Channel estimation and training design for MIMO two-way multi-relay systems

Abstract

In this dissertation, we study the channel estimation and training design for MIMO two-way multi-relay systems under various fading environments including flat fading, frequency-selective fading and time-selective fading. Unlike the single-relay scenario investigated in most existing studies, a severe problem in the multi-relay scenario is that the inter-link interference among the training/pilot sequences is present, which significantly degrades the channel estimation quality. For this reason, a critical issue in channel estimation for multi-relay systems is to resolve the inter-link interference issue. Unfortunately, unlike the other types of interference such as the inter-antenna and inter-source interferences, the inter-link interference is very difficult to eliminate, because it is physically not feasible to assign orthogonal sequences over different relay links owing to the transmission mechanism of multicasting, and then, forwarding. In this dissertation, we propose novel training schemes to solve the challenging inter-link interference problem utilizing the degrees of freedom offered by multiple relay nodes. The main focus of this dissertation is to estimate the channel state information (CSI) of bidirectional links, which is essential for self-interference cancellation and data detection. We adopt the linear minimum mean square error (LMMSE) criterion for channel estimation. We resolve the interference issue as well as improve the quality of the channel estimates by minimizing the total mean square error (MSE) of the LMMSE estimator under the transmit power constraints at two source nodes and multiple relays. Firstly, we address the problems of channel estimation and training design for flat fading MIMO-two-way relay systems. To solve the inter-link interference problem, we propose to apply the precoding technique at each relay. The optimal form of training signals and precoding matrices is presented in the sense of removing the inter-link interference as well as minimizing the total MSE. Using the proposed structure, we convert the optimal training design problem into a tractable convex form, from which the optimal training sequences are designed efficiently. For ease of practical implementation and complexity reduction, a low-complexity training scheme is also developed in closed-form. This scheme is shown to be asymptotically optimal in the high signal-to-noise (SNR) regime and gives useful insights into the optimal training design. Secondly, we investigate the problems of channel estimation and pilot design for MIMO-two-way relay systems in frequency-selective fading environments. To solve the inter-link interference problem, we propose to apply the phase rotation technique at each relay. The optimal form of pilot signals, phase rotations and pilot placement is derived in the sense that the inter-link interference is completely removed as well as the total MSE is minimized. Using this form, we convert the optimal pilot design problem into a tractable convex form, from which the optimal pilot sequences are designed efficiently. For an important special scenario, the optimal pilot design is presented in semi-closed form with a lower complexity, which provides us useful insights. For ease of practical implementation and complexity reduction, a low-complexity pilot design is also proposed in closed-form. This scheme is shown to be asymptotically optimal in the high signal-to-noise (SNR) regime and gives further insights into the optimal pilot design. Thirdly, we consider the problems of channel estimation and pilot design in time-selective fading environments. To solve the inter-link interference problem, we propose to apply the phase rotation technique at each relay. The optimal form of pilot signals, phase rotations and pilot placement is presented in the sense that the inter-link interference is completely eliminated as well as the total MSE is minimized. Using this form, we recast the optimal pilot design problem as a tractable convex form, from which the optimal pilot sequences is designed efficiently. For ease of practical implementation and complexity reduction, a low complexity pilot design is also proposed in closed-form. This method is shown to be asymptotically optimal in the high SNR regime and provides useful insights into the optimal pilot design. The performance of the proposed schemes is evaluated through simulations. Numerical results show that under various fading scenarios, the proposed schemes significantly improve the performance of channel estimation and data transmission compared to the existing methods. Finally, we discuss several practical issues related to the implementation of the proposed schemes, such as the spatial correlation estimation, the individual channel estimation, the feedback and the relay selection problem.