Temporally Correlated Compressed Sensing Using Generative Models for Channel Estimation in Unmanned Aerial Vehicles

Bayesian modelling of the channel distribution is a crucial step before channel recovery specially in the underdetermined scenario in multiple input multiple output (MIMO) antenna setups. In complicated dynamic propagation environments such as the ones encountered in Unmanned Aerial Vehicles (UAVs) Air to Ground (A2G) channels, Bayesian modelling might not be feasible or the model may not be able to approximate the different aspects of the true distribution well enough. Thus, estimation performance will be affected irrespective of the efficiency of recovery algorithm. To exploit the temporal correlations and imperfections in the real channels in such a scenario, we design a temporally correlated adversarial regulariser using Variational recurrent neural networks (VRNN) and train the framework on simulated channel dataset. The framework can be trained directly with channel samples, thus, allowing channel modelling and estimation without explicit tractable Bayesian models in highly dynamic systems. We then propose a temporally correlated deep compressed sensing algorithm which does not depend on the expressibility of the networks and provide theoretical results for existence and recovery. Numerical experiments demonstrate its effectiveness for channel estimation in A2G channels and show superior channel recovery and improved modelling even for out-of-distribution channels.