On a geometric view of multiuser detection for synchronous DS/CDMA channels

We consider a geometric view of multiuser detection and present results on the problem of efficient computation of the optimal decision regions (Voronoi diagram) for synchronous direct-sequence code division multiple access (DS/CDMA). Among other results, it is shown that Verdu's (1986) algebraic notion of "indecomposable error sequences" relates directly to the geometric construction of the Voronoi diagram for multiuser detection. Based on the presented geometric results we introduce two multiuser detectors whose performance compares favorably to some popular existing detectors.