Transmit beamforming for MISO frequency-selective channels with total and per-antenna power constraints

We consider the problem of transmit beamforming (BF) design for cyclic prefixed (CP) transmissions over MISO frequency selective channels. Both CP single carriers (SC) and orthogonal frequency-division multiplexing (OFDM) systems are investigated. To reduce receiver complexity, frequency domain BF is adopted. The BF is designed by minimizing the arithmetic mean of the error probabilities at the receiver, first under the total power constraint (TPC) and then under the per-antenna power constraint (PPC). The solutions under the PPC are obtained using convex optimization tools. The simulation results show that although BF for SC only slightly outperforms BF for OFDM under TPC, the gap in performance becomes large under PPC. It is also shown that for large number of transmit antennas, the phase-rotation BF (PRB) is nearly optimal under PPC.