Abstract-This paper addresses the problem of source and relay transmit covariance optimization on the Gaussian MIMO relay channel with full channel state information (CSI), i.e., assuming perfect knowledge of all channels. For full-duplex relaying, we show that the cut-set bound on capacity can be computed as the solution of a convex problem, thus providing a tighter bound than previously published. For time division duplex (TDD) relaying, both upper and lower bounds on capacity are derived, and the transmit covariance matrices are optimized for decode-and-forward (DF) strategies with either partial or full decoding at the relay. A generic procedure is introduced to formulate these problems into a standard convex form, and to solve them efficiently. Suboptimum precoders are also proposed which have a specific matrix structure that either leads to a closed-form expression or at least reduces the dimension of the optimization problem. Practical aspects related to transmit power constraints and CSI availability are then discussed. Finally, simulations in a cellular downlink scenario show that the partial DF strategy can achieve a rate very close to capacity for realistic values of the source to relay SNR, and that the rate loss due to suboptimum precoder structures remains small for typical antenna configurations.Index Terms-Cooperative, relay, channel state information (CSI), MIMO.
Abstract-This paper addresses cooperative Time Division Duplex (TDD) relaying in the multiple-antenna case with full Channel State Information (CSI), i.e. assuming perfect knowledge of all channels. The main focus of the paper is on the Compress-and-Forward (CF) strategy, for which an achievable rate on the Gaussian MIMO relay channel can be derived by applying distributed vector compression techniques. The processing at the CF relay consists in a Conditional Karhunen-Loève Transform (CKLT) followed by a separate Wyner-Ziv (WZ) coding of each output stream at a different rate. The paper provides a simple analytical expression for the optimum WZ coding rates, and also proposes an iterative procedure to perform this optimization jointly with that of the transmit covariance matrices at the source and relay. The Multiple Access Channel (MAC) formed by the source and relay transmitting simultaneously to the destination is considered, and it is shown that an optimal decoding order exists at least in the single-antenna case. We discuss the extension to MIMO-OFDM, as well as practical source coding implementation. The CF achievable rates are benchmarked with other upper and lower bounds on capacity.Simulation results show that CF can outperform Decode-and-Forward (DF) and approach capacity for realistic SNR values, which validates the performance of the proposed optimization procedure.
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