Semidefinite Relaxation for Millimeter Wave Massive MIMO Detection

Abstract

In this paper, we consider the application of semidefinite relaxation (SDR) to millimeter wave (mmWave) massive multiple input multiple output (MIMO) systems. In particular, we focus on the use of SDR as a computationally efficient approximation of maximum likelihood (ML) detection in mmWave massive MIMO for high order modulations. The SDR detector is a convex relaxation of the ML problem. To mitigate the high path loss at mmWave frequencies and the poor scattering nature of the mmWave channel, this paper proposes the use of a uniform planar array (UPA) hybrid beamforming technique with large antenna arrays and the SDR detector to improve the performance of 16-quadrature amplitude modulation (16-QAM) mmWave massive MIMO systems. When perfect Channel State Information (CSI) is available at the base station (BS) and mobile station (MS), computer simulations have shown that a gain exceeding 5 dB can be achieved with reasonable complexity by using the SDR algorithm compared to a linear detection system with Zero-forcing (ZF) or minimum mean-square error (MMSE) detection. Moreover, the SDR applied in this paper has fewer constraints and a lower complexity than the other SDRs used for conventional MIMO, and it can be solved in polynomial time using any of the available SDR solvers.