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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-Loeve 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 …