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Spread spectrum communications and CDMA



L. Vandendorpe

L. Vandendorpe
UCL Communications and Remote Sensing Lab.



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    Spread spectrum communications and CDMA Spread spectrum communications and CDMA Presentation Transcript

    • Spread spectrum communications and CDMA L. Vandendorpe UCL Communications and Remote Sensing Lab. 1
    • 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
    • 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
    • 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
    • Block diagram of analog BPSK DS/SS transmitter and receiver 5
    • Illustration of the spreading/despreading process 6
    • Power spectra before and after DS/SS 7
    • Spectra in the presence of narrowband jamming 8
    • 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
    • Example of offset QPSK for DS/SS• Block diagram a(n) N c 1 (n) u(t) cos(ωc t ) sin(ωc t ) + b(n) N c 2 (n) u ( t - T c/ 2 ) 10
    • Frequency hopping 11
    • M-ary FSK and Slow Frequency hopping 12
    • M-ary FSK and Fast Frequency hopping 13
    • 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
    • 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
    • M-sequences• Map the {0, 1} values onto bi = {−1, 1}• Define the periodic correlation function φ(j) = n b b 1 i i+j (periodic in j, period n)• Ideally φ(j) = δ(j) (for the main period)• For an m sequence n j=0 φ(j) = (1) −1 1 ≤ j ≤ n − 1 16
    • 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 2(m+1)/2 + 1 m odd t(m) = (2) 2(m+2)/2 + 1 m even• Example: m = 10, t(10) = 65, −1, −t(m), t(m) − 2 = −1, −65, 63• Such sequences are called preferred sequences 17
    • 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
    • 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