On the Autocorrelation Properties of Truncated Maximum-Length Sequences and Their Effect on the Power Spectrum

Truncated maximum-length binary sequences are studied in this paper. The impact of truncation on their autocorrelation properties and power spectral density is investigated. Several new analytical results are given and validated through simulation. The first- and second-order statistics of the periodic autocorrelation function and the spectral peak amplitudes over the ensemble of all possible starting seeds are analyzed. Explicit bounds are found for the mean square of the periodic autocorrelation function. An analytical technique for evaluating the maximum spectral peak values is derived. As a case study, high data rate space links using LFSR randomizers are considered. Truncation may induce high peaks in the spectrum, requiring suitable margins to comply with power flux density constraints. The new results allow to analytically estimate the margin, providing useful information for the link design.