Matrix Differential Calculus with Applications in Statistics and Econometrics

Interference alignment (IA) has evolved as a powerful technique in the information theoretic framework for achieving the optimal degrees of freedom of interference channel. In practical systems, the design of specific interference alignment schemes is subject to various criteria and constraints. In this paper, we propose novel transceiver schemes for the MIMO interference channel based on the mean square error (MSE) criterion. Our objective is to optimize the system performance under a given and feasible degree of freedom. Both the total MSE and the maximum per-user MSE are chosen to be the objective functions to minimize. We show that the joint design of transmit precoding matrices and receiving filter matrices with both objectives can be realized through efficient iterative algorithms. The convergence of the proposed algorithms is proven as well. Simulation results show that the proposed schemes outperform the existing IA schemes in terms of BER performance. Considering the imperfection of channel state information (CSI), we also extend the MSE-based transceiver schemes for the MIMO interference channel with CSI estimation error. The robustness of the proposed algorithms is confirmed by simulations.

MSE-Based Transceiver Designs for the MIMO Interference Channel

This paper studies linear precoding and decoding schemes for K-user interference channel systems. It was shown by Cadambe and Jafar that the interference alignment (IA) algorithm achieves a theoretical bound on degrees of freedom (DOF) for interference channel systems. Based on this, we first introduce a non-iterative solution for the precoding and decoding scheme. To this end, we determine the orthonormal basis vectors of each user's precoding matrix to achieve the maximum DOF, then we optimize precoding matrices in the IA method according to two different decoding schemes with respect to individual rate. Second, an iterative processing algorithm is proposed which maximizes the weighted sum rate. Deriving the gradient of the weighted sum rate and applying the gradient descent method, the proposed scheme identifies a local-optimal solution iteratively. Simulation results show that the proposed iterative algorithm outperforms other existing methods in terms of sum rate. Also, we exhibit that the proposed non-iterative method approaches a local optimal solution at high signal-to-noise ratio with reduced complexity.

Linear precoder designs for K-user interference channels

This paper considers both one-way and two-way relaying systems with multiple relays between two terminal nodes where all nodes have multiple-input multiple-output (MIMO) antennas. We propose a unified algorithm which computes the optimal linear transceivers jointly at the source node and the relay nodes for amplify-and-forward (AF) protocols. First, optimization designs based on the sum-rate and the mean-square error (MSE) criteria are formulated for the two-way AF relaying channel. Due to non-convexity of the given problems, the proposed schemes iteratively identify local-optimal source and relay filters by deriving the gradients of the cost functions for a gradient descent algorithm. Then, the proposed algorithm can optimize a one-way multiple relay system as a special case of the two-way channel. Finally, we prove the global optimality of the maximum sum-rate scheme under an asymptotically large antenna assumption. From simulation results, it is confirmed that the proposed methods yield the near optimum result for the MIMO multiple relay channel even with a moderate number of antennas. Consequently, we show that the proposed algorithm outperforms conventional schemes in terms of the sum-rate and the error performance for both one-way and two-way protocols.

Joint Optimization for One and Two-Way MIMO AF Multiple-Relay Systems

Properly designed precoders can significantly improve the spectral efficiency of multiple-input multiple-output (MIMO) relay systems. In this paper, we investigate joint source and relay precoding design based on the mean-square-error (MSE) criterion in MIMO two-way relay systems, where two multiantenna source nodes exchange information via a multiantenna amplify-and-forward relay node. This problem is non-convex and its optimal solution remains unsolved. Aiming to find an efficient way to solve the problem, we first decouple the primal problem into three tractable subproblems, and then propose an iterative precoding design algorithm based on alternating optimization. The solution to each subproblem is optimal and unique, thus the convergence of the iterative algorithm is guaranteed. Second, we propose a structured precoding design to lower the computational complexity. The proposed precoding structure is able to parallelize the channels in the multiple access (MAC) phase and broadcast (BC) phase. It thus reduces the precoding design to a simple power allocation problem. Last, for the special case where only a single data stream is transmitted from each source node, we present a source-antenna-selection (SAS)-based precoding design algorithm. This algorithm selects only one antenna for transmission from each source and thus requires lower signalling overhead. Comprehensive simulation is conducted to evaluate the effectiveness of all the proposed precoding designs.

