SPREAD SPECTRUM MODULATION

• Pseudonoise Sequences• Direct Sequence Spread Spectrum• Signal space dimensionality and Processing gain• Probability of error• Frequency hop spread spectrum• Applications

Definition of Spread SpectrumSpread spectrum is a modulation

method applied to digitally modulated signals that increases the transmit signal bandwidth to a value much larger than is needed to transmit the underlying information bits.

1. They are difficult to intercept for unauthorized person.

2. They are easily hidden, it is difficult to even detect their presence in many cases.

3. They are resistant to jamming.4. They have an asynchronous multiple-

access capability.5. They provide a measure of immunity to

distortion due to multipath propagation

Spread Spectrum Signal Characteristics :

Spread Spectrum Conditions• The signal occupies a bandwidth much

larger than is needed for the information signal.

• The spread spectrum modulation is done using a spreading code, which is independent of the data in the signal.

• Despreading at the receiver is done by correlating the received signal with a synchronized copy of the spreading code.

Pseudo-Noise Sequence A pseudo-noise ( PN ) sequence is a periodic binary

sequence with a noise like waveform that is usually generated by a means of a feed back shift register. It consists of a shift register made up of m flip-flops and a logic circuit to form a multiloop feedback circuit. The maximam-length sequence represents a commonly used periodic PN sequence.

Feedback shift register

x1 x2 x3 O/P

Fig : Maximum-length sequence generatorIt is periodic with a period of N= - 1 m- length of the shift register

+

2m

m N

7 127 8 255 9 511 10 1023 11 2047 12 4095 13 8191 17 131071 19 524287

Properties of the PN sequences : Balance property : In each period of a

maximum-length sequence, the number of 1s is always one more than the number of 0s.

Run property: Among the runs of 1s and 0s in each period of a maximum-length sequence, ½ runs of each kind are of length 1, ¼ are of length 2, 1/8 are of length 3, and so on as long as these fractions represent meaningful numbers of runs.

Correlation property: The autocorrelation function of a maximum-length sequence is periodic and binary valued.

k=lN k=lN

The autocorrelation function of a bipolar waveform three-stage pseudo noise generator

Spread Spectrum TechniquesThere are several forms of spread

Spectrums :1. Direct sequence spread spectrum

(DS/SS)2. Frequency hopping spread spectrum

(FH/SS)

Direct sequence spread spectrum SS modulation can provide protection against

externally generated interfering (jamming- broadband noise/multitone waveform) signals with finite power.

Purposely making the information bearing signal occupy a bandwidth far in excess bandwidth require to transmit it.

Noise-like apperance The transmitted signal is thus enabled to

propagate through the channel undetected by anyone who may be litening.

Therefore SS as a method of “camouflaging” the information bearing signal.

Idealized model of baseband spread-spectrum systemb(t) m(t)=c(t) b(t)Data seq modulator c(t) PN seq is wideband (a) TransmitterBy multiplying the information-bearing signal b(t) the spreading code

c(t), each information bit is “chopped” up into a number of small time increments. These small time increments are referred to as chips.

m(t) r(t) = m(t) + i(t)Modulated signal = c(t)b(t) + i(t) i(t) interference (b) Channel

x

∑

The waveforms in the transmitter

Demodulator:r(t) z(t) o/p rxed s/l c(t)

z(t)=c(t)r(t) = c(t)c(t)b(t)+c(t)i(t) ; c(t)c(t)=1 for all t

z(t) =b(t) + c(t)i(t) ; b(t) – NB & c(t)i(t)-WB

Use of LPF z(t) = b(t)

Pay for the improved protection against interference is increased transmission bandwidth, system complexity and processing gain. Here, our primary concern is the security of transmission.

x Base band (Low pass)

filter

The waveforms in the receiver

Direct sequence spread coherent binary phase shift keyingTo provide DSSS over a baseband channel,

coherent binary phase shift keying (psk) is added into the transmitter and receiver.

