Tracking a frequency hopped signal using particle filtering

The problem of tracking the frequency and complex amplitude of a frequency-hopped complex sinusoid is considered, using a novel stochastic state-space formulation and particle filtering tools. The problem is of considerable interest for interference mitigation in frequency-hopped wireless networks, and in military communications. The proposed particle filtering approach has a number of desirable features. It affords high-resolution estimates of carrier frequency and hop timing, manageable complexity (linear in the number of processed samples), and flexibility in tracking signals with irregular hopping patterns due to intentional timing jitter. The proposed state-space model is not only parsimonious, but fortuitous as well: it turns out that the associated optimal importance function can be computed in closed form, and thus samples from it can be drawn using rejection techniques. Both prior and optimal importance sampling versions are developed and illustrated in pertinent simulations.