Source-relay optimization for a two-way MIMO relay system

This paper addresses a non-regenerative two-way MIMO relay system where two sources exchange information via a common relay. Both sources and the relay are each equipped with multiple antennas. In the first phase (time or frequency), both sources transmit their signals and the relay receives. In the second phase, the relay transmits towards both sources a transformed signal. The optimization of the source covariance matrices and the optimization of the relay transformation matrix can be performed alternately until convergence. The former can be achieved by a generalized water filling algorithm, and the latter can be achieved by two algorithms discussed in this paper. The first algorithm is a hybrid gradient optimization. The second algorithm is an iterative weighted MMSE equalization. It is shown in simulation that both algorithms converge to the same results and are much faster than a prior algorithm developed for single-antenna sources.