Two-way relay systems are known to be capable of providing higher spectral efficiency compared with conventional one-way relay systems. However, the channel estimation problem for two-way relay systems is more complicated than that of one-way relay systems. In this paper, we propose and compare two channel estimation algorithms, namely the superimposed channel training scheme and the two-stage channel estimation algorithm, for two-way multiple-input multiple-output (MIMO) relay communication systems, where the individual channel state information (CSI) for the first-hop and second-hop links is estimated. For both algorithms, we derive the optimal structure of the source and relay training sequences which minimize the mean-squared error (MSE) of channel estimation. In the superimposed channel training scheme, the power allocation between the source and relay training sequences is optimized. For the two-stage channel estimation algorithm, we optimize the power allocation at the relay node between two stages to improve the performance of the algorithm. Numerical examples are shown to demonstrate and compare the performance of the proposed channel training algorithms.

In this paper, we investigate a dual-hop simultaneous wireless information and power transfer (SWIPT) based amplifying-and-forward (AF) multiple-input multiple-output (MIMO) relay communication system where the relay node harvests energy based on radio frequency (RF) signals transmitted from the source node through the hybridized power-time splitting-based relaying (HPTSR) protocol to forward information to the destination node. The joint optimization of the time-switching (TS) factor, source and relay precoding matrices, and the power-splitting (PS) ratio vector is proposed to maximize the mutual information (MI) between the source and destination nodes. We derive the optimal structure for the source and relay precoding matrices to simplify the transceiver optimization problem. Two algorithms based on the upper bound and lower bound of the objective function are proposed to efficiently solve the optimization problem with low computational complexity. Numerical examples demonstrate that the proposed algorithms provide a better MI performance compared with TS based and PS based energy harvesting (EH) relay systems. INDEX TERMS Amplify-and-forward (AF) relay, energy harvesting, hybridized power-time switching relaying (HPTSR), multiple-input multiple-output (MIMO) relay, simultaneous wireless information and power transfer (SWIPT)

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In this article, the transceiver design optimization problem is investigated for multi-hop multicasting amplifyand-forward (AF) multiple-input multiple-output (MIMO) relay systems, where multiple source nodes broadcast their message to multiple destination nodes via multiple serial relay nodes. Multiple antennas are installed at the sources, relays, and the destination nodes. In the transceiver design, we consider the mismatch between the true and the estimated channel state information (CSI), where the CSI mismatch follows the Gaussian-Kronecker model. A robust transceiver design algorithm is developed to jointly optimize the source, relay, and destination matrices to minimize the maximal weighted mean-squared error (WMSE) of the received message at all destination nodes. In particular, the WMSE is made statistically robust against the CSI mismatch by averaging through the distributions of the true CSI. Moreover, the WMSE decomposition is exploited to reduce the computational complexity of the transceiver optimization. Numerical simulations show a better performance of the proposed robust transceiver design against the channel mismatch.

In this paper, we investigate the channel estimation problem for multiple-input multiple-output (MIMO) relay communication systems with time-varying channels. The time-varying characteristic of the channels is described by the complexexponential basis expansion model (CE-BEM). We propose a superimposed channel training algorithm to estimate the individual first-hop and second-hop time-varying channel matrices for MIMO relay systems. In particular, the estimation of the secondhop time-varying channel matrix is performed by exploiting the superimposed training sequence at the relay node, while the first-hop time-varying channel matrix is estimated through the source node training sequence and the estimated second-hop channel. To improve the performance of channel estimation, we derive the optimal structure of the source and relay training sequences that minimize the mean-squared error (MSE) of channel estimation. We also optimize the relay amplification factor that governs the power allocation between the source and relay training sequences. Numerical simulations demonstrate that the proposed superimposed channel training algorithm for MIMO relay systems with time-varying channels outperforms the conventional two-stage channel estimation scheme.