Research On Algorithms Of Spatial Spectrum Estimation Based On Sparse Signal Reconstruction

Spatial spectrum estimation has been a topic having important applications in thearray signal processing fields. Since recent years, sparse signal reconstruction andcompressed sensing have obtained wide attention of signal processing community. Byutilizing the sparseness or compressive characters of signals, they can achieve signalreconstruction or approximation with requiring only a small amount of observation dataand hence has also applicability of superresolution. The spatial sparseness of targets orsources makes it possible that sparse signal reconstruction and compressed sensing canbe applied to the superresolution spatial spectrum estimation. Since the sparse signalreconstruction algorithms can still obtain more accurate estimates of spatial angles inthe case of small samples, low signal-to-noise ratio and high correlations of sources, theapplication of sparse signal reconstruction to spatial spectrum estimation has drawnmore and more interests in the array signal processing fields. This dissertation discussesthe spatial spectrum estimation problem from this new view of sparse signalreconstruction, with emphasis on spectrum estimation algorithms based on sparse signalreconstruction. The main research results include the followings:1. A fast orthogonal matching pursuit algorithm for2D angle estimation in aMIMO radar is proposed. When the orthogonal matching pursuit algorithm in thecontext of sparse signal reconstruction is applied to the2D angle estimation in MIMOradar, the corresponding2D sparse signal reconstruction problem is required to betranslated into a1D sparse signal reconstruction problem. However, this way seems notefficient. Utilizing the projections of a2D sparse signal onto its each dimension usuallyare also sparse, this dissertation improves the atom search process in the orthogonalmatching pursuit algorithm then obtains a fast algorithm for2D sparse signal. Theproposed algorithm is applied not only to the2D angle estimation in MIMO radar, butalso to other2D sparse signal models in which the corresponding dictionary can bedecomposed into the Kronecker product of two sub-dictionaries. This algorithm canachieve performance approximating to the orthogonal matching pursuit algorithm withsignificantly lower computational complexity.2. An ESPRIT matching pursuit algorithm utilizing the information provided bythe signal subspace is proposed. In the case of single snapshot, the performance ofclassical subspace-based direction-of-arrival (DOA) estimation algorithms and theorthogonal matching pursuit algorithm are compared. At high signal-to noise ratios, thesubspace-based ESPRIT algorithm and MUSIC algorithm can obtain finer DOA estimates than the orthogonal matching pursuit algorithm, even with a reduced effectiveaperture due to a spatial smoothing process required by them. This dissertation embedsthe ESPRIT algorithm into the iteration process of orthogonal matching pursuitalgorithm and proposes a novel ESPRIT matching pursuit algorithm. The proposedalgorithm can improve both the performance of the ESPRIT algorithm at lowsignal-to-noise ratios and the orthogonal matching pursuit algorithm at highsignal-to-noise ratios and simultaneously has advantages of both the algorithms atdifferent signal-to-noise ratios. Additionally, skipping the process of atom correlationsearch in the presented ESPRIT matching pursuit algorithm and selecting only theatoms provided by ESPRIT algorithm in each iteration, a simplified version can beobtained. It can effectively reduce the computation complexity of the ESPRIT matchingpursuit algorithm and still obtain a performance improvement compared to the ESPRITalgorithm.3. A multiple dictionaries sparse Bayesian learning algorithm which can beapplied to wideband DOA estimation is proposed. For the DOA estimation of widebandsources, among classical signal subspace based algorithms, algorithms of incoherentprocessing can not applied to resolve conherent sources while coherent signal subspacebased algorithms can work even in the case of coherent wideband sources, but theyrequire pre-estimates of DOA for focusing processing hence are significantly sensitiveto the accuracy of these pre-estimates of DOA. When consider the sparse Bayesianlearning algorithm, an algorithm which has good performance and has nouser-parameters, it can be applied only to the narrawband DOA estimation. Forwideband sources, it no longer can be applied. Considering the DOA estimation ofwideband sources, this dissertation jointly exploits the common sparse pattern ofmultiple sub-bands, and derives a multiple dictionaries sparse Bayesian learningalgorithm. Simulation results indicates that compared with classical subspace-basedwideband DOA estimation methods, this algorithm can still achieve better DOAestimation performance in the case of low signal-to-noise ratios, high correlations ofsources and small samples. Besides that, unlike the coherent signal subspace algorithm,this algorithm has no requirement of pre-estimation of angles and focusing translation,and at the same time, it is insensitive to estimates of source number. All of this make ithave a robust performance.