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The sparse uniform linear array (SULA) with larger array aperture is adopted to improve the accuracy of direction of arrival (DOA) estimation with a limited number of physical antennas. In the case of single working frequency configuration, spatial aliasing problem occurs due to the spatial under-sampling. However, with a sufficient anti-aliasing condition for multiple frequencies, the unique DOA estimations can be obtained without ambiguity by using multiple integer frequencies. The multiple equivalent array structures of the multiple integer frequencies are analyzed. To perform DOA estimation, in the first part of the paper, a pair of fast DOA estimation methods are proposed. Based on the fact that a real DOA and its ambiguous positions are periodic distributed in the sine domain, the two proposed methods are applied to each equivalent array separately to obtain the real DOA positions as well as their replica positions. Then, an effective matching algorithm is proposed to pick out the real DOAs from the ambiguous ones. The first algorithm is a partial spectral search-based algorithm, and the second algorithm is a search-free-based method. These two algorithms are referred to as matching partial spectral search-based algorithm (matching PPS) and matching root-multiple signal classification algorithm (matching root-MUSIC), respectively. Our third proposed algorithm is a combined root-MUSIC which is applied to the multiple equivalent arrays by taking them as sub-arrays of a common filled ULA. The combined root-MUSIC algorithm utilizes the MUSIC null-spectrum functions of all equivalent arrays to form a new polynomial, and the DOA estimations can be obtained efficiently without any spatial ambiguity by applying polynomial rooting to the new polynomial. Simulations are provided to verify the validity of the proposed algorithms.

Fast DOA Estimation Algorithms for Sparse Uniform Linear Array With Multiple Integer Frequencies