Abstract-In this paper, we consider the fundamental problem of channel estimation in multiple-input multiple-output (MIMO) amplify-and-forward (AF) relaying systems operating over random channels. Using the Bayesian framework, linear minimum mean square error (LMMSE) and expectation-maximization (EM) based maximum a posteriori (MAP) channel estimation algorithms are developed, that provide the destination with full knowledge of all channel parameters involved in the transmission. The performance of the proposed algorithms is evaluated in terms of the mean square error (MSE) as a function of the signal-tonoise ratio (SNR) during the training interval. Our simulation results show that the incorporation of prior knowledge into the channel estimation algorithm offers improved performance, especially in the low SNR regime.
I. INTRODUCTIONRecently, the introduction of relaying nodes in wireless channels has triggered a significant research interest [1]. The deployment of relays has been identified as a suitable technique for providing broader coverage, higher transmission rates, and increased reliability. Moreover, when the source and destination are equipped with multiple antennas, the concept of relaying is combined with that of multiple-input multipleoutput (MIMO) systems. Then, the system's performance can be further enhanced by exploiting the spatial dimension [2].For different relaying strategies, the problem of power allocation and network beamforming has been well studied in the existing literature [3]. Several designs for the optimal relay amplifying factor have been proposed for maximizing the received signal-to-noise ratio (SNR) or some other performance measure, such as the channel capacity [3], [4]. Most existing relaying schemes, however, assume that perfect instantaneous channel state information (CSI) is available at the receiver. Therefore, it becomes clear that to exploit the advantages of MIMO relaying networks, an accurate CSI of all involved links is required. Despite the importance of this prerequisite, channel estimation is often ignored by either assuming perfect CSI or by considering only the estimation of the compound (from source to destination) channel [5]. While CSI of the compound channel guarantees feasible data detection at the destination, the knowledge of the individual channel responses can be utilized to further improve the overall system performance.In this paper, we study stochastic channel estimation techniques for MIMO relaying systems with random channels. In particular, we develop linear minimum mean square error (LMMSE) and expectation-maximization (EM) based maximum a posteriori (MAP) channel estimation schemes for