Given the cost and complexity associated with the deployment of a large number of radio frequency (RF) chains in millimeter wave (mmW) multi-input multi-output (MIMO) systems, this paper addresses the question of network efficiency considerations for hybrid precoding. We first establish the relevance of directional precoding structures as a low-complexity and robust solution to meet the data rate demands of single-user MIMO systems relative to the more complex and less robust eigen-mode-based precoding structures. Key to the relevance of the directional precoding structures is the sparsity of the mmW channel coupled with higher antenna dimensionality affordable due to smaller wavelengths. We then leverage the directional structure of the channel to propose a simple class of directional schedulers that offers a low-complexity and yet approximately fair separation plane in the user space. We then compare the performance of single-user precoding schemes with multi-user precoding schemes and show that from network efficiency considerations, it would be more worthwhile to expend the RF chain resource on multi-user transmissions.

The focus of this work is on cost and complexity- induced rank-constrained precoding for millimeter- wave (mmW) multi-input multi-output (MIMO) systems. The higher antenna dimensionality and sparse channel structure of mmW systems motivate directional precoding schemes over more complex and less robust eigen-mode-based precoding schemes. Building on a prior work that illustrated the superiority in design, robustness and performance of a directional rank-1 beamformer, this work considers higher-rank directional precoding structures for mmW systems. It is shown that directional precoders continue to enjoy similar properties in single-user MIMO (SU-MIMO) systems. But from a network efficiency consideration, it would be more worthwhile to expend the radio frequency (RF) chain resource on multi-user transmissions. Towards this goal, a directional scheduler and different directional beamforming structures are proposed here. These structures are shown to result in significant performance improvement over higher-rank SU-MIMO schemes.

The focus of this paper is on beamforming in a millimeter-wave (mmW) multi-input multi-output (MIMO) set-up that has gained increasing traction in meeting the high data-rate requirements of next- generation wireless systems. For a given MIMO channel matrix, the optimality of beamforming with the dominant right-singular vector (RSV) at the transmit end and with the matched filter to the RSV at the receive end has been well-understood. When the channel matrix can be accurately captured by a physical (geometric) scattering model across multiple clusters/paths as is the case in mmW MIMO systems, we provide a physical interpretation for this optimal structure: beam steering across the different paths with appropriate power allocation and phase compensation. While such an explicit physical interpretation has not been provided hitherto, practical implementation of such a structure in a mmW system is fraught with considerable difficulties (complexity as well as cost) as it requires the use of per-antenna gain and phase control. This paper characterizes the loss in received SNR with an alternate low-complexity beamforming solution that needs only per-antenna phase control and corresponds to steering the beam to the dominant path at the transmit and receive ends. While the loss in received SNR can be arbitrarily large (theoretically), this loss is minimal in a large fraction of the channel realizations reinforcing the utility of directional beamforming as a good candidate solution for mmW MIMO systems.