A subarray signal processing scheme is described for a large-scale two-dimensional analog-digital hybrid beamformer to be used in quasi-millimeter-wave-band mobile communication systems. Multiple analog phased arrays direct their respective beams to multiple users, enabling space-division multiple access (SDMA). An iterative soft-input soft-output (SISO) multi-user detector recovers multi-user signals from subarray output signals corrupted by inter-user interference (IUI). In addition, a phased-array directivity control algorithm is derived based on inter-subarray signal phase-difference estimation from inter-beam-interference (IBI)-cancelled subarray output signals. Simulation results demonstrate that our proposed scheme achieves reduced hardware complexity, IUI-resistant multi-user signal detection, and IBI-resistant multi-user-tracking phased-array directivity control.