A robust compressive sensing based technique for reconstruction of sparse radar scenes

Abstract

Pulse-Doppler radar has been successfully applied to surveillance and tracking of both moving and stationary targets. For efficient processing of radar returns, delay-Doppler plane is discretized and FFT techniques are employed to compute matched filter output on this discrete grid. However, for targets whose delay-Doppler values do not coincide with the computation grid, the detection performance degrades considerably. Especially for detecting strong and closely spaced targets this causes miss detections and false alarms. This phenomena is known as the off-grid problem. Although compressive sensing based techniques provide sparse and high resolution results at sub-Nyquist sampling rates, straightforward application of these techniques is significantly more sensitive to the off-grid problem. Here a novel parameter perturbation based sparse reconstruction technique is proposed for robust delay-Doppler radar processing even under the off-grid case. Although the perturbation idea is general and can be implemented in association with other greedy techniques, presently it is used within an orthogonal matching pursuit (OMP) framework. In the proposed technique, the selected dictionary parameters are perturbed towards directions to decrease the orthogonal residual norm. The obtained results show that accurate and sparse reconstructions can be obtained for off-grid multi target cases. A new performance metric based on Kullback-Leibler Divergence (KLD) is proposed to better characterize the error between actual and reconstructed parameter spaces. Increased performance with lower reconstruction errors are obtained for all the tested performance criteria for the proposed technique compared to conventional OMP and ℓ1 minimization techniques. © 2013 Elsevier Inc

Sparse delay-Doppler image reconstruction under off-grid problem

“…When sparsity levels of the actual and reconstructed signals do not match, classical error criterions become inappropriate. Here, we propose to use Kullback-Leibler Divergence(KLD) between the actual and reconstructed target scenes, which is detailed in [5].…”

“…If the gradient of a function is Lipschitz continuous with a constant L, gradient descent steps converges to a local optima by using constant step size that satisfies µ < 2/L [7], [8]. As shown in [5], normalized form of the non-linear objective function in (10) is Lipschitz continuous with L = 10 π 2 . In the presented results, step size is selected selected as µ i,l ≤ 0.01 < 2/L and decreases throughout the iterations, thus our selection of the step size is guaranteed to converge to a local minima.…”

“…More details about proposed technique is presented in [5]. For a general non-parametric case, a reconstruction algorithm and some performance bounds are provided in [6].…”

Design of CFAR radars using compressive sensing

“…However, much of the literature in CS techniques addressing localization of sparse targets (e.g. [9], [10], [11]) fails to explain how CS techniques affect parameters of interest to radar, specifically the probabilities of false alarm and detection.…”

Range-Doppler radar target detection using compressive sensing

“…SA yaklaşımının kullanıldıgı alanlardan birisi de radar hedef tespit sistemleridir. Radar hedef tespiti ve SA ile ilgili bazı araştırıl-malar yapılmıştır [5]. SA yaklaşımı, radar sinyal işlemede dogal olarak seyrek sinyalleri kullanıldıgından dolayı uygundur [6].…”