Address assignment for a time-frequency-coded, spread-spectrum system

In a multiple-access, spread-spectrum system, the messages intended for a particular user are distinguished by a specific signal pattern called the address. Here we consider such a system where an address is a sequence of L tones, chosen from Q possible frequencies. It can be described as a pattern in an L X Q time-frequency matrix. We study the problem of assigning addresses to the user in such a system using an algebraic approach which provides Q distinct addresses that guarantee minimum interference among Q or fewer system users. Both a synchronous and a nonsynchronous situation are considered. In the latter case, we have derived an address assignment that prevents interference from time-shifted signals from other users. We evaluate the performance of the system by studying the message error probability caused by interference among users and present upper bounds that give the maximum number of simultaneous users the system can accommodate at a certain error probability.