Coding for the MIMO multi-hop amplify-and-forward fading channel with limited feedback

In this paper, coding techniques for the multiple-input multiple-output multi-hop amplify-and-forward (MIMO-MH-AF) quasi-static fading channel with perfect feedback are proposed. First, the diversity orders that can be achieved over this channel are investigated. The study is based on the partitioning of the channel onto several paths whose individual diversity order add to attain the maximum diversity carried by the channel. Next, we study the performance of space-time bit-interleaved coded modulation (ST-BICM), consisting of a coded modulation concatenated to a space-time rotation, over the MIMO-MH-AF quasi-static fading channel with perfect feedback. We propose upper bounds on the diversity orders that a ST-BICM can attain if a limited feedback from the destination to all the nodes is available. These bounds provide a tradeoff between attainable diversity, detector complexity, and coding rates. Finally, word error rate performances of several schemes with up to three bits of feedback are compared to outage probabilities, which represents the fundamental limit over quasi-static fading channels.