Omnidirectional Transmit Beamforming for Massive MIMO with Uniform Rectangular Array

In public channels, common signals are required to transmit omnidirectionally to ensure cell-wide coverage. In this paper, we focus on omnidirectional beamforming for common signal transmission in a massive multiple-input multiple-output (MIMO) system equipped with a uniform rectangular array (URA). We first model the omnidirectional transmission as a feasibility optimization problem in a matrix form. By counting the number of equality constraints and the degrees of freedom of the matrix variable, we conjecture that it takes at least three beamforming vectors to achieve constant-power signal transmission at any direction for a URA with more than two rows/columns. We then propose an efficient iterative rank-reduction algorithm, which can obtain three beamforming vectors that can generate a perfectly flat radiation beampattern, but cannot reduce further for a URA with more than two rows/columns. That is, the algorithm numerically verifies the conjecture. The numerical results validate the superior performance of the proposed scheme over the existing alternatives.