Study On Algorithms For Spatial Signal Detection And Parameters Estimation

The estimation of signal parameters is an important research field of modern signal processing. It finds wide applications in many fields, such as radar, communications, sonar, seismology, radio astronomy, biomedicine engineering, etc. So, its study is of great theoretical and practical value. This dissertation aims at the development of high-resolution and robust parameters estimation methods, involving direction-of-arrival (DOA), frequency and range in different practical environments, and then verifies these methods by computer simulations. The main work can be summarized as follows:1. In the case of spatially uncorrelated signals while the signals have temporally relations (or the length of correlation time of signals is larger than that of noise), a novel multistage decomposition and reconstruction approach for estimation of DOA in unknown correlated noise fields is proposed. Based on the biorthogonality between a matrix and its Moore-Penrose pseudo inverse, the proposed method makes no assumptions on the spatial covariance matrix of the noise. It exploits the structural information of a set of spatio-temporal correlation matrices, and gives a robust and precise estimation of signal subspace to obtain the DOA estimation with high accuracy. Theoretic analysis and computer simulation results show the efficiency of the proposed algorithm.2. In Chapter 3, we develop a generalized version of the multistage decomposition and reconstruction algorithm proposed in Chapter 2. The convergence of the proposed algorithm is proven by use of the idea of cyclic minimization, and its applications to two-dimensional (2-D) frequency estimation and harmonic retrieval are discussed. On one hand, for 2-D frequency estimation, we construct an interesting cost function and present a novel iterative algorithm by use of the biorthogonality of matrices and rotational invariance property. The algorithm obtains one 2-D frequency component at each stage. Therefore, the proposed algorithm can pair the 2-D frequencies automatically. Moreover, all the columns of the frequency matrices can be obtained by systematic multistage decomposition and multistage reconstruction. On the other hand,for harmonic retrieval, we define a novel efficient cost function based on the structural information of a set of correlation matrices, and apply the multistage algorithm to find all the frequency components. Simulation results are provided to show the good performance and efficiency of the proposed algorithm.3. Based on the property of non-circular sources and information theoretic criteria, a modified algorithm for the determination of the number of non-circular signals is proposed. The complex-valued operations can be converted into real-valued operations by use of unitary transformation, which decreases the computational complexity to a great extent. Computer simulation results show that the detection performance of the proposed algorithm is much better than that of the conventional algorithms. Secondly, we exploit the feature of non-circular sources and convert the received data matrix of array into a real-valued one. Then a real-valued root-MUSIC-type DOA estimation algorithm is presented, which has much lower computational complexity than the conventional algorithms. Simulation results are provided to verify the performance of the proposed algorithm.4. Based on higher-order cumulant of the received data of array, we discuss theproblem of joint parameter estimation of near-field signal sources. In the case of carrierfrequency is known, two matrix pencils are elaborately constructed. The phases of thegeneralized eigenvalues of these two matrix pencils give the estimation of DOA andrange, while their amplitudes can automatically pair among parameters. Withoutspectral peak searching and pairing procedure, the proposed algorithm givesclosed-form solutions to the parameters. Furthermore, in order to improve theestimation performance, we present a new algorithm to jointly parameters estimation.Firstly, a whiten matrix is constructed by second order statistics, and then the arraysteering matrix is estimated by use of jointly diagonalization of the array cumulantmatrices, which exploits the structural information of the higher order statistics matrices.Thus the DOA and range can be estimated from the array steering vectorssimultaneously. Compared with the higher-order ESPRIT method, the new algorithmcan improve the efficiency of elements. In addition, it does not need any operation ofparameters pairing. In the case of carrier frequency is unknown, a new algorithm forjointly estimate frequency, DOA and range of near field sources is presented. Weconstruct three matrix pencils. The phases of the generalized eigenvalues of thesematrix pencils give the estimates of frequency, DOA and range, while their amplitudescan automatically pair the three dimensional parameters. Without spectral peak searching and pairing among parameters, the proposed algorithm gives closed-form solutions to the three dimensional parameters. The effectiveness of these algorithms is verified by computer simulation results.