  Channel estimation and signal detection are very challenging for an
orthogonal frequency division multiplexing (OFDM) system without cyclic prefix
(CP). In this article, deep learning based on orthogonal approximate message
passing (DL-OAMP) is used to address these problems. The DL-OAMP receiver
includes a channel estimation neural network (CE-Net) and a signal detection
neural network based on OAMP, called OAMP-Net. The CE-Net is initialized by the
least square channel estimation algorithm and refined by minimum mean-squared
error (MMSE) neural network. The OAMP-Net is established by unfolding the
iterative OAMP algorithm and adding some trainable parameters to improve the
detection performance. The DL-OAMP receiver is with low complexity and can
estimate time-varying channels with only a single training. Simulation results
demonstrate that the bit-error rate (BER) of the proposed scheme is lower than
those of competitive algorithms for high-order modulation.
