This paper addresses the robust design of a multiple-input multiple-output amplify-and-forward relay system against channel state information (CSI) mismatch due to estimation error and feedback delay. The estimation error and feedback delay are expressed using appropriate models, from which we derive the conditional mean square error (MSE) between the desired and the received signals upon the estimated CSI. The conditional MSE is then minimized to optimize the relay beamforming matrix with relay transmission power constraint. It is shown that the proposed optimization problem reduces to the conventional minimum MSE problem when CSI mismatch vanishes. By analyzing the structure of the optimal beamforming matrix, the optimization problem is simplified so that it can be directly solved using the genetic algorithm (GA). To further reduce the computational load, we develop a relaxed version of the optimization problem. It is found that the relaxation enables us to efficiently solve the problem using water filling strategy. Computer simulations show that both GA and water filling solutions are superior to conventional solutions without CSI mismatch consideration, while the water filling is 1000 times faster than the GA.
In this paper, we consider optimization of a two-way multiple-input multiple-output (MIMO) amplify-and-forward relay network which consists of a pair of transceivers and several relay nodes. Multiple antennas are equipped on the transceivers and relays. Multiple access broadcast scheme which finishes communication in two time slots is considered. In the first time slot, signals received by the relays are scaled by several beamforming matrices. In the second time slot, the relays transmit the scaled signals to the two transceivers. Upon receiving these signals, a MIMO equalizer is implemented at each transceiver to recover the desired signal. In this paper, zero forcing equalizers are used. Joint optimization of the beamforming matrices and the equalizers are realized using the following criteria: 1) the total relay transmission power is minimized subject to the minimal output signal-to-noise ratio (SNR) constraint at each transceiver, 2) the minimal output SNR of the two transceivers is maximized subject to total relay transmission power constraint, and 3) the minimal output SNR of the two transceivers is maximized subject to individual relay transmission power constraint. It is shown that the proposed optimization problems can be formulated as the second-order cone programming problems which can be solved efficiently. The validity of the proposed algorithm is verified by computer simulations.
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