Abstract
Direction-of-arrival (DOA) estimation with a co-prime linear array, composed of two uniform linear arrays with inter-element spacing larger than half-wavelength of incoming signals, has been investigated a lot thanks to its high-resolution performance. For better computational efficiency, one class of methods treat the co-prime linear array as two sparse uniform linear subarrays. From each of them, high-precision but ambiguous DOA estimation is obtained, and the ambiguities are eliminated according to the co-prime property. However, the existing methods of this kind suffer from the insufficient reliability and high complexity. In this paper, the potential problems associated with the DOA estimation with two co-prime subarrays are discussed, and a reliable and efficient DOA estimation method is proposed. For each subarray, the true DOAs are treated as their equivalent angles and the pair matching of them is accomplished by exploring the cross-correlations between the equivalent signals associated with the equivalent angles. Compared with other existing methods, the proposed method is able to achieve a better estimation performance in all situations, in terms of accuracy and complexity.
Highlights
Direction-of-arrival (DOA) estimation is one of the most crucial problems in radar, wireless communication and other applications [1]–[3]
The Root Mean Square Error (RMSE) performance of the proposed method and the method in [15] is compared in a normal situation, where two signals are assumed to come from θ1 = 10.00◦ and θ2 = 40.00◦, and a grating angles problem situation, where three signals are assumed to impinge from θ1 = 10.00◦, θ2 = 27.35◦ and θ3 = 35.01◦, versus signal-to-noise ratio (SNR) and snapshots number (SNR is 10dB)
In this paper, the existing problems associated to the DOA estimation with co-prime linear arrays, including ambiguity, pair matching errors and grating angles problem, are discussed
Summary
Direction-of-arrival (DOA) estimation is one of the most crucial problems in radar, wireless communication and other applications [1]–[3]. By dividing the co-prime array into two ULAs, and finding the common peaks of their MUSIC-spectrums, the DOAs can be uniquely obtained and the ambiguities caused by the large inter-element spacing can be eliminated based on the co-prime property. Because of the large inter-element spacing, when two or more source signals come from a set of specific angles, for which they have exactly a same directional vector for one subarray, the directional matrix of this subarray will be rank deficient, it is challenging to find the true DOAs for all the above mentioned methods These specific angles are called grating angles, and this problem is called grating angles problem, which is discussed in [15], where a joint singular value decomposition (JSVD) based method is proposed. Superscript (·)T , (·)∗ and (·)+ denote the transpose, complex conjugate and pseudo-inverse operator, respectively. | · | denotes the modulus operator and IM stands for the identity matrix with dimension M × M
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