Low rank approximation based hybrid precoding schemes for multi-carrier single-user massive MIMO systems

In this paper we study the hybrid precoding design problem for a frequency selective massive MIMO channel, e.g., the millimeter wave (mmWave) massive MIMO channel. In contrast to a traditional MIMO system, a hybrid analog-digital MIMO scheme is preferred for massive MIMO systems due to the high cost and power consumption of the radio frequency (RF) chains. The RF analog precoding is implemented using only phase shift networks, which impose constant modulus constraints on the RF precoding and decoding matrices. Moreover, there is just one common equivalent RF beamforming matrix for all subcarriers. The resulting sum rate maximization problem is non-convex and, therefore we resort to suboptimal solutions. Two methods are introduced, namely, the higher order SVD (HOSVD) based design and the sequential low rank unimodular approximation based design. The former approach exploits the truncated HOSVD of the equivalent channel while the latter approach approximates optimal unconstrained solutions by low rank unimodular approximations. Simulation results show that when the mmWave channel model is used, both approaches outperform the extension of the state of the art compressed sensing based algorithm to the multi-carrier case.