Underdetermined DOA Estimation of Wideband LFM Signals Based on Gridless Sparse Reconstruction in the FRF Domain

Abstract

An underdetermined direction of arrival (DOA) estimation method of wideband linear frequency modulated (LFM) signals is proposed without grid mismatch. According to the concentration property of LFM signal in the fractional Fourier (FRF) domain, the received sparse model of wideband signals with time-variant steering vector is firstly derived based on a coprime array. Afterwards, by interpolating virtual sensors, a virtual extended uniform linear array (ULA) is constructed with more degrees of freedom, and its covariance matrix in the FRF domain is recovered by employing sparse matrix reconstruction. Meanwhile, in order to avoid the grid mismatch problem, the modified atomic norm minimization is used to retrieve the covariance matrix with the consecutive basis. Different from the existing methods that approximately assume the frequency and the steering vector of the wideband signals are time-invariant in every narrowband frequency bin, the proposed method not only can directly solve more DOAs of LFM signals than the number of physical sensors with time-variant frequency and steering vector, but also obtain higher resolution and more accurate DOA estimation performance by the gridless sparse reconstruction. Simulation results demonstrate the effectiveness of the proposed method.

Super-Resolution DoA Estimation on a Co-Prime Array via Positive Atomic Norm Minimization

“…The co-prime array with M 1 = 3, M 2 = 5 is used. In this case, the antenna elements are physically located as [0, 3,5,6,9,10,12,15,20,25] ∆, where ∆ = λ/2. Under this array configuration, V = 35.…”

“…Since the resolution is proportional to the array cardinality [18], the usage of the sparse array results in resolution improvement. The sparse array has been exploited in the seminal works of CS-based DOA estimation [21][22][23] and ANM-based DOA estimation [24,25]. The other approaches to increase the resolution were introduced in [26][27][28].…”

Robust Sparse Bayesian Learning-Based Off-Grid DOA Estimation Method for Vehicle Localization

“…The other two categories, namely, gridless methods and off-grid methods, can eliminate or narrow this gap. Gridless methods [37][38][39][40][41][42] operate in the continuous domain directly so that they can avoid the grid mismatch problem. Gridless methods have strong theoretical guarantees and can only be applied to the uniform or sparse linear arrays.…”

Wideband DOA Estimation on Co-prime Array via Atomic Norm Minimization

“…The ANM-based algorithm also extended to 2D-DOA estimation, including azimuth and elevation estimation [24] and multiple-input-multiple-output (MIMO) radar [25]. The ANM-based wideband DOA estimation has been studied in [26]. However, the idea of reducing complexity has not been discussed.…”

“…However, the idea of reducing complexity has not been discussed. In addition, [26] targets linear frequency modulated (LFM) signals and thus is difficult to be used in the general scenario.…”