Generalized likelihood detection on multiple access channels

The problem of detecting the presence of a user on a multiple access channel and the problem of decoding this user's symbol sequence for both coherent and incoherent communications with M-ary signal sets are considered jointly. A test is proposed which solves this problem in two stages. The first stage is a threshold test based on the generalized likelihood ratio test with a threshold chosen to achieve a specified probability of false alarm. The second stage of the detector consists of a generalized maximum a posteriori probability decision rule. This stage is shown to be asymptotically efficient, conditioned on a correct detection of the user's presence.