Reduced State Sequence Detection Asynchronous Gaussian Multiple-Access Channels

The problem of coherent multiuser detection is considered for the K-user asynchronous Gaussian Code-Division multiple Access (CDMA) channel. The maximum likelihood sequence detector (MLSD) is asymptotically optimal in that it achieves the highest error exponent of the bit error probability for each user. However, the MLSD can only be implemented by a dynamic programming algorithm whose complexity depends exponentially on K. In order to mitigate the complexity of this scheme, a class of group detection strategies is derived based on optimal statistical inferential procedures. Each member of this class of detectors corresponds to a L group partition of the K users, and consists of a bank of L group detectors, one for demodulating the information symbols of users in each group. Each group detector is a reduced state sequence detector with the dominant complexity determined by the computation of the solution of a combinatorial optimization problem via a forward dynamic programming algorithm. This algorithm has a complexity that is exponential in the number of users in the corresponding group. The overall complexity is determined by the size of the largest group which is a design parameter that can be chosen to be only as large as complexity considerations allow. The performance analysis of the group detection scheme is obtained by deriving asymptotically tight upper and lower bounds on the bit error probability, thereby characterizing its multiuser asymptotic efficiency.