Abstract
There is a problem that complex operation which leads to a heavy calculation burden is required when the direction of arrival (DOA) of a sparse signal is estimated by using the array covariance matrix. The solution of the multiple measurement vectors (MMV) model is difficult. In this paper, a real-valued sparse DOA estimation algorithm based on the Khatri-Rao (KR) product called the L1-RVSKR is proposed. The proposed algorithm is based on the sparse representation of the array covariance matrix. The array covariance matrix is transformed to a real-valued matrix via a unitary transformation so that a real-valued sparse model is achieved. The real-valued sparse model is vectorized for transforming to a single measurement vector (SMV) model, and a new virtual overcomplete dictionary is constructed according to the KR product’s property. Finally, the sparse DOA estimation is solved by utilizing the idea of a sparse representation of array covariance vectors (SRACV). The simulation results demonstrate the superior performance and the low computational complexity of the proposed algorithm.
Highlights
The direction of arrival (DOA) estimation is an important area of research in array signal processing
We propose a real-valued sparse DOA estimation algorithm by using the KR
The array aperture is extended, and the estimation accuracy is improved by using the KR product
Summary
The direction of arrival (DOA) estimation is an important area of research in array signal processing. There are many DOA estimation algorithms with good performance, such as the multiple signal classification (MUSIC) algorithm, the estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm, etc. Introduces the idea of a sparse representation of array covariance vectors (SRACV) to propose a method called the L1 -SRACV algorithm for estimating sparse signals’ DOAs. Compared to L1 -SVD, the L1 -SRACV algorithm does not need to determine the regularization parameter and has a higher stability. Sensors 2016, 16, 693 sparse model based on the array covariance matrix is transformed to a real-valued sparse model via a unitary transformation so that the amount of calculation is reduced by at least four times.
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