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Unformatted text preview: IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 58, NO. 2, FEBRUARY 2010 781 Compress-and-Forward Cooperative MIMO Relaying With Full Channel State Information Sbastien Simoens , Member, IEEE , Olga Muoz-Medina, Josep Vidal , Member, IEEE , and Aitor Del Coso , Member, IEEE 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 chan- nels. 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 com- pression techniques. The processing at the CF relay consists in a conditional Karhunen-Love transform (CKLT) followed by a sep- arate 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 proce- dure 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 simul- taneously 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 bench- marked with other upper and lower bounds on capacity. Simu- lation results show that CF can outperform decode-and-forward (DF) and approach capacity for realistic SNR values, which vali- dates the performance of the proposed optimization procedure. Index Terms Compress, channel state information (CSI), for- ward, MIMO, relay. I. INTRODUCTION C OOPERATIVE Relaying (see, e.g.,  for an overview) is regarded as a promising technique for next generation cellular wireless systems and is being considered by several standardization groups (e.g., IEEE802.16 Task Groups j and m ). In cooperative relaying, a node on a multihop path from a source to a destination can receive and process the signals transmitted by several predecessors. The latter can thus transmit cooperatively to maximize the end-to-end information rate. In the aforementioned standards, it is also envisioned that both infrastructure devices (e.g., base stations, fixed relay stations) and mobile devices (e.g., handsets) will be equipped with mul- Manuscript received November 23, 2008; accepted July 20, 2009. First pub- lished August 18, 2009; current version published January 13, 2010. This work was supported in part by the ICT ROCKET Project of the 7Th European Re- search Framework, by the Spanish/Catalan Science and Technology Commis- sions, and by the FEDER funds from the EC: TEC2006-06481/TCM, TEC2004- 04526, and 2005SGR-00639. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Geert Leus....
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