A Low-Complexity ESPRIT-Based DOA Estimation Method for Co-Prime Linear Arrays

Abstract

The problem of direction-of-arrival (DOA) estimation is investigated for co-prime array, where the co-prime array consists of two uniform sparse linear subarrays with extended inter-element spacing. For each sparse subarray, true DOAs are mapped into several equivalent angles impinging on the traditional uniform linear array with half-wavelength spacing. Then, by applying the estimation of signal parameters via rotational invariance technique (ESPRIT), the equivalent DOAs are estimated, and the candidate DOAs are recovered according to the relationship among equivalent and true DOAs. Finally, the true DOAs are estimated by combining the results of the two subarrays. The proposed method achieves a better complexity–performance tradeoff as compared to other existing methods.

A Sum-of-Squares and Semidefinite Programming Approach for Maximum Likelihood DOA Estimation

“…The corresponding resolution probabilities against SNR are given in Figure 2b. The two sources are said to be resolvable [29,30] if $|{\widehat{\theta }}_i-{\theta }_i|\le |{\theta }_1-{\theta }_2|/2$ for both $i=1,2$, where ${\hat{\theta }}_i$ denotes the estimate of ${\theta }_i$. We can see that the resolution probabilities of different methods are enhanced with the increase of SNR.…”

DOA Estimation Based on Real-Valued Cross Correlation Matrix of Coprime Arrays

“…However, as ${\Sigma }_1$ and ${\Sigma }_2$ are processed separately, and their eigenvalues are mis-pairing, which will cause the interference between the angles when determining the unique DOA. Sun et al [20] proposed an additional processing method relying on peak search and angle difference chosen to deal with this problem, but this procedure also adds computation complexity. We will analyse the relationship between ${\Sigma }_1$ and ${\Sigma }_2$ below, and conduct a method to simultaneously obtain the eigenvalues of ${\Sigma }_1$ and ${\Sigma }_2$ with automatically pairing.…”

“…To overcome the ambiguity problem of DOA estimation using sparse arrays, the common peaks of the MUSIC spectra obtained from the two coprime subarrays are selected to uniquely determine the DOA estimations [18], but the high-computational peak searches are required. Thereafter, in order to reduce the complexity involved in the peak search of whole angular space, a partial spectral search (PSS) MUSIC method was proposed in [19] to reduce the search range, and an ESPRIT-based method was proposed in [20] to estimate the DOA without peak search. However, these methods all process the subarrays separately, and the obtained results from the two subarrays are mis-pairing, which result in angular interference between different sources and degradation of the DOA estimation performance, especially with low signal to noise ratio (SNR).…”

“…To deal with this problem, Ref. [20] proposed an additional processing procedure relying on peak search and angle difference chosen, but this makes the algorithm inefficient.…”

“…The automatically paired solutions make it simple and accurate to determine the unique DOA estimation. Compared to the PSS method in [19] and ESPRIT-based method in [20], the proposed algorithm requires lower complexity, achieves better DOA estimation performance and handles more sources. Multiple simulations are conducted to verify the effectiveness of our approach.…”