Spread Sprectrum Modulation
RAGHUDATHESH G P
Asst Professor
DIGITAL COMMUNICATION (VTU)-10EC61 UNIT – 8: Spread Spectrum Modulation: Pseudo noise sequences, notion of spread spectrum, direct
sequence spread spectrum, coherent binary PSK, frequency hop spread spectrum, applications. 7 Hours TEXT BOOK:
1. Digital communications , Simon Haykin, John Wiley India Pvt. Ltd, 2008. REFERENCE BOOKS:
1. Digital and Analog communication systems , Simon Haykin, John Wildy India Lts, 2008 2. An introduction to Analog and Digital Communication , K. Sam Shanmugam, John Wiley India Pvt. Ltd, 2008. 3. Digital communications - Bernard Sklar: Pearson education 2007 Special Thanks To:
1. Raviteja B, Rajendra Soloni , Venkatasumana C H PREPARED PREPARED BY:
RAGHUDATHESH G P Asst Prof ECE Dept, GMIT Davangere 577004 Cell: +917411459249 Mail:
[email protected] Thoughts:
Work like a clock but do esn’t sit like like a rock. ro ck.
If you don’t make mistakes, you’re not working on hard enough problems. enough problems.
Never leave that till tomorrow which which you can do today. Time is money don’t waste it. No change of circumstances can repair a defect of character.
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Spread Sprectrum Modulation
RAGHUDATHESH G P
Asst Professor
Spread-Spectrum Modulation
In any communication system, two important considerations are :
1. transmitted power 2. channel bandwidth
The task of the designer is to utilize these considerations, considerations, effectively.
Even though, it is desirable to have systems with minimum transmission bandwidth, there are situations, where the transmission bandwidth is deliberately increased to a value much higher than the baseband signal bandwidth and this technique is known as spreadspectrum modulation.
The main advantages of spread-spectrum modulation techniques are: 1. They provide immunity against, intentional jamming by another hostile source. 2. They provide immunity against interference from other channels. 3. They provide immunity against eavesdropping as the transmitted signal will be buried in the background noise. 4. They provide immunity against degradation of performance in a fading multi-path channel. 5. They provide asynchronous multiple access capability, because of which several users can use the same transmission channel simultaneously. 6. Readily available IC components. 7. Lower cost of Implementation.
Definition of Spread-Spectrum System:
It is defined in two parts: 1. Spread-Spectrum is a means of transmission in which the data of interest occupies a bandwidth in excess of the minimum bandwidth necessary to send the data. 2. The spectrum spreading is accomplished before transmission through the use of code that is independent of the data sequence. The same code is used in the receiver (operating in synchronism with the transmitter) to despread the received signal so that the original data may be recovered.
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Spread Sprectrum Modulation
RAGHUDATHESH G P
Asst Professor
Standard modulation techniques like frequency modulation and pulse code modulation also spread the spectrum of an information bearing signal, but they do not qualify as spread-spectrum systems because they do not satisfy all the conditions mentioned above.
Application of Spread-Spectrum System: 1. Multipath rejection in a ground – ground – based mobile radio environment. 2. Multiple access communication in which a number of independent users are required to share a common channel without an external synchronizing mechanism. 3. Secure communication. 4. Antijam capability.
Types of spread-spectrum techniques: 1. Direct sequence spread-spectrum: here 2 stages of modulation are used a. The incoming data sequence is used to modulate a wideband code. This code transforms the narrowband data sequence into a noise-like wideband signal. b. The resulting wideband signal undergoes a second modulation using frequency shift keying technique. 2. Frequency hop spread-spectrum: the spectrum of a data modulated carrier is widened by changing the carrier frequency in a pseudo-random manner. 3. Time hopping spread-spectrum. 4. Chrip spread-spectrum. 5. Hybrid method spread-spectrum. 6. Pulsed FM spread-spectrum.
For their operation first two methods relay on the availability of a noise-like spreading code called a pseudo-noise a pseudo-noise or pseudorandom sequence (PN sequence).
Pseudo-noise Sequence:
Definition: it is a code sequence of 1s and a nd 0s with certain autocorrelation properties.
We know that random signals cannot be predicted; its future values can only be described by a statistical model. model.
A pseudorandom signal is not random at all; it is a deterministic, periodic signal that is known to both the transmitter and the receiver.
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Spread Sprectrum Modulation
RAGHUDATHESH G P
Asst Professor
Even though it is deterministic, it appears to have the statistical properties of sampled white noise.
It appears to an unauthorized listener, as a truly random signal.
Generation:
1. These sequences are generated using shift registers having feedback connections. 2. Using an m-stage shift register having appropriate linear feedback signals, it is possible to generate a periodic sequence with a period equal to 2m - 1 bits.
Maximum length (ML) sequences : It is a Pseudo-noise Sequence generated by linear
feedback shit resistor having a length of 2m - 1.
A shift register of length m consists of m flip-flops (two-state memory stages) regulated by a single timing clock. At each pulse of the clock, the state of each flipflip-flop flop is shifted shifted to the next one down the line.
