Sensor Array Calibration in Presence of Mutual Coupling and Gain/Phase Errors by Combining the Spatial-Domain and Time-D
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Sensor Array Calibration in Presence of Mutual Coupling and Gain/Phase Errors by Combining the Spatial-Domain and Time-Domain Waveform Information of the Calibration Sources Ding Wang
Received: 5 May 2012 / Revised: 14 September 2012 / Published online: 17 October 2012 © Springer Science+Business Media New York 2012
Abstract This paper is concerned with the maximum-likelihood (ML) calibration methods tailored to the antenna arrays whose spatial responses are perturbed by mutual coupling effects and unknown sensor gain/phase responses. Unlike the existing work, the proposed methods are capable of jointly exploiting the spatial-domain information and time-domain waveform information of the calibration sources. Two kinds of numerical optimization algorithm are devised dependent on different array geometries. One is suitable for arbitrary irregular array manifold, while the other applies to some particular uniform arrays. Additionally, based on the maximum a posteriori probability (MAP) criterion, we extend the two algorithms to the scenario where the true values of the calibration source azimuths deviate slightly from the nominal ones with a priori known Gaussian distribution. The Cramér–Rao bound (CRB) expressions for the unknowns are derived in the absence and presence of the azimuth deviations, respectively. Simulation results support that the performances of the proposed algorithms are preferable to the ones which merely employs the spatial-domain information of the calibration sources, and are able to attain the corresponding CRB. Keywords Active calibration · Gain/phase errors · Mutual coupling effects · Spatial-domain information · Time-domain waveform information · Maximum likelihood (ML)
1 Introduction It is well known that the super-resolution direction-of-arrival (DOA) estimation algorithms based on the eigenstructure technique and maximum-likelihood (ML) criterion D. Wang () Department of Communication Engineering, Zhengzhou Information Science and Technology Institute, Zhengzhou, Henan 450002, P.R. China e-mail: [email protected]
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Circuits Syst Signal Process (2013) 32:1257–1292
are sensitive to the perturbations in the array’s spatial response [3–6]. Therefore, the array errors calibration technique has attracted extensive research interest in the last decades, among which a significant research community is to view the errors calibration as a problem of parameter estimation. The parametric array errors calibration methods can be classified as self-calibration [7, 9, 12, 14, 15, 19, 20, 24, 27, 29– 31] and active calibration [1, 2, 8, 10, 11, 13, 16–18, 21–23, 25, 28]. Either of the methods possesses its own advantages. In this paper, we concentrate on the latter. Over the last three decades, the problem of calibrating the array errors with auxiliary sources has been sufficiently investigated in the open literature. The examples of the active calibration method include those in [1, 2, 8, 10, 11, 13, 16–18, 21–23, 25, 28]. The algorithms in [2, 25] are proposed to compensate for the sens
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