DOA Estimation Algorithm Based on Compressed-Sensing
A novel kind of method using in the DOA estimate of array signal processing is proposed. This method is based on constructing matrix with random selection of the rows of DFT transformation matrix. Such matrix satisfies the RIP condition (restricted isomet
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DOA Estimation Algorithm Based on Compressed-Sensing Yao Luo and Qun Wan
Abstract A novel kind of method using in the DOA estimate of array signal processing is proposed. This method is based on constructing matrix with random selection of the rows of DFT transformation matrix. Such matrix satisfies the RIP condition (restricted isometry property). Due to the sparsity of space signal, the amount of array sensor is reduced significantly, which results in a lower complexity of the array system. SVD decomposition is used in processing the sampling signal to minimize its dimension and the final performance is much better than traditional algorithms. Keywords Compressed sensing • DOA estimation • SVD decomposition
46.1
Introduction
Compressed Sensing (CS) is a novel theory which has been widely used in many areas. It shows that sampling rate of one system can be significantly reduced if observed signal satisfy some the sparsity condition [1] and reconstruction of original signal will be exactly the same. Estimation of direction-of-arrival (DOA) is an important area in array signal processing. Traditional algorithms aiming in solving this problem include multiple classification method (MUSIC) and minimum variance distortionless response (MVDR), etc. But both of them perform unsatisfactory when SNR < 0. In many cases, sources accounted for only a few angular resolution units, which makes the targets’ distribution in space sparse and satisfies the requirement of sparsity in CS and makes the reconstruction feasible. In this chaper, we set the array antenna randomly in a direct line, which uses much fewer antennas comparing
Y. Luo (*) • Q. Wan School of Electronic Engineering, UESTC, Cheng Du 611731, China e-mail: [email protected] Q. Liang et al. (eds.), Communications, Signal Processing, and Systems, Lecture Notes in Electrical Engineering 202, DOI 10.1007/978-1-4614-5803-6_46, # Springer Science+Business Media New York 2012
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to the uniform linear array (ULA) and makes the corresponding matrix satisfy RIP condition [2] as well. SVD singular value decomposition is used to reduce dimensions of receiving signal. M-FOCUSS algorithm is used to reconstruct receiving signal and simulation comparing with traditional methods are given.
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The Model of Compressed Sensing
The problems of sparse signal computations appear in many applications. A signal is a sparse one if most values of entries are almost zero, or in some cases equal to zero. For signals that are not sparse enough on some certain basis, transformations that lead to a sparse representation can satisfy the requirement. Consider a vector x 2 Rm with m nonzero entries. This vector can be the expression of any kind of signal we interested in such as the array signal. For a standard orthonormal basis ðci : i ¼ 1; ; mÞ and related coefficients yi ¼ hx; ci i, the vector is said to be a sparse vector based on the transformation with such basis in the following sense that, for some 0 < p < 2 and for some R > 0 [1]. kykp
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