In order to prevent the shift register from emptying by the end of m clock pulses, a logical (i.e., Boolean) function of the states of the m flip-flops are used to compute a feedback term, and apply it to the t he input of the first flip-flop.
In a feedback shift register of the linear type, the feedback function is obtained using modulo-2 addition of the outputs of the various flip-flops. This operation is illustrated in Figure below for the case of m = 3.
Representing the states of the three flip-flops as x1, x2, and x3, we see that in Figure the feedback function is equal to the modulo-2 sum of x1 and x3.
A maximum-length sequence so generated is always periodic periodic with a per iod of
Here, m = the length of the shift register (equivalent to the degree of the generator polynomial)
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Spread Sprectrum Modulation
RAGHUDATHESH G P
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For parameter values of a PN consider the 3-stage FB shit register. It is assumed that the initial state of the shift register is 100 (by reading the content of the 2 FF’s from left to right). Then, the succession sates will be as fo llows: llows:
State of filp-flop
1
0 1 1 1 0 1 0 0
1 1 0 0 1
Output PN sequence equal to
0 0 1 1 1 0 1 0
0 0 1 1 1 0 1 0 The Sequence repeats
Initial State: S 1 = 1, S2 = 0 and S3 = 0
Input values are 100, 110, 111, 011, 101, 010, 001, 100 …
The output sequence (the last positi pos ition on of each state of the Shift register) is 0011101.
The sequence repeats itself with period 7.
The choice of 100 as the initial state is an arbitrary one. Any of the other six states could serve equally well as an initial state. The resulting output sequence would then be some cyclic shift of the sequence given.
It should be noted that 000 is not a state of the shift register sequence since this results
in a catastrophic cyclic code, (i.e., once the 000 state is entered, the shift register sequence cannot leave this state).
Problem: A PN sequence is generated using a FB shift register of length 4 (4 stages). Find the generated output sequences if the initial contents of the shift register are 1000. If the 7
chip rate is 10 chips/sec, calculate the chip and PN sequence duration and period of the output sequence. Draw its schematic arrangement. Solution: i. To obtain the PN sequence:
Assuming the FB taps on (4,1) gives maximum length sequence, thus output of stage 4 and stage 1 are mod-2 added and given to input of stage 1 as shown in the figure below
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Spread Sprectrum Modulation
RAGHUDATHESH G P
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Table below shows the PN sequence generated.
Shift No 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
State of Shift Register S1 S2 S3 S4 1 0 0 0 1 1 0 0 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 0 0 1 1 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 1 1 0 0 0
Mod 2 adder output
PN Sequence
1 1 1 0 1 0 1 1 0 0 1 0 0 0 1 1
0 0 0 1 1 1 1 0 1 0 1 1 0 0 1 0
Generated PN Sequence for m = 4 Thus the generated PN sequence = 000111101011001…… ii. To obtain Chip Duration:
Chip rate is, 7
R c = 10 chips/sec. Thus chip duration is,
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Spread Sprectrum Modulation
RAGHUDATHESH G P
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iii. To obtain period of PN sequence:
Properties of Maximum-length Sequence:
Maximum length sequences have properties similar to those exhibited by truly random binary sequences.
A random binary sequence is a sequence in which the presence of a binary symbol 1 or 0 is equally probable
Some properties of maximum-length sequences are listed listed below: 1. Balance property : o
In each period of a maximum length sequence, the number of 1 s is always more by one number than the number of 0 s.
o o o o o
o o
For an ML sequence generated ge nerated by a m-stage shift register with linear feedback: m Period N = 2 – 1 1 bits. Number of 1’s = 2m-1 bits. m-1 Number of 0’s = 2 – 1 1 bits. Ex.: For 3-stage 3-stage Shift Shift register, i.e, 0010111 Number of 1’s 4 Number of 0’s 3
2. Run property:
Among the runs of 1 s and of 0 s in each period of a maximum-length 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 as long as t hese fractions represent meaningful numbers of runs. A "run” mean a subsequence o f identical symbols (1s or 0s) within one period of the sequence. The length of this subsequence is the length of the run. For a maximum-length sequence generated generat ed by a feedback shift register of length N, the total number of runs is (N + 1)/2. Ex.: let PN sequence = 0010111 Thus,
00, 1, 0, 111 = 4 runs.
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Spread Sprectrum Modulation
RAGHUDATHESH G P
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1, 0 two runs are of length one (50%) (50% ) 00 one runs are of length one (25%) 111 one runs are of length one (25%) 3. Correlations property:
The autocorrelation function of a maximum-length sequence is periodic and binary-valued. Let binary symbols 0 and 1 be represented by -1 volt and +1 volt, respectively. By definition, the autocorrelation sequence of a binary sequence {cn} , so represented, equals
Here,
N = the length or period of the sequence and k = the lag of the autocorrelation sequence.
