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Spread Spectrum Techniques

Spread Spectrum Techniques. Frequency Hopping Direct Sequence. Shannon’s Theorem and Nyquist’s Theorem. channel capacity, [ bps ]. channel bandwidth, [Hz]. SNR is the signal-to-Noise ratio [ Unitless ]. Shannon’s theorem has some interesting implications: For a given capacity, :

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Spread Spectrum Techniques

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  1. Spread Spectrum Techniques Frequency Hopping Direct Sequence

  2. Shannon’s Theorem and Nyquist’s Theorem • channel capacity, [bps]. • channel bandwidth, [Hz]. • SNR is the signal-to-Noise ratio [Unitless]. • Shannon’s theorem has some interesting implications: • For a given capacity, : • There is no limit to how small the bandwidth can be, provided that SNR is sufficiently large. • There is no limit to how small the SNR can be, provided that the bandwidth is sufficiently large. • For a given Bandwidth, : • There is no limit to the capacity provided that SNR is sufficiently large. • There is no limit to how small SNR can be, provided that the Capacity is reduced accordingly.

  3. Cont. • Rearranging Shannon’s equation gives: For large :

  4. Graph C/B vs. SNR (dB) C/B SNR (dB)

  5. Negative SNR • Shannon’s theorem acknowledges the possibility that the noise power can be at a higher level than the signal’s power, this situation does not make data transmission impossible. • Considering the equation, data transmission is possible as long as is positive, that is when there is some signal power. • Shannon’s theorem therefore tells us that data transmission is possible under these conditions. • For negative values of however, will be less than 1. • e.g., for an SNR of -30 dB, a bandwidth of 714 kHz would be required to carry data at 1 kbps.

  6. Nyquist’s Theorem • Although Shannon’s theorem places a limit on the data that can be carried, it is not the only limit. • Nyquist’s theorem places an absolute limit on the symbol (baud) rate for a channel of a particular bandwidth regardless of noise levels. • According to Nyquist’s theorem a channel of bandwidth can carry a maximum of symbols per second.

  7. Example • It is required to transmit data at a rate of 9600 bps over a channel of bandwidth 2000 Hz. Use Shannon’s theorem to determine the minimum signal to noise ratio required and, referring to Nyquist’s theorem. Comment on a suitable modulation scheme. • Solution: • Therefore a SNR of at least 14.3 dB is required. • The bandwidth 2000 Hz limits the baud rate to 4000 Baud • Thus there must be at least 3 bits per symbol.

  8. Spread Spectrum • Spread spectrum is a communication technique that spreads a narrowband communication signal over a wide range of frequencies for transmission then de-spreads it into the original data bandwidth at the receive. • Makes jamming and interception harder • Two Techniques: • Frequency hoping • Signal broadcast over seemingly random series of frequencies • Direct Sequence • Each bit is represented by multiple bits in transmitted signal • Chipping (spreading)code/sequence

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

  10. General Model of Spread Spectrum System

  11. Spread spectrum Concept

  12. 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 HedyLamarr

  13. Basic Operation • Typically 2k carriers frequencies forming 2k channels • Channel spacing 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 • May be fractions of bit (see later) • Sequence dictated by spreading code

  14. f4 f3 f2 f1 Time Frequency FHSS Repeating period Spreading Factor

  15. f4 f3 f2 f1 Time Frequency FHSS Repeating period

  16. f4 f3 f2 f1 Time Frequency Multiplexing Repeating period User1 User2

  17. f4 f3 f2 f1 Time Frequency Multiplexing Repeating period User1 User2

  18. Frequency Hopping Spread Spectrum System

  19. Frequency Hopping Spread Spectrum System

  20. Slow and Fast FHSS • Frequency shifted every Tc seconds • Duration of signal symbol is TM seconds • Slow FHSS has Tc TM • Fast FHSS has Tc < TM • Generally fast FHSS gives improved performance in noise (or jamming)

