Transmitter Optimization for Per-Antenna Power Constrained Multi-Antenna Downlinks:An SLNR Maximization Methodology

Abstract

In this paper, we consider signal-to-leakage-plus-noise ratio (SLNR) maximized precoding for multi-antenna downlinks under per-antenna power constraints (PAPCs). In contrast to the conventional sum power constraint, the per-antenna power constrained SLNR precoder design problem no longer admits a simple closed-form solution and achieving its optimal solution turns out to be much more challenging. To conquer the difficulty, we first propose to perform the Charnes–Cooper transformation on the problem of interest, which yields a solvable simpler second-order cone program (SOCP). Moving beyond this approach, we are then able to obtain a semi-closed form solution to the optimal SLNR precoder. The power allocation among users is also optimized for further performance enhancement, for which we devise two numerical methods based on gradient projection and a low-complexity approximation. Finally, focusing on the imperfect channel state information (CSI) scenario, we develop a robust SLNR-based precoder to combat the performance degradation caused by random CSI errors. The superiority of all proposed precoder designs in this work is confirmed by numerical simulations.