Direction Of Arrival Estimation Algorithm In Multipath Propagation

Array signal processing is a important branch of the modern signal processing, and its applications include radar, communication, sonar, radio astronomy and so on. The direction estimation technique for the incident signals is called DOA (direction of arrival) estimation, and has been widely developed over the past more than thirty years. In real environments, the scenario of multipath propagation is very common due to var-ious reflective surfaces, such as clouds, hills, buildings and some other man-made in-terference. Therefore, there are more and more researchers engage in the topic of DOA estimation, and hope to obtain more information to be directly used by military or civil-ian. High estimation accuracy, low computational complexity, few number of needed array sensors and robust DOA estimation algorithm is the goal of many researchers. In this paper, we study the DOA estimation algorithm in multipath propagation and propose some more superior and effective algorithms. The main contributions in this paper are illustrated as follows:Firstly, by modifying the structure of spatial difference matrix, we study and pro-pose two algorithms to overcome the rank deficient problem of difference smoothed matrix. The first algorithm uses the method of MUSIC (multiple signal classification) to estimate the DOAs of uncorrelated signals, and then a new matrix is constructed by squaring the spatial difference matrix to resolve the coherent signals. In the second algorithm, we propose a new method of modified TLS-ESPRIT (total least squares es-timation of signal parameters via rotation invariance techniques) to estimate the DOAs of uncorrelated signals. Afterwards, a new matrix is constructed by taking the absolute value of the eigenvalues of spatial difference matrix. Then the coherent signals can be resolved using the new matrix. The two algorithms are all supported by strict theoret-ical proof, and the simulations also show high DOA estimation accuracy. Moreover, since part of the power of coherent signals will also be eliminated when eliminating the uncorrelated signals in the operation of spatial difference, the DOA estimation per-formance of coherent signals will be restricted inevitably. With further research, we find that we can construct the array covariance matrix of uncorrelated signals after esti-mating the DOAs and power of uncorrelated signals. Then we can subtract it from the array covariance matrix to avoid this problem. In the follows, we propose an improved method of DOAM (DOA matrix), and this method can be applied in the mixed signal situations. The DOAs of uncorrelated signals are first estimated by our proposed crite-rion and the related eigenvalues of DOA matrix. Afterwards, with the eigenvectors of DOA matrix that related to coherent signals and the orthogonal projection technique, we can resolve the coherent signals. Since the signals in each coherent group can be re-solved separately, this algorithm needs fewer sensors than the existing algorithms that resolve all the coherent signals simultaneously.Second, in multipath environments, most of the existing DOA estimation algo-rithms pay no attention to the great information in fading coefficients. Then we study and propose two effective algorithms to estimate the fading coefficients in multipath propagation. The first method converts the estimation to a quadratic minimization problem, and then solves it by the method of Lagrange multipliers. The second method constructs a matrix, the null space of which is identical with the column space of the fading coefficient matrix. Then the fading coefficients can be calculated using the rela-tionship between the two spaces. From the simulations, the two algorithms are all with high estimation accuracy. Moreover, by utilizing the estimated DOAs and fading coef-ficients, their estimation accuracy can be further improved. In the follows, we combine the spatial difference technique and the matrix reconstruction technique together. The proposed algorithm constructs a new Toeplitz matrix by rearranging the elements in the spatial difference matrix, and then use it to estimate the DOAs of coherent signals. As the uncorrelated and coherent signals are resolved separately, this algorithm can largely reduce the number of needed array sensors. Furthermore, we study and propose an im-proved algorithm based on spatial difference and the matrix reconstruction technique. By modifying the structure of the above constructed Toeplitz matrices, the improved algorithm can utilize all the constructed Toeplitz matrices and improve the DOA esti-mation obviously. Afterwards, we deduce the CRB (Cramer-Rao lower bound) for the 1D (one dimension) DOA estimation in the scenario of multipath propagation. Then we give the CRB for the DOA estimation of uncorrelated and coherent signals, and the relative CRB of fading coefficients estimation, respectively.At last, we study the 2D (two-dimension) DOA estimation in multipath prop-agation. Firstly, we propose a new array configuration-Z shaped array, and a high resolution 2D DOA estimation algorithm based on DOAM and spatial difference technique. In this algorithm, we construct a DOA matrix, which is applicable to the 2D DOA estimation in the mixed signal situation. The DOAs of uncorrelated signals are estimated firstly using the nonzero eigenvalues and corresponding eigenvectors of the DOA matrix combined with our proposed criterion. Then we can utilize the spatial difference matrix and smoothing technique that based on submatrices to construct a new DOA matrix to resolve the coherent signals. As this algorithm does not need 2D spatial spectrum calculation and peak searching, it has low computational complexity. Moreover, it does not need the pair matching of the estimated 2D DOAs, and the Z shaped array can save more sensors than the uniform plane array. In the follows, we combine the spatial difference technique and the matrix reconstruction technique together, and apply them to the 2D DOA estimation in multipath propagation. The proposed algorithm uses a new method of modified TLS-ESPRIT to estimate the DOAs of uncorrelated signals, and then construct a new Toeplitz matrix by rearranging the elements in spatial difference matrix. Using the product of the Toeplitz matrix and its conjugate transpose matrix, the remaining coherent signals can be resolved. Similarly, this algorithm does not need 2D spatial spectrum calculation and peak searching, so it also has low computational complexity. In the end, we deduce the CRB for the 2D DOA estimation in the scenario of multipath propagation. Then we give the CRB for the DOA estimation of uncorrelated and coherent signals, and the relative CRB of fading coefficients estimation, respectively.