Elsevier

Signal Processing

Volume 122, May 2016, Pages 87-92
Signal Processing

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Improved MUSIC algorithm for high resolution angle estimation

https://doi.org/10.1016/j.sigpro.2015.12.002Get rights and content

Highlights

  • A set of spatial temporal correlation matrices are constructed.

  • A uniform expression is established by the above matrices.

  • A cyclic optimization algorithm is designed to calculate the signal subspace.

  • Proposed algorithm possesses better subspace accuracy and RMSE than the MUSIC.

  • Proposed algorithm has a higher resolution compared with the MUSIC algorithm.

Abstract

By using a single correlation matrix, classic MUSIC algorithm estimates subspaces through traditional eigenvalue decomposition. Its performances suffered from these inaccurate subspaces greatly. In this paper, a set of spatial temporal correlation matrices are firstly constructed by exploiting the array received data. Secondly, in order to get more accurate subspace, we establish a uniform cost function that exploits these matrices. Thirdly, a cyclic optimization algorithm is designed to jointly estimate the signal subspace. Moreover, by the relation between signal and noise subspace, the corresponding projection matrix of noise subspace is obtained, hence an improved MUSIC algorithm is implemented by this projection matrix. Finally three experiments are conducted to validate the performances of the proposed algorithm.

Introduction

MUltiple SIgnal Classification (MUSIC) algorithm [1] is a well-known high resolution direction of arrival (DOA) estimation method. Its performances mainly depend on the accuracy of estimated subspace [2]. However, the subspace in classic MUSIC is obtained by the traditional eigenvalue decomposition of the single zero delay correlation matrix. Such a subspace will dramatically decline [3] the performances of MUSIC in some cases. One is the signal to noise ratio (SNR) lower than 0 dB, which makes the signal and noise subspace be difficultly distinguished. Therefore, an incorrect subspace is obtained. Another case is in small snapshots, an imprecise correlation matrix is derived, and its eigvalue decomposition estimates a coarse subspace. Both critically limit the performances [4] of MUSIC algorithm.

This paper sufficiently utilizes the spatial temporal domain information. By exploiting two subarrays and their multiple delay received data, a set of spatial temporal correlation matrices are constructed. These matrices are written into a uniform expression for establishing a cost function. A novel cyclic optimization algorithm is proposed to jointly estimate the signal subspace. Then the projection matrix of noise subspace is obtained, from which the improved MUSIC algorithm is proposed. All these are the main contributions of this paper.

In the simulations, the accuracy of estimated subspace by the proposed cyclic optimization is compared with the traditional eigenvalue decomposition. Then the spatial spectrums of the improved MUSIC and the classical MUSIC are also simulated to demonstrate the improvement of the resolution. The root mean square error (RMSE) of estimated angle is also presented. Each of the performance is analyzed versus SNR, snapshots and the number of sensors. Simulations show that the proposed algorithm possesses better performances than classic MUSIC algorithm in the same scenarios.

Section snippets

Problem formulation

Consider a uniform linear array (ULA) composed of M (m=1,2,,M) sensors on which P narrow band noncoherent far field signals are impinging with different DOAs. The signal arriving at the mth sensor isxm(t)=p=1Pampsp(t)+nm(t)where amp=exp[j(2π/λ)(m1)dsinθp], d is the spacing between adjacent sensor elements, λ is the wavelength and θp is the DOA relative to the array broadside. The array output at tth snapshot can be expressed asx(t)=[x1(t),x2(t),,xM(t)]T=As(t)+n(t)where T represents the

Improved MUSIC algorithm

In the proposed algorithm, we separate the above mentioned ULA into two subarrays. Let the first and second subarrays be composed of the sensors with the indices 1,2,,M1 and 2,3,,M, respectively. The received signal vector of the first and second subarray can be written asx1(t)=A1(θ)s(t)+n1(t)x2(t)=A2(θ)s(t)+n2(t)=A1(θ)Φs(t)+n2(t)where A2=A1Φ, Φ=diag[exp(jω1),exp(jω2),,exp(jωP)], ωp=2πd(sinθp)/λ. Let Rs(k) represent the sample correlation matrix of the source signal vector which is given byE

Simulation results

In this section, simulations are presented to illustrate the performances of the improved MUSIC algorithm. A uniform linear array is used and two narrow band noncoherent far field signals come from θ1=-3o and θ2=3o. K in Eq. (10) is set to be 4, i.e. 20 spatial temporal correlation matrices are constructed. Except the performance simulations versus sensor number, we fixed the sensor number in other experiments to be 13. Experiments 1 and 2 have been averaged over 100 Monte Carlo runs. And

Conclusions

In this paper, a cyclic optimization algorithm is proposed to calculate the signal subspace, the corresponding projection matrix of noise subspace is deduced, and an improved MUSIC algorithm is proposed. Experimental results show that the cyclic optimization algorithm can increase the accuracy of estimated signal subspace. The improved MUSIC algorithm has stronger ability to distinguish the closely set sources, and can obtain higher spatial spectrum peaks compared with the conventional MUSIC in

Acknowledgments

The authors would like to thank very much the Handling Editor Dr Ana Isabel Perez-Neira, Editor Chitra and the anonymous reviewers for their valuable comments and suggestions that have significantly improved the manuscript.

This work was supported by the National Natural Science Foundation of China under Grants 61373177 and 61271293; the Scientific Research Plan of Education Department of Shaanxi Province (11JK0903).

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