference affects the probability of error and
following assumptions are made:

1. The chip frequencies are the same for all the n- systems.
2. The transmitted powers are the same for all the systems.
3. The data rates fb = 1/Tb are the same for all the systems.
4. Thermal noise introduced by the channel is not taken into account
5. The power presented by each DS SS signal at its receiver input is the same for all the
receivers.
6. The random phases of the n carrier signals are statistically independent.
Let f0 Hz be the common carrier frequency, di(t) be the data transmitted and ci(t) be the PN
sequence signal of the ith
user, and P0 be the power presented by each signal at the input
of its receiver. The data rate is fb for all users and let i
 be the random phase of the carrier
of the ith
user. Then the signal present at the input of each receiver is given by
0 0
1
( ) 2 ( ) ( )cos( )
n
i i i
i
z t P c t d t t
 

 

The output of the integrate and dumb filter at the kth receiver is given by
0 0
1
( ) ( ) ( ) ( )cos( )
n
i k i i k
i
v t P c t c t d t  

 

0 0
1,
( ) ( ) ( ) ( )cos( )
n
k i k i i k
i i k
P d t P c t c t d t  
 
  

The above equation has written by making all PN sequence waveforms ( )
i
c t ’s make
transitions at the same time. Rewriting as:
0 0 0 , ,
1,
( ) ( ) ( ) ( )cos( )
n
k i k i k i
i i k
v t P d t P c t c t 
 
  
The PSD of one interfering signal is given by,
0
1
(f) ;
4
j c
b
b
PT
S f f
T
  
The total PSD for (n-1) statistically independent interfering signals as,
0
0
( 1) 1
( ) ;
4
c
T
b
n PT
S f f
T

 
The probability of error for (n-1) interferers is given as;
0
1 1 1
2 2
2 2 1
b b
e
j c c
P T T
P erfc erfc
P T n T
    
 
 
    
 
  
 
   
 
In order to minimize the probability of bit error, we have to maximize
( 1)
2
c
b
f n
f


Advantages of DS-SS System
1. This system combats the intentional interference (jamming) most effectively.
2. This system has a very high degree of discrimination against the multipath signals.
Therefore, the interference caused by the multipath reception is minimized successfully.
3. The performance of DS-SS system in the presence of noise is superior to other systems.

Disadvantages of DS-SS system
1. The PN code generator output must have a high rate. The length of such a sequence needs
to be long enough to make the sequence truly random.
2. With the serial search system, the acquisition time is too large. This makes the DS-SS system
be slow.
3. Synchronization is affected by the variable distance between the transmitter and receiver.
4. The DS-SS signal is not very effective against broadband interference.
Major applications of DS-SS system
1. Providing immunity against a jamming signal – Anti-jamming application.
2. Low detectability signal transmission – the signal is purposely transmitted at a very low
power level. Hence the signal has a Low Probability of being intercepted (LPI) and it is called
an LPI signal.
3. Accommodating a number of simultaneous signal transmissions on the same channel, i.e.
Code Division Multiple Access (CDMA) or spread spectrum multiple access (SSMA).
PERFORMANCE PARAMETERS OF DS-SS SYSTEM
The important performance parameters of a direct sequence spread spectrum system are
1) Processing gain, 2) Probability of Error and 3) Jamming Margin.
1) Processing Gain
The processing gain of a DS-SS system represents the gain achieved by processing a
spread spectrum signal over an unspread signal. It may also be defined as the ratio of the
bandwidth of the spread spectrum signal to the bandwidth of the unspread signal.
Therefore, Processing gain Gp =
𝑏𝑎𝑛𝑑𝑤𝑖𝑑𝑡ℎ 𝑜𝑓 𝑠𝑝𝑟𝑒𝑎𝑑 𝑠𝑖𝑔𝑛𝑎𝑙
𝑏𝑎𝑛𝑑𝑤𝑖𝑑𝑡ℎ 𝑜𝑓 𝑢𝑛𝑠𝑝𝑟𝑒𝑎𝑑 𝑠𝑖𝑔𝑛𝑎𝑙
The bit rate of the binary data entering the transmitter input refers to the bandwidth of unspread
signal. It is given by
1
b
b
R
T
 … (5.29)
The chip rate of the PN sequence refers to the bandwidth of spread spectrum signal. It is
given by
1
c
c
R
T
 … (5.30)
Therefore, processing gain is given by
b
p
c
T
G
T
 … (5.31)
We note that Tb = NTc. where N is the number of chips per information bit, and also called as
the spread factor.

