CROSSCORRELATION OF A MAXIMAL LENGTH BINARY SEQUENCE AND ITS SUBSEQUENCES.
ROME AIR DEVELOPMENT CENTER GRIFFISS AFB N Y
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One method of synchronizing a communication system uses the cross correlation between a maximal length pseudorandom, binary sequence and a portion of that sequence. Using only part of the sequence causes the correlation function to have peaks when the sequences are not aligned, and thus may cause a threshold decision scheme to synchronize incorrectly. This report describes several methods that compute the histogram of the correlation values for all unique integral bit shifts, using any maximal length sequence and any subsequence length. The report also derives exact analytical results for very short subsequences and for subsequences which are almost as long as the main sequence. The report shows that for any main sequence, if the subsequence length remains constant, the choice of the particular subsequence within the main sequence will have little effect on the histogram of the correlation values. Finally the report gives several analogies between the subsequence correlation problem and coding theory. Author
- Operations Research