Spread Spectrum Chapter 7. Spread Spectrum Form of communication Can be used to transmit analog or digital data using an ANALOG signal Idea: spread the

Spread Spectrum

Chapter 7

Spread Spectrum Form of communication Can be used to transmit analog or digital data using an

ANALOG signal

Idea: spread the signal over a wider bandwidth to make jamming and interception more difficult. First: Frequency hopping Recently: Direct Sequence

Spread Spectrum Jamming: deliberate noise to block reception of

transmitted signals and to cause a nuisance at the receiving station.

Spread Spectrum First: Input is fed into a channel encoder

Produces analog signal with narrow bandwidth around some centre frequency=> first modulation

Second: Signal is further modulated using a sequence of digits Spreading code or spreading sequence (called PN) Generated by pseudo-random number generator

=> Effect of the second modulation is to increase bandwidth of signal to be transmitted

On the receiving end, the same code is used to demodulate the spread spectrum signal

Spread Spectrum

Spread Spectrum What can be gained from apparent waste of

spectrum? Can be used for hiding and encrypting signals

Only a recipient who knows the spreading code can recover the encoded information

Several users can independently use the same wider bandwidth with very little interference (CDMA)

Spread Spectrum

Spread SpectrumFirst: Frequency hoppingRecently: Direct Sequence

Frequency Hoping

Spread Spectrum (FHSS)

What could you suggest??

0101 0100 0111 0010 1010 0101 01010

Frequency Hoping Spread Spectrum (FHSS)

Signal is broadcast over seemingly random series of radio frequencies Transmitter hopping from frequency to frequency at fixed

intervals Tc

A receiver hopping between frequencies in synchronization with the transmitter picks up the message

Eavesdroppers hear only unintelligible bits Attempts to jam the signal on one frequency succeed only at

knocking out a few bits

Frequency Hoping Spread Spectrum (FHSS)

Signal is broadcast over seemingly random series of radio frequencies

A number of channels allocated for the FH signal Width of each channel corresponds to bandwidth of

input signal (output of the first modulation) Signal hops from frequency to frequency at fixed

intervals Tc

Transmitter operates in one channel at a time for Tc During Tc, some number of bits are transmitted using

some encoding scheme After each Tc, a new carrier frequency is selected

Frequency Hoping Spread Spectrum

Channels sequence dictated by spreading code 00 11 01 10 How many channels (bands) Needed number of bits? What is the length of the spreading code?

In the example, How many bands? What is the number of needed bits (k) to generate the spreading code ? The transmission duration on every band is Tc Generate your own spreading code Note that, in the spreading code, every k bits decides one specific band


First modulation : For transmission, binary data are fed into a modulator

using some digital-to-analog encoding scheme (FSK) or (BPSK).

The resulting signal sd(t) is centered on some base frequency.


Second Modulation: A pseudonoise (PN), or pseudorandom number,

serves as an index into a table of frequencies; this is the spreading code

01 00 11 10 Each k bits of the PN specifies one of the 2^k

carrier frequencies. The duration of each frequency hop is Tc

At each successive interval Tc (each k PN bits), a new carrier frequency c(t) is selected.


The frequency carrier specified by the code is used to modulated the signal produced from the initial modulator to produce a new signal s(t) s(t) is now centered on the selected carrier frequency.

On reception, the spread spectrum signal is demodulated using the same sequence of PN-derived frequencies and then demodulated to produce the output data.

FHSS Using MFSK

f i = f c + (2i – 1 – M)f d

f c = the carrier frequency f d = the difference frequency M = number of different signal elements = 2 L

L = number of bits per signal element

tfAts ii 2cos Mi 1

Reminder: MFSK MFSK example with M = 4 During Ts, 2 bit signal elements are transmitted M = 4, four different frequencies are used to encode the data

input 2 bits at a time. Each signal element is a discrete frequency tone around fc the total MFSK bandwidth is Wd = M fd .

FHSS Using MFSK MFSK signal (with a bandwidth of Wd = M fd ) is translated to a new

frequency band every Tc seconds by modulating the MFSK signal with the FHSS carrier signal Tc is the transmission duration on every FHSS band Remember that with FHSS, width of each channel corresponds to

bandwidth of input signal (output of the first modulation) For data rate of R:

duration of a bit: T = 1/R seconds duration of signal element: Ts = LT seconds

Tc Ts - slow-frequency-hop spread spectrum

Tc < Ts - fast-frequency-hop spread spectrum

Slow FHSS

Thus, for the first pair of columns, governed by PN sequence 00, the lowest band of frequencies is used. For the second pair of columns, governed by PN sequence 11, the highest band of frequencies is used.

Each pair of columns corresponds to the selection of a frequency band based on a 2-bit PN sequence.

Slow FHSS MFSK example with M = 4 During Ts, 2 bit signal elements are transmitted Each pair of columns corresponds to the selection of

a frequency band based on a 2-bit PN sequence. Thus, for the first pair of columns, governed by PN

sequence 00, the lowest band of frequencies is used.

For the second pair of columns, governed by PN sequence 11, the highest band of frequencies is used.

