L. Vandendorpe UCL Communications and Remote Sensing Lab.

1. Spread spectrum communications and CDMA
L. Vandendorpe
UCL Communications and Remote Sensing Lab.
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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
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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)
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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
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5. Block diagram of analog BPSK DS/SS transmitter and
receiver
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6. Illustration of the spreading/despreading process
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7. Power spectra before and after DS/SS
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8. Spectra in the presence of narrowband jamming
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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
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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) +
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11. Frequency hopping
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12. M-ary FSK and Slow Frequency hopping
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13. M-ary FSK and Fast Frequency hopping
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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 ...
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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
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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)
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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
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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
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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
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