Deep Learning Detection Networks in MIMO Decode-Forward Relay Channels

In this paper, we consider signal detection algorithms in a multiple-input multiple-output (MIMO) decode-forward (DF) relay channel with one source, one relay, and one destination. The existing suboptimal near maximum likelihood (NML) detector and the NML with two-level pair-wise error probability (NMLw2PEP) detector achieve excellent performance with instantaneous channel state information (CSI) of the source-relay (SR) link and with statistical CSI of the SR link, respectively. However, the NML detectors require an exponentially increasing complexity as the number of transmit antennas increases. Using deep learning algorithms, NML-based detection networks (NMLDNs) are proposed with and without the CSI of the SR link at the destination. The NMLDNs detect signals in changing channels after a single training using a large number of randomly distributed channels. The detection networks require much lower detection complexity than the exhaustive search NML detectors while exhibiting good performance. To evaluate the performance, we introduce semidefinite relaxation detectors with polynomial complexity based on the NML detectors. Additionally, new linear detectors based on the zero gradient of the NML metrics are proposed. Applying various detection algorithms at the relay (DetR) and detection algorithms at the destination (DetD), we present some DetR-DetD methods in MIMO DF relay channels. An appropriate DetR-DetD method can be employed according to the required error probability and detection complexity. The complexity analysis and simulation results validate the arguments of this paper.