ACHIEVABLE RATES OF MULTI-HOP AND COOPERATIVEMIMO AMPLIFY-AND-FORWARD RELAY SYSTEMS WITH FULL CSI Nicola Varanese*, Osvaldo Simeone*, Yeheskel Bar-Ness *CWCSPR - NJIT {nv35, osvaldo.simeone}@njit.edu barness@yegal.njit.edu Umberto Spagnolini *DEI Politecnico di Milano spagnoli@elet.polimi.it ABSTRACT In this paper 1 , two types of MIMO Amplify-and-Forward relay systems are considered: multi-hop and cooperative. For both cases, the problem of maximizing the achievable rate over the covariance matrices of the symbols transmitted by the source and relay linear processing matrix is formu- lated under the assumption of full channel state information at each node. A sub-optimal iterative algorithm is proposed and proved by numerical simulations to outperform known schemes. 1. INTRODUCTION Cooperation is a new paradigm for reliable and high- through- put multi-user wireless communications. The building block of cooperative systems is the relay channel, introduced in [1], where a max-flow-min-cut upper bound for its capacity was derived. To date, the capacity-achieving coding strat- egy for this channel is still unknown, and simplified cooper- ative communication schemes have been recently proposed in [2], namely Amplify-and-Forward (AF) and Decode-and- Forward (DF). The main difference between these coopera- tive schemes and conventional multi-hop regenerative (DF) or non-regenerative (AF) relaying schemes is that the desti- nation decodes the source message from the signals received from both the source and the relay node. Modified versions of the original DF and AF collaborative protocols, capable of achieving higher rates, have been introduced in [3]. Both [2] and [3] focus on the case where each node is deployed with a single antenna. The multi-antenna relay channel has been recently in- vestigated from different perspectives. The authors of [4] extended the information-theoretic results of [1] to a multi- antenna scenario and devised an algorithm to compute the input covariance matrices that maximize the max-flow-min- cut upper bound. Performance of the AF scheme of [2] in a multi-antenna setting was analyzed in [5]. In particular, [5] 1 This work was partially supported by grant from Samsung Electronics Co., LTD. x n R n D H 1 G H 2 y x R y R (a) x n R n D H 1 G H 2 H 0 y x R y R (b) Fig. 1. Block diagram of a multi-hop (a) and cooperative (b) MIMO Amplify-and-Forward relay system. derived the optimal linear processing matrix at the relay, for both multi-hop and cooperative MIMO AF relay systems, under the assumption of perfect channel state information (CSI) at each node and isotropic covariance matrix for the symbol transmitted by the source. In this paper, we consider multi-hop and cooperative MIMO AF relay systems with perfect CSI at each node as in [5]. However, differently from [5]: (i) for both multi- hop and cooperative systems, the covariance matrix of the symbols transmitted by the source is not constrained to be isotropic; (ii) for the cooperative scenario, the considered AF protocol is the one presented in [3], whereby the source transmits in both time-slots (not only in the first). The prob- lem of maximizing the achievable rate over the source co- variance matrices and linear processing matrix at the relay is formulated. An iterative algorithm, capable of finding a sub-optimal feasible solution, is proposed for both multi- hop and cooperative cases, and proved by numerical simu- lations to outperform known schemes under broad channel conditions.