Study On Sparse Super-resolutive Methods For Array-based Direction Of Arrival Estimation

In the spatial electromagnetic scenarios,the emitters distribute densely or move rapidly,and so many short-time and frequency-hopping and stealth signals appear.As the important part of the electronic reconnaissance and countermeasure,the field of radio direction finding and location faces the unprecedented difficulties and challenges.In this thesis,we study and perfect the theory of compressive sensing,then exploit it to present some sparse and super-resolution methods for array direction finding and tracking in the scenarios of low signal-to-noise ratio?SNR?and a few number of snapshots and moving targets.Firstly,we study the ?-RIP condition for ?₁-analysis sparse reconstruction.Aiming at the problem that the current ?-RIP condition for ?₁-analysis sparse reconstruction requires the strongly incoherent sensing matrix,we give a tight bound for ?-RIC,which relaxes the coherence condition of sensing matrix and guarantees the theoretical foundation for the application of ?₁-analysis sparse reconstruction.Secondly,we present the denoise method based on ?₁-analysis sparse reconstruction for the array receiving data in low SNR scenario.When the SNR is quit low,the performances of the traditional spatial spectrum estimation and sparse direction-of-arrival?DOA?estimation are unideal.The array manifold matrix was constructed as a redundant dictionary in which the array receiving signals were sparse through the appropriate spatial sparse division,and the corresponding sparse recovery model was established to reconstruct the array output data.It was proved that the manifold matrix was a tight frame and satisfied the condition which guaranteed accurate recovery of signals through sparse recovery so that it was reasonable enough to use sparsity optimization to reconstruct the array output data.The upper bound of reconstruction error was given.The effectiveness of this presented method for improving the performance of DOA estimation with low SNR were verified by the experiments.Thirdly,we propose two sparse DOA estimation methods based on signal subspace and signal structure information respectively.For almost all of the sparsity-based methods,the measurement domain is either the array output or the array covariance matrix.In this thesis,we propose a novel sparsity-based method for DOA estimation by exploiting the source signal subspace as the measurement domain.We present a sparse representation of the signal subspace and establish the sparse reconstruction model of the source powers,and finally a second-order cone programming is applied to formulate this problem.In order to exploit the spatial sparsity and the temporal correlation,we propose a new DOA estimation method based on block-sparse bayesian methodology and grid refined strategy.This grid refined strategy reduces the error of DOA estimation due to the off-grid effect of sources and mismatch of the sparse representation model.Fourthly,we propose two sparse continuous-field methods for DOA estimation.The performance of sparsity-based methods is limited by the off-grid effect of sources and mismatch of the sparse representation model.In order to overcome this problem,we propose a sparse continuous-field and super-resolution method using only single snapshot.Moreover,we provide the conditions that guarantee the exact DOA estimation using one snapshot,including the theoretical low-bound of the required number of sensors and the minimum angle-distance between two consecutive sources.On the other hand,a Sparse Continuous-field and Super-resolution Method?SCSM?is proposed without dircretization.SCSM estimates DOA in the continuous bearing-field by solving a semidefinite programming?SDP?using single or multiple snapshots,which connects the covariance fitting criterion with the sparsity of sources.Finaly,we propose a novel method to track the DOA of moving sources named as TvLSR?Tracking via Low-rank and Sparse Recovery?.Currently,the sparsity-based method for DOA tracking is rare.Exploiting the theory of redundancy compressive sensing,TvLSR reformulated DOA tracking as an optimization problem of recovering a lowrank matrix and a sparse matrix from a low-dimensional array observation data.A fast algorithm was proposed to recover these matrices.The DOA tracking was accomplished by finding the peaks of each column of the recovered signal-matrix.