Hence,
b
p
c
T
G N
T
  …(5.32)
The Processing Gain (PG) is also called as the bandwidth expansion factor (Be) since it
represents the advantage gained over the jammer that is obtained by expanding the bandwidth
of the transmitted signal.
2) Probability of Error
The probability of error Pe for a coherent BPSK system is given by
1
2
b
e
E
P erfc

 … (5.33)
Where Eb is the energy per bit and
2

is the power spectral density of white noise.
In a DS-SS BPSK system, the interference may be treated as a wideband noise signal with a
power spectral density of
2

.For the spread signal, we may write
 =JTc (5.34)
Where J refers to average information power and Tc chip duration or interval.
Therefore the probability of error for DS-spread spectrum is given by
1
2
b
e
c
E
P erfc
JT
 (5.35)
3)Jamming Margin (Antijam characteristics)
Let b s b
E PT
 …(5.36)
Where Ps is the average signal power and Tb is the bit duration.
Hence, ( )( )
b s b s b
c c
E PT P T
JT J T

  …(5.37)
b
p
c
b b
s
T
G
T
J
E E
P
 
 
…(5.38)
The ratio
s
J
P
is called as the jamming margin. Therefore, the jamming margin may be
defined as the ratio of average interference power J and the average signal power Ps.
JM(dB) = 10 10 min
10log 10log ( )
b
p
E
G

 …(5.39)
Where min
( )
b
E
 is the minimum bit energy-to-noise density ratio needed to support a
prescribed average probability of error.

FREQUENCY HOPPING SPREAD SPECTRUM SYSTEMS (FH-SS)
In the Direct sequence spread spectrum systems (DS-SS), the use of a PN sequence to
modulate a phase shift keyed signal achieves instantaneous spreading of the transmission
bandwidth. The frequency hopping spread spectrum (FH-SS) system is an alternative method.
In FH-SS, the spectrum of the transmitted signal is spread sequentially by randomly hopping
the data modulated carrier from one frequency to the next. Hence, the type of spread spectrum
in which the carrier hops randomly from one frequency to another is called Frequency-hopped
Spread Spectrum (FH-SS) system.
Basic Principle
In a FH-SS communication system the available channel bandwidth is subdivided into
a large number of contiguous frequency slots. In any signalling interval, the transmitted signal
occupies one or more of the available frequency slots. The selection of the frequency slot(s) in
each signalling interval is made pseudorandomly according to the output from a PN generator.
The figure 5.12 illustrates a particular FH pattern in the time-frequency plane.
Figure 5.12 Example of Frequency-hopped pattern
A common modulation format for FH systems is that of M-ary frequency shift keying (MFSK).
The combination is referred to simply as FH/MFSK. Although PSK modulation gives better
performance than FSK in AWGN channel, it is difficult to maintain phase coherence in
i) The synthesis of frequencies used in the hopping pattern.
ii) The propagation of the signal over the channel as the signal is hopped from one
frequency to another frequency over a wide bandwidth.

Therefore, FSK modulation with non-coherent detection is usually employed with
FH spread spectrum signals.
Types of Frequency hopping
Since frequency hopping does not cover the entire spread spectrum instantaneously, we
consider the rate at which the hops occur. We identify two basic (technology-independent)
characterizations of frequency-hopping. They are
1) Slow-frequency hopping
2) Fast-frequency hopping.
Slow-frequency hopping
In FH system, if the hopping is performed at the symbol rate, we have a slow hopped
signal. Hence in slow-frequency hopping, the symbol rate Rs of the MFSK signal is an integer
multiple of the hop rate Rc i.e. several symbols are transmitted on each frequency hop.
Transmitter:
Figure 5.13 shows the block diagram of a slow-frequency hopping FH-MFSK
transmitter. First, the incoming binary data are applied to an M-ary FSK modulator. The
resulting M-ary FSK modulated signal is applied to a Mixer. The Mixer consists of a
multiplier followed by a band pass filter (BPF)
Figure 5.13FHSS/M-ary FSK Transmitter
The other input to the mixer block is obtained from a digital frequency synthesizer. The
frequency synthesiser is controlled by a PN code generator. Hence the M-ary FSK modulated
signal is again modulated by a carrier produced by the frequency synthesizer. The Mixer
produces two outputs of the sum frequency and the difference frequency. The band pass filter
that follows the mixer selects only the sum frequency signal, which is the FH-MFSK signal.
This signal is then transmitted.
 Using the M-ary FSK system, M symbols can be transmitted, where M=2K.
Here k is
the number of bits of the input binary data that form one symbol.

