Study about Improvement of Direction of Arrival (DoA) Estimation by Using Compressed Sensing Based on Covariance Matrix

The present paper describes a new method for the direction of arrival (DoA) estimation using sparse representation of covariance matrix is proposed by using a non-uniform linear array. A new vector will be derived by vectoring the covariance matrix of a non-uniform linear array. This vector is identical to the received vector of a large-scale virtual uniform linear array. The DoA of one source will be estimated because the covariance matrix of this vector is rank one. The spatial smoothing technique is one way to overcome this problem. In this method, the obtained array is divided into multiple sub-arrays and the covariance matrix of each sub-array will be estimated. Using the average of sub-arrays covariance matrix, a new full rank covariance matrix will be obtained. By quantizing the continuous angle space into a discrete set, DoA estimation can be modeled as a compressed sensing problem. The difference between the derived covariance matrix and its estimation will be used to estimate the DoA of sources. Due to the quantization of continuous angle space, the estimated DoAs has an inaccuracy. To improve the estimation accuracy, we propose a method. Simulation results show that the proposed method can improve the estimation accuracy. To increase the accuracy of estimation, it is necessary to divide the steps into a very small size. By dividing the steps by small size, there is a problem called coherence of the measurement matrix columns.