Optimization of MIMO Relays for Multipoint-to-Multipoint Communications: Nonrobust and Robust Designs

In this paper, we propose algorithms to jointly optimize the multiple multiantenna relays which assist multipoint-to-multipoint communications in wireless networks. Assuming that the knowledge of the second order statistics of the channels such as covariance matrices are available, the multiple-input-multiple-output (MIMO) relays are designed using two different methods: (1) minimize the sum of the powers of the relays while fulfilling the signal-to-interference-plus-noise ratio (SINR) requirements for all destinations and (2) maximize the minimum of the SINRs of all destinations satisfying the transmit power constraint of each MIMO relay. Furthermore, considering the fact that the covariance matrices of the channels between the MIMO relays and destinations are subject to uncertainty due to feedback and quantization errors, the robust versions of the aforementioned methods based on worst-case concept are proposed. It is shown that the proposed nonrobust as well as robust designs are nonconvex optimization problems but they can be solved accurately and efficiently using the standard semidefinite relaxation and randomization techniques. Computer simulations verify the improved performance of the robust designs over nonrobust methods.