 The M-ary FSK modulator will assign a distinct frequency for each of these Msymbols.
The synthesizer output at a given instant of time is the frequency hop.
 The output bits of the PN generator change randomly. Hence the synthesizer output
frequency will also change randomly.
 Each frequency hop is mixed with the MFSK signal to produce the transmitted signal.
 If the number of successive bits at the output of PN generator is n, then thetotal number
of frequency hops will be 2n
.
 The total bandwidth of the transmitted FH-MFSK signal is equal to the sum of all the
frequency hops. Therefore, the bandwidth of the transmitted FH-MFSK signal is very
large of the order of few GHz.
Receiver:
Figure 5.14 shows the block diagram of a slow-frequency hopping FH-MFSK
receiver
Figure 5.14 FHSS/M-ary FSK Receiver
The received signal is applied as input to the Mixer. The other input to the mixer is obtained
from the digital frequency synthesizer. The frequency synthesizer is driven by a PN code
generator. This generator is synchronized with the PN code generator at the transmitter.
Therefore, the frequency hops produced at the synthesizer output will be identical to those at
the transmitter. The mixer produces two outputs of the sum frequency and the difference
frequency. The band pass filter selects only the difference frequency, which is the MFSK
signal. Thus the mixer removes the frequency hopping. The MFSK signal is then applied to a
non-coherent MFSK detector. A bank of M, non-coherent matched filters are used for non-
coherent MFSK detection. Each matched filter is matched to one of the tones of the MFSK
signal. An estimate of the original symbol transmitted is obtained by selecting the largest filter
output.

The FHSS signal and spreading Factor:
Let Ts denote the symbol period for an M-ary FSK modulation. Let f0 denote the unmodulated
carrier frequency of the M-ary FSK modulation. Then the M-ary FSK angular frequencies are
0 0 0 0
1 3 5 ( 1)
, , ,.........
2 2 2 2
k
M
        

         … (5.40)
and the M-ary FSK modulated signal itself can be written as
0
(t) 2 cos( ) ( 1)
MFSK k k s s
S P t forkT t k T
 
     … (5.41)
after each chip period Tc, the frequency synthesizer output hops to a new value, then during that chip
period the FH/MFSK signal is given as
/ 0
(t) 2 cos[( ) )
FH MFSK k i k
S P t
  
   … (5.42)
The mixing of the MFSK signal with the synthesizer output signal having a frequency of fi
increases the bandwidth occupancy. If the MFSK signal has a bandwidth Ws then
. .ofFH/ MFSKsignal LW
c s
W BW
  … (5.43)
Where L>1, is called the spreading factor or processing gain. 2m
L  , m is length of PN
segment to select frequency hop.
For a slow-hoping FHSS, the symbol rate Rs=1/Ts of the MFSK signal is an interger multiple
of the hop rate Rc=1/Tc . the bitrate Rb and the symbol rate Rs in a MFSK sytem are related
2
log
b
s
R
R
M
 … (5.44)
Since Tc ≥ Ts in slow hopping FHSS, there can bne several symbols in one hop interval Tc.
In slow FHSS the hop rate i.e the chip frequency fc is less than the message bit rate fb.
Therefore two or more baseband bits are transmitted at the same frequency.
Let Δf be the separation between adjacent frequencies of the frequency synthesizer and let BT
be the bandwidth of the modulated carrier wave before spreading. Then Δf has to be larger
than or atleast to BT . if there are 2m
discrete frequencies among which the synthesizer
frequency hops, the bandwidth of the transmitter signal(after hoping) is
BT(FHSS)=2m
* Δf=2m
* BT(say) …(5.45)
L=
BT(FHSS)
BT
=Gp the processing gain=2m
… (5.46)

