Fast Subspace and DOA Estimation Method for the Case of High-Dimensional and Small Samples

Abstract

It is well-known that classical direction of arrival (DOA) estimation methods work well in the case of large samples. However, these methods may be theoretically invalid in the case of small samples, which frequently occur in large array systems. Such a large array has two effects: i) The number of samples is relatively quite small, and ii) the dimension of samples is very large. To handle the above problems, a more appropriate method for solving DOA estimators in the case of high-dimensional and small samples is proposed in this paper. First, considering the special structure of received samples, an alternative well-estimated second-order statistic, known as the Gram matrix, is originally constructed to better utilize the spatial and statistical information of signals and noise contained by small samples. Second, two novel methods for estimating the number of targets are derived by combining the Gram matrix and information-theoretic criteria. Third, a novel object function and the corresponding algorithm based on the Gram matrix are designed to estimate the signal subspace more efficiently, and then the DOAs of targets are obtained by multiple signal classification methods. In particular, the theoretical analysis indicates that the improved signal subspace estimation algorithm only needs to decompose the low-dimensional Gram matrix instead of the high-dimensional sample covariance matrix. Finally, simulation results are provided to demonstrate the high accuracy and lower computational complexity of the proposed methods in the case of high-dimensional and small samples.