Linear feedback shift registers (LFSR) are a simple method of generating sequences, including pseudorandom number sequences. Some of these LFSR sequences have special properties; a maximal length sequence (MLS or m-sequence) has a large autocorrelation at zero lag, with near zero autocorrelation elsewhere. This 'impulsive' autocorrelation function allows one to quickly determine the impulse response of a linear time invariant (LTI) system.

Maximal length sequences are also the base for sets of sequences with good correlation properties. One such set is the small set of Kasami sequences. These sequences have small off-peak autocorrelations and also small cross correlations between sequences. This property allows for code-division multiplexing as well as accurately determining the arrival time of a transmitted sequence, even in the presence of other interfering transmissions.

I've uploaded some Matlab code for generating LFSR sequences, m-sequences, and sets of Kasami sequences, as well as examples. As alwasy, find it here. Please review, rate, or leave feedback so that I know people are finding these uploads interesting.

## Monday, January 19, 2009

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