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In this paper, we consider signal detection algorithms in a multiple-inputmultiple-output (MIMO) decode-forward (DF) relay channel with one source, onerelay, 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 channelstate information (CSI) of the source-relay (SR) link and with statistical CSIof the SR link, respectively. However, the NML detectors require anexponentially increasing complexity as the number of transmit antennasincreases. Using deep learning algorithms, NML-based detection networks(NMLDNs) are proposed with and without the CSI of the SR link at thedestination. The NMLDNs detect signals in changing channels after a singletraining using a large number of randomly distributed channels. The detectionnetworks require much lower detection complexity than the exhaustive search NMLdetectors while exhibiting good performance. To evaluate the performance, weintroduce semidefinite relaxation detectors with polynomial complexity based onthe NML detectors. Additionally, new linear detectors based on the zerogradient of the NML metrics are proposed. Applying various detection algorithmsat the relay (DetR) and detection algorithms at the destination (DetD), wepresent some DetR-DetD methods in MIMO DF relay channels. An appropriateDetR-DetD method can be employed according to the required error probabilityand detection complexity. The complexity analysis and simulation resultsvalidate the arguments of this paper.

Deep Learning Detection Networks in MIMO Decode-Forward Relay Channels