Transmit beamforming for EIRP-limited MIMO systems based on golay sequence

We study a transmit beamforming for multiple antenna systems under the per-antenna power and the equivalent isotropic radiation power (EIRP) constraints. Finding the optimal beamforming vector maximizing SNR in such case is known to be NP-hard, and its semi-definite programming (SDP) approximation can be still complex due to the large number of the inequality constraints. This work considers a low complexity transmit beamforming technique, called Golay beamforming, based on the structured codebook consisting of the Golay sequences with the bounded EIRP guarantee. We discuss the specific structure and the performance bounds of the Golay beamforming, and propose the weighted Golay beamforming which can further improve the received SNR by using a specific set of the weighted Golay sequences which enjoys the same bounded low EIRP. Numerical results show that the proposed Golay beamforming provides an efficient low complexity solution with the graceful performance degradation under moderate EIRP constraints, and can be further improved by the weighted Golay beamforming.