Active Constraints Inspired Zero-Forcing Precoder Design under Per-Antenna Power Constraints

This paper investigates the problem of linear zero-forcing (ZF) precoder design for sum rate maximization under per-antenna power constraints (PAPCs). A conventional method to tackle this problem is to lift it into a convex determinant maximization program with respect to the transmit covariance matrices, whose complexity, however, increases dramatically as the problem size increases. A suboptimal alternative is to adopt a semi-closed-form pseudo-inverse solution, whose performance, however, becomes dramatically inferior to the optimal design as the number of transmit antennas goes large. A new low-complexity high-performance ZF precoder design under PAPCs is proposed in this paper. Specifically, we first investigate the power usage at each transmit antenna for ZF precoding under PAPCs and identify a lower bound on the number of power constraints that should be active (i.e., satisfied with equality) at the optimal ZF precoder. Then, we devise a low-complexity iterative algorithm to find a ZF precoder satisfying PAPCs, at which the number of active power constraints meets the lower bound requirement for optimality. Simulation results show that the proposed ZF precoder achieves the near-optimal sum rate with significantly reduced computational complexity.