A Stochastic Particle Variational Bayesian Inference Inspired Deep-Unfolding Network for Sensing Over Wireless Networks

Future wireless networks are envisioned to provide ubiquitous sensing services, driving a substantial demand for multi-dimensional non-convex parameter estimation. This entails dealing with non-convex likelihood functions containing numerous local optima. Variational Bayesian inference (VBI) provides a powerful tool for modeling complex estimation problems and leveraging prior information, but poses a long-standing challenge on computing intractable posterior distributions. Most existing variational methods depend on specific distribution assumptions for obtaining closed-form solutions, and are difficult to apply in practical scenarios. Given these challenges, firstly, we propose a parallel stochastic particle VBI (PSPVBI) algorithm. Due to innovations like particle approximation, added updates of particle positions, and parallel stochastic successive convex approximation (PSSCA), PSPVBI can flexibly drive particles to fit the posterior distribution with acceptable complexity, yielding high-precision estimates of the target parameters. Furthermore, additional speedup can be obtained by deep-unfolding this algorithm. Specifically, superior hyperparameters are learned to dramatically reduce iterations. In this PSPVBI-induced deep-unfolding network, some techniques related to gradient computation, data sub-sampling, differentiable sampling, and generalization ability are also employed to facilitate the practical deployment. Finally, we apply the learnable PSPVBI (LPSPVBI) to solve two important positioning/sensing problems over wireless networks. Simulations indicate that the LPSPVBI algorithm outperforms existing solutions.