Wideband directions of arrival estimation of chirp sources using compressive sensing

Classical Directions of Arrival (DoA) algorithms estimate the time delays associated with the signal received at an array of sensors through phase information. Most existing wideband algorithms decompose the signals received by an antenna array into multiple narrowband frequencies, and then the wideband DOAs are estimated by coherent or incoherent combination of signal and noise subspace information at multiple source frequencies. A novel algorithm for finding the direction of arrival (DoA) for wide-band chirp sources is introduced in this study, where frequency shift rather than phase shift is utilized to estimate the signal time delays between sensors, eliminating many limitations due to phase ambiguity like spatial sampling, leading to finer angular resolution between multiple sources. The proposed algorithm processes the data using Discrete Chirp Fourier Transform (DCFT) that invokes the exact chirp model in the signal leading to more precise estimates compared to general wideband DoA methods that do not exploit the chirp model. Use of Compressed Sensing (CS) enables exploitation of the sparsity in the DCFT-domain data for highly accurate DoA estimation. Reduced number of measurements are required for CS optimization processing by making use of the sparsity of the DCFT coefficients. The proposed approach eliminates the need for correlation, iterations, and time-frequency analysis needed by many classical chirp signal parameter estimation algorithms. Theoretical derivation is given and simulation results of the new algorithm for single and multiple wide-band chirp sources show significant performance enhancement even in highly noisy environment.