  Future wireless networks are envisioned to provide ubiquitous sensing
services, which also gives rise to a substantial demand for high-dimensional
non-convex parameter estimation, i.e., the associated likelihood function is
non-convex and contains numerous local optima. Variational Bayesian inference
(VBI) provides a powerful tool for modeling complex estimation problems and
reasoning with prior information, but poses a long-standing challenge on
computing intractable posteriori distributions. Most existing variational
methods generally rely on assumptions about specific distribution families to
derive closed-form solutions, and are difficult to apply in high-dimensional,
non-convex scenarios. Given these challenges, firstly, we propose a parallel
stochastic particle variational Bayesian inference (PSPVBI) algorithm. Thanks
to innovations such as particle approximation, additional updates of particle
positions, and parallel stochastic successive convex approximation (PSSCA),
PSPVBI can flexibly drive particles to fit the posteriori distribution with
acceptable complexity, yielding high-precision estimates of the target
parameters. Furthermore, additional speedup can be obtained by deep-unfolding
(DU) the PSPVBI algorithm. Specifically, superior hyperparameters are learned
to dramatically reduce the number of algorithmic iterations. In this
PSPVBI-induced Deep-Unfolding Networks, 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 LPSPVBI to solve several important parameter estimation problems in
wireless sensing scenarios. Simulations indicate that the LPSPVBI algorithm
outperforms existing solutions.