Transmitter – two stages (modulator & binary PSK modulator)

The transmitted signal x(t) is DS/BPSK signal.The phase modulation (t) of x(t)

Polarity of data seq b(t) at time t + -

Polarity of PN seq c(t) at time t

+ 0 π - π 0

The channel output given by: y(t) = x(t) + j(t) = c(t) s(t)+

j(t)The Coherent detector input u(t) : u(t) =c(t) y(t) = s(t)+ c(t)

j(t) where for all t

Signal space dimentionality and Processing gain It is based on the signal space approach. Signal space representations of the transmitted signal and the interfering signal

(jammer). Consider a set of orthonormal basis functions,

----- 1 ------ 2 K=0,1……………..,N-1. -chip duration, N- number of chips per bit

The transmitted signal x(t) for the interval of an information bit, -signal energy per bit, + -> 1, - -> 0 the code seq denotes the PN seq +/- 1 N-D req N orthonormal functions

0 --------- 3

X(t) = c(t)s(t) = ± c(t) cos(2πt)

= ±

The jammer, j(t) = ---- 4

Where, ---- 5

= (t) dt k = 0,1,…….., N – 1 ----- 6

j(t) is 2N-D The avg power of the interference j(t),

------- 7

Lack of knowledge of signal phase, the jammer can only place equal energy in the cosine and sine coordinates

------------ 8

rewrite eqn 4 , ------------ 10The coherent detector output is, ----------- 11

Where, ------ 12

------ 13

The despread binary PSK signal s(t), ----

14

Plus sign – 1 & minus sign – 0. Assuming

------- 15The component due to interference,

------- 16 using eqn 1 and eqn 5

-------- 17

Approximate the PN seq ------ 18Where & are RVs

The probability of the event = + or – 1 equals ------ 19

The mean of the RV is zero since, for fixed k,

------ 20

For a fixed vector j, the variance of is given by, ------ 21

Since the spread factor , the variance in terms of the avgInterference power J as ------ 22

The output signal-to-noise ratio, ------ 23 An input signal-to-noise ratio, ------ 24

The output signal-to-noise ration in terms of the input signal-to-noise ratio, ------- 25

The signal-to-noise ratio in decibles, ------

26Where,

The processing gain in another way,1. The bit rate of the binary data entering the transmitter

input is given by ------- 27

2. The bandwidth of the PN seq c(t), defined in terms of the main lobe of its spectrum ------ 28

The processing gain ------ 29

PG=

PG=

Probability of error Let the coherent detector output v and noise component

are the sample value of a random variable V and ------- 1 The decision rule used by the coherent detector is to declare

that the received bit in an interval (0, ) is 1 or 0. With both information bits assumed equally likely, the average

probability of error is same as the conditional probability of the receiver making a decision in favor of symbol 1, given that symbol 0 was sent.

= --------- 2 is the sum of N identically distributed random variables.

According to the central limit theorem, for large N, the random variable assumes a Gaussian variable with zero mean and variance , where J is the average interference power and

is the chip duration. The average probability of error, ) -------

3 is appropirate for DS/BPSK binary systems with large spread

factor N.

Antijam characteristics: The average probability of error for a coherent binary

PSK system reproduced -------- 4

The calculation of bit error rate in a direct-sequence spread binary PSK system, the interference may be treated as wideband noise of power spectral density

-------- 5 The bit energy , where P is the average

signal power and is the bit duration. The bit energy-to-noise density

ratio --------- 6

The jamming margin, The jamming margin in terms of decibels,

FHSSThe wide bandwidth is divided

into narrow sub-bands or channels

The message signal is hopped from one channel to another.

At the transmitter, the modulated message signal is transmitter at a transmit frequency determined by certain hopping algorithm.

FHSS Example

PN sequence generatorA PN sequence generator generates a

periodic PN sequence based on a hopping algorithm.

The generated PN sequence is fed to a frequency synthesizer, which then determines the frequency channel at which to transmit the message frame.

m bit PN generator identifies 2m -1 possible frequencies.

FHSS ReceiverAt the receiver there is an identical

PN generator synchronized with the received signal.

Receiver therefore knows which at frequency current frame will be transmitted.

Thus enabling correct detection and demodulation of the received signal.

FHSS block diagram (transmitter)

FHSS block diagram (receiver)

Fast and Slow FHSSTwo types of FHSS, Fast and SlowIf the hopping rate > message

symbol rate, it is fast FHSSIf message symbol rate

hopping rate, it is slow FHSSfast FHSS gives improved

performance in noise (or jamming)

Fast and Slow FHSS

Example: Slow FHSS with M =4 and m = 2

Fast and Slow FHSS

Example: Fast FHSS with M =4 and m = 2

ApplicationsCode division multiple accessMultipath suppression