Fast-frequency hopping:
In FH system, if there are multiple hops per symbol, we have fast-hopped signal. Hence in fast-
frequency hopping, the hop rate Rc is an integer multiple of the MFSK symbol rate Rs ie., the
carrier frequency will change or hop several times during the transmission of one symbol.
Hence, in a fast FH-MFSK system, each hop is a chip.
Figure5.15 Fast-FHSS-MFSK demodulator
In general, fast frequency hopping is used to defeat a smart jammer’s tactic that involves
two functions: measurement of the spectral content of the transmitted signal, and returning of
the interfering signal to that portion of the frequency band.
To overcome the jammer, the transmitted signal must be hopped to a new carrier
frequency before the jammer is able to complete the processing of these two functions. For data
recovery at the receiver, non-coherent detection is used. However, the detection procedure is
different from that used in a slow FH-MFSK receiver. The Figure 5.15 shows a typical fast
FH-MFSK demodulator.
First, the signal is dehopped using a PN generator identical to that used in transmitter.
Then, filtering is done with a low pass filter having a bandwidth equal to the data bandwidth.
The filtered signal is demodulated using a bank of ’M’ envelope detectors.
Each envelope detector is followed by a clipping circuit and an accumulator. The
clipping circuit serves an important function in the presence of an intentional jammer or other
strong unpredictable interference. The demodulator does not make symbol decisions on a chip-
by-chip basis. The energy from the N chips are accumulated. After the energy from the Nth chip
is added to the N-1 earlier ones, the demodulator makes a symbol decision by choosing the
symbol that corresponds to the accumulator with maximum energy

Advantages of FH-SS system:
 The processing gain PG is higher than that of DS-SS system.
 Synchronization is not greatly dependent on the distance.
 The serial search system with FH-SS needs shorter time for acquisition.
Disadvantages of FH-SS system:
 The bandwidth of FH-SS system is too large (in GHz).
 Complex and expensive digital frequency synthesizers are required.
Applications of FHSS system:
 CDMA systems based on FH spread spectrum signals are particularly attractive for
mobile communication.
 Wireless local area networks (WLAN) standard for Wi-Fi.
 Wireless Personal area network (WPAN) standard for Bluetooth.
Fast hopping Versus Slow hopping:
Table 5.4 compares the performance of fast hopping and slow hopping systems.
Table 5.4 comparison of slow and fast hopping
Slow hopping and fast hopping performance may also compared by the following two
examples: 1) Figure 5.16 shows chip in the context of an FH-MFSK system.

Figure 5.16 Chip context in FH-MFSK
Figure 5.16(a) illustrates an example of fast frequency hopping. The data symbol rate is 30
symbol/s and the frequency hopping rate is 60 hops/s. The figure illustrates the waveform s(t)
over one symbol duration ( 1/30 s).The waveform change in (the middle of) s(t) is due to a new
frequency hop.
Figure 5.16(b) illustrates an example of slow frequency hopping. The data symbol rate is still
30symbols/s, but the frequency hopping rate has been reduced to 10hops/s. The waveform s(t)
is shown over a duration of three symbols ( 1/10 s)
Figure 5.17 shows the comparison for a binary FSK system. Figure 5.17(a) illustrates an
example of fast frequency hopping for a binary FSK system. The diversity is N=4. There are 4
chips transmitted per bit. Here, the chip duration is the hop duration.
Figure 5.17 comparison for binary system
Figure 5.17(b) illustrates an example of slow frequency hopping for a binary
FSK system. In this case, there are 3 bits transmitted during the time duration
of a single hop. Here, the chip duration is the bit duration.

White or Barrage Jamming: ‘White noise, or ‘barrage jamming’, which covers the entire
bandwidth Wc of the FHSS signal. let J be the jamming power which is spread over the full
bandwidth Wc of the FHSS signal.
In the barrage jamming case, the jamming signal
appears as white noise. Since we are considering
FHSS with M-ary FSK, the bit-error probability in the
presence of white noise of two-sided PSD of 2

2
1
2
b
E
e
P e 

 . Hence, in the presence of barrage jamming signal with a PSD of Nj, the
bit-error probability becomes,
2( )
1
,
2
b
j
E
N
ej j
c
J
P e whereN
W



 
Partial-band Jamming: If α denotes the fraction of the FHSS signal bandwidth, Wc, which
is covered by the jamming signal, assuming J to be the total jamming power as in the previous
case, the jamming PSD j
N
 and it has bandwidth αWc.
Pe = (prob. of error in case of jamming) * (Probability of jamming) + (prob. of error if there
is no jamming)* (Prob. of not being jammed)
(1 )
exp exp
2 2( / ) 2 2
b b
e
j
E E
P
N
 
  
 
  

 
   
  
 
 
SYNCHRONIZATION
Need for Synchronization
The process in which the locally generated carrier at the receiver must be in frequency and
phase synchronism with the carrier at the transmitter is called synchronization. In spread
spectrum communication systems, there should be perfect alignment between the transmitted
and received PN codes, for satisfactory operation, because
(i) Carrier frequency as well as the PN clock may drift with time.
(ii) If there is relative motion between the transmitter and receiver, as in the case of mobile
and satellite spread spectrum systems, the carrier and PN clock will suffer Doppler
frequency shift.
Hence, synchronization of the PN sequence of the receiver with that of the transmitter is
essential.
Synchronization steps:
The process of synchronizing the locally generated spreading signal with the received spread
spectrum signal is usually accomplished in two steps. They are
1) Acquisition: The first step, called acquisition, consists of bringing the two spreading signals
into coarse alignment with one another.

