Spread Spectrum Techniques. Class Contents Spread Spectrum Concept Key Characteristics Frequency...

Spread Spectrum Techniques

Class Contents Spread Spectrum Concept

Key Characteristics Frequency Hopping Spread Spectrum

Mathematical Treatment using BPSK Example of FHSS using MFSK

Slow FHSS Fast FHSS

FHSS bandwidth Direct Sequence Spread Spectrum

Example using BPSK DSSS bandwidth

Spreading Sequences PN Sequences Properties of the PN sequences

Spread Spectrum Transmission technique invented in 1940 for

military type applications. It can be used to transmit analogue or digital

data using an analogue signal. Immune to frequency jamming Immune to various kinds of noise and multipath

distortion.

Spread Spectrum Can be used to hide encrypting signals

Only a receiver with the same spreading code can recover the information

Several users can independently use the same higher bandwidth with very little interference

Key Characteristics of SS system.

Input data is modulated around a carrier frequency. (typically: BFSK,MFSK,BPSK)

Sequence of bits is further modulated using a sequence of bits known as “spreading code”

Signal is transmitted over a broader BW.

TRANSMITTER:

Key Characteristics of SS system

The spreading code is used to demodulate the SS signal

The modulated signal is fed into a demodulator to recover the original data.

RECEIVER:

Spread Spectrum System

Frequency Hopping Spread Spectrum. The signal is broadcast over a seemingly

random series of radio frequencies. The signal is hopping from frequency to

frequency at fixed intervals. To recover the signal, the receiver needs to be

switching frequencies in a synchronous manner with the transmitter

Attempts to jam the signal in a frequency band only knock a few bits

Frequency Hopping Spread Spectrum.

Frequency Hopping Spread Spectrum. The width of each channel corresponds to the bandwidth

of the input signal

The sequence of channels is dictated by the spreading code.

The transmitter uses a frequency channel for a fixed time interval and then changes to another according to the spreading sequence

Frequency Hopping Spread Spectrum.

Frequency Hopping Spread SpectrumMathematical Treatment:

Using BFSK, the input signal is:

)T1(Tfor)))1(5.0(2cos()( 0 ititfbfAts id

where: A: Amplitude of signalf0: base frequencybi: value of the ith bit of data (+1 and -1, for binary 1 and 0)f: frequency separationT: bit duration; data rate = 1/T


1binary for ))(2cos()( 0 tffAtsd

0binary for))(2cos()( 0 tfAtsd

)T1(Tfor)))1(5.0(2cos()( 0 ititfbfAts id


The frequency synthesizer generates a constant frequency tone whose Frequency hopes between the set of 2k frequencies.

During the ith bit interval and the ith hop:


This signal is multiplied by the spreading sequence:

)2cos()))1(5.0(2cos()()()( 0 tftfbfAtctstp iid

Using the trigonometric Identity: )cos()cos(2

1)cos()cos( yxyxyx

)))1(5.0(2cos(5.0

)))1(5.0(2cos(5.0)(

0

0

tffbfA

tffbfAtp

ii

ii

Frequency Hopping Spread SpectrumMathematical Treatment:In Frequency this product signal is the same signal spread to a different frequency

On the transmitter a band pass filter centred on the sum frequency is usedTo generate the signal to be transmitted (FHSS signal).


)))1(5.0(2cos(5.0)( 0 tffbfAts ii

FHSS signal out of the transmitter:


)))1(5.0(2cos(5.0)( 0 tffbfAts ii At the receiver, the signal is again multiplied by the spreading code:

)2cos()))1(5.0(2cos(5.0)( 0 tftffbfAtp iii

)))1(5.0(2cos(25.0

)))1(5.0(2cos(25.0)()()(

0

0

tfbfA

tfffbfAtctstp

i

iii


Using the same trigonometric Identity:

Again a bandpass filter is used, but this time to block the difference frequency

)))1(5.0(2cos(25.0)( 0 tfbfAts id

This is an attenuated version of the original signal.

