Abstract
The coarray techniques, e.g., nested and coprime arrays, can significantly improve degrees of freedom (DOFs) via constructing a so-called difference coarray, which enables underdetermined direction-of-arrival (DOA) estimation within reach in the presence of unknown nonuniform noise. There are repeated lags in the difference coarray, which also contain useful statistical information. In this paper, the repeated lags are properly used for DOA estimation algorithm design in unknown nonuniform noise environments. Specifically, the number of repeated lags in the difference coarray is rigorously given. Then these repeated lags and unique lags are judiciously rearranged to form a pseudo data set, which is composed of linearly independent vectors. Based on the pseudo data set, we propose two algorithms for DOA estimation in the presence of unknown nonuniform noise. One is a searching algorithm without source number knowledge (SASNK), and the other is a multi-snapshot compressive sensing method (MSCS) with better DOA estimation performance. The MSCS also does not require source number information. Numerical results are included to showcase the effectiveness of the proposed algorithms.
Highlights
Underdetermined direction-of-arrival (DOA) estimation, i.e., estimating K DOAs from N < K sensors, is a problem of significance in engineering and science [1]–[4]
In practical applications, since we know the number of sensors of the given prototype coprime array (PCA) and coprime array, it is viable to pre-calculate the number of lags appearing more than once and twice and store them in the system
NUMERICAL EXAMPLES we evaluate the performance of the searching algorithm without source number knowledge (SASNK) and MSCS by comparing them with the SORTE-MUSIC, MUSIC [21], compressive sensing (CS) [14], and covariance matrix reconstruction based CS method (CMRCS) [20] methods
Summary
Underdetermined direction-of-arrival (DOA) estimation, i.e., estimating K DOAs from N < K sensors, is a problem of significance in engineering and science [1]–[4]. The noise covariance matrix is a diagonal matrix with unequal diagonal elements [18] In this case, the DOA estimation performance of many existing methods based on nested and coprime arrays suffer severe degradation. The DOA performance still needs to be improved in small sample or low signal-to-noise ratio (SNR) cases It is seen in the above nested array example that there are N 2 lags in the difference coarray. The methods in [10]–[12] use all the covariance values for DOA estimation without source number knowledge under the assumption that the noise is uniform, i.e., noise power at each sensor is the same
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