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-Lo