A Class of Composite Sequences and its Implications for Matched Filter Signal Processing

Abstract

In direct-sequence spread-spectrum multiple-access (SSMA) communication systems, a unique code sequence is assigned to each user (transmitter-receiver pair). A transmitter modulates its code sequence with the data to be transmitted, usually by sequence-inversion keying (SIK), and then procedes with RF carrier modulation (e.g., using PSK or MSK). The corresponding receiver recovers the data by either matched filtering (using a filter matched to the code sequence) or active correlation (using a locally-generated synchronous replica of the code sequence). The performance of such a system depends upon the correlation properties of the set of sequences used. Specifically, the out-of-phase values of the autocorrelation function (ACF) of each sequence are required to be small in magnitude to ease problems associated with the synchronisation circuits at a receiver and, in some applications, to provide protection against multipath interference. Also, the cross-correlation function (CCF) between each pair of sequences in the set must be small in magnitude, for all relative phase-shifts, to minimise interference between users in the face of unpredictable (often time-varying) delays in the communication channel.