Research On Efficient Direction-of-arrival Estimation Algorithms Based On Polynomial Rooting

The publication of the Multiple Signal Classification(MUSIC)algorithm has witnessed a revolution of Direction of Arrival(DOA)from the traditional algorithm to super-resolution.Though MUSIC algorithm is nearly perfect in theory,it is limited in practice because of the computational complexity of the spectral search process.The Root Multiple Signal Classification(Root-MUSIC)algorithm uses polynomial rooting instead of spectral search to reduce the complexity of DOA estimation.It has a better performance compared to MUSIC,but it only can be applied to Uniform Linear Array(ULA).The polynomial rooting super-resolution algorithms apply the thought of Root-MUSIC to arbitrary array,such as Array Interpolation(AI),Manifold Separation Technique(MST)and Fourier-Domain Root-MUSIC(FD-Root-MUSIC).Those algorithms are time-consuming because the constructed polynomials are complex and their dimensions are relatively high.Therefore,the research on efficient DOA estimation algorithms based on polynomial rooting is of great importance.The main contents of this paper and innovations are as follows:First,the mathematical model of DOA estimation,two classic super-resolution algorithms,MUSIC and Root-MUSIC,and polynomial rooting super-resolution algorithms are presented.The advantages and disadvantages of MUSIC and Root-MUSIC are pointed out.The polynomial rooting super-resolution algorithms use polynomial rooting to estimate the DOA.However the constructed polynomials' dimension is high,and the computation is huge,to ensure a certain degree of accuracy.It is of great practical significance to reduce the dimension of the polynomials or transformed the polynomials into real-valued.Next,a novel Reduced-Dimension Root-MUSIC(RD-Root-MUSIC)algorithm based on spectral factorization is proposed,in which the dimension of polynomial involved in the rooting step is efficiently reduced to half.A companion matrix whose eigenvalues correspond to the roots of the reduced-dimension polynomial is further constructed.Arnoldi iteration is finally used to calculate only the L largest eigenvalues containing DOA information,where L is the number of signals.Simulation results show that RD-Root-MUSIC has a similar performance to Root-MUSIC,with much lower complexity.The simulations are also given to show the influence of different parameters' selection on RD-Root-MUSIC.Finally,Real Coefficient MUSIC(RC-MUSIC)and Real Coefficient Root-MUSIC(RC-Root-MUSIC)are proposed,which are based on the correspondence between the derivative and primitive function and the mapping between the coordinate systems.The two algorithms both estimate the signal DOA through real coefficient polynomial rooting.Simulation results show that RC-MUSIC and RC-Root-MUSIC not only have a high accuracy,but also have a low complexity.Bairstow is used to work out the polynomials constructed by RC-MUSIC and RC-Root-MUSIC,which is an efficient algorithm in engineering applications for solving real coefficient polynomials.