For a maximum-length sequence of o f length N, the autocorrelation sequence is periodic with period N and two-valued, as shown by
Here,
Where l is any integer. When the length N is infinitely large, the autocorrelation sequence R c(k) approaches that of a completely random binary sequence. Problem: For a linear Fb Fb SR with 3 stage (m = 3), evaluate the maximum length length PN sequence for FB taps = (3, 1). Draw the schematic arrangement and verify all the properties of PN sequence output. Sketch the sequence and its autocorrelation function. Solution: i. Schematic arrangement:
As there is 3 stages in the SR’s let, the Feedback taps will be taken from outputs of 1
st
and 3rd stage and schematic as shown below .
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Spread Sprectrum Modulation
RAGHUDATHESH G P
Asst Professor
ii. To obtain PN sequence: Let in the initial states of SR’s be S 1 = 1, S2 = 0 and S3 = 0. Table below shows the generated sequence:
Sl.No 1 2 3 4 5 6 7 8
State of shift register S1 S2 S3 1 0 0 1 1 0 1 1 1 0 1 1 1 0 1 0 1 0 0 0 1 1 0 0
Mod-2 adder output
S1
S3
1 0 0 1 1
PN-Sequence S3 0 0 1 1 1 0 1 0 Sequence repeat from above
Generation of PN Sequence Thus the generated pseudo random sequence is, 0011101…….. Length of the sequence is
iii. To verify the properties of maximum length sequence:
The generated PN sequence is,
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RAGHUDATHESH G P
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a. Balance property: In the above sequence for each period, number of 1 s is one more
than number of 0 s. This satisfi sat isfies es balance property. b. Run property : When there are 'm' stages in the shift shift register, then generated sequence m-1
contains 2
3-1
runs. Here in = 3. Hence there will be 2
=4 runs. These are given g iven below:
Run = 1
Run = 2
Run = 3
Run = 4
Thus there are total 4 runs, Run 1 = {0 0} Run 2 = {1 11} Run 3 = {0} Run 4 = {1} i) Here two runs (i.e. half of total 4 runs) are o f length 1. These runs are run-3 and run-4. ii) One run (i.e. one fourth of total 4 runs) is of length 2. This run is run-1. Thus run property is satisfied. c. Correlation Property:
Problem: Figure DP9.5 shows a 4-stage linear feedback shift register. If the initial state is I111, find the output sequence of the shift register.
Solution
Successive states of the linear feedback shift register is tabulated in Table below
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Shift 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 (THE STATE REPEAT) 15
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State of shift register C3 C2 C1 C0 1 1 1 1 0 1 1 1 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 0 0 1 1 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 1 0 0 1 1 1 0 1 1 1 1
Asst Professor
Feedback bit C3 C0 0 1 0 1 1 0 0 1 0 0 0 1 1 1 1 0
Output bit 1 1 1 1 0 1 0 1 1 0 0 1 0 0 0 1
The output sequence is taken from last stage and is shown in the last column. 111101011001000 1111 ---------------------One period
A Basic Idea (Notion) of Spread Spectrum :
The spread-spectrum technique described in this section is referred to as direct-sequence spread spectrum. The discussion presented here in context of baseband transmission .
An important aspect of spread-spectrum modulation is that it can provide protection against externally generated interfering interfering (jamming) signals with finite finite power. po wer.
The jamming signal may consist of a fairly powerful broadband noise or multitone waveform that is directed at the receiver for the purpo se of disrupting communications.
Protection against jamming waveforms is provided by purposely making the information bearing signal occupy oc cupy a bandwidth far in excess of o f the minimum bandwidth necessary to transmit transmit it.
This has the effect of making the transmitted signal assume a noise like appearance so as to blend into the background.
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Spread Sprectrum Modulation
RAGHUDATHESH G P
Asst Professor
The transmitted signal is thus enabled to propagate through the channel undetected by anyone who may be listening. We may therefore think of spread spectrum as a method of "camouflaging " the information-bearing signal.
One method of widening the bandwidth of an information-bearing (data) sequence
involves the use of modulation using spreading code (PN sequence).
Let b(t) = a binary data sequence
c(t) = a pseudo-noise (PN) sequence
Both signals are represented in their polar non return-to-zero forms, in terms of two levels equal in amplitude and opposite in polarity, namely, ± 1.
Applying baseband signal b(t) which is a narrowband and wideband signal c(t) sequences to a product modulator or multiplier as shown below to obtain Spread spectrum signal m(t) given by
Waveforms of b(t), c(t) and m(t) are as shown below
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The m(t) is transmitted through the channel where additive noise is added as shown in figure below
Received signal r(t) consists of the transmitted signal m(t) plus an additive interference denoted by i(t), as shown above.
To recover the original data sequence b(t), the received signal r(t) is applied to a demodulator that consists of a multiplier followed followed by a low-pass filter, filter, as in figure below
The multiplier is supplied with a locally generated PN sequence is an exact replica of that used in the transmitter. The resulting demodulated signal is therefore given by
Above Equation shows that the desired signal b(t) is multiplied twice by the spreading code c(t), whereas the unwanted signal i(t) is multiplied only once. Spreading code c(t) alternates between the levels - 1 and + 1, and the alteration is destroyed when it is squared; thus
Thus,
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RAGHUDATHESH G P
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We thus see from above Equation that the data sequence b(t) is reproduced at the multiplier output in the receiver, except for the effect of the interference represented by the additive term c(t) i(t).
