Detecting matrices for random CDMA systems

This paper studies detecting matrices in random dense and sparse Code Division Multiple Access (CDMA) systems. Detecting matrices were originally introduced in the coin weighing problem. Such matrices can be used in CDMA systems in over-loaded scheme where the number of users is greater than the number of chips. We drive some conditions in the large system limit for binary and bipolar random CDMA systems to ensure that any random matrix is a detecting matrix. Furthermore, we extend our results to sparse random ternary matrices that have been using in the sparse CDMA literature. Finally, a construction method for the sparse detecting matrices is introduced.