Aliasing-Free Wideband Beamforming Using Sparse Signal Representation

• Published in: IEEE transactions on signal processing Vol. 59; no. 7; pp. 3464 - 3469
• Main Authors: Zijian Tang, Blacquiere, G, Leus, G
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.07.2011; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Aliasing; Ambiguity; Applied sciences; Array signal processing; Arrays; Beamforming; Detection, estimation, filtering, equalization, prediction; Dictionaries; Direction of arrival estimation; Exact sciences and technology; Information, signal and communications theory; Mathematical analysis; multiple-dictionary; orthogonal matching pursuit; Representations; Signal and communications theory; Signal representation. Spectral analysis; Signal representations; Signal, noise; sparse signal representation; spatial aliasing; Spatial resolution; Telecommunications and information theory; uniform linear array; Wideband; wideband beamforming; Parameter estimation; Dictionaries; Direction-of-arrival estimation; multiple-dictionary; spatial aliasing; Signal estimation; uniform linear array; Iterative method; Signal representation; wideband beamforming; Algorithm; Beam forming; orthogonal matching pursuit; Wide band; Aliasing; Matching pursuit; Signal processing; Sparse representation; sparse signal representation; Linear antenna arrays
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2011.2140108

Sparse signal representation (SSR) is considered to be an appealing alternative to classical beamforming for direction-of-arrival (DOA) estimation. For wideband signals, the SSR-based approach constructs steering matrices, referred to as dictionaries in this paper, corresponding to different frequency components of the target signal. However, the SSR-based approach is subject to ambiguity resulting from not only spatial aliasing, just like in classical beamforming, but also from the over-completeness of the dictionary, which is typical to SSR. We show that the ambiguity caused by the over-completeness of the dictionary can be alleviated by using multiple measurement vectors. In addition, by considering the uniform linear array (ULA) structure, we argue that if the target signal contains at least two frequencies, whose absolute difference phrased in wavelengths is larger than twice the array spacing, the spatial aliasing corresponding to these frequencies will be completely distinct. These properties enable us to adapt the existing ℓ 1 algorithms to extract the target DOAs without ambiguity.