Study On Fast Algorithm For Super-resolution Doa Estimation

In array signal processing, the fundamental task is to construct the effientfilter for spatial signals and exacting information by a sensor array which isdistributed in space. Direction-of-arrival （DOA） estimation which is an integralpart of array signal processing has attracted widespread attention around theworld. With the development of science and technology, it is desired to increasethe aperture of the antenna array to improvie the performance. However,traditional estimation algorithms usually cannot meet the actual applicationrequirements due to its enormous computational complexity. Therefore, more andmore domestic and foreign researchers have investigated the low-complexityand/or robust DOA estimation algorithms. In this paper, two efficient DOAestiamtion methods have been proposed from perspective of low-complexity andhigh estimation accuracy.The traditional DOA estimators require an estimate of the covariance matrixand perform its eigenvalue decomposition （EVD） to obtain the signal or noisesubspace. As the ML estimate of the covariance matrix, the sample covariancematrix （SCM） is ususally employed for this task. The total computationalcomplexity is around（M²N+M³）with M and N being the number ofsensors and snapshots, respectively. Obviously, when the number of sensors islarge, the complexity will be proportional to. To solve this problem, we haveproposed a low-complexity DOA estimation algorithm in Chapter.4. Unlike theconventional subspace based methods, the proposed scheme only needs tocalculate two sub-matrices of the sample covariance matrix, that is,R₁₁∈（?）^K×KandR₂₁∈（?）^M-K×K, avoiding its complete computation. Here, K is auser-definite parameter and satisfies P≦K≦min{M,N}with P being thenumber of source signals. Meanwhile, a Nystr m-based approach is utilized tocorrectly compute the signal subspace which only requires（?）（MK²）flops. Thus,the proposed method is computationally advantageous, particularly whenK＜M. Furthermore, we derive the asymptotic variances of the estimatedDOAs.In order to further reduce the complexity and improve the accuracy of DOAestimation algorithm, we have proposed a low-complexity unitary ESPRITalsorithm 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 methodand use this signal subspace to derive a low-complexity unitary ESPRITalgorithm. It should be demonstrated that in this algorithm, all the matrixoperations are in the real number field, so the complexity is much smaller thanthe complex ESPRIT algorithm. Furthermore, the process of building thereal-valued submatrices（?）₁₁and（?）₂₁is equivalent to the forward andbackword smoothing method, thus the proposed unitary ESPRIT can also handlethe problem of coherent sources. Numerical results are included to demonstratethe efficiency of the DOA estimator.