2) Tracking: Once the received spread spectrum signal has been acquired, the second step,
called tracking, takes over for fine alignment.
Both acquisition and tracking make use of the feedback loop.
Acquisition:
A) DS Spread spectrum systems:
Figure 5.18 shows the serial search scheme for Direct Sequence spread spectrum
systems. There is always an initial timing uncertainty between the receiver and the transmitter.
Let us suppose that the transmitter has N chips and the chip duration is Tc. If initial
synchronization is to take place in the presence of additive noise and other interference, it is
necessary to dwell for Td=NTc in order to test synchronism at each time instant. We search over
the time uncertainty interval in(coarse) time steps of ½ Tc.
Figure 5.18 DSSS- acquisition
The locally generated PN signal is correlated with the incoming PN signal. At fixed search
intervals of NTc (search dwell time), the output signal is compared to a preset threshold. If the
output is below the threshold, the locally generated code signal is advanced in time by (½) Tc
seconds. The correlation process is repeated again. These operations are performed until a
signal is detected or the threshold is exceeded. Then the PN code is assumed to have been
acquired. Thus, if initially the misalignment between the two codes was n chips, the total time
taken for acquisition is given by Tacq = 2nNTc seconds.
B) FH spread spectrum systems
Figure 5.19 shows the serial search scheme for frequency hopping spread spectrum
systems. Here the non-coherent matched filter consists of a mixer followed by a bandpass filter
(BPF) and a square law envelope detector. The PN code generator controls the frequency
hopper. Acquisition is accomplished when the local hopping is aligned with that of the received
signal.
Let fi be the frequency of the frequency synthesizer at the transmitter. Suppose fj be the
frequency of the signal produced by the frequency synthesizer in the acquisition circuit of the
receiver. If fi ≠ fj, then only a small voltage less than the threshold will be produced at the output
of BPF. At a later instant of time during searching, if fi = fj, then a large voltage exceeding the

threshold will be produced at the output of BPF. This indicates the alignment of local hopping
with that of the received signal.
Figure 5.19 “camp-and-wait” FHSS –Acquisition
Tracking
Once the signal is acquired, the initial search process is stopped and fine
synchronization and tracking begins. The tracking maintains the PN Code generator
at the receiver in synchronism with the incoming signal. Tracking includes both fine
chip synchronization and, for coherent demodulation, carrier phase tracking.
A) DS Spread spectrum system: The commonly used tracking loop for a direct sequence
spectrum signal is the Delay-locked loop (DLL) as shown in the Figure 5.20.
Figure 5.20 DLL for PN tracking
The received DS spread spectrum signal is applied simultaneously to two
multipliers. One of the multipliers is fed with PN code delayed by , a fraction of the
chip interval. The other multiplier is fed with the same PN code advanced by . The
output from each multiplier is fed to a BPF centred on f0.

The output of each BPF is envelope detected and subtracted. This difference signal is
applied to the loop filter that drives the VCO. The VCO serves as the clock for the PN code
generator. If the synchronization is not exact, the filtered output from one correlator will exceed
the other. Hence the VCO will be appropriately advanced or delayed. At the equilibrium point,
the two filtered correlator outputs will be equally displaced from the peak value. Then the PN
code generator output will be exactly synchronized to the received signal that is fed to the
demodulator.
FH Spread spectrum system:
A typical tracking technique for FH spread spectrum signals is illustrated in
Figure 5.21. Although initial acquisition has been achieved, there is a small timing error
between the received signal and the receiver clock. The BPF is tuned to a single
intermediate frequency and its bandwidth is of the order of 1/Tc . Its output is envelope detected
and then multiplied by the clock signal to produce a three-level signal. This drives the loop
filter.
Figure 5.21 Early –late gate -Tracking loop for FHSS
Suppose that the chip transitions from the locally
generated sinusoidal waveform do not occur at
the same time as the transitions in the incoming
signal. Then the output of the loop filter will be
either positive or negative, depending on
whether the VCO is lagging or advanced relative
to the timing of the input signal.
This error signal from the loop filter will provide
the control signal for adjusting the
VCO timing signal so as to drive the frequency
synthesizer output to proper
synchronism with the received signal.

