Fast gridless direction-of-arrival estimation for wideband linear frequency modulated signals Based on fractional Fourier transform

A novel fast direction-of-arrival (DOA) estimation method of wideband Linear Frequency Modulated (LFM) signals without grid mismatch is proposed. Leveraging the aggregation traits inherent in wideband LFM signals within the Fractional Fourier (FRF) domain, the received model of LFM signals with time-invariant steering vector is drived. To counter the impact of grid mismatch on DOA estimation, this method utilizes atomic norms with continuous space dictionaries as sparse constraints, constructing a sparse recovery optimization problem. By transforming the minimization of atomic norms into a semipositive definite programming problem, the method effectively solves this optimization problem, reconstructing the covariance matrix from limited snapshot data in the FRF domain. Furthermore, addressing the efficiency challenge of solving semi-positive definite programming problems with multiple elements, a fast solution framework considering multiple measurement vectors and partial observation model is derived based on the interior point method theory, Karush-Kuhn-Tucke conditions and Toeplitz matrix characteristics. Compared to existing methods, the proposed method achieves heightened resolution and enhanced accuracy in DOA estimation through gridless sparse reconstruction, notably reducing computational complexity. The effectiveness of this method is robustly validated through simulation results.