Abstract
Sparse array arrangement has been widely used in vector-sensor arrays because of increased degree-of-freedoms for identifying more sources than sensors. For large-size sparse vector-sensor arrays, one-bit measurements can further reduce the receiver system complexity by using low-resolution ADCs. In this paper, we present a sparse cross-dipole array with one-bit measurements to estimate Direction of Arrivals (DOA) of electromagnetic sources. Based on the independence assumption of sources, we establish the relation between the covariance matrix of one-bit measurements and that of unquantized measurements by Bussgang Theorem. Then we develop a Spatial-Smooth MUSIC (SS-MUSIC) based method, One-Bit MUSIC (OB-MUSIC), to estimate the DOAs. By jointly utilizing the covariance matrices of two dipole arrays, we find that OB-MUSIC is robust against polarization states. We also derive the Cramer-Rao bound (CRB) of DOA estimation for the proposed scheme. Furthermore, we theoretically analyze the applicability of the independence assumption of sources, which is the fundamental of the proposed and other typical methods, and verify the assumption in typical communication applications. Numerical results show that, with the same number of sensors, one-bit sparse cross-dipole arrays have comparable performance with unquantized uniform linear arrays and thus provide a compromise between the DOA estimation performance and the system complexity.
Highlights
Signal processing for electromagnetic (EM) signals has attracted attention as the reason of carrying more information than traditional signals in the past decades [1]–[3]
We focus on the direction of arrival (DOA) estimation using one-bit measurements for sparse vector-sensor arrays, since sparse array arrangement increases degrees of freedom (DOF) and one-bit measurements reduce the cost of analog-todigital converters (ADC)
We find that one-bit sparse cross-dipole arrays provide a compromise between the DOA estimation performance and the system complexity
Summary
Signal processing for electromagnetic (EM) signals has attracted attention as the reason of carrying more information than traditional signals in the past decades [1]–[3]. 2) A subspace algorithm called OB-MUSIC is developed for the proposed array to estimate DOAs. By exploiting the structure of the covariance matrix, this algorithm is robust to both PP and CP signals and its performance is comparable with that of unquantized measurements on ULAs. 3) The CRB of one-bit sparse cross-dipole arrays is derived. AS denotes the L × K array steering matrix, sK,m(t) and nS,m(t) are the signals vector and the noise vector received by dipoles on the x-axis or y-axis, respectively. The unknown Nm has no effect on the DOA estimation since the following proposed method is based on the normalized covariance matrix RxS,m. The information loss caused by one-bit measurements is more than 2dB. 2) When the signals are fixed, w(x) is a decrease function as the noise power σ 2 increased, which means the information loss in one-bit measurements is larger in low SNR regime than in the high SNR regime
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