Estimating Multiple Frequency-Hopping Signal Parameters via Sparse Linear Regression

Frequency hopping (FH) signals have well-documented merits for commercial and military applications due to their near-far resistance and robustness to jamming. Estimating FH signal parameters (e.g., hopping instants, carriers, and amplitudes) is an important and challenging task, but optimum estimation incurs an unrealistic computational burden. The spectrogram has long been the starting non-parametric estimator in this context, followed by line spectra refinements. The problem is that hop timing estimates derived from the spectrogram are coarse and unreliable, thus severely limiting performance. A novel approach is developed in this paper, based on sparse linear regression (SLR). Using a dense frequency grid, the problem is formulated as one of under-determined linear regression with a dual sparsity penalty, and its exact solution is obtained using the alternating direction method of multipliers (ADMoM). The SLR-based approach is further broadened to encompass polynomial-phase hopping (PPH) signals, encountered in chirp spread spectrum modulation. Simulations demonstrate that the developed estimator outperforms spectrogram-based alternatives, especially with regard to hop timing estimation, which is the crux of the problem.