Spread spectrum communications and CDMA

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L. Vandendorpe
UCL Communications and Remote Sensing Lab.

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Spread spectrum communications and CDMA

  1. 1. Spread spectrum communications and CDMA L. Vandendorpe UCL Communications and Remote Sensing Lab. 1
  2. 2. Spread spectrum techniques (1) • Definition: – Transmission BW much wider than the signal BW • Motivation behind this apparently wasteful approach ? – To provide resistance against interference/jamming – To mask the signal in the noise (low prob. of intercept) – Resistance against multipath propagation (not all) – Allow multiple access – Also used for range measurement 2
  3. 3. Spread spectrum techniques (2) • Types – Direct sequence spectrum spreading (DS/SS) – Frequency hopping (FH), slow (SFH) or fast (FFH) – Time hopping – Hybrid techniques (both FH and DS) • All techniques use codes in some way • When each user has its own code (any technique) : Code Division Multiple Acces (CDMA) 3
  4. 4. Spread spectrum techniques (3) • In the beginning (past) : Modulation first then spreading – No specific link between data modulation and spreading waveform – Problem of spectrum limitation – See block diagram 4
  5. 5. Block diagram of analog BPSK DS/SS transmitter and receiver 5
  6. 6. Illustration of the spreading/despreading process 6
  7. 7. Power spectra before and after DS/SS 7
  8. 8. Spectra in the presence of narrowband jamming 8
  9. 9. Spread spectrum techniques (4) • Presently (IS-95, UTRA-WCDMA) – DS/SS CDMA implemented as digital data shaping (before mixer) – Followed by chip half root Nyquist filter 9
  10. 10. Example of offset QPSK for DS/SS • Block diagram N c1(n) u(t) cos(ωct) a(n) N c2(n) u(t-Tc/2) b(n) sin(ωct) + 10
  11. 11. Frequency hopping 11
  12. 12. M-ary FSK and Slow Frequency hopping 12
  13. 13. M-ary FSK and Fast Frequency hopping 13
  14. 14. About the codes • If correlation only is performed at the receiver – Autocorrelation as close as possible to Dirac pulse – If several synchronous (downlink) : orthogonal codes – If several asynchronous users : as low as possible cross-correlations for any delay – Families : Gold, Kasami, etc ... 14
  15. 15. M-sequences • Most popular sequences: maximum length shift register sequences or m sequence • Sequence of length n = 2m − 1 and generated by an m-stage shift register with linear feedback (and primitive polynomial) • Sequence periodic with period n • Each period contains 2m−1 ones and 2m−1 − 1 zeros pulse 15
  16. 16. M-sequences • Map the {0, 1} values onto bi = {−1, 1} • Define the periodic correlation function φ(j) = n 1 bi bi+j (periodic in j, period n) • Ideally φ(j) = δ(j) (for the main period) • For an m sequence φ(j) = n j = 0 −1 1 ≤ j ≤ n − 1 (1) 16
  17. 17. Codes • In CDMA, not only autocorrelation matters but also cross-correlation • The periodic cross-correlation between any pair of m sequences of the same period can have large peaks: not acceptable in CDMA • Gold and Kasami proved that certain pairs of m sequences of length n have 3 valued cross-correlations (−1, −t(m), t(m) − 2) where t(m) = 2(m+1)/2 + 1 m odd 2(m+2)/2 + 1 m even (2) • Example: m = 10, t(10) = 65, −1, −t(m), t(m) − 2 = −1, −65, 63 • Such sequences are called preferred sequences 17
  18. 18. Codes • From a pair of preferred sequences, we can generate new sequences by the modulo-2 sum of the first with shifted versions of the second (or vice-versa). • For period n, n = 2m − 1 possibilities • with the 2 original sequences, one get n + 2 sequences, called Gold codes or sequences • Apart from the 2 original sequences, the other are not m sequences; hence the autocorrelation is not two-valued • The cross-correlation of any pair of Gold sequences taken from the n = 2 is three-valued −1, −t(m), t(m) − 2 18
  19. 19. Codes: to be revisited ? • All these considerations are mainly motivated by the fact that corre- lation based reception is supposed to be implemented • So correlation properties matter • If more advanced receivers are considered one can wonder whether correlation properties are still of the same importance 19

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