Transmit Beamforming for MISO Frequency-Selective Channels With Per-Antenna Power Constraint and Limited-Rate Feedback

In this paper, we consider transmit beamforming (BF) design under per-antenna power constraint (PPC) for multiple-input-single-output (MISO) frequency-selective channels. Both cyclic-prefixed (CP) single carriers and orthogonal frequency-division-multiplexing (OFDM) systems are investigated. Since there is no closed-form expression for the optimal PPC BF coefficients, and the optimization tools employed to find the PPC solution are usually complicated, here, we propose three computationally more effective suboptimal solutions to minimize the arithmetic mean of the effective error probabilities. Moreover, we address the issue of limited-rate feedback, and a simple codebook design method for frequency-selective channels is proposed. Unlike conventional methods where the codebook is directly designed for BF vectors, here, we construct codebooks for the amplitude and phase of the time-domain channel state information (CSI) to reduce the rate of feedback. Further, the nonuniform feedback strategy is investigated. Simulation results show that the proposed suboptimal solutions have much lower complexities than the convex optimization-based PPC solutions. The effectiveness of the proposed uniform and nonuniform limited-rate feedback methods is also demonstrated via simulations.