On Linear Precoding of Nonregenerative MIMO Relay Networks for Finite-Alphabet Source

Multiple input and multiple output (MIMO) relay could provide broader wireless coverage, better diversity, and higher throughput. Most existing precoder designs for either source or relay node are based on the assumption of Gaussian input signals. However, recent works have revealed possible performance loss of MIMO systems originally optimized for Gaussian source signals when applied to practical finite-alphabet source signals. In this work, we investigate the design problem of joint MIMO precoding for wireless two-hop nonregenerative cooperative relay networks under finite-alphabet source signals. We identify several structural properties of optimal precoders. Specifically, we provided the optimal left singular vectors of the relay precoder, and proved the convexity of mutual information with respect to the square of relay precoder singular value. These results generalize the two-hop relay networks in Gaussian input assumption to the cooperative relay networks in arbitrary finite-alphabet input signals. Furthermore, we propose gradient-based numerical iterative optimization algorithms not only for arbitrary finite-alphabet source signal precoding but also for cooperative relay networks which may or may not have a direct source to destination link. Our results demonstrate substantial performance improvement over existing precoder designed traditionally under Gaussian input assumption, which indicates that the waterfilling based precoding strategy is not suitable for finite-alphabet constellation source inputs.