Spread spectrum communications and CDMA
L. Vandendorpe UCL Communications and Remote Sensing Lab.
Spread spectrum techniques (1)
Denition: 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
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)
Spread spectrum techniques (3)
In the beginning (past) : Modulation rst then spreading No specic link between data modulation and spreading waveform Problem of spectrum limitation See block diagram
Block diagram of analog BPSK DS/SS transmitter and receiver
Illustration of the spreading/despreading process
Power spectra before and after DS/SS
Spectra in the presence of narrowband jamming
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 lter
Example of oset QPSK for DS/SS
Block diagram
a(n) N c 1 (n) u(t) cos(c t ) sin(c t ) b(n) N c 2 (n) u ( t - T c/ 2 )
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Frequency hopping
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M-ary FSK and Slow Frequency hopping
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M-ary FSK and Fast Frequency hopping
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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 ...
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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 2m1 ones and 2m1 1 zeros pulse
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M-sequences
Map the {0, 1} values onto bi = {1, 1} Dene the periodic correlation function (j) = j, period n) Ideally (j) = (j) (for the main period) For an m sequence (j) = n j=0 1 1 j n 1 (1)
n b b 1 i i+j (periodic in
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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
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Codes
From a pair of preferred sequences, we can generate new sequences by the modulo-2 sum of the rst 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
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Codes: to be revisited ?
All these considerations are mainly motivated by the fact that correlation 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
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