Underdetermined Direction Of Arrival Estimation Based On Co-prime Array

Due to its outstanding advantage in enhancing the degree of freedom(DOF),co-prime array(CPA)has been a research hotspot in the field of underdetermined direction of arrival(DOA)estimation since it was proposed in 2010.Over several years,optimization of array configuration and elevation of the number of signals that can be estimated have been two of the most important topics for CPA.To provide a theoretical basis for one-dimensional(1-D)and two-dimensional(2-D)underdetermined DOA estimation,this paper aims to enhance the DOF of CPA in terms of two aspects of developments including array configuration and co-prime algorithm.The primary contributions of this work are as follows:(1)For the problem of 1-D underdetermined DOA estimation,in-depth analysis and comprehensive comparison are made to reveal the phenomenon that holes can result in delay waste,which is further found out as a common problem for conventional CPA and state-of-the-art modifications.To solve such a problem,a novel 1-D successive CPA(S-CPA)without holes based on a triple nesting technique(TNT)using four sub-arrays is proposed.Exploiting the fourth-order cross difference set of the S-CPA,a virtual linear array with equivalent signal model for DOA estimation at hand is obtained accordingly.Moreover,by analyzing the computation details of its cross fourth-order difference set,the optimal configuration of the S-CPA is derived,based on which all the holes in the virtual linear array can be filled without delay waste.A theoretical expression is also provided to predict the DOF of the S-CPA,and numerical simulations are conducted to demonstrate the performances of the proposed S-CPA.It is shown that S-CPA is able to eliminate all the holes thoroughly and enhance the DOF significantly.Compared with state-of-the-art CPAs,the proposed S-CPA also provides improvements on higher accuracy,fewer physical sensors and smaller array aperture.(2)To address the problem of more practical 2-D underdetermined DOA estimation,L-shaped CPA(L-CPA)with much fewer physical sensors than rectangular CPA is considered.Firstly,the basic theory of L-CPA enhancing its DOF by the virtual cross array constructed from second-order difference set is analyzed.Inspired by this,a new fourth-order L-CPA(4th-L-CPA)algorithm exploiting again the second-order difference set between the two virtual cross sub-arrays of the original L-CPA is presented.Compared with state-of-the-art methods with virtual cross array,the proposed technique obtains virtual rectangular array with significantly enhanced DOF.Secondly,the manifold of the virtual rectangular array is derived and available signal model based on the proposed 4th-L-CPA is constructed for DOA estimation.Finally,numerical simulations are conducted to evaluate the performance of the proposed algorithm,which demonstrate that 4th-L-CPA is able to enhance the DOF significantly.In addition,the proposed approach also shows advantages in many aspects including comparable accuracy,fewer physical sensors and smaller array aperture than L-CPA and other plane CPAs...