Study On Large Scale Array Adaptive Signal Processing Under Small Sample Support

In the past several decades, array signal processing has been widely used in many application areas such as radar, sonar, wireless communication, microphone array speech processing, medical imaging and so on. Firstly, to obtain higher resolution and better interference suppressing capability, the element number of the modern antenna array are quickly increasing, which causes the computation loads of many conventional adaptive processing methods too heavy for real-time processing. Secondly, due to limitation of the exterior environment and the technics of hardware, the number of training samples for adaptive processing does not increase synchronously. In order to handle the high-dimension small sample support problem for large-scale array, we study the three important areas of array processing (direction of arrival estimation, adaptive beamforming and space-time adaptive processing) from two aspects:improving the convergence rate and reducing the computational complexity. The main contribution and significant results are summarized as follows.1. Using the spatial sparsity of the source signals, we propose two direction of arrival (DOA) estimation methods based on the sparse representation of multiple measurement vectors (MMV). The first method estimates the signal subspace by stacking the left singular eigenvectors of samples matrix corresponding to the big singular eigenvalues and computes the DOA of the signals by ultilizing the proposed re-weighted iterative minimum variance (RIMV) method to sparsely represent the signal subspace. In the second method, we improve the sparse representation model of the covariance matrix and propose a new DOA estiamation method. Without the prior-knowledge about the noise level, the proposed method only utilizes partial information of the covariance matrix for the DOA estimation and provides robustness to noise level at the cost of an element aperture loss. Furthemore, the proposed methods can effectively distinguish the coherent signals without decorrelation processing.2. By analyzing the construction of the optimal adaptive beamforming weight, we find that the optimal adaptive weight only lies in a low-dimension subspace composed of the desired signal steering vector and the interferences subspace. Experientially speaking, the number of interferences designed to suppress is much smaller than that of the array sensors. Consequently, once the interference-plus-signal subspace (IPSS) is obtained, only a low-dimension combination vector is needed to compute, which will lead to a reduction of the computational complexity. First, we construct a complete IPSS.And then the sparse constraint is imposed on the combination vector to select the least number of column vectors of the complete IPSS to form the adaptive weight. Comparing with the conventional reduce-rank methods, the proposed method requires no prior-knowledge on the number of interferences and is robust to many common mismatches.3. One of the key problems of space-time adaptive processing (STAP) is how to estimate the clutter covariance matrix (CCM) accurately with small samples when the clutter environment is heterogeneous. By using the sparsity characteristic of the clutter spectrum, the CCM estimation methods based on sparse representation (CCM-SR) can estimate the clutter spectrum and yield an good estimation of the CCM. The CCM-SR can achieve a good estimation performance with only one or a few samples, which significantly improves the convergence rate of the STAP. However, there are often many pseudo-peaks in the clutter spectrum estimated by the sparse representation (SR), which will cause a CCM estimation error. By exploiting the special relationship of clutter ridge curve between space domain and Doppler domain, we can eliminate the pseudo-peaks in clutter spectrum effectively via fitting the curve of clutter ridge and improve the estimation accuracy of the CCM. In addition, a byproduct of our method is the estimation of the flying parameters (the velocity of the radar platform, the crab angle and so on).4. To reduce the heavy computational load of the conventional STAP, a fast Space-Time Adaptive Processing (STAP) algorithm based on low-rank approximation of the weight matrix is proposed. Unlike the traditional Low-Rank Approximation (LRA) algorithm for STAP, the weight matrix is reconstructed so that the numbers of its columns and rows are the same or close to each other by utilizing the special Kronecker property of the space-time steering vector. By using the LRA method to approximate the adaptive weight matrix, the original quadratic optimal problem is convertered into a bi-quadratic optimal problem which can be solved by bi-iterative method.5. Although the conventional reduce-dimension/reduce-rank methods can significantly improve the convergence rate and reduce the computation load, the adaptive weight for each direction and Doppler needs to be recomputed. For small sample support problem, the adaptive weight vector is formulated as a linear combination of the training sample vectors plus the desired signal steering vector, based on the fact that the optimal adaptive weight completely depends on signal-plus-interference (ground clutter) subspace and the training samples are mainly composed by interference. Therefore, we only need to compute a lower dimension combination vector instead of the fully adaptive weight vector. Moreover, our method saves significantly computation load by avoiding the inversion of high-dimension sample covariance matrix (SCM). When the number of samples is greater than the degree of freedom (DOF) of the interference subspace, three well-known regularization methods are used to find a stable solution, since the excessive large variation of the combination vector can be caused by the ill-conditioned Gram matrix.