Matching pursuit decomposition for high-resolution direction of arrival

Time-frequency analysis was combined with array processing to develop a direction of arrival (DOA) estimation method. Spatial time-frequency distribution (STFD) was introduced as the natural means to deal with source signals that are localizable in the time-frequency (TF) domain. It was shown that estimating the signal and noise subspaces are improved by constructing the subspaces from the TF signatures of the signal arrivals rather than from the spatial data covariance matrix, which is commonly used in conventional multiple signal classification (MUSIC). However, the instantaneous frequency signature is needed in real application of STFD. For this purpose, identification of auto-term regions are needed and it is often difficult for really closed space sources because cross terms mask the auto terms. It means the cross term amplitude is greater than the auto terms. In this paper, three high-resolution DOA estimation approaches of non-stationary narrowband signals using matching pursuit (MP), are developed. We demonstrate the proposed technique's source discriminatory capability, its robustness against noise, and employing for underdetermined problem as well. In this paper, we consider the first sensor output as reference and decompose it by using MP decomposition based on Gabor and chirplet dictionaries. The coefficients of MP contain the steering vector information and so they can be used to estimate the DOA. In addition, the chosen MP atoms are used to implement the modified STFD based on Wigner Ville distribution and Rihaczek time frequency distribution as well. We show that using either coefficients or chosen atoms to estimate the DOA in array processing outperforms the conventional MUSIC for different scenarios. Some simulation results, showing the performance of three proposed approaches based on MP and also showing their advantages and drawbacks, are presented.