Slow FHSS

Each 2 bits of the PN sequence is used to select one of the four channels. That band is held for a duration of two signal elements, or four bits (Tc = 2 Ts = 4T).

We use an FHSS scheme with k = 2. That is, there are 4 = 2^k different channels, each of width Wd .The total FHSS bandwidth is Ws = 2^k Wd .

Slow FHSS Here we have M = 4, which means that four different frequencies are

used to encode the data input 2 bits at a time. Each signal element is a discrete frequency tone, and the total

MFSK bandwidth is Wd = M fd . We use an FHSS scheme with k = 2. That is, there are 4 = 2^k

different channels, each of width Wd .

The total FHSS bandwidth is Ws = 2^k Wd . Each 2 bits of the PN sequence is used to select one of the four

channels (bands).

That band is held for a duration of two signal elements, or four bits (Tc = 2 Ts = 4T).

Fast FHSSIn this case, however, each signal element is represented by two frequency bands.

Fast FHSS Again, M = 4 and k = 2. In this case, however, each signal element is

represented by two frequency bands tones. Again, Wd = M fd and Ws = 2^k Wd . In this

example (Ts = 2 Tc = 2T). In general, fast FHSS provides improved

performance compared to slow FHSS in the face of noise or jamming.

FHSS Performance Considerations

Large number of frequencies used Results in a system that is quite resistant to

jamming Jammer must jam all frequencies With fixed power, this reduces the jamming power

in any one frequency band

Direct Sequence Spread Spectrum (DSSS)

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


Spreading code spreads signal across a wider frequency band Spread is in direct proportion to number of bits used Therefore, a 10-bit spreading code spreads the signal

across a frequency band that is 10 times greater than a 1-bit spreading code.

- The duration of each chip in the code is Tc<<T (the information bit duration)


One technique combines digital information stream with the spreading code bit stream using exclusive-OR (Figure 7.6)


Try to apply the exclusive-Or between the data input and the generated spreading code




What does an information bit of one cause? What does an information bit of zero cause? What is the bit rate of the resulting combination?

Compared to the information rate!


Note that an information bit of one inverts the spreading code bits in the combination, while an information bit of zero causes the spreading code bits to be transmitted without inversion.

The combination bit stream has the data rate of the original spreading code sequence, so it has a wider bandwidth than the information stream.

In this example, the spreading code bit stream is clocked at four times the information rate.

Reminder: Phase-Shift Keying (PSK)

Two-level PSK (BPSK) Uses two phases to represent binary digits

Rather than representing binary data with 1 and 0, it is more convenient for our purpose to use +1 and -1 to represent the two binary digits

tsd

tfA c2cos tfA c2cos

1binary 0binary

tfA c2cos

tfA c2cos1binary 0binary

DSSS Using BPSK

BPSK signal can be written as ,

sd(t) = A d(t) cos(2 fct) A = amplitude of signalfc = carrier frequencyd(t) = discrete function [+1, -1], +1 refers to bit 1 and -1 refers to bit 0

DSSS Using BPSK To produce DSSS signal, Multiply BPSK signal,

sd(t) = A d(t) cos(2 fct)

by c(t) [PN sequence that takes values +1, -1] to get

s(t) = A d(t)c(t) cos(2 fct) A = amplitude of signal fc = carrier frequency

d(t) = discrete function [+1, -1] At receiver, incoming signal multiplied by c(t)

Since, c(t) x c(t) = 1, incoming signal is recovered s(t) c(t)= A d(t) c(t) c(t) cos(2 fct) = sd(t)

DSSS Using BPSK Try to find s(t)

DSSS Using BPSK

DSSS Using BPSK The spectrum of the data signal is

What is the bandwidth of the data signal?

Could you express sd(t)!!

DSSS Using BPSK The spectrum of the spread signal is

What is the bandwidth of the spread signal?

Knowing that T = k Tc, What is the relationship between both bandwidth?

Code-Division Multiple Access (CDMA)

Multiplexing technique used with spread spectrum

Basic Principles of CDMA D = rate of data signal Break each bit into k chips

Chips are a user-specific fixed pattern What is the chip rate? Chip data rate of new channel = kD

CDMA Example If k=6 and code is a sequence of 1s and -1s <c1, c2, c3, c4, c5, c6>

For a ‘1’ bit, A sends code as chip pattern <c1, c2, c3, c4, c5, c6>

For a ‘0’ bit, A sends complement of code <-c1, -c2, -c3, -c4, -c5, -c6>

Receiver knows sender’s code and performs electronic decode function

<d1, d2, d3, d4, d5, d6> = received chip pattern <c1, c2, c3, c4, c5, c6> = sender’s code u refers to the user

665544332211 cdcdcdcdcdcddSu

CDMA Example User A code = <1, –1, –1, 1, –1, 1>

What is the pattern to be send to communicate a 1 bit? What is the pattern to be send to communicate a 0 bit?