By applying the multiplier output to a baseband (low-pass) filter with a bandwidth just large enough to accommodate the recovery of the data signal b (t), the spurious component c (t) i (t) is thereby removed.
Direct-Sequence Spread Coherent Binary Phase-Shift Keying:
Figure above shows that the transmitter involves two stages of modulation: 1. The first stage consists of a product modulator or multiplier with the data sequence and PN sequence as inputs. 2. Second stage consists of a binary PSK modulator.
The transmitted signal x (t) is thus a direct-sequence spread binary phase-shift-keyed (DS/BPSK) signal.
The phase modulation θ(t) of x(t) has one of two values, 0 and π, depending on the polarities of the data sequence seque nce b(t) and PN sequence c(t) at time t in accordance with w ith the truth table of Table below
Polarity of PN sequence + c(t) at time t -
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Polarity of Data Sequence b(t) at Time t + 0 π π 0
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RAGHUDATHESH G P
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The receiver, shown in Figure below, consists of two stages of demodulation.
The received signal y (t) and a locally generated replica of the PN sequence are applied to a multiplier. This multiplication represents the first stage of demodulation in the receiver.
The second stage of demodulation consists of a coherent detector, the output of which provides an estimate of the original data sequence.
Figure below illustrates the input data waveform for the first stage of modulation.
Figure below shows the waveform of o f a sinusoidal carrier.
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Figure below shows the DS/BPSK waveform that result from the second stage of modulation.
Model for Analysis:
In the normal form of the DSS transmitter, the spectrum spreading is performed prior to phase modulation.
But for analysis, it more convenient to interchange the order of these two operations, as in the model of Figure below.
The figure above shows that the transmitter section involves two stage o f modulation: st
1. 1 stage consists of binary PSK modulator. nd
2. 2 stage consists of a product modulator or multiplier with input sequence s (t) and PN sequence c (t) as inputs.
Swapping is performed as both spectrum spreading and the binary phase shift keying are both linear operations.
Hence x(t) is a direct sequence spread binary phase shift keyed signal i.e.,
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The phase modulation θ(t) of x(t) has one of two values, 0 and π, depending on the polarities of the data d ata sequence seque nce b(t) and PN sequence c(t) at time t in accordance w ith the truth table as shown Polarity of Data Sequence b(t) at Time t + 0 π π 0
Polarity of PN sequence + c(t) at time t -
In this model, it is assumed that the interference j(t) limits performance, so that the effect of channel noise may be ignored.
Thus channel output is given by
Here,
s(t) binary PSK signal c(t) PN sequence
In the receiver the received signal y(t) is first multiplied by the PN sequence c(t) yielding output that equals the coherent detector input u(t). Thus,
But Hence
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Spread Sprectrum Modulation
RAGHUDATHESH G P
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The above equation shows that the coherent detector input u (t) consists of a binary PSK signal s (t) imbedded in additive code-modulated code -modulated interference denoted by c(t)j(t).
The modulated nature of the latter component forces the interference signal (jammer) to spread its spectrum, thus, the information bits at the receiver output is afforded increased reliability.
Performance of Direct Sequence Spread Spectrum System:
The performance of direct sequence spread spectrum system can be evaluated on the basis of processing processing gain and probability of error.
Proces Processin g Gai n:
Definition: Processing Gain (PG) is defined as the ratio of the bandwidth of spread
message signal to the bandwidth of unspreaded data signal.
BW of unspreaded or data signal : For the NRZ bipolar signals the bandwidth of the
signal is equal to
BW of spreaded signal: The spreading pseudo-noise signal c(t) is multiplied by data
signal and the spreaded message signal m(t) m(t) is produced. Thus any one bit period in message signal m(t) is same as that in spreading pseudo -noise signal c(t) and is given by:
Putting the values of the both bandwidth obtained in processing gain equation then:
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Spread Sprectrum Modulation
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One bit period ‘Tb’ of ‘Tb’ of data signal is equal to ‘N’ bits periods of spreading pseudo-noise pseudo -noise signal, thus
Putting the value of
in processing gain we get,
Probabil ity of Er ror of DS/BPSK Sys Syste tem: m:
Expression Expression for the probability of error of coherent BPSK system given as,
Here,
= noise spectral density and
= the bit energy
For direct sequence spread spectrum modulation the no ise ise spectral density is given as,
Here J = the average interference power
Hence Probability of Error of DS/BPSK System is:
Jamming M argin (A nti jam Characte Characteri ri stics): tics):
The average probability of error for a coherent b inary PSK system is
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The bit error rate in a direct-sequence spread binary PSK system is concerned; the interference may be treated as wideband no ise of power spectral density N0/2, defined by
Bit energy E b is given by,
Here,
P = average signal power
T b = the bit duration.
Hence, we may express the bit energ y-to-noise density ratio as
Here, J/P = jamming margin.
