High Precision Large Aperture Array Calibration Method for Residual Separation of Near-field Effects in Darkroom

XU Libing; LIU Kaixin

doi:10.11999/JEIT241084

Volume 47 Issue 7

Jul. 2025

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XU Libing, LIU Kaixin. High Precision Large Aperture Array Calibration Method for Residual Separation of Near-field Effects in Darkroom[J]. Journal of Electronics & Information Technology, 2025, 47(7): 2140-2148. doi: 10.11999/JEIT241084

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XU Libing, LIU Kaixin. High Precision Large Aperture Array Calibration Method for Residual Separation of Near-field Effects in Darkroom[J]. Journal of Electronics & Information Technology, 2025, 47(7): 2140-2148. doi: 10.11999/JEIT241084

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High Precision Large Aperture Array Calibration Method for Residual Separation of Near-field Effects in Darkroom

doi: 10.11999/JEIT241084 cstr: 32379.14.JEIT241084

XU Libing,
LIU Kaixin^,

Southwest China Research Institute of Electronic Equipment, Chengdu 610036, China

Received Date: 2024-12-09
Rev Recd Date: 2025-03-30

Available Online: 2025-04-19

Publish Date: 2025-07-22

Abstract

Abstract

Objective Direction estimation is a critical aspect of array signal processing technology. Array errors are inevitably introduced during the manufacturing and installation processes. To mitigate the negative effects of these errors on the accuracy and resolution of direction estimation, arrays must be calibrated before deployment. In practical engineering applications, active array calibration is the primary method, and performing calibration in a darkroom, which shields against electromagnetic wave interference, enhances calibration performance. However, the size of the darkroom is limited. As the array aperture increases, the distance between the calibration source and the array may fail to meet the far-field condition, leading to the introduction of nonlinear near-field phase components in the received signal. Moreover, the absence of a precise positioning system in the darkroom may result in the actual installation position of the calibration source differing from its nominal position, further compromising calibration performance. To address these issues, this paper proposes a high-precision large aperture array calibration method that separates residual near-field effects in the darkroom. This method eliminates the phase residuals caused by deviations in the calibration source position and the near-field distance of the source, effectively calibrates the amplitude and phase errors of large aperture arrays in the darkroom, and thereby improves the accuracy of direction estimation. Methods The proposed method utilizes the nominal coordinates of the calibration source to compensate for the phase difference caused by the near-field distance and derives the formula for the near-field effect residual resulting from source position deviations. Next, an array amplitude and phase error estimation technique at nominal coordinates is proposed to solve for the array amplitude and phase error matrix containing the phase residual. This technique constructs a cost function based on the orthogonality between the subspace spanned by the array manifold vector with amplitude-phase errors and the noise subspace of the array’s received signals. The least squares method is then applied to solve for the low-precision array error estimation results. To enhance precision, this method employs a near-field effect residual separation technique to separate the phase residuals from the solved array error matrix, thereby achieving high-precision array error estimation results. Through differential operations, the technique verifies that the near-field effect residual of each element in a uniform linear array is approximately proportional to the element’s serial number. High-precision array calibration improves the accuracy of direction estimation. Results and Discussions This paper proposes a high-precision near-field calibration method for large-aperture uniform linear arrays. The method addresses the calibration problem under near-field conditions and mitigates the negative effects of calibration source position deviation on the active calibration algorithm. It requires only a single calibration source, demonstrating both innovation and practicality.In Section 5, the performance of the proposed method is analyzed in detail through simulation. First, Fig. 2 verifies an important conclusion of this algorithm: the near-field effect residual of each element in a uniform linear array is approximately proportional to the element’s serial number. Figs. 4 to 7 examine the influences of various factors on array calibration performance, including calibration source position deviation, array aperture, distance between the calibration source and the array, and signal frequency. All four factors significantly impact the magnitude of the near-field residual. Specifically, increasing source position deviation, array aperture, and signal frequency, as well as decreasing the distance of the calibration source, will all increase the phase residual, which negatively affects array calibration. In Fig. 4, the proposed method demonstrates greater tolerance to severe source position deviations, maintaining high accuracy in array error estimation even under such conditions. Fig. 5 shows that increasing the number of array elements, which is equivalent to enlarging the array aperture, increases the near-field effect residual. However, this method effectively removes the residual, aiding in achieving high-precision array error estimation and restoring high-precision direction estimation for the large-aperture array. Fig. 6 investigates the influence of the distance between the calibration source and the array. Without removal of the near-field effect residual, the array error estimation accuracy rapidly decreases as the distance decreases. However, the proposed method ensures that the accuracy decreases only slowly. When the near-field distance ranges from 20m to 50m, the accuracy remains nearly unchanged. This simulation clearly demonstrates the effectiveness of the method in removing near-field effect residuals. High-frequency signals theoretically provide excellent direction estimation accuracy. However, higher signal frequencies lead to more severe near-field phase residuals, and inefficient array calibration can further degrade direction estimation accuracy. In Fig. 7, without removing the near-field phase residual, the direction estimation accuracy does not improve even with an increase in signal frequency. Fortunately, after removing the near-field effect residual with the proposed method, high-precision direction estimation performance is restored for high-frequency signals. Conclusions This paper addresses the challenge that large-aperture arrays often fail to satisfy the far-field distance condition in a darkroom. Additionally, due to instrument measurement errors, obtaining precise calibration source position coordinates in the darkroom is difficult, which complicates array calibration. To address these issues, a high-precision large-aperture array calibration method for residual separation of near-field effects in a darkroom is proposed. This method not only achieves near-field array calibration but also mitigates the phase errors caused by source position deviation, resulting in high-precision estimation of array amplitude and phase errors.The method compensates for the phase difference of the near-field path and constructs a cost function to estimate array amplitude and phase errors using the orthogonality of the signal subspace. The calibration source position deviation introduces near-field effect phase residuals. This paper analyzes the relationship between the phase residual and the array element serial number, solves for and removes the phase residual, thus obtaining high-precision array error estimation results.Simulation results demonstrate that the proposed method has a high tolerance for source position deviation. Even under conditions of large array aperture, high signal frequency, and close proximity between the calibration source and the array, the method remains effective in calibrating the array and significantly improves the accuracy of direction estimation.
- Near-field array calibration,
- Amplitude and phase errors,
- Calibration source position deviation,
- Target azimuth estimation

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References(17)

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