TUNALIData Communication1 Spread Spectrum Chapter 9

TUNALIData Communication2 Spread Spectrum Can be used to transmit either analog or digital data Analog signal Spread data over wide bandwidth Makes jamming and interception harder Frequency hoping —Signal broadcast over seemingly random series of frequencies Direct Sequence —Each bit is represented by multiple bits in transmitted signal —Chipping code

TUNALIData Communication3 Spread Spectrum Concept Input fed into channel encoder —Produces narrow bandwidth analog signal around central frequency Signal modulated using sequence of digits —Spreading code/sequence —Typically generated by pseudonoise/pseudorandom number generator Increases bandwidth significantly —Spreads spectrum Receiver uses same sequence to demodulate signal Demodulated signal fed into channel decoder

TUNALIData Communication4 General Model of Spread Spectrum System

TUNALIData Communication5 Gains Immunity from various noise and multipath distortion —Including jamming Can hide/encrypt signals —Only receiver who knows spreading code can retrieve signal Several users can share same higher bandwidth with little interference —Cellular telephones —Code division multiplexing (CDM) —Code division multiple access (CDMA)

TUNALIData Communication6 Pseudorandom Numbers Generated by algorithm using initial seed Deterministic algorithm —Not actually random —If algorithm is good, results pass reasonable tests of randomness Need to know algorithm and seed to predict sequence

TUNALIData Communication7 Frequency Hopping Spread Spectrum (FHSS) Signal broadcast over seemingly random series of frequencies Receiver hops between frequencies in sync with transmitter Eavesdroppers hear unintelligible blips Jamming on one frequency affects only a few bits

TUNALIData Communication8 Basic Operation Typically 2 k carriers frequencies forming 2 k channels Channel spacing between carrier frequencies corresponds with bandwidth of input Each channel used for fixed interval —300 ms in IEEE —Some number of bits transmitted using some encoding scheme —Sequence dictated by spreading code

TUNALIData Communication9 Frequency Hopping Example

TUNALIData Communication10 Frequency Hopping Spread Spectrum System (Transmitter)

TUNALIData Communication11 Frequency Hopping Spread Spectrum System (Receiver)

TUNALIData Communication12 Spread Spectrum Math 1 FSK input to the FHSS —s d (t) = A cos(2  (f (b i +1)  f)t) iT<t<(i+1)T —A = amplitude of signal —f 0 = base frequency —b i = value of the ith bit of data —  f = frequency separation —T = bit duration

TUNALIData Communication13 Spread Spectrum Math 2 Product signal during i th bit —p(t)= s d (t)c(t)= A cos(2  (f (b i +1)  f)t) cos(2  f i t) —Using cos(x)cos(y)=1/2(cos(x+y)+cos(x-y) —p(t)=0.5A[ cos(2  (f (b i +1)  f + f i )t + cos(2  (f (b i +1)  f - f i )t ] —Using a bandpass filter difference frequency can be blocked yielding —s(t)=0.5A cos(2  (f (b i +1)  f + f i ) t At the receiver, s(t) is multiplied by c(t). We again use the above trigonometric identity. This time sum frequency is blocked to obtain the original signal.

TUNALIData Communication14 FHSS Using MFSK Transmitted signal —s i (t) = A cos 2  f i t 1 ≤ i ≤ M —f i =f c + (2i -1-M) f d —f d = denotes difference frequency —M = number of different signal elements = 2 L —L = number of bits per signal element

TUNALIData Communication15 Slow and Fast FHSS Frequency shifted every T c seconds Duration of signal element is T s seconds Slow FHSS has T c  T s Fast FHSS has T c < T s Generally fast FHSS gives improved performance in noise (or jamming)

TUNALIData Communication16 Slow Frequency Hop Spread Spectrum Using MFSK (M=4, k=2)

TUNALIData Communication17 Fast Frequency Hop Spread Spectrum Using MFSK (M=4, k=2)

TUNALIData Communication18 FHSS Performance Considerations Typically large number of frequencies used —Improved resistance to jamming —Suppose that we have an MFSK transmitter with bandwidth W d Noise jammer with same bandwidth and fixed power S j on the signal carrier frequency —Then the signal energy per bit to noise power density per Hertz is If frequency hopping is used, the jammer must jam all 2 k frequencies reducing jamming power at a frequency to S j /2 k. Processing (Signal to noise ratio) gain is 2 k = W s /W d

TUNALIData Communication19 Direct Sequence Spread Spectrum (DSSS) Each bit represented by multiple bits using spreading code Spreading code spreads signal across wider frequency band —In proportion to number of bits used —10 bit spreading code spreads signal across 10 times bandwidth of 1 bit code One method: —Combine input with spreading code using XOR —Input bit 1 inverts spreading code bit —Input zero bit doesn’t alter spreading code bit —Data rate equal to original spreading code Performance similar to FHSS

TUNALIData Communication20 Direct Sequence Spread Spectrum Example

TUNALIData Communication21 DSSS Using BPSK Use +1 and -1 The signal is Where A= amplitude of the signal f c = carrier frequency d(t)= discrete function converting 1 to +1 and 0 to -1 With c(t) being the previous spreading signal At the receiver, since c(t)  c(t)=1

TUNALIData Communication22 Direct Sequence Spread Spectrum Transmitter

TUNALIData Communication23 Direct Sequence Spread Spectrum Receiver

TUNALIData Communication24 Direct Sequence Spread Spectrum Using BPSK Example

TUNALIData Communication25 Approximate Spectrum of DSSS Signal

TUNALIData Communication26 DSSS Performance Considerations 1 Let the jamming signal be of the form The received signal is where s(t)=transmitted signal s j (t)=jamming signal n(t)=additive white noise S j =jamming signal power

TUNALIData Communication27 DSSS Performance Considerations 2 The signal component due to jamming signal is This is BPSK modulation of the carrier tone and carrier power S j is spread over a bandwidth of 2/T c. BPSK demodulator has bandpass filter of 2/T width, thus most of the jamming power is filtered. Passing jamming power Gain in signal to noise ratio is T/T c = R c /R which is approximately W s /W d

TUNALIData Communication28 Code Division Multiple Access (CDMA) Multiplexing Technique used with spread spectrum Start with data signal rate D —Called bit data rate Break each bit into k chips according to fixed pattern specific to each user —User’s code New channel has chip data rate kD chips per second E.g. k=6, three users (A,B,C) communicating with base receiver R Code for A = Code for B = Code for C =

TUNALIData Communication29 CDMA Example

TUNALIData Communication30 CDMA Explanation Consider A communicating with base Base knows A’s code Assume communication already synchronized A wants to send a 1 —Send chip pattern A’s code A wants to send 0 —Send chip pattern Complement of A’s code Decoder ignores other sources when using A’s code to decode —Orthogonal codes —S A (s A )+ S A (s B ) = S A (s A )

TUNALIData Communication31 CDMA for DSSS n users each using different orthogonal PN sequence Modulate each users data stream —Using BPSK Multiply by spreading code of user

TUNALIData Communication32 CDMA in a DSSS Environment

TUNALIData Communication33 Required Reading Stallings chapter 9