Limited Feedback-Based Multi-Antenna Relay Broadcast Channels with Block Diagonalization

The relay technology is effective in extending radio coverage and improving the performance of cell edge users. In multi-antenna relay channels, good knowledge of the channel state information (CSI) at the transmitter is important to achieve multiplexing gains of the multiple-input multiple-output technique. In this paper, we study the multi-antenna relay downlink channel with limited feedback CSI from both two-hop links. Data streams from the base station (BS) are first transmitted to a relay station (RS) with singular value decomposition-based precoding and receiver pulse shaping at the BS and RS, respectively. The block diagonalization precoding is then applied at the RS to forward the received signals to the remote multi-antenna users. We derive an upper bound for the system throughput loss due to CSI quantization error, and then propose a feedback quality control strategy to maintain a bounded rate loss relative to the perfect CSI case. It reveals that the feedback size B-1 from the RS to BS needs to scale in proportion to both transmit power at the BS and RS while the feedback size B-2 from each user to the RS only needs to scale linearly with the transmit power at the RS.