Data and Computer Communications

1. Data and Computer Communications Chapter 9 – Spread Spectrum Eighth Edition by William Stallings Lecture slides by Lawrie Brown

2. Spread Spectrum • important encoding method for wireless communications • analog & digital data with analog signal • spreads data over wide bandwidth • makes jamming and interception harder • two approaches, both in use: • Frequency Hopping • Direct Sequence

3. Spread Spectrum • Input is fed into a channel encoder • Produces analog signal with narrow bandwidth • Signal is further modulated using sequence of digits • Spreading code or spreading sequence • Generated by pseudonoise, or pseudo-random number generator • Effect of modulation is to increase bandwidth of signal to be transmitted

4. Spread Spectrum • On receiving end, digit sequence is used to demodulate the spread spectrum signal • Signal is fed into a channel decoder to recover data

5. Spread Spectrum Advantages • What can be gained from apparent waste of spectrum? • Immunity from various kinds of noise and multipath distortion • Can be used for hiding and encrypting signals • Several users can independently use the same higher bandwidth with very little interference • CDM/CDMA Mobile telephones

6. Pseudorandom Numbers • generated by a deterministic algorithm • not actually random • but if algorithm good, results pass reasonable tests of randomness • starting from an initial seed • need to know algorithm and seed to predict sequence • hence only receiver can decode signal

7. Frequency Hoping Spread Spectrum (FHSS) • Signal is broadcast over seemingly random series of radio frequencies • A number of channels allocated for the FH signal (2k) • Width of each channel corresponds to bandwidth of input signal • Signal hops from frequency to frequency at fixed intervals • Transmitter operates in one channel at a time • Bits are transmitted using some encoding scheme • At each successive interval (300 ms for LAN 802.11), a new carrier frequency is selected

8. Frequency Hoping Spread Spectrum • Channel sequence dictated by spreading code • Receiver, hopping between frequencies in synchronization with transmitter, picks up message • Advantages • Eavesdroppers hear only unintelligible blips • Attempts to jam signal on one frequency succeed only at knocking out a few bits

9. Frequency Hoping Spread Spectrum

10. Frequency Hoping Spread Spectrum

11. Frequency Hoping Spread Spectrum

12. Frequency Hoping Spread Spectrum • Define the FSK input to the FHSS system as

13. Frequency Hoping Spread Spectrum • Assume the duration of one hop is the same as the duration of one bit • ignore phase differences between the data signal and the spreading signal, also called a chipping signal, c(t) . • The product signal during the ith hop • Using the trigonometric identity • A bandpass filter is used to block the difference frequency and pass the sum frequency, yielding an FHSS signal of

14. Frequency Hoping Spread Spectrum • At a receiver • A bandpass filter is used to block the sum frequency and pass the difference frequency • The same form as

15. Multiple Frequency-Shift Keying (MFSK) • More than two frequencies are used • More bandwidth efficient but more susceptible to error • 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

16. FHSS Using MFSK • MFSK signal is translated to a new frequency every Tcseconds by modulating the MFSK signal with the FHSS carrier signal • 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 • multiple data bits per frequency hop • Tc < Ts - fast-frequency-hop spread spectrum • multiple frequency hops per data bit

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

18. Multiple Frequency-Shift Keying (MFSK) • total MFSK bandwidth Wd = Mfd • Total FHSS bandwidth Ws = 2kWd

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

20. FHSS Performance Considerations • Large number of frequencies used • Large value of k 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 • Ex. MFSK transmitter with BW Wd and noise jammer of the same BW then • Eb/Nj = EbWd/Sj • If frequency hopping is used, jammer must jam 2k frequencies. With fixed power, jammed frequency will be reduced Sj/2k. • The gain in SNR or processing gain is • Gp = 2k = Ws/Wd

21. Direct Sequence Spread Spectrum (DSSS) • Each bit in original signal is represented by multiple bits in the transmitted signal • Spreading code spreads signal across a wider frequency band • Spread is in direct proportion to number of bits used • One technique combines digital information stream with the spreading code bit stream using exclusive-OR (Figure 7.6)

22. Direct Sequence Spread Spectrum (DSSS)

23. Phase-Shift Keying (PSK) • Two-level PSK (BPSK) • Uses two phases to represent binary digits

24. Phase-Shift Keying (PSK) • BPSK signal can be represented

25. DSSS Using BPSK • Multiply BPSK signal, sd(t) = A d(t) cos(2fct) by c(t)[takes values +1, -1] to get s(t) = A d(t)c(t) cos(2fct) • At receiver, incoming signal multiplied by c(t) • Since, c(t) x c(t) = 1, incoming signal is recovered

26. DSSS Using BPSK

27. DSSS Using BPSK

28. DSSS Performance Consideration

29. DSSS Performance Consideration • assume a simple jamming signal at the center frequency of the DSSS system with a form • the received signal is • where

30. DSSS Performance Consideration • The despreader at the receiver multiplies sr(t) by c(t), for jamming • Which is simply a BPSK modulation of the carrier tone • the carrier power Sj is spread over a bandwidth of approximately 2/Tc • Using Bandpass filter with BW 2/T, most of the jamming power is filtered

31. DSSS Performance Consideration • as an approximation, we can say that the jamming power passed by the filter is • The jamming is reduced by (Tc/T) • The inverse of this factor is the gain in SNR

32. Code-Division Multiple Access (CDMA) • CDMA is a multiplexing technique used with spread spectrum • Basic Principles of CDMA • D = rate of data signal • Break each bit into kchips • Chips are a user-specific fixed pattern • Chip data rate of new channel = kD

33. CDMA Example

34. CDMA Example • If k=6 and code is a sequence of 1s and -1s • 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 • u is the user that we are interested in • <d1, d2, d3, d4, d5, d6> = received chip pattern • <c1, c2, c3, c4, c5, c6> = sender’s code

35. 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

36. CDMA Example • the preceding computation using SA becomes • If A sends a 0 bit that corresponds to • no matter what sequence of 1s and -1s, it is always

37. CDMA Example • If B sends a 1 bit, then • Thus, the unwanted signal (from B) does not show up at all • if the decoder is linear and if A and B transmit signals SA and SB , respectively, at the same time, then • The codes of A and B that have the property that • are called orthogonal • In practice, the CDMA receiver can filter out the contribution from unwanted users or they appear as low-level noise

38. CDMA Example • User’s codes • Transmission from A

39. CDMA Example • Transmission from B, receiver attempts to recover A’s transmission • Transmission from C, receiver attempts to recover B’s transmission

40. CDMA Example • Transmission from B and C, receiver attempts to recover B’s transmission

41. CDMA for Direct Sequence Spread Spectrum

42. 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

43. 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

44. Important PN Properties • Randomness • Uniform distribution • Balance property : • in long sequence the fraction of binary ones should approach 1/2 • Run property: run is defined as a sequence of all 1-s or a sequence of all 0-s • about 1/2 of runs of each type should be of length 1,1/4 of length 2, 1/8 of length 3, etc. • Independence • no one value in sequence can be inferredfrom the others • Correlation property • good auto-and cross-correlation properties • Unpredictability

45. Implementation of PN sequences

46. Linear Feedback Shift Register Implementation

47. Problem Assignments • Solve all the review questions • Try the following problems: • 9.1, 9.2, 9.3, 9.4, 9.5, 9.6, 9.7