Optimal linear receivers for synchronizing pseudo random sequences

Much research work has been done in finding sequences with good autocorrelation properties. The conventional receiver structure for synchronizing with such a sequence transmitted periodically is a matched filter matched to the sequence. However, the synchronization performance of the receiver can be further improved if the receiver tries to match to the sequence and dematch the circular shifts of the sequence. In the problem at hand the data preceding the synchronization sequence is known. We derive the optimal linear receiver to synchronize with a given sequence and demonstrate the synchronization gain achieved by employing such a receiver over the conventional receiver. This gain is obtained by simply changing the receiver coefficients, leaving the receiver structure unchanged