caa a22 4500 606204989 CHVBK 20210128101005.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s00034-014-9926-y doi (NATIONALLICENCE)springer-10.1007/s00034-014-9926-y Wang Ding Department of Communication Engineering, Zhengzhou Information Science and Technology Institute, Zhengzhou, 450002, Henan, People's Republic of China aut Improved Active Calibration Algorithms in the Presence of Channel Gain/Phase Uncertainties and Sensor Mutual Coupling Effects [Elektronische Daten] [Ding Wang] This paper deals with the problem of active calibration when channel gain/phase uncertainties and sensor mutual coupling effects are simultaneously present. The numerical algorithms used to compensate for array error matrix, which is formed by the product of mutual coupling matrix and channel gain/phase error matrix, are presented especially tailored to uniform linear array (ULA) and uniform circular array (UCA). First, the array spatial responses corresponding to different azimuths are numerically evaluated using a set of time-disjoint auxiliary sources at known locations. Subsequently, a least-squares (LS) minimization model with respect to array error matrix is established. To solve this LS problem, two novel algorithms, namely algorithm I and algorithm II, are developed. In algorithm I, the array error matrix is considered as a whole matrix parameter to be optimized and an explicit closed-form solution to the error matrix is obtained. Compared with some existing algorithms with similar computation framework, algorithm I is able to utilize all potentially linear characteristics of ULA's and UCA's error matrix, and the calibration accuracy can be increased. Unlike algorithm I, algorithm II decomposes the array error matrix into two matrix parameters (i.e., mutual coupling matrix and channel gain/phase error matrix) to be optimized and all (nonlinear) numerical properties of the error matrix can be exploited. Therefore, algorithm II is able to achieve better calibration precision than algorithm I. However, algorithm II is more computationally demanding as a closed-form solution is no longer available and iteration computation is involved. In addition, the compact Cramér-Rao bound (CRB) expressions for all array error parameters are deduced in the case where auxiliary sources are assumed to be complex circular Gaussian distributed. Finally, the two novel algorithms are appropriately extended to the scenario where non-circular auxiliary sources are used, and the estimation variances of the array error parameters can be further decreased if the non-circularity is properly employed. Simulation experiments show the superiority of the presented algorithms. Springer Science+Business Media New York, 2014 Array error calibration nationallicence Active calibration nationallicence Mutual coupling nationallicence Channel gain/phase errors nationallicence Closed-form solution nationallicence Alternating iteration nationallicence Cramér-Rao bound (CRB) nationallicence Non-circular sources nationallicence Circuits, Systems, and Signal Processing Springer US; http://www.springer-ny.com 34/6(2015-06-01), 1825-1868 0278-081X 34:6<1825 2015 34 34 https://doi.org/10.1007/s00034-014-9926-y text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00034-014-9926-y text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Wang Ding Department of Communication Engineering, Zhengzhou Information Science and Technology Institute, Zhengzhou, 450002, Henan, People's Republic of China aut NATIONALLICENCE 773 0- Circuits, Systems, and Signal Processing Springer US; http://www.springer-ny.com 34/6(2015-06-01), 1825-1868 0278-081X 34:6<1825 2015 34 34