Precoder and Capacity Expressions for Optimal Two-User MIMO Transmission with Per-Antenna Power Constraints

In this letter, multiuser multiple-input multiple-output (MIMO) precoding which achieves the Gaussian broadcast channel (GBC) capacity under the per-antenna power constraint (PAPC) is investigated. In particular, closed-form expressions for both the MIMO precoder and the corresponding sum capacity are presented for the two-user case. We show that the result can also be utilized to provide the two-user capacity expression under the total power constraint (TPC) of transmit antennas.