Minimizing the worst-case interuser interference experienced by any user in CDMA systems: a matrix approach

The problem of designing signature sequences that minimize the worst-case interuser interference experienced by any user in CDMA systems is traditionally considered to be a very important but difficult problem. The problem for synchronous CDMA was recently solved by Massey and Mittelholzer (1993). We show that their results can be derived in a simple way by properly applying the matrix notation. This matrix approach is used to solve the sequence design problem for synchronous CDMA with orthogonal coding, and a necessary and sufficient condition for optimal sequence sets is obtained for the first time. It turns out that optimal sequence sets are very easy to construct. The method is then applied to solve the sequence design problem for asynchronous CDMA in a simple way. This last result was previously used to explain why so many famous sequence sets possess very similar SNR performance. For the above three CDMA systems, the optimal sequence sets not only minimize the worst-case interuser interference, but also ensure that the interuser interference experienced by every user is (nearly) the same-the uniformly good property. However, the results also indicate that the conventional SNR measures, if used as the sole performance criterion, are insufficient.