Sum-rate maximization and sum-power minimization for 2-user (2,2) downlink systems using generalized zero-forcing

The paper analyzes a downlink system where a 2-antenna base station is sending independent signals to two 2-antenna mobile users simultaneously in the same physical (time and frequency) channel. To multiplex the signals in the spatial domain, we consider the use of orthogonal space-division multiplexing (OSDM), broadly known as generalized zero-forcing (GZF), that allows the users to be completely separated before decoding. The paper's main contribution is that we derive the optimal array processing solutions for both the sum-rate maximization problem, subject to a fixed transmit power constraint, and the sum-power minimization problem, subject to a fixed rate constraint. The capacity and signal-to-noise ratio (SNR) regions for the OSDM system are also derived, and results for dirty-paper coding (DPC) and time-division systems are provided for comparison.