LiST-BF Design for Downlink Beamforming with Arbitrary Shaping Constraints

This paper considers the beamforming design for a multiuser multiple-input single-output (MU-MISO) downlink with an arbitrary number of (context-specific) shaping constraints. In this setup, the state-of-the- art beamforming schemes cannot attain the well-known performance bound promised by the semidefinite program (SDP) relaxation technique. To close the gap, we propose a linear space-time beamforming (LiST-BF) scheme, consisting of a circulant space-time symbol mapper followed by the beamforming design with orthogonality constraints. It is shown that the proposed LiST-BF scheme can perform general rank-$K$ beamforming for user symbols in a low-complexity and structured manner. Sufficient conditions are derived to guarantee that the LiST-BF scheme always achieves the SDP bound for linear beamforming schemes. Based on such conditions, an efficient algorithm is then developed to obtain the optimal LiST-BF solution in polynomial time. Numerical results demonstrate that the proposed scheme enjoys substantial performance gains over the existing alternatives.