Direction-of-Arrival Estimation of Multiple Linear Frequency Modulation Signals Based on Quadratic Time–Frequency Distributions and the Hough Transform

The direction-of-arrival (DOA) estimation of multiple linear frequency modulation (LFM) signals typically requires the construction of a spatial time–frequency distribution (STFD) matrix via linear transforms or quadratic time–frequency distributions (QTFD) before joint spatial time–frequency estimation. Extensive research has been conducted on DOA estimation of LFM signals with overlapped instantaneous frequency (IF) trajectories and significantly different chirp rates. However, when LFM signals have the same chirp rate and slightly different initial frequencies with parallel and close IF trajectories, their linear transforms suffer from low resolution and quadratic distributions and are affected by cross-terms, both of which reduce accuracy. To address this problem, this study proposes a DOA estimation algorithm based on QTFD and the Hough transform. First, QTFD is used to improve the resolution and apply both spatial and directional smoothing to eliminate cross-terms. Second, the Hough transform is employed for IF estimation instead of threshold filtering to enhance accuracy. Finally, DOA results are obtained via time–frequency filtering and the multiple signal classification (MUSIC) algorithm. Experiments show that for two LFM signals at a −5 dB signal-to-noise ratio (SNR), the proposed algorithm improves accuracy by approximately 43.2% compared to similar algorithms and effectively estimates the DOA in underdetermined cases. Thus, the proposed algorithm enhances the DOA estimation accuracy for multiple LFM signals, is robust to noise, and expands the application scenarios of joint spatial time–frequency estimation.