Convergence study of an iterative joint detector for wavelet packet multiple-access communication

The joint detection of all users in a multiple access communication system is known to greatly enhance the system performance. The optimal joint detector has a complexity which is exponential in the number of users and is, therefore, impractical. Suboptimal algorithms attempt to achieve near optimal performance with reduced computational complexity. The suboptimal joint detection literature deals only with receiver design, allowing for the use of any set of signature waveforms. Using the structure of the wavelet packet transform we are able to choose signal sets and design a detection algorithm which results in significantly lower computational complexity than other proposed suboptimal joint detectors. The wedding of detector development and wavelet packet signal set design, therefore, becomes an interesting problem. The convergence, performance and receiver complexity of suboptimal MA detectors crucially depend upon the signal set structure; it is, thus, of paramount importance to study the convergence of our iterative algorithm for our signal structure. Sufficient conditions for the convergence of an iterative joint detection scheme are developed