The jamming margin and the processing gain, both expressed in decibels, are related by
Here,
(Eb/N0)min = minimum bit energy-to-noise density ratio needed to support a prescribed average probability of error.
Advantages and Disadvantages of DS-SS System: Advantages of direct sequence system:
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1. This system has best noise and antijam performance. 2. Unrecognized receivers find it most difficult to detect direct sequence signals. It has best discrimination against multipath signals. Disadvantages of direct sequence systems:
1. It requires wideband channel with small phase distortion. 2. It has long acquisi acqu isition tion time. t ime. 3. The pseudo-noise generator should generate sequence at high rates. 4. This system is distance relative.
Problems on Direct Sequence Spread Spectrum System: 1. In a Direct Sequence Spread Spectrum modulation scheme, a 14-stage linear feedback shift register is used to generate the PN sequence. Find (i) the period of code sequence and (ii) processing gain. Solution:
(i) The period of code sequence: (ii) Processing gain:
We know that one bit period ‘Tb’ of data signal is equal to ‘N’ bits periods of spreading
pseudo-noise signal, thus
Hence Processing gain is:
2. The direct sequence spread spectrum communication system has following parameters. Data sequence bit duration, T b = 4.095 ms PN Chip duration, T c = 1 µs
-5
for average probability of error less than 10 .
Calculate processing gain and jamming margin Solution:
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One bit period of pseudo-noise sequence is also called as one 'Chip'. Here one chip duration is Tc. i.e. Tc = 1 µs and T b = 4.095 ms.
Processing Gain:
Since PG = N, the length of the bit sequence is 4095. Jamming margin:
The jamming margin is given by,
Comment on result: This shows that information bits at the receiver output can be detected with -5
the probability of error less than 10 even when noise interference is upto 409.5 times the received signal power. The jamming margin calculated in dB ,
3. In a direct sequence spread-spectrum modulation, it is required to have a jamming margin greater than 26 dB. The ratio
is set at 10. Determine the minimum processing
gain and the minimum number of stages required to generate the maximum length sequence.
Solution:
Thus,
We know that one bit period ‘Tb’ of data signal is equal to ‘N’ bits periods of spreading pseudopseudonoise signal Tc, thus
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If n = 11, we have N = 2047 If n = 12, we have N = 4095.
To have PG of 4000, n = 12 is the minimum number of stages. However, with n = 12, the actual processing gain 4095. 4. A PN sequence is generated using linear feedback shift register with number of stages 7
equal to 10. The chip rate is 10 per sec. Find the following. i.
PN sequence length.
ii.
Chip duration of the PN sequence.
iii.
Period of the PN sequence.
Solution:
i. ii. iii.
PN sequence length= N =
= 1023
7
Chip duration is Tc = 1/10 = 0.1 µsec Period of the PN sequence
5. A direct sequence spread-spectrum system uses a linear feedback shift register of 20 stages for the generation of PN sequence. Calculate the processing gain of the sequence, in dB. Solution:
Number of stages of shift shift register n = 20. Periodic length
- 1 ≈ 220
Processing gain of the sequence, in dB is:
= 60 dB
6. In a DS/BPSK system, the feedback shift register used to generate the PN sequence has length m = 19. The system is required to have a probability of error due to externally -5
generated interfering signals that does not exceed 10 . Calculate the following system parameters in decibels: a. Processing gain
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b. Antijam margin
Solution:
a.
b.
WKT, the probability of error is,
With
we we get
. Thus,
FREQUENCY-HOP SPREAD SPECTRUM: Notion of Frequency-Hop Spread Spectrum:
In the spread-spectrum systems discussed previously (DSS), the use of a PN sequence to modulate a phase-shift keyed signal achieves instantaneous spreading of the transmission bandwidth.
The ability of such a system to combat the effects of jammers is determined by the processing gain of the system which is a function of the PN sequence length .
The processing gain can be made larger by employing a PN sequence with narrow chip duration, which, in turn, permits a greater transmission bandwidth and more chips per bit.
However, the capabilities of physical devices used to generate the PN spread-spectrum signals impose a practical limit on the attainable processing gain .
Thus, it turns out that the processing gain so attained is still not large enough to overcome the effects of some jammers of concern, in which case we have to resort to other methods.
An alternative method is to force the jammer to cover a wider spectrum by randomly hopping the data-modulated carrier from one frequency to the next. In effect, the spectrum of the transmitted signal is spread sequentially rather than instantaneously.
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The term "sequentially " refers to the pseudo-random-ordered sequence of frequency hops. The type of spread spectrum in which the carrier hops randomly from one frequency to another is called frequency-hop (FH) spread spectrum .
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.
Classification of frequency-hop (FH) spread spectrum:
Based on the rate of o f frequency hopping it is classified into 2 types: 1. Slow-frequency hopping: Here the symbol rate R s of the MFSK signal is an integer multiple of the hop rate R h. Thus, several symbols are transmitted on each frequency hop. 2. Fast-frequency hopping: Here the hop rate R h is an integer multiple of the MFSK symbol rate R s. Thus, the carrier frequency will change or hop several times during the transmission transmission of o f one symbol. Thus, slow-frequency hopping and fast-frequency hopping are the converse of one another.
