Doubly Iterative Turbo Equalization: Optimization through Deep Unfolding

This paper analyzes some emerging techniques from the broad area of Bayesian learning for the design of iterative receivers for single-carrier transmissions using bit-interleaved coded-modulation (BICM) in wideband channels. In particular, approximate Bayesian inference methods, such as expectation propagation (EP), and iterative signal-recovery methods, such as approximate message passing (AMP) algorithms are evaluated as frequency domain equalizers (FDE). These algorithms show that decoding performance can be improved by going beyond the established turbo-detection principles, by iterating over inner detection loops before decoding. A comparative analysis is performed for the case of quasistatic wideband communications channels, showing that the EP-based approach is more advantageous. Moreover, recent advances in structured learning are revisited for the iterative EP-based receiver by unfolding the inner detection loop, and obtaining a deep detection network with learnable parameters. To this end, a novel, mutual-information dependent learning cost function is proposed, suited to turbo detectors, and through learning, the detection performance of the deep EP network is optimized.