Binary Sequences for Spread-Spectrum Multiple-Access Communication

The communication capacity of a single wideband satellite channel can be simultaneously shared by a number of users by means of spread-spectrum multiple-access (SSMA). In phase-coded SSMA the multiple-access capability is provided by phase modulating a distinct signature sequence onto the user's carrier which spreads the user data over a wide bandwidth. All of the important code parameters for the analysis of such a system can be derived from the aperiodic correlation functions of the signature sequences. The asymptotic behavior such code parameters is considered for random binary sequences for which the sequence length grows very large. New sets of pseudo-random or m- sequences with optimal aperiodic autocorrelation and cross-correlation properties are obtained. The relationship between the first few central moments of the aperiodic correlation functions and the characteristic polynomials generating the m-sequences is analyzed and the results are compared with actual sequence data. Gauss's product of cyclotomic cosets is used to establish new analytical results on the periodic correlation properties of Gold sequences and Kasami sequences yielding subsets of sequences whose correlation parameters satisfy tighter bounds than previously established for the entire sequence sets. Numerical data on the relevant correlation parameters is obtained for a large number of good signature sequences.