Research On DOA Estimation Methods Based On Sparse Representation

Direction-of-arrival(DOA)estimation is a very important research direction of array signal processing,in particular it has been widely used in many fields of radar,sonar,remote sensing,communications,etc.Although traditional DOA estimation methods based on subspace can achieve high accuracy and super-resolution capability,but these methods also have many limitations and shortcomings,for example,they usually require a lot of snapshots,precisely known the number of sources,pre-processing of decoherence for coherent signals and their estimation error is large under low signal-to-noise ratio(SNR)condition,and so on.However,with the development and improvement of the compressed sensing(CS)theory and sparse representation(SR)theory,it provides people with a new perspective to look at the DOA estimation problem — to transform the DOA estimation problem into a problem of sparse representation.Compared with the traditional subspace methods,DOA estimation based on sparse representation has the angle super-resolution ability,does not require a lot of snapshots to estimate the covariance matrix of array signal,and the estimation performance will not be affected by the coherence of signals.Therefore the class method provides a new way to solve the problems of the traditional methods.In the dissertation,DOA estimation problem is discussed and researched from the perspective of sparse representation.One-dimensional(1-D)and twodimensional(2-D)DOA estimation methods for narrow-band signals and 1-D DOA estimation methods for wideband signals were researched respectively.The main research results of this dissertation can be summarized as follows:Firstly,a single-snapshot DOA estimation method based on sparse representation in pulse compression system is proposed in order to solve the problem that the target DOA can not be effectively estimated due to too much targets in the pulse compression radar system.DOA estimation in pulse compression radar systems exist in the problem in which the SNR before pulse compression is very low due to no coherent accumulation and the number of signals can be estimated is limited by the number of array sensors,whereas the snapshots available after pulse compression are few even single snapshot,and the correlation of echo signals in the same range cell is very strong even coherent.To solve this problem,a single-snapshot DOA estimation method is proposed based on sparse representation.This method allows DOA estimation being performed after pulse compression,so not only SNR but also the number of signals can be estimated will be greatly enhanced.In theory,the maximum number of signals can be estimated in each range cell is the number of array elements minus one.Simulation analysis and measured data processing show that the proposed method is better than the traditional MUSIC method in the estimation accuracy and the angle resolution,especially under the condition of low SNR and small angle difference.Secondly,based on the idea of dimension reduction estimation,a 2-D DOA estimation method is proposed based on a pair-matching algorithm of spatial spectrum reconstruction of sub-dictionary,in order to solve the problem of high computational complexity and pairing failure.Currently DOA estimation methods based on sparse representation are mostly for uniform linear array(ULA),which can only estimate the one-dimensional orientation angle,whereas for two-dimensional array such as planar array,etc.,this class DOA estimation methods are very few.One of the main reasons is the complexity of sparse reconstruction algorithm is too high caused by the dimension of dredundant dictionary is too large in 2-D DOA estimation based on direct sparse representation.To solve the problem of high complexity,we decouple the relationship between the two-dimensional DOA,so that the construction of the redundant dictionary of two-dimensional DOA will be transformed into the construction of redundancy dictionary of one-dimensional DOA,which will greatly reduce the complexity of the sparse reconstruction algorithm and provides the premise for practical algorithm.Aiming at the problem of angle matching brought by dimension reduction processing,a pair-matching algorithm is proposed based on spatial spectrum reconstruction of sub-dictionary,which can improve the pairing probability of success and estimation accuracy,especially in the case of similar power signals.Theoretical analysis and simulation results show that this method not only can greatly reduce the computational complexity of the algorithm,and has better estimation performance compared with the traditional methods,especially under the condition of low SNR and small angle difference,its advantages are more obvious.Finally,the DOA estimation of wideband signal is studied.By using matched filter and FRFT transform respectively,two new DOA estimation methods for wideband signals are proposed,at the same time,a off-grid DOA estimation method via alternating descent iteration is proposed based on modified fractional domain sparse model in order to resolve the grid mismatch problem.Aiming at the problem that traditional DOA estimation methods can cannot work when the number of received signals is more than the number of array elements,a regularized FOCUSS method based on matched filtering and sparse representation is proposed under the condition of known signal information a priori,and in this method the DOA estimation model is constructed in time domain by the filtered signal and the array manifold matrix is only related to the center frequency of the wideband signal,but not related to the other frequencies.Aiming at the problem that there are the cross-term interference and time-frequency selection in DOA estimation based on time-frequency analysis,a regularized FOCUSS method based on fractional domain sparse model is proposed,where both the DOA estimation model and the new array manifold matrix are constructed in fractional domain.Both of these two methods can improve signal-to-noise ratio and signal-to interference ratio,thus improving the performance of the DOA estimation,while also increasing the number of signals that can be estimated.The simulation results show that the two methods can deal with both coherent and non-coherent wideband signals,and have better estimation accuracy and angle resolution,especially in low SNR condition.In addition,in order to solve the problem of grid mismatch,a novel off-grid DOA estimation method via alternating descent iteration is proposed based on modified fractional domain sparse model,which compensates for the mismatched grid error by alternating descending iterations.The simulation results show that the proposed method has better estimation accuracy and angular resolution,and also has the advantage of being less sensitive to the size of the grid.