Slow-frequency Hopping:
Here the symbol rate R s of the MFSK signal is an integer multiple of the hop rate R h.
Several symbols are transmitted on each frequency hop.
Transmitter:
1. Figure above shows the block diagram of an FH/MFSK transmitter, which involves frequency modulation followed by mixing. 2. First, the incoming binary data are applied to an M-ary FSK modulator. The resulting modulated wave and the output from a digital frequency synthesizer are then applied to a mixer that consists of a multiplier multiplier followed by a filter. filter.
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3. The filter is designed to select the sum frequency component resulting from the multiplication process as the transmitted signal. signal. 4. In particular, successive (not necessarily disjoint) k-bit segments of a PN sequence k
drive the frequency synthesizer, which enables the carrier frequency hop over 2 distinct values.
5. On a single hop, the bandwidth of the transmitted signal is the same as that resulting from the use of a conventional M-ary frequency-shift-keying (MFSK) format with an alphabet of M = 2K orthogonal signals. 6. However, for a complete range of 2k-frequency hops, the transmitted FH/MFSK signal occupies a much larger bandwidth.
With present-day technology, FH bandwidths of the order of several GHz are attainable, which is an order of magnitude larger than that achievable with direct-sequence spread spectra.
An implication of these large FH bandwidths is that coherent detection is possible only within each hop, because frequency synthesizers are unable to maintain phase coherence over successive hops.
Accordingly, most frequency-hop spread-spectrum communication systems use noncoherent M-ary modulation schemes.
Receiver:
1. In receiver shown in the figure above, the frequency hopping is first removed by mixing (down-converting) the received signal with the output of a local frequency synthesizer that is synchronously controlled in the same manner that in the transmitter. 2. The resulting output is then band-pass filtered, and subsequently processed by a noncoherent M-ary FSK detector.
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3. To implement this M-ary detector, we may use a bank of M noncoherent matched filters each of which is matched to one o ne of the MFSK tones. 4. An estimate of the original symbol transmitted is obtained by selecting the largest filter output. Chip rate for Slow Frequency Hopping:
An individual FH/MFSK tone of shortest duration is referred to as a Chip.
The chip rate, R c, for an FH/MFSK system is defined by
Here,
R h = hope rate R s = symbol rate
A slow FH/MFSK signal is characterized by having multiple symbols transmitted per hop. Thus, each symbol of a slow FH/MFSK signal is a c hip.
Thus, in a slow FH/MFSK system, the bit rate R b of the incoming binary data, the symbol rate R s of the MFSK symbol, the chip rate R c, and the hop rate R h are related by
Here,
Processing Gain(PG):
PG is defined as,
Let f s =frequency hops generated because of ‘t’ bits ‘t’ bits of PN sequence.
Thus the BW of the spread signal will be 2 f s.
Also BW of unsuppressed signal = f s.
Thus PG is given as,
The processing gain (expressed in decibels) is equal to
Here k = length of the PN segment employed to select a frequency hop.
t
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Example of slow frequency hopping:
Figure (a) below shows an example of the FH/MFSK system for slow frequency hopping.
It shows the variation of the frequency of the output with respect to the input binary data symbols.
In the Figure (a) above, 3 bits of PN sequence are used to select a hop. Therefore there 3
are 2 = 8 different hops over the complete FH bandw idth.
Two bits of input binary data represent one symbol. As shown in Figure (b) above, two symbols are transmitted in one frequency hop.
2
There will be total M = 2 = 4 symbols. Thus in a single frequency hop there are four different frequencies. Those four frequencies correspond to four possible symbols. Figure (b) illustrates this for first first hop of o f Figure (a).
As shown in Figure two symbols occupy any two frequencies in one hop out of four. The chip rate is equal to symbol rate.
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The symbol 01 has FSK frequency of F2. And because of frequency hopping this frequency is increased to f H + f 2. Similarly symbol 11 has frequency of f H +f 4. The hop frequency f H is controlled by bits of PN sequence.
Fast-frequency Hopping:
Here the hop rate R h is an integer multiple of the MFSK symbol rate R s.
Thus, the carrier frequency will change or hop several times during the transmission of one symbol.
Thus, A fast FH/MFSK system differs from a slow FH/MFSK system in that there are multiple hops per M-ary symbol. Hence, in a fast FH/MFSK system, each hop is a chip.
Fast-frequency hopping is used to defeat a smarter jammer's tactic that involves two functions: 1. Measurement of the spectral con-tent of o f the transmitted transmitted signal 2. Retuning of the interfering signal to that portion of the frequency band.
Clearly, 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, noncoherent detection is used.
But the detection procedure is quite different from that used in a slow FH/MFSK receiver. In particular, two procedures may be considered: 1. For each FH/MFSK symbol, separate decisions are made on the K frequency-hop chips received, and a simple rule based on majority vote is used to make an estimate of the dehopped MFSK symbol. 2. For each FH/MFSK symbol, likelihood functions a re computed as functions of the total signal received over K chips, and the larger one is selected.