Performance Comparison of DSSS and FHSS
COMMERCIAL APPLICATIONS OF SPREAD SPECTRUM TECHNIQUES
Spread spectrum signals are used for
1) Combating or suppressing the detrimental effects of interference due to jamming
(Intentional interference). It can be used in military applications also.
2) Accommodating multiple users to transmit messages simultaneously over the same
channel bandwidth. This type of digital communication in which each user (transmitter-
receiver pair) has a distinct PN code for transmitting over a common channel bandwidth
is called as Code Division Multiple Access (CDMA) or Spread Spectrum Multiple
Access (SSMA). This technique is popularly used in digital cellular communications.
3) Reducing the unintentional interference arising from other users of the channel.
4) Suppressing self-interference due to multipath propagation.
5) Hiding a signal by transmitting it at low power and, thus, making it difficult for an
unintended listener to detect in the presence of background noise. It is also called a Low
Probability of Intercept (LPI) signal.
6) Achieving message privacy in the presence of other listeners.
7) Obtaining accurate range (time delay) and range rate (velocity) measurements in radar
and navigation.

Drill Problems
1. An FHSS system employs a total bandwidth of 400 MHz and an individual
channel bandwidth of 100Hz. What is the minimum number of PN bits
required for each frequency hop?
Sol: Given BT(FHSS)=400MHz, Channel bandwidth, BT = 100 Hz
Processing gain, ( ) 6
400
4 10
100
T FHSS
p
T
B MHz
G
B Hz
   
6 22
2 4 10 2
m
p
G    
Hence, minimum number of PN bits, m=22bits.
2. A 3-stage shift register with linear feedback generates the sequence:
0 1 0 1 1 1 0 0 1 0 1 1 1 0
(i) Determine the period of the given infinite sequence.
(ii) Verify the three properties of the PN sequence for the given sequence.
Sol: (a) given
0 1 0 1 1 1 0 0 1 0 1 1 1 0
one period
  
The given sequence has a period N=7, after every 7-bits the patterns repeats.
Therefore, 2 1 3
m
N m
   
(b) Balance Property: In one period we have,
Number of 1s = 4 , Number of 0s = 3.
Run Property: Total runs =
1
4
2
N 

To get correct runs take circular shift to right, we get sequence of 0010111. Read
from left to right so, a total of four runs are there in one period of sequence. The four runs are
00, 1, 0,111.
Autocorrelation Property: one period of sequence:
   
0 1 2 3 4 5 6
, , , , , , 0,1,0,1,1,1,0
C C C C C C C 
Let us represent symbol 0 by +1 volt and symbol 1 by -1 volt.
We know that,
1
(i )modN
0
1
( ) , 0,1, , 1
N
c i
i
R C C N
N

 



  

6
(i )mod7
0
1
( ) , 0,1, ,6
7
c i
i
R C C 
 


 

Compute R(0):
0 1 2 3 4 5 6
:
i
C C C C C C C C
( 0)mod7
i
C  0 1 2 3 4 5 6
:C C C C C C C
0 2 6 1 3 4 5
=-1volts; 1
C C C C C C C volts
      
 
2 2 2 2 2 2 2
0 1 2 3 4 5 6
1
(0) 1
7
R C C C C C C C
       

To compute R(1) do one circular right shift and to compute remaining also same procedure is
followed , i.e, do circular right shifts by i-index times.
Compute R(1) : 0 1 2 3 4 5 6
:
i
C C C C C C C C
( 1)mod7 1 2 3 4 5 6 0
:
i
C C C C C C C C

 
0 1 1 2 2 3 3 4 4 5 5 6 6 0
1 1
(1)
7 7
R C C C C C C C C C C C C C C
        
Proceeding in same manner , R(2)=R(3)=R(4)=R(5)=R(6)=
1
7

Thus ACR has only two values, is periodic with a period equal to 7.
1, 0, 7, 14, 21,...
( ) 1
, 0, 7, 14, 21,...
7
R



   


 
    


3. A DSS uses LFSR of 20 stages for the generation of PN sequence. Calculate
the processing gain of the sequence, in dB.
Sol: Given, n=20
20 20
20
2 1 2 1 2
10log 10log2 60
m
N
N dB
    
 

UNIT-5 Spread Spectrum Communication.pdf

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UNIT-5 Spread Spectrum Communication.pdf