Theoretical analysis of M-ary/SS communication systems using racing counters and a Hadamard matrix

The performance of M-ary spread spectrum (M-ary/SS) communication systems is discussed. Firstly, the initial acquisition time is evaluated. Secondly, the retention time, which is the average number of frames holding correct frame timing, and the recovery time, which is the average number of frames required to establish synchronization, are derived. Lastly, the bit-error rate (BER) performance is evaluated. M-ary/SS communication systems, which have more than one spreading code, can improve the BER performance under conditions in which there is additive white Gaussian noise (AWGN). However, the synchronization of M-ary/SS communication systems is difficult because they have several spreading codes. The frame synchronization method uses a Hadamard matrix and "racing counters." As a result, the retention time becomes longer than the recovery time when the size of the lower counter differs greatly from that of the upper counter in the racing counters. Then the BER gets close to the performance which is achieved under complete synchronization.