A Hybrid Inference Architecture Incorporating Neural Network with Belief Propagation for AI Receivers

Conventional wireless communication receivers guided by Bayesian inference methods need to know the exact statistical relationship among variables, which is hard to obtain accurately in wireless contexts, thus limiting the system performance. The recently emerging artificial intelligence (AI)-empowered algorithms have shown striking performances in exploring the implicit relationship among variables with specially designed Neural Networks (NNs). Therefore, it is preferable to integrate NNs with BPs in receiver design. Such approaches also leverage NNs' lack of reasoning ability in large state spaces and traditional BPs' lack of reasoning depth. However, conventional receiver modules are usually designed based on explicit mathematical derivations, which cannot be easily substituted with datadriven NNs as they may break the overall inner relationship of the algorithm. In this paper, we investigate how to beneficially incorporate NNs into the existing Belief Propagation (BP)-based framework, taking the traditional semi-blind estimation problem in an Orthogonal Frequency-Division Multiplexing (OFDM) receiver as an example. Unlike existing deep-unfolding approaches, we simply utilize NNs as embedded functional units rather than duplicate denoising modules. Through qualitative discussions and numerical results, we illustrate the characteristics, principles, and differences of our proposed architecture compared to the traditional BP framework and show the dramatic performance improvements brought by incorporating NNs with BP in this well-investigated problem. Recalling that the state evolution of NNs is different from that of traditional BP methods, we give some new insights and design principles which are somehow counterfactual. We also raise some open issues on the incorporated framework.