Receiver based on the second procedure is optimum in the sense that it miniimizes the average probability of symbol error for a given Eb/No .
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Example of Fast frequency hopping:
Figure above shows the variation of transmitted frequency of fast hopping with respect to time.
The data sequence used is same as that of slow frequency hopping. But here hopping rate (hence frequency of PN sequence) is higher.
The first two bits 01 of the input binary data form one symbol (since symbol is two). Two hops are used to transmit one symbol.
As shown in Figure above the frequency of FSK signal for symbol 01 is f 2. This symbol is transmitted in first hop (f H1 H1 +f 2) and also in some other hop (f H6 H6 + f 2). One chip is equal to one hop.
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Problems on Frequency-Hop Spread Spectrum: 1. A slow FH/MFSK system has the following parameters: The number of bits per MFSK symbol = 4 The number of MFSK symbol per hour = 5 Calculate the processing gain of the system. Solution:
Let f s be the symbol frequency. There are 4-bits per MFSK symbol. Thus, bandwidth of unspresded signal will be f s/4. Also, there are 5 MFSK symbol per hop. Thus, bandwidth of the spreaded signal will be 5f s. Thus Processing gain (PG) is,
Thus, expressed in dB,
2. A fast FH/MFSK system has the following parameters: The number of bits per MFSK symbol = 4 The number of MFSK symbol per hour = 4 Calculate the processing gain of the system. Solution:
Let f s be the symbol frequency. There are 4-bits per MFSK symbol. Thus, bandwidth of unspresded signal will be f s/4. Also, there are 4 MFSK symbol per hop. Thus, bandwidth of the spreaded signal will be 4f s. Processing gain (PG) is,
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Thus, expressed in dB,
Advantages and Disadvantages of FH-SS system: Advantages of frequency hopping system:
1. These systems bandwidth (spreads) are very large. 2. They can be programmed to avoid some portions of the spectrum. 3. They have relatively short acquisition time. 4. The distance effect is less. Disadvantages of frequency hopping systems
1. Those systems need complex frequency synthesizers. 2. They are not useful for range and range-rate measurement. 3. They need error correction.
Comparison between Stow and Fast Frequency Hopping:
Sl. No
Parameter
1
Definition
2 3
Chip rate R h and R s
4
Carrier frequencies
5
Jammer interference
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Slow frequency hopping
Fast frequency hopping
Multiple symbols are transmitted in one frequency hop. Symbol rate is equal to chip rate. Hop rate is lower than symbol rate. One or more symbols are transmitted over the same carrier frequency. This signal can be detected by jammer if carrier frequency in one hop is known.
Multiple hops are taken to transmit transmit one symbol. Hop rate is equal to chip rate. Hop rate is higher than symbol rate. One symbol is transmitted over multiple carriers in different hops. This signal is difficult to detect since one symbol is transmitted on multiple carrier frequencies.
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Comparison between DS-SS and FH-SS:
Sl. No
Parameter
Direct sequence spread spectrum
Frequency hop spread spectrum
1
Definition
2
Spectrum of signal
3
Chip rate R c
PN sequence of large bandwidth is multiplied multiplied with narrowband data signal. Data sequence is spread over entire bandwidth of spread spectrum signal. Chip rate is fixed. It is the rate at which bits of PN sequence occur.
Data bits are transmitted in different frequency slots which are changed by PN sequence. Data sequence is spread over small frequency slots of the spread spectrum signal. Chip rate is maximum of hop rate or symbol rate.
4 5
Modulation technique Processing gain
Normally modulation
uses
BPSK Normally uses M-ary FSK modulation . Here t = bits in PN sequence.
Applications: 1. Code-division Multiple Accesses:
The two most common multiple access techniques for satellite communications are frequency-division multiple access (FDMA) and time-division multiple access (TDMA).
In FDMA, all users access the satellite channel by transmitting simultaneously but using joint frequency bands.
In TDMA, all users occupy the same RF bandwidth of the satellite channel, but they transmit transmit sequentially sequent ially in time.
When, however users are permitted to transmit simultaneously and also occupy the same bandwidth of the satellite channel, then some other method must be provided for separating the individual signals at the receiver.
Code-division multiple access (CDMA) is the method that makes it possible to perform this separation.
To accomplish CDMA, spread spectrum is always used. In particular, each user is assigned a code of its own, which performs the direct-sequence or frequency-hop spreadspectrum modulation.
The design of the codes has to cater for two provisions:
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1. Each code is approximately orthogonal (i.e., has low cross-correlation) with all the other codes. 2. The CDMA system operates asynchronously, which means that the transition times of a user's data symbols do not have to coincide with those of the other users.
The second requirement complicates the design of good codes for CDMA. The use of CDMA offers three attractive features over TDMA: 1. CDMA does not require an external synchronization network, which essential feature of TDMA. 2. CDMA offers a gradual degradation in performance as the number of users is increased. It is therefore relatively easy to add new users to the system. 3. CDMA offers an external interference rejection capability (e.g., multipath
rejection or resistance to deliberate jamming). Multipath Suppression:
In many radio channels, the transmitted signal reaches the receiver input via more than one path.