User B code = <1, 1, –1, – 1, 1, 1> Receiver receiving with A’s code

If User A sends ‘1’ bit, What is the resulting SA(d) If User A sends ‘0’ bit: What is the resulting SA(d) If User B sends ‘1’ bit: What is the resulting SA(d)


CDMA Example User A code = <1, –1, –1, 1, –1, 1>

To send a 1 bit = <1, –1, –1, 1, –1, 1> To send a 0 bit = <–1, 1, 1, –1, 1, –1>

User B code = <1, 1, –1, – 1, 1, 1> To send a 1 bit = <1, 1, –1, –1, 1, 1>

Receiver receiving with A’s code (A’s code) x (received chip pattern)

User A ‘1’ bit: 6 -> 1 User A ‘0’ bit: -6 -> 0 User B ‘1’ bit: 0 -> unwanted signal ignored

CDMA Example

If the Data message is 1101 what should be sent by every user??

Draw it!

CDMA Example Receiver knows sender’s code and performs electronic

decode function

<d1, d2, d3, d4, d5, d6> = received chip pattern <c1, c2, c3, c4, c5, c6> = sender’s code u refers to the user

Let's suppose the receiver is actually interested in user A signal and see what happens.??


CDMA Example A sends 1

A sends 0

So if SA produces a +6, we say that we have received a 1 bit

from A; if SA produces a -6, we say that we have received a 0 bit from user A; otherwise, we assure that someone else is sending information or there is an error.

CDMA Example what happens if user B is sending and we try to receive it

with SA, that is, we are decoding with the wrong code, A's.

Thus, the unwanted signal (from B) does not show up at all. You can easily verify that if B had sent a 0 bit, the decoder would

produce a value of 0 for SA again.

CDMA Example If the decoder is linear and if A and B transmit signals sA and sB, respectively, at the

same time, then SA(sA + sB) = SA(sA) + SA(sB) = SA(sA) The decoder ignores B when it is using A's code. The codes of A and B that have the property that

SA(cB) = SB(cA) = 0 are called orthogonal.

END

Appendix

CDMA for Direct Sequence Spread Spectrum

Categories of Spreading Sequences Spreading Sequence Categories

PN sequences Orthogonal codes

For FHSS systems PN sequences most common

For DSSS systems not employing CDMA PN sequences most common

For DSSS CDMA systems PN sequences Orthogonal codes

PN Sequences PN generator produces periodic sequence that

appears to be random PN Sequences

Generated by an algorithm using initial seed Sequence isn’t statistically random but will pass many

test of randomness Sequences referred to as pseudorandom numbers or

pseudonoise sequences Unless algorithm and seed are known, the sequence is

impractical to predict

Important PN Properties Randomness

Uniform distribution Balance property Run property

Independence Correlation property

Unpredictability

Linear Feedback Shift Register Implementation

Properties of M-Sequences Property 1:

Has 2n-1 ones and 2n-1-1 zeros Property 2:

For a window of length n slid along output for N (=2n-1) shifts, each n-tuple appears once, except for the all zeros sequence

Property 3: Sequence contains one run of ones, length n One run of zeros, length n-1 One run of ones and one run of zeros, length n-2 Two runs of ones and two runs of zeros, length n-3 2n-3 runs of ones and 2n-3 runs of zeros, length 1

Properties of M-Sequences Property 4:

The periodic autocorrelation of a ±1 m-sequence is

otherwise

... 2N, N,0, 1

1

τ

NR

Definitions Correlation

The concept of determining how much similarity one set of data has with another

Range between –1 and 1 1 The second sequence matches the first sequence 0 There is no relation at all between the two sequences -1 The two sequences are mirror images

Cross correlation The comparison between two sequences from different

sources rather than a shifted copy of a sequence with itself

Advantages of Cross Correlation The cross correlation between an m-sequence and

noise is low This property is useful to the receiver in filtering out

noise The cross correlation between two different m-

sequences is low This property is useful for CDMA applications Enables a receiver to discriminate among spread

spectrum signals generated by different m-sequences

Gold Sequences Gold sequences constructed by the XOR of two

m-sequences with the same clocking Codes have well-defined cross correlation

properties Only simple circuitry needed to generate large

number of unique codes In following example (Figure 7.16a) two shift

registers generate the two m-sequences and these are then bitwise XORed

Gold Sequences

Orthogonal Codes Orthogonal codes

All pairwise cross correlations are zero Fixed- and variable-length codes used in CDMA

systems For CDMA application, each mobile user uses one

sequence in the set as a spreading code Provides zero cross correlation among all users

Types Welsh codes Variable-Length Orthogonal codes

Walsh Codes

Set of Walsh codes of length n consists of the n rows of an n ´ n Walsh matrix:

W1 = (0)

n = dimension of the matrix Every row is orthogonal to every other row and to

the logical not of every other row Requires tight synchronization

Cross correlation between different shifts of Walsh sequences is not zero

nn

nnn WW

WWW 2

2

Typical Multiple Spreading Approach Spread data rate by an orthogonal code

(channelization code) Provides mutual orthogonality among all users

in the same cell Further spread result by a PN sequence

(scrambling code) Provides mutual randomness (low cross

correlation) between users in different cells


Documents

Spread Spectrum Chapter 7. Spread Spectrum Form of communication Can be used to transmit analog or digital data using an ANALOG signal Idea: spread the