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Spread Spectrum

Spread Spectrum. Chapter 9. Spread Spectrum. Can be used to transmit either a nalog 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

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Spread Spectrum

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  1. Spread Spectrum Chapter 9 Data Communication

  2. 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 Data Communication

  3. 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 Data Communication

  4. General Model of Spread Spectrum System Data Communication

  5. 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) Data Communication

  6. 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 Data Communication

  7. 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 Data Communication

  8. Basic Operation • Typically 2k carriers frequencies forming 2kchannels • Channel spacing between carrier frequencies corresponds with bandwidth of input • Each channel used for fixed interval • 300 ms in IEEE 802.11 • Some number of bits transmitted using some encoding scheme • Sequence dictated by spreading code Data Communication

  9. Frequency Hopping Example Data Communication

  10. Frequency Hopping Spread Spectrum System (Transmitter) Data Communication

  11. Frequency Hopping Spread Spectrum System (Receiver) Data Communication

  12. Spread Spectrum Math 1 • FSK input to the FHSS • sd(t) = A cos(2(f0+0.5(bi+1)f)t) iT<t<(i+1)T • A = amplitude of signal • f0 = base frequency • bi = value of the ith bit of data • f = frequency separation • T = bit duration Data Communication

  13. Spread Spectrum Math 2 • Product signal during i th bit • p(t)= sd(t)c(t)= A cos(2(f0+0.5(bi+1)f)t) cos(2fit) • Using cos(x)cos(y)=1/2(cos(x+y)+cos(x-y) • p(t)=0.5A[ cos(2(f0+0.5(bi+1)f + fi)t + cos(2(f0+0.5(bi+1)f - fi)t ] • Using a bandpass filter difference frequency can be blocked yielding • s(t)=0.5A cos(2(f0+0.5(bi+1)f + fi) 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. Data Communication

  14. FHSS Using MFSK • Transmitted signal • si (t) = A cos 2 f i t 1 ≤ i ≤ M • fi =f c + (2i -1-M) fd • f d= denotes difference frequency • M = number of different signal elements = 2 L • L = number of bits per signal element Data Communication

  15. Slow and Fast FHSS • Frequency shifted every Tc seconds • Duration of signal element is Ts seconds • Slow FHSS has Tc Ts • Fast FHSS has Tc < Ts • Generally fast FHSS gives improved performance in noise (or jamming) Data Communication

  16. Slow Frequency Hop Spread Spectrum Using MFSK (M=4, k=2) Data Communication

  17. Fast Frequency Hop Spread Spectrum Using MFSK (M=4, k=2) Data Communication

  18. FHSS Performance Considerations • Typically large number of frequencies used • Improved resistance to jamming • Suppose that we have an MFSK transmitter with • bandwidth Wd • Noise jammer with same bandwidth and fixed power Sj 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 2k frequencies reducing jamming power at a frequency to Sj/2k. Processing (Signal to noise ratio) gain is 2k = Ws/Wd Data Communication

  19. 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 Data Communication

  20. Direct Sequence Spread Spectrum Example Data Communication

  21. DSSS Using BPSK • Use +1 and -1 • The signal is Where A= amplitude of the signal fc= 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 Data Communication

  22. Direct Sequence Spread Spectrum Transmitter Data Communication

  23. Direct Sequence Spread Spectrum Receiver Data Communication

  24. Direct Sequence Spread Spectrum Using BPSK Example Data Communication

  25. ApproximateSpectrum of DSSS Signal Data Communication

  26. DSSS Performance Considerations 1 • Let the jamming signal be of the form The received signal is where s(t)=transmitted signal sj(t)=jamming signal n(t)=additive white noise Sj=jamming signal power Data Communication

  27. DSSS Performance Considerations 2 • The signal component due to jamming signal is This is BPSK modulation of the carrier tone and carrier power Sj is spread over a bandwidth of 2/Tc. 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/Tc= Rc/R which is approximately Ws/Wd Data Communication

  28. 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 = <1,-1,-1,1,-1,1> • Code for B = <1,1,-1,-1,1,1> • Code for C = <1,1,-1,1,1,-1> Data Communication

  29. CDMA Example Data Communication

  30. 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 <1,-1,-1,1,-1,1> • A’s code • A wants to send 0 • Send chip pattern <-1,1,1,-1,1,-1> • Complement of A’s code • Decoder ignores other sources when using A’s code to decode • Orthogonal codes • SA(sA)+ SA(sB) = SA(sA) Data Communication

  31. CDMA for DSSS • n users each using different orthogonal PN sequence • Modulate each users data stream • Using BPSK • Multiply by spreading code of user Data Communication

  32. CDMA in a DSSS Environment Data Communication

  33. Required Reading • Stallings chapter 9 Data Communication

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