Blind source separation using dictionary learning over time-varying channels

Distributed sensors observe radio frequency (RF) sources over flat-fading channels. The activity pattern is sparse and intermittent in the sense that while the number of latent sources may be larger than the number of sensors, only a few of them may be active at any particular time instant. It is further assumed that the source activity is modeled by a Hidden Markov Model. In previous work, the Blind Source Separation (BSS) problem solved for stationary channels using Dictionary Learning (DL). This thesis studies the effect of time-varying channels on the performance of DL algorithms. The performance metric is the probability of detection, where a correct detection is the event that the estimated value of a source exceeds a threshold at a time instant when the true source is active. Using the probability of detection when the channels are stationary as a baseline, it is shown that there is significant degradation for time-varying channels and observation intervals much longer than the time coherence. Detection performance improves when the observation time is approximately equal to the time coherence. Performance is again degraded when the observation is shorter and there is not sufficient information for the DL algorithms to learn from