A Generalized Framework on Beamformer Design and CSI Acquisition for Single-Carrier Massive MIMO Systems in Millimeter Wave Channels

In this paper, we establish a general framework on the reduced dimensional channel state information (CSI) estimation and pre-beamformer design for frequency-selective massive multiple-input multiple-output MIMO systems employing single-carrier (SC) modulation in time division duplex (TDD) mode by exploiting the joint angle-delay domain channel sparsity in millimeter (mm) wave frequencies. First, based on a generic subspace projection taking the joint angle-delay power profile and user-grouping into account, the reduced rank minimum mean square error (RR-MMSE) instantaneous CSI estimator is derived for spatially correlated wideband MIMO channels. Second, the statistical pre-beamformer design is considered for frequency-selective SC massive MIMO channels. We examine the dimension reduction problem and subspace (beamspace) construction on which the RR-MMSE estimation can be realized as accurately as possible. Finally, a spatio-temporal domain correlator type reduced rank channel estimator, as an approximation of the RR-MMSE estimate, is obtained by carrying out least square (LS) estimation in a proper reduced dimensional beamspace. It is observed that the proposed techniques show remarkable robustness to the pilot interference (or contamination) with a significant reduction in pilot overhead

Receive Combining vs. Multi-Stream Multiplexing in Downlink Systems with Multi-Antenna Users

In downlink multi-antenna systems with many users, the multiplexing gain is strictly limited by the number of transmit antennas $N$ and the use of these antennas. Assuming that the total number of receive antennas at the multi-antenna users is much larger than $N$, the maximal multiplexing gain can be achieved with many different transmission/reception strategies. For example, the excess number of receive antennas can be utilized to schedule users with effective channels that are near-orthogonal, for multi-stream multiplexing to users with well-conditioned channels, and/or to enable interference-aware receive combining. In this paper, we try to answer the question if the $N$ data streams should be divided among few users (many streams per user) or many users (few streams per user, enabling receive combining). Analytic results are derived to show how user selection, spatial correlation, heterogeneous user conditions, and imperfect channel acquisition (quantization or estimation errors) affect the performance when sending the maximal number of streams or one stream per scheduled user---the two extremes in data stream allocation. While contradicting observations on this topic have been reported in prior works, we show that selecting many users and allocating one stream per user (i.e., exploiting receive combining) is the best candidate under realistic conditions. This is explained by the provably stronger resilience towards spatial correlation and the larger benefit from multi-user diversity. This fundamental result has positive implications for the design of downlink systems as it reduces the hardware requirements at the user devices and simplifies the throughput optimization.Comment: Published in IEEE Transactions on Signal Processing, 16 pages, 11 figures. The results can be reproduced using the following Matlab code: https://github.com/emilbjornson/one-or-multiple-stream

Optimized Training Design for Wireless Energy Transfer

Radio-frequency (RF) enabled wireless energy transfer (WET), as a promising solution to provide cost-effective and reliable power supplies for energy-constrained wireless networks, has drawn growing interests recently. To overcome the significant propagation loss over distance, employing multi-antennas at the energy transmitter (ET) to more efficiently direct wireless energy to desired energy receivers (ERs), termed \emph{energy beamforming}, is an essential technique for enabling WET. However, the achievable gain of energy beamforming crucially depends on the available channel state information (CSI) at the ET, which needs to be acquired practically. In this paper, we study the design of an efficient channel acquisition method for a point-to-point multiple-input multiple-output (MIMO) WET system by exploiting the channel reciprocity, i.e., the ET estimates the CSI via dedicated reverse-link training from the ER. Considering the limited energy availability at the ER, the training strategy should be carefully designed so that the channel can be estimated with sufficient accuracy, and yet without consuming excessive energy at the ER. To this end, we propose to maximize the \emph{net} harvested energy at the ER, which is the average harvested energy offset by that used for channel training. An optimization problem is formulated for the training design over MIMO Rician fading channels, including the subset of ER antennas to be trained, as well as the training time and power allocated. Closed-form solutions are obtained for some special scenarios, based on which useful insights are drawn on when training should be employed to improve the net transferred energy in MIMO WET systems.Comment: 30 pages, 9 figures, to appear in IEEE Trans. on Communication

Two-Way Training for Discriminatory Channel Estimation in Wireless MIMO Systems

This work examines the use of two-way training to efficiently discriminate the channel estimation performances at a legitimate receiver (LR) and an unauthorized receiver (UR) in a multiple-input multiple-output (MIMO) wireless system. This work improves upon the original discriminatory channel estimation (DCE) scheme proposed by Chang et al where multiple stages of feedback and retraining were used. While most studies on physical layer secrecy are under the information-theoretic framework and focus directly on the data transmission phase, studies on DCE focus on the training phase and aim to provide a practical signal processing technique to discriminate between the channel estimation performances at LR and UR. A key feature of DCE designs is the insertion of artificial noise (AN) in the training signal to degrade the channel estimation performance at UR. To do so, AN must be placed in a carefully chosen subspace based on the transmitter's knowledge of LR's channel in order to minimize its effect on LR. In this paper, we adopt the idea of two-way training that allows both the transmitter and LR to send training signals to facilitate channel estimation at both ends. Both reciprocal and non-reciprocal channels are considered and a two-way DCE scheme is proposed for each scenario. {For mathematical tractability, we assume that all terminals employ the linear minimum mean square error criterion for channel estimation. Based on the mean square error (MSE) of the channel estimates at all terminals,} we formulate and solve an optimization problem where the optimal power allocation between the training signal and AN is found by minimizing the MSE of LR's channel estimate subject to a constraint on the MSE achievable at UR. Numerical results show that the proposed DCE schemes can effectively discriminate between the channel estimation and hence the data detection performances at LR and UR.Comment: 1