Ex., in a mobile communication environment, the transmitted signal is reflected off a variety of scatterers such as buildings, trees, and moving vehicles.
Thus, in addition to the direct path from the transmitter to the receiver, there are several other indirect paths (arising from the presence of the scatterers) that contribute to the composition of the received signal.
The contributions from these indirect paths exhibit different signal attenuations and time delays relative to that from the direct path. Indeed, they may interfere with the contribution from the direct path either constructively or destructively at the receiver input.
The interference caused by these indirect paths is called multipath interference or simply multipath .
The variation in received signal amplitude due to this interference is called fading , as the signal amplitude tends to fade away when destructive interference occurs between the contributions from the direct and indirect paths.
The description of multi-path fading is also complicated by whether the mobile receiving unit and nearby scatterers are all standing still, whether the mobile receiving unit is standing still but some of the scatterers are moving, or whether the mobile receiving unit is moving as well as some (or all) all) of the t he scatterers.
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In a slow-fading channel, we may combat the effects of multipath by applying spread spectrum.
Specifically, in a direct-sequence spread-spectrum system, we find that if the reflected signals at the receiver input are delayed (compared with the direct-path signal) by more than one chip duration of the PN code, n the reflected signals are treated by the matched filter filter or correlator of the receiver in the same way as any other uncorrelated input signal.
Indeed, the higher the chip rate of the PN code, the smaller will the degradation due to multipath be.
In a frequency-hop spread-spectrum system, improvement in system performance in the presence of multipath is again po ssible, but through a mechanism different d ifferent from that in a direct-sequence spread-spectrum system.
In particular, effect of multipath is diminished, provided that the carrier frequency of the transmitted signal hops fast enough relative to the differential time delay between the desired signal from the direct path and the undesired signals from the indirect paths.
Under the above condition, all (or most) of the multipath energy will (on the average) fall in frequency slots that are orthogonal to the slot occupied currently by the desired signal, and degradation due to multipath is thereby minimized. VTU QUESTIONS
1. Explain the slow frequency hopping spread spectru m system. December 2010 (10 M) 2. Define processing gain and jamming margin.
December 2010 (4 M)
3. Consider the PN sequence 000100110101111. Demonstrate the properties of the PN sequence.
December 2010 (6 M)
4. Write a short note on :
December 2010 (6 M)
a. Pseudo noise (PN) sequence b. Frequency hopping. c. Spread binary PSK system. d. Application of spread spectrum. 5. Explain fast frequency hop spread spectrum system.
January 2011 (10 M)
6. What is spread spectrum technique. Explain the working of direct sequence spread
spectrum transmitter and receiver. January 2014 (8 M), January 2006 (8 M), January 2008 (10 M), June 2012 (10 M)
7. Explain the properties of PN sequence.
June 2012 (6 M)
8. Compare slow and fast frequency hopping.
June 2012 (4 M)
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9. Explain the properties of maximum length sequence generated from 3 stage shift register
with linear feedback. Verify these properties and determine the period of the given PN sequence 01011100101110.
June 2012(6 M), December 2012 (8 M)
10. Explain with a block diagram the model of direct sequence spread binary PSK system. June 2008(10 M), December 2012 (8 M) 11. Highlight the application of spread spectrum technique. June 2007(8M), December 2012 (4 M)
12. Explain:
January 2008 (8 M)
a. Slow frequency hopping. b. Fast frequency hopping. 13. A slow FH/MFSK has the following parameters: Number of bits/MFSK symbol symbol = 4 Number of MFSK symbols/hop symbols/hop = 5 Find the processing gain of the system.
January 2006 (4 M), January 2008 (3 M)
14. What is spread spectrum? How they are classified? What is the role of PN code in spread spectrum?
July 2008(8 M)
15. Explain the frequency hop spread M-ary FSK transmitter and receiver. June 2007 (8 M) 16. In a direct sequence spread spectrum modulation scheme, a 14 stage linear feedback shift register is used to generate the PN code sequence. Find a. The period of code sequence. b. Processing gain.
June 2007 (4 M)
17. Specify the requirements of spread spectrum communication and mention the types of SS.
December 2010 (6 M)
18. What is meant by Processing gain and jamming margin in the case of DS speared spectrum signal? Explain with related equations.
January
2009
(4
M),
December 2010 (6 M)
19. Draw and explain a FH spread spectrum system, using block hopping. December 2010 (8 M) 20. With related block diagrams, explain slow frequency hopping SS system. July 2009 (6 M)
21. The direct sequence spread spectrum communication co mmunication system has following following parameters: para meters: Data sequence bit duration, T b = 4.095 ms Pin chip duration, Tc = 1 µs -5
E b/No = 10 for average probability of errors less than 10 . Calculate processing gain and jamming margin.
December 2014 (4 M)
22. Explain the principle of slow frequency hopping, and list advantages and disadvantages of FH-SS system.
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December 2014 (8 M)
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