Frequency Hopping Spread SpectrumExample using MFSK:

The data is encoded using MFSK M=4

element signalper bits ofnumber L

2elements signaldifferent ofnumber

frequency difference

frequencycarrier

)12(

1)2cos()(MFSK

L

M

f

f

fMiff

MitfAts

d

c

dci

i

For FHSS, the MFSK signal is translated to a new frequency every Tc seconds

Frequency Hopping Spread SpectrumExample using MFSK:

For a data rate of R, the duration of a bit is T = 1/R

The duration of a signal element is Ts = L . T

Comparing Ts and Tc, FHSS can be classified in two:

• Slow-frequency-hop spread spectrumTc ≥ Ts

• Fast-frequency-hop spread spectrum Tc < Ts

Frequency Hopping Spread SpectrumExample using MFSK – Slow FHSS:

For slow FHSS, we set Tc=2Ts. And we will use k=2 (jump every 2 symbols)

Example using MFSK – Slow FHSS:

Frequency Hopping Spread SpectrumExample using MFSK – Fast FHSS:

For fast FHSS, we set Tc=Ts/ 2.

And we will keep k=2

Example using MFSK – Fast FHSS:

Frequency Hopping Spread SpectrumBandwidth :

• MFSK bandwidth is Wd = 4.fd.

• FHSS scheme has k=2 22 blocks of frequencies with 4 frequencies in each block.

• The total FHSS bandwidth is:

dk

s W2W

• Each 2 bits of the PN sequence is used to select one block of channels.

Direct Sequence Spread Spectrum

Each bit of the original sequence is represented by multiple bits in the transmitted signal using a spreading code.

The spreading code “spreads” the signal across a wider frequency band in direct proportion to the number of bits used.


And exclusive or (XOR) is used to combine the signal with the spreadingcode

AB 0 1

0 0 1

1 1 0

XOR truth table


Example:

Direct Sequence Spread SpectrumExample using BPSK:

Binary data is represented using +1 and -1 to represent binary 1 and 0

0binary for 1

1binary for 1)(

with

)2cos()()(

-td

tftdAts cd

To generate the DSSS signal, sd(t) is multiplied by the PN sequence c(t),

which takes values of +1 and -1.

)2cos()()()()()( tftctdAtctsts cd


incoming signal s(t), is multiplied again by c(t).

for any bit stream c(t).c(t) = 1.That recovers the original signal:

)2cos()()()(

)2cos()()()()()(

tftdAtcts

tftctctdAtcts

c

c

Direct Sequence Spread SpectrumBandwidth Considerations:

The information signal has a bit width of T. The data rate will be 1/T

The frequency spectrum width of the signal, depending on the encoding Technique is roughly 2/T:

Direct Sequence Spread SpectrumBandwidth Considerations:

The spectrum of the PN signal is roughly 2/Tc:


Bandwidth Considerations:

The amount of spreading that is achieved is a direct result of the data rate of the PN sequence:

Spreading Sequences

The spreading sequence c(t), is a sequence of binary bits shared by the transmitter and receiver

Spreading consists of multiplying (XOR) the input data by the spreading sequence.

The bit rate of the spreading sequence is higher than that of the data.

Spreading Sequences

At the receiver, the spreading is removed by multiplying by an exact copy of the spreading code synchronized with the transmitter.

The spreading codes are chosen so that the resulting signal is noise like:

There should be an approximately equal number of 0s and 1s, and few or no repeated patterns

PN sequences

Ideal sequence is a random sequence

The transmitter and receiver must have an exact copy of the sequence: a predictable way is needed to generate the same bit stream at transmitter and receiver

A PN generator will produce a periodic sequence that eventually repeats but that appears to be random.

PN sequences PN sequences are generated by an algorithm using

some initial value called “SEED”

The algorithm is deterministic and therefore produces sequential numbers that are not statistically random.

If the algorithm is good, the sequence will pass many reasonable tests of randomness.

These numbers are referred to as “Pseudorandom numbers of Pseudonoise sequences”

Properties of the PN sequence

The two must important properties of a PN sequence are RANDOMNESS & UNPREDICTABILITY

To validate randomness the following criteria are used:

Uniform Distribution: The frequency of occurrence of each number should be approximately the same. On a binary sequence, this is expanded in:

Balance Property: In a long sequence, the fraction of binary 1s should approach ½

Properties of the PN sequence Run Property: A run is defined as a sequence of all 1s or all 0s.

The appearance of alternate digits signal the beginning of a new run. About ½ of the runs of each type should be of length 1, ¼ of length 2, 1/8 of length 3, and so on.

Independence: No one value in the sequence can be inferred from others.

In spread spectrum, the correlation property also applies to a PN sequence:

Correlation Property: If a period of a sequence is compared term by term with a cycle shift of itself, the number of terms that are the same differs from those that are different by at most 1.

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