Fast CS algorithm for chirp signals parameters estimation using multi-resolution DCFT atom transformation

Abstract

Estimation of linear Time-Frequency varying signal parameters is a computationally expensive process. Traditional estimation methods have several drawbacks that affect the performance of these estimators. Compressive sensing is a novel statistical approach that can make use of signal sparsity in a certain domain to fully recover the signal from fewer coefficients or measurements. Recent work on applying compressive sensing (CS) for chirp estimation has been reported in literature [1] [2], but these methods require super-resolution transformation causing a high post processing burden especially for real-time wide-band signals. To address this limitation, we propose to use a lower resolution measurements matrix with a wide range of estimated parameters. We apply low resolution Discrete Chirp Fourier Transform (DCFT) [3] with selected number of measurements to obtain prior signal information. Next, constrained high resolution transformation matrix is used by making use of the prior information obtained earlier. This would reduce the computational burden applied using super resolution of direct CS method. Multiple chirp signals are also considered, the effect of minimum signal separation, difference in amplitude of chirp signals and transformation resolution was studied based on simulation results and driven equations. Effect of noise has been studied, and the results show high immunity in the recovery process because CS had performed as filter for low side-lopes coefficients, even with very few measurements deployed.