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Unformatted text preview: h the autocorrelation
properties of Barker codes. EE102A:Signal Processing and Linear Systems I; Win 0910, Pauly 16 PseudoNoise Codes
Pseudonoise codes approximate the ideal sharp autocorrelation, orthogonal
codes. These are deterministic codes that approximate the characteristics
of a noise sequence.
They are ±1 with probability of 1/2, and have the run lengths of −1’s and
1’s of a random sequence. = At zero shift, the product of the two is a contant ”1”, and the autocorrelation
is ”N”. At other shifts, the product of each interval is just is likely to be
+1 as −1, so the autocorrelation is small. EE102A:Signal Processing and Linear Systems I; Win 0910, Pauly 17 They are not completely orthogonal, although
1
T T φn(t)φk (t)dt 0 should be small (again, ±1 equally likely, so the integral will be small).
Other channels appear as noiselike interference.
If we correlate the received signal with φn(t) we get a large signal for the
nth channel, with a peak at the delay for the nth channel.
Adding users looks likes like an increased background noise level, which
softly degrades performance. EE102A:Signal Processing and Linear Systems I; Win 0910, Pauly 18 y(t ) (!1 y)(t ) (!2 y)(t ) EE102A:Signal Processing and Linear Systems I; Win 0910, Pauly 19 Summary
Orthogonal codes allow users to share a channel.
Hadamard codes work well when the channels can be synchronized, such as
when the basestation is talking to multiple handsets.
For unsynchronized channels, we want both orthogonality, and good
autocorrelations. Psuedorandom codes are a good approximation.
We can continue to add users by handing out more codes, with a soft
degradation of performance. Other users look like an increased noise level. EE102A:Signal Processing and Linear Systems I; Win 0910, Pauly 20...
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 Fall '13
 Mukamel
 Signal Processing

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