Study On Fast Algorithm For Super-resolution DOA Estimation

In array signal processing, the fundamental task is to construct the efficient filter for spatial signals and exacting information by a sensor array which is distributed in space. Direction-of-arrival(DOA) estimation which is an integral part of array signal processing has attracted widespread attention around the world. With the development of science and technology, it is desired to increase the aperture of the antenna array to improve the performance. However, traditional estimation algorithms usually cannot meet the actual application requirements due to its enormous computational complexity. Therefore, more and more domestic and foreign researchers have investigated the low-complexity and/or robust DOA estimation algorithms. In this paper, two efficient DOA estimation methods have been proposed from perspective of low-complexity and high estimation accuracy.The traditional DOA estimators require an estimate of the covariance matrix and perform its eigenvalue decomposition(EVD) to obtain the signal or noise subspace. As the ML estimate of the covariance matrix, the sample covariance matrix(SCM) is usually employed for this task. The total computational complexity is around 2 3(M N +M) with M and N being the number of sensors and snapshots, respectively. Obviously, when the number of sensors is large, the complexity will be proportional to M. To solve this problem, we have proposed a low-complexity DOA estimation algorithm in Chapter. 4. Unlike the conventional subspace based methods, the proposed scheme only needs to calculate two sub-matrices of the sample covariance matrix, that is, 11K′KR? and()21M -K ′KR?, avoiding its complete computation. Here, K is a user-definite parameter and satisfies ￡K ￡min{M, NP} with P being the number of source signals. Meanwhile, a Nystr?m-based approach is utilized to correctly compute the signal subspace which only requires 2(MK) flops. Thus, the proposed method is computationally advantageous, particularly when K M. Furthermore, we derive the asymptotic variances of the estimated DOAs.In order to further reduce the complexity and improve the accuracy of DOA estimation algorithm, we have proposed a low-complexity unitary ESPRIT algorithm which is based on the Nystr?m method. First of all, we transform the complex sample data into real-valued data by a unitary transformation. Secondly, we construct the signal subspace of the real-valued data by the Nystr?m method and use this signal subspace to derive a low-complexity unitary ESPRIT algorithm. It should be demonstrated that in this algorithm, all the matrix operations are in the real number field, so the complexity is much smaller than the complex ESPRIT algorithm. Furthermore, the process of building the real-valued submatrices 11 R and 21 R is equivalent to the forward and backward smoothing method, thus the proposed unitary ESPRIT can also handle the problem of coherent sources. Numerical results are included to demonstrate the efficiency of the DOA estimator.