An antenna array is overloaded when the number of cochannel signals in its operating environment exceeds the number of elements. This paper proposes an iterative joint detection technique, spatially reduced search joint detection (SRSJD), that well approximates the joint maximum likelihood (JML) receiver, while reducing its computational complexity by several orders of magnitude. This complexity reduction is achieved by first exploiting the spatial separation between interfering signals with a linear preprocessing stage, and second, performing iterative joint detection with a reduced-state trellis formed over space instead of time. These novel joint detection trellises are possibly tail-biting and vary in structure from stage to stage. Through simulation, SRSJD is shown to demodulate over 2M synchronous quaternary phase-shift keying signals of zero excess bandwidth with an M element circular array. The channels of all users are assumed known.