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

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

  23. Direct Sequence Spread Spectrum (DSSS) • Each bit represented by multiple bits using spreading (chipping)code/sequence. This process is called Processing Gain. • The bits resulting from combining the information bits with the chipping code are called chips - the result- which is then transmitted. • 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  Processing Gain Spreading Factor (SF) =10 • SF is the number of chips within each symbol duration , let be the chip duration : chipping rate, : Baud rate. • 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

  24. Direct Sequence Spread Spectrum Example : XOR

  25. Another method (polar)

  26. Approximate Spectrum of DSSS Signal BW: The BW of is

  27. Direct Sequence Spread Spectrum Transmitter

  28. Direct Sequence Spread Spectrum Receiver Spread Signal Original Signal

  29. DSSS Overall Transmit/Receive transmit signal spread spectrum signal user data modulator X chipping sequence radio carrier : we can look at it as a pulse shaping PN generator transmitter correlator lowpass filtered signal sampled sums products received signal data demodulator integrator decision X chipping sequence receiver radio carrier PN generator

  30. DSSS Using BPSK • Multiply BPSK signal, by [takes values +1, -1] to get • amplitude of signal • carrier frequency • digital baseband signal • pulse shaping signal • bit duration • At receiver, incoming signal multiplied by • Since, , original signal is recovered

  31. Direct Sequence Spread Spectrum Using BPSK Example

  32. Narrowband vs. Spread Spectrum Narrowband (High Peak Power) Power Spread Spectrum (Low Peak Power) Frequency The bandwidth increases with spreading but spectral power density necessary for transmission decreases. Spread spectrum needs only very small power densities, often below the level of natural background noise.

  33. Gains • Immunity from various noise and multipath distortion • Including jamming • Can hide/encrypt signals • Only receiver who knows spreading code can retrieve signal • Advantages • reduces frequency selective fading • in cellular networks • base stations can use the same frequency range • several base stations can detect and recover the signal • soft handover • Disadvantages • precise power control necessary

  34. signal Interference or noise power spread signal power spread Interference or noise detection at receiver f f Gains (cont.) • Problem of radio transmission: frequency dependent fading can wipe out narrow band signals for duration of the interference • Solution: spread the narrow band signal into a broad band signal using a special code - protection against narrow band interference spread spectrum channels channelquality channelquality narrowband channels 2 2 2 2 1 5 6 2 2 3 1 4 frequency frequency Narrowband signal spreadspectrum guard space

  35. Effects of spreading on noise and interference Rx x + The noise is spread

  36. Effects of spreading and interference PSD PSD user signal broadband interference narrowband interference i) ii) f f sender PSD PSD PSD iii) iv) v) f f f receiver

  37. Code Division Multiple Access (CDMA) • Multiplexing Technique used with spread spectrum • Start with data signal rate • Buad rate (symbols per second) • Break each symbol into SF chips according to fixed pattern specific to each user (User’s spreading code) • SF is the number of chips within each symbol duration , let be the chip duration • New channel has chip data rate chips per second (cps). • Spreading code repetition period (code length) : • Short code: an exact pattern of the PN will repeat each data symbol. • Long code:

  38. Short vs. Long Code Short 1 0 1 1 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 0 0 1 0 1 0 1 1 0 0 1 0 1 1 0 1 1 0 Long 1 0 0 1 1 0 0 1 1 0 0 1 0 1 0 0 0 1 0 1 1 1 0 0 1 0 0 1 0 0 1 1

  39. CDMA Example • e.g. SF=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> Short code

  40. 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 <c1, c2, c3, c4, c5, c6>, e.g.<1,-1,-1,1,-1,1> • A’s code • A wants to send 0 • Send chip pattern <-c1, -c2, -c3, -c4, -c5, -c6>, e.g.<-1,1,1,-1,1,-1> • Complement of A’s code • 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 • Decoder ignores other sources when using A’s code to decode • Orthogonal codes

  41. 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> • To send a 0 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: <1, –1, –1, 1, –1, 1>X<1, 1, –1, –1, 1, 1>=0 unwanted signal ignored

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

  43. CDMA in a DSSS Environment

  44. Seven Channel CDMA Encoding and Decoding

  45. correlator lowpass filtered signal sampled sums products received signal data demodulator integrator decision X chipping sequence receiver radio carrier PN generator

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