Semidefinite programming based omnidirectional beamforming for massive MIMO

In public channels, common signals need to be transmitted omnidirectionally to achieve cell-wide coverage. In this paper, we consider omnidirectional beamforming for common signal transmission in the massive multi-input multi-output (MIMO) scenario. After formulating the task as a max-min optimization problem, we propose a semidefinite programming (SDP) based technique to maximize the minimum received power over all directions under transmit power constraints. We show that the problem can be efficiently solved using the semidefinite relaxation technique. Relying on a small number of beamformers, the proposed scheme can generate a perfectly flat beampattern to ensure reliable omnidirectional transmission with equal transmit-power per beamformer and equal average transmit-power per antenna. The proposed approach can be applied to any antenna array configuration, including uniform linear array (ULA) and uniform rectangular array (URA). The numerical results validate the effectiveness of the proposed schemes.