Linear systems i win 09 10 pauly 15 we would like

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Unformatted text preview: h the autocorrelation properties of Barker codes. EE102A:Signal Processing and Linear Systems I; Win 09-10, Pauly 16 Pseudo-Noise Codes Pseudo-noise codes approximate the ideal sharp auto-correlation, 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 09-10, 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 noise-like 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 09-10, Pauly 18 y(t ) (!1 ￿ y)(t ) (!2 ￿ y)(t ) EE102A:Signal Processing and Linear Systems I; Win 09-10, 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. Psuedo-random 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 09-10, Pauly 20...
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