On the capacity of MIMO relay channels

Bo Wang, Junshan Zhang, A. Host-Madsen
2005 IEEE Transactions on Information Theory  
We study the capacity of multiple-input multipleoutput (MIMO) relay channels. We first consider the Gaussian MIMO relay channel with fixed channel conditions, and derive upper bounds and lower bounds that can be obtained numerically by convex programming. We present algorithms to compute the bounds. Next, we generalize the study to the Rayleigh fading case. We find an upper bound and a lower bound on the ergodic capacity. It is somewhat surprising that the upper bound can meet the lower bound
more » ... der certain regularity conditions (not necessarily degradedness), and therefore the capacity can be characterized exactly; previously this has been proven only for the degraded Gaussian relay channel. We investigate sufficient conditions for achieving the ergodic capacity; and in particular, for the case where all nodes have the same number of antennas, the capacity can be achieved under certain signal-to-noise ratio (SNR) conditions. Numerical results are also provided to illustrate the bounds on the ergodic capacity of the MIMO relay channel over Rayleigh fading. Finally, we present a potential application of the MIMO relay channel for cooperative communications in ad hoc networks. Index Terms-Cooperative communications, ergodic capacity, multiple-input multiple-output (MIMO), relay channel. I. INTRODUCTION W IRELESS networking constitutes an important component of future information technology applications. Recently, the use of multiple antennas at wireless transmitters and receivers has been identified as an enabling technique for high-rate multimedia transmissions over wireless channels. Although the point-to-point multiple-input multiple-output (MIMO) channel is relatively well understood (particularly the information-theoretic aspects therein), the general area of multiuser MIMO communications, i.e., the field of communications involving a network of many users using multiple antennas, is still at a stage of its infancy and poses a rich set of challenges to the research community. We consider MIMO relay channels because this application has great potential in wireless networks. For example, for transmissions from a base station (access point) to users, relay stations can be exploited to relay messages for end users. The motivation for using relay stations can be simply put as follows.
doi:10.1109/tit.2004.839487 fatcat:d5xjjltq2jfmjkyb2aqg2ezz4m