Maximizing the Sum-Rate and Minimizing the Sum-Power of a Broadcast 2-User 2-Input Multiple-Output Antenna System Using a Generalized Zeroforcing Approach

While information theory tells us that a broadcast multiple-input multiple-output (MIMO) channel may be shared spatially to maximize the utilization of the channel by dirty-paper coding (DPC) techniques as opposed to time-only or frequency-only division, the associated complexity of a DPC codec is problematic for some practical applications. A more feasible alternative is to use generalized zeroforcing (GZF) which beams the signals to the targeted receivers while ensuring no inter-user interference at all the receiver outputs. Our objective of this letter is to study the GZF optimization of a broadcast 2-user 2-input many-output antenna system for both 1) sum-rate maximization subject to a total transmit power constraint and 2) sum-power minimization subject to rate constraints of the users. We shall derive the optimal GZF solutions for both problems. The capacity and signal-to-noise ratio (SNR) regions for the optimized GZF systems are also derived, and results for DPC and time-division systems are provided for comparisons