On the weight distributions of m-sequences in AWGN

An analysis and simulation is performed on the effect of additive white Gaussian noise (AWGN) on the weight distribution of the cross-correlation function between two maximal-length sequences (m-sequences) for direct-sequence spread-spectrum modulation, with specific examples cited for the m-sequences of linear span eight. The decimation, cross-correlation, and weight distribution properties of m-sequences are examined and integrated to characterize these functions in an efficient manner, requiring only O(N) functions instead of O(N²) to describe all possible weight distributions achievable for N m-sequences of a given length. Mean-squared difference (MSD) and skewness criteria to describe the degradation of weight distributions in noise are presented. The results of these criteria are summarized in weight distribution merge graphs, indicating that weight distributions in AWGN approach a Gaussian distribution at or above -15-dB signal-to-noise ratios