Research On Array Signal Parameter Estimation Based On Co-Prime Sampling And Low Rank Constraint

Signal parameter estimation is an important research topic in array signal processing,which is widely used in many fields such as communications,radar,sonar,seismic exploration,and radio astronomy.The arrival of direction(DOA)and frequency of the space signal are two important characteristic information of the signal.This paper studies the DOA estimation method based on co-prime parallel array and the space-frequency parameter joint estimation method for wideband distributed source based on the space-time coprime sampling respectively,which provide theoretical basis and application reference for array signal parameter estimation technology based on co-prime sampling and low-rank matrix recovery.The main research contents of this thesis includes:1.The signal receiving model of narrow band point sources and the DOA estimation method based on uniform linear array are studied.Considering that the number of estimable signals in this method is limited by the number of physical sensors.We use the co-prime array structure and utilize high-order statistics of the received signal to improve the degree of freedom(DOF)of the array.The principle of DOA estimation for narrow band point sources based on the co-prime linear array is also studied.Through the simulation experiment of DOA estimation based on uniform linear array and co-prime linear array,the advantages of co-prime linear are illustrated.2.A new co-prime parallel array structure is proposed.Based on this array and using conjugate space-time extension technique,we propose an improved two-dimensional(2-D)DOA estimation method.The proposed array consists of a co-prime parallel array and two extra sensors placed along vertical axis,and the degree of freedom of the array is extended through two steps: Firstly,a symmetrical virtual parallel coprime array is constructed by computing the signal auto-correlation between the output of the co-prime parallel array and the sensors at vertical axis and the conjugate augmented technique.The virtual array is composed of two symmetric one-dimensional linear co-prime arrays arranged in parallel;Secondly,by vectorizing the signal covariance matrix corresponding to the virtual parallel coprime array,a one-dimensional virtual difference array is constructed.The one-dimensional virtual array contains the sum and difference array between the sub-arrays of the co-prime parallel array,which further expands the aperture and transforms the two-dimensional DOA estimation problem into a one-dimensional DOA estimation problem at the same time.In particular,in order to quantificationally evaluate and compare the DOF of the proposed array and the coprime parallel array,we derive the analytical formulas for the realizable number of continuous virtual array sensors and unique virtual array sensors of the resultant one-dimensional virtual arrays which are based on the co-prime parallel array and the proposed array,respectively.The simulation results verify that the proposed method has higher estimation accuracy and resolution.3.In order to realize the space-frequency joint distribution spectrum estimation of wideband distributed sources,the array signal receiving model of the wideband distributed sources with spatial-frequency joint distribution is derived firstly.Considering that sampling at uniform array and Nyquist rate in wideband array signals requires very high hardware and software consumption.We consider joint time and space co-prime sampling of the signal.We observe that the angular expansion and frequency spread of the wideband distributed signal reduce the sparseness of the source in the angular and frequency domains,which will reduce the performance of traditional sparsity-based reconstruction algorithms.However,we proved that the space-frequency joint distribution spectrum of wideband distributed source has lowrank characteristic,which is independent of the type of the space-frequency distribution and its spread.With this observation,we propose a space-frequency joint spectrum estimation method for wideband distributed source based on space-time joint co-prime sampler and low-rank constaint.The DOF of the estimation method based on space-time joint co-prime sampling and that of uniform sampling are analyzed and compared,and the quantitative analysis of DOF is given.The simulation experiments show that the space-time joint co-prime sampling and the low-rank matrix recovery algorithm are effective in the space-frequency joint estimation of wideband distributed sources.