Geometric interpretation of multiaccess joint detection and the alternating projection algorithm

The joint detection of all users in a multiple access (MA) communication system in which user transmissions are correlated has been shown in recent literature to enhance the system performance relative to that achieved without joint detection. Over the past several years the area of low complexity joint detectors has received much attention. This paper explains the problem of multiple access joint detection in geometrical terms. Geometric interpretation leads to the proposal of an alternating projection joint detection algorithm (APJD). Due to some similarities between our APJD and the multistage joint detector (MJD) of Varansi and Aazhang (1990), the MJD is also discussed. The APJD is guaranteed to converge and a proof is given. The geometric interpretation of the MA joint detection problem allows for the exploration of determining, a priori, the error probability of a joint detector and user waveform set in the absence of noise. Simulations offer empirical characterization of the error behavior of both detectors