A sparsity detection framework for on-off random access channels

This paper considers a simple on-off random multiple access channel (MAC), where n users communicate simultaneously to a single receiver. Each user is assigned a single codeword which it transmits with some probability lambda over m degrees of freedom. The receiver must detect which users transmitted. We show that detection for this random MAC is mathematically equivalent to a standard sparsity detection problem. Using new results in sparse estimation we are able to estimate the capacity of these channels and compare the achieved performance of various detection algorithms. The analysis provides insight into the roles of power control and multi-user detection.