1. Spread Spectrum Chapter 7

2. 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

3. Spread Spectrum Jamming: deliberate noise to block reception of transmitted signals and to cause a nuisance at the receiving station.

4. 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

5. Spread Spectrum

6. 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)

7. Spread Spectrum First: Frequency hopping Recently: Direct Sequence

8. Frequency Hoping Spread Spectrum (FHSS) What could you suggest?? 0101 0100 0111 0010 1010 0101 01010

9. Frequency Hoping Spread Spectrum (FHSS) Signal is broadcast over seemingly random series of radio frequencies Transmitter hopping from frequency to frequency at fixed intervals T c 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

11. 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 T c Transmitter operates in one channel at a time for T c During T c, some number of bits are transmitted using some encoding scheme After each T c, a new carrier frequency is selected

12. 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 T c  Generate your own spreading code  Note that, in the spreading code, every k bits decides one specific band

13. Frequency Hoping Spread Spectrum First modulation : For transmission, binary data are fed into a modulator using some digital-to-analog encoding scheme (FSK) or (BPSK). The resulting signal s d (t) is centered on some base frequency.

14. Frequency Hoping Spread Spectrum 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 T c At each successive interval T c (each k PN bits), a new carrier frequency c(t) is selected.

15. Frequency Hoping Spread Spectrum 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.

16. 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

17. Reminder: MFSK MFSK example with M = 4 During T s, 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 W d = M f d.

18. FHSS Using MFSK MFSK signal (with a bandwidth of W d = M f d ) is translated to a new frequency band every T c seconds by modulating the MFSK signal with the FHSS carrier signal T c 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: T s = LT seconds T c  T s - slow-frequency-hop spread spectrum T c < T s - fast-frequency-hop spread spectrum

19. 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.

20. Slow FHSS MFSK example with M = 4 During T s, 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.

21. 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 (T c = 2 T s = 4T). We use an FHSS scheme with k = 2. That is, there are 4 = 2^k different channels, each of width W d. The total FHSS bandwidth is W s = 2^k W d.

22. 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 W d = M f d. We use an FHSS scheme with k = 2. That is, there are 4 = 2^k different channels, each of width W d. The total FHSS bandwidth is W s = 2^k W d. 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 (T c = 2 T s = 4T).

23. Fast FHSS In this case, however, each signal element is represented by two frequency bands.

24. Fast FHSS Again, M = 4 and k = 2. In this case, however, each signal element is represented by two frequency bands tones. Again, W d = M f d and W s = 2^k W d. In this example (T s = 2 T c = 2T). In general, fast FHSS provides improved performance compared to slow FHSS in the face of noise or jamming.

25. 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

26. Direct Sequence Spread Spectrum (DSSS) Each bit in original signal is represented by multiple bits in the transmitted signal using a spreading code

27. Direct Sequence Spread Spectrum (DSSS) 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)

28. Direct Sequence Spread Spectrum (DSSS) One technique combines digital information stream with the spreading code bit stream using exclusive-OR (Figure 7.6)

29. Direct Sequence Spread Spectrum (DSSS) Try to apply the exclusive-Or between the data input and the generated spreading code

30. Direct Sequence Spread Spectrum (DSSS)

32. 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!

33. Direct Sequence Spread Spectrum (DSSS) 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.

35. 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

36. DSSS Using BPSK BPSK signal can be written as, s d (t) = A d(t) cos(2  f c t) A = amplitude of signal f c = carrier frequency d(t) = discrete function [+1, -1], +1 refers to bit 1 and -1 refers to bit 0

37. DSSS Using BPSK To produce DSSS signal, Multiply BPSK signal, s d (t) = A d(t) cos(2  f c t) by c(t) [PN sequence that takes values +1, -1] to get s(t) = A d(t)c(t) cos(2  f c t) A = amplitude of signal f c = 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  f c t) = s d (t)

38. DSSS Using BPSK Try to find s(t)

39. DSSS Using BPSK

40. The spectrum of the data signal is What is the bandwidth of the data signal? Could you express s d (t)!!

41. 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?

42. 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

43. CDMA Example If k=6 and code is a sequence of 1s and -1s For a ‘1’ bit, A sends code as chip pattern For a ‘0’ bit, A sends complement of code Receiver knows sender’s code and performs electronic decode function = received chip pattern = sender’s code u refers to the user

44. CDMA Example User A code = 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 = Receiver receiving with A’s code If User A sends ‘1’ bit, What is the resulting S A (d) If User A sends ‘0’ bit: What is the resulting S A (d) If User B sends ‘1’ bit: What is the resulting S A (d)

45. CDMA Example User A code = To send a 1 bit = To send a 0 bit = User B code = To send a 1 bit = 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

46. CDMA Example If the Data message is 1101 what should be sent by every user?? Draw it!

48. CDMA Example Receiver knows sender’s code and performs electronic decode function = received chip pattern = sender’s code u refers to the user Let's suppose the receiver is actually interested in user A signal and see what happens.??

49. CDMA Example A sends 1 A sends 0 So if S A produces a +6, we say that we have received a 1 bit from A; if S A 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.

50. CDMA Example what happens if user B is sending and we try to receive it with S A, 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 S A again.

51. CDMA Example If the decoder is linear and if A and B transmit signals s A and s B, respectively, at the same time, then S A (s A + s B ) = S A (s A ) + S A (s B ) = S A (s A ) The decoder ignores B when it is using A's code. The codes of A and B that have the property that S A (c B ) = S B (c A ) = 0 are called orthogonal.

52. END

53. Appendix

54. CDMA for Direct Sequence Spread Spectrum

55. 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

56. 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

57. Important PN Properties Randomness Uniform distribution Balance property Run property Independence Correlation property Unpredictability

58. Linear Feedback Shift Register Implementation

59. Properties of M-Sequences Property 1: Has 2 n-1 ones and 2 n-1 -1 zeros Property 2: For a window of length n slid along output for N (=2 n-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 2 n-3 runs of ones and 2 n-3 runs of zeros, length 1

60. Properties of M-Sequences Property 4: The periodic autocorrelation of a ±1 m- sequence is

61. 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

62. 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

63. 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

64. Gold Sequences

65. 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

66. Walsh Codes Set of Walsh codes of length n consists of the n rows of an n ´ n Walsh matrix: W 1 = (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

67. 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

68. Frequency Hoping Spread Spectrum