Joint Source and Relay Precoding Designs for MIMO Two-Way Relaying Based on MSE Criterion

Block diagonalization (BD) is a well-known precoding method in multiuser multi-input multi-output (MIMO) broadcast channels. This scheme can be considered as a extension of the zero-forcing (ZF) channel inversion to the case where each receiver is equipped with multiple antennas. One of the limitation of the BD is that the sum rate does not grow linearly with the number of users and transmit antennas at low and medium signal-to-noise ratio regime, since the complete suppression of multi-user interference is achieved at the expense of noise enhancement. Also it performs poorly under imperfect channel state information. In this paper, we propose a generalized minimum mean-squared error (MMSE) channel inversion algorithm for users with multiple antennas to overcome the drawbacks of the BD for multiuser MIMO systems. We first introduce a generalized ZF channel inversion algorithm as a new approach of the conventional BD. Applying this idea to the MMSE channel inversion for identifying orthonormal basis vectors of the precoder, and employing the MMSE criterion for finding its combining matrix, the proposed scheme increases the signal-to-interference-plus-noise ratio at each user's receiver. Simulation results confirm that the proposed scheme exhibits a linear growth of the sum rate, as opposed to the BD scheme. For block fading channels with four transmit antennas, the proposed scheme provides a 3 dB gain over the conventional BD scheme at 1% frame error rate. Also, we present a modified precoding method for systems with channel estimation errors and show that the proposed algorithm is robust to channel estimation errors.

Generalized channel inversion methods for multiuser MIMO systems

This paper considers two-way relaying systems with a multiple-input multiple-output (MIMO) relay between two MIMO terminal nodes. The two-way relaying protocol can en- hance the spectral efficiency compared with the one-way protocol by compensating the loss from half-duplex signaling. In this paper, we propose an iterative scheme to find a relay weighting matrix maximizing the sum-rate for two-way relay channels. Due to the non-convexity of the given problem, the proposed scheme iteratively identifies a local optimal solution by deriving the gradient of the sum-rate and applying the gradient descent algorithm. Simulation results show that the proposed iterative scheme with provable convergence achieves a near-optimal sum- rate for the two-way MIMO relay channels. Also, we show that the proposed scheme with a few iterations still outperforms the conventional schemes.

Sum-Rate Maximization for Two-Way MIMO Amplify-and-Forward Relaying Systems

In this paper, we develop linear precoding methods for cognitive radio (CR) multi-user multiple-input multiple-output (MU-MIMO) broadcast systems where unlicensed secondary users (SUs) simultaneously use the same spectrum of the licensed primary user (PU). When the zero-forcing block diagonalization (ZF-BD) precoder is extended to the CR network, a noise enhancement problem occurs. Therefore, we propose a regularized BD precoder based on the minimum mean-square error (MMSE) criteria subject to zero interference constraint for the PU. As a result, the proposed MMSE-BD scheme improves the signal-to-interference-plus-noise ratio at each SU's receiver compared to the ZF-BD based method. Simulation results demonstrate that the proposed algorithm outperforms the ZF based technique by more than 5 dB at the sum-rate 10 bps/Hz for CR MU-MIMO downlink systems.

Hakjea Sung

Papers

Generalized channel inversion methods for multiuser MIMO systems

Linear precoder designs for K-user interference channels

Joint Optimization for One and Two-Way MIMO AF Multiple-Relay Systems

Sum-Rate Maximization for Two-Way MIMO Amplify-and-Forward Relaying Systems

Linear Precoder Designs for Cognitive Radio Multiuser MIMO Downlink Systems