Linear transceiver design for relay-assisted broadcast systems with diagonal scaling

In this paper, we study the linear transceiver design for the downlink of a cellular network assisted by a multi-antenna relay. A diagonal scaling scheme is proposed in which multiple single-antenna users apply different complex-valued scaling to their signals before decoding, as represented by an equivalent diagonal equalizer matrix. This equalizer is designed together with a linear precoder at the base station (BS) and a linear processing matrix at the relay. The objective is to minimize the weighted minimum mean square error (MMSE) between the precoder input and the equalizer output, subject to power constraints at the BS and the relay. In particular, the optimal relaying matrix is first derived in closed form as a function of the precoder and the equalizer. The latter two can then be jointly designed in an efficient iterative manner. Simulation results demonstrate lower bit-error rates (BERs) than previous design methods.