Algorithm for calculating the nonperiodic autocorrelation of maximal length sequences

In a spread-spectrum multiple-access communication system it is desirable to permit a number of users to simultaneously utilise the same channel. This can be achieved using code-division multiple-access techniques where the codes are very often maximal-length sequences. To permit reliable code-bit synchronisation and prevent multipath distortion, knowledge of the nonperiodic autocorrelation is necessary. The required autocorrelation may be obtained by simple modulo-two addition bit by bit, which, however, requires a large number of calculations even for moderate code lengths. From a computational aspect it is therefore of interest to obtain a simple algorithmic procedure which may lead to time saving. This paper discusses one such algorithm to ease the computation of the nonperiodic autocorrelation for maximal-length sequences.