Gridless Underdetermined DOA Estimation of Wideband LFM Signals With Unknown Amplitude Distortion Based on Fractional Fourier Transform

In this article, a wideband Direction-of-Arrival (DOA) estimation method for underdetermined scenarios is proposed, which effectively solves the basis mismatch problem. Based on the fractional Fourier transform (FRFT), the wideband received signal model with a coprime array is first derived by exploiting the aggregation characteristic of wideband linear frequency modulated (LFM) signals in the fractional Fourier (FRF) domain. Then, in order to increase the degree of freedom, an extended uniform linear array is built, and the covariance matrix of the signal is reconstructed by employing the penalized atomic norm minimization with the consecutive spatial dictionary. Meanwhile, without the knowledge of the noise level, the noise variance is estimated from the noisy incomplete data, which is utilized to improve the covariance matrix reconstruction performance. Additionally, for the unconditional model, the Cramér–Rao bound for the wideband DOA estimation based on a coprime array is derived. Different from the existing methods, the proposed method not only can estimate more DOAs of wideband signals than the number of physical sensors in the presence of unknown amplitude distortion but also can obtain more accurate DOA estimation performance without basis mismatch. The effectiveness of the proposed method is verified by our numerical results.