Robust Adaptive Beamforming with Eigenspace Bases Transition for Mixed-Near-and-Far Field Scenarios

CHEN Peng; ZHANG Qian; LIU Yaoming; HU Xin; WANG Wei

doi:10.11999/JEIT260968

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CHEN Peng, ZHANG Qian, LIU Yaoming, HU Xin, WANG Wei. Robust Adaptive Beamforming with Eigenspace Bases Transition for Mixed-Near-and-Far Field Scenarios[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT260968

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CHEN Peng, ZHANG Qian, LIU Yaoming, HU Xin, WANG Wei. Robust Adaptive Beamforming with Eigenspace Bases Transition for Mixed-Near-and-Far Field Scenarios[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT260968

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Robust Adaptive Beamforming with Eigenspace Bases Transition for Mixed-Near-and-Far Field Scenarios

doi: 10.11999/JEIT260968 cstr: 32379.14.JEIT260968

CHEN Peng^1
,,
ZHANG Qian¹,
LIU Yaoming¹,
HU Xin^{2
,
,},
WANG Wei¹

1.
School of Information Engineering, Chang’an University, Xi’an 710064, China
2.
School of Future Transportation, Chang’an University, Xi’an 710064, China

Funds: Natural Science Basic Research Program of Shaanxi (2025JC-YBQN-947), Fundamental Research Funds for the Central Universities, Chang’an University (300102244203, 300102243401)

Received Date: 2026-07-14
Accepted Date: 2026-09-28
Rev Recd Date: 2026-09-18

Available Online: 2026-10-08

Abstract

Abstract

Objective The rapid evolution of modern communication and sensing technologies, such as 6G communication-sensing integration, 5G ultra-dense networking, and indoor Internet of Things (IoT) applications, has rendered the operating environment of array antenna systems increasingly complex, and Mixed-Near-and-Far (MNF) field scenarios with the coexistence of far-field and near-field targets have become the norm. As the core technology of array signal processing, beamforming includes adaptive beamforming and static beamforming. Unlike static beamforming, adaptive beamforming can automatically adjust the weight vector according to changes in the actual environment, allowing the desired signal to pass without distortion while suppressing interference and noise. Existing adaptive beamforming algorithms tailored for either single far-field or single near-field scenarios are limited to signal processing in a single-distance scenario and suffer from performance limitations when addressing the filtering problem in MNF field scenarios. Therefore, it is imperative to carry out research on adaptive beamforming algorithms for the MNF field. Current studies on the MNF field mainly focus on source localization or communication precoding, while research on MNF-field beamforming for interference suppression remains insufficient. Moreover, the source position parameters are generally unknown and coupled, i.e., the response vector depends simultaneously on the angle and the distance, which causes traditional angle-only methods to suffer from significant model mismatch when processing near-field sources. Aiming at the degradation of beamforming performance caused by this coupling problem, this paper proposes a Robust Adaptive Beamforming Using Eigenspace Bases Transition in MNF field. Methods Consider a uniform linear array (ULA) composed of M isotropic sensor elements with a fixed spacing, which receives one desired signal, J interferences, and additive white Gaussian noise in the MNF field; the Fresnel first-order approximation is adopted for near-field sources. The algorithm reconstructs the interference-plus-noise covariance matrix (INCM) by estimating the eigenspace of the received data and directly removing the desired signal component from the Sample Covariance Matrix (SCM). Unlike the reconstruction algorithms based on subspace basis transition, the reconstruction algorithm based on eigenspace bases transition can avoid the direct estimation of the noise covariance matrix and improve the accuracy of INCM reconstruction. To tackle the issue of coupled source position parameters within the MNF field, a multi-start L-BFGS-B optimization strategy is employed to solve the space distance minimization problem, resulting in an estimated source response vector set (SRVS). Specifically, multiple initial points are randomly sampled within the search space bounded by nominal DOA prior information, and each point independently undergoes L-BFGS-B optimization to convergence; the solution with the minimum objective value among all runs is then selected as the parameter estimation result. This multi-start mechanism effectively overcomes the local minimum issue caused by permutation symmetry. Additionally, an eigenspace bases transition (EBT) method is proposed to compute the reconstructed INCM, thereby circumventing the need for power estimation of interference and noise. With the basis transition matrix, the reconstructed INCM is obtained by attenuating the desired-signal component and nulling the noise-subspace components through a diagonal attenuation matrix, and the noise-subspace term is then added back to compensate for the missing noise components. In typical scenarios with large arrays and controlled optimization parameters, the computational complexity of the proposed algorithm is on the same order as that of classical adaptive beamforming methods. Subsequently, the modified steering vector (SV) is derived through eigendecomposition of the desired signal covariance matrix, and the weighting vector for the MNF field beamformer is produced. Results and Discussions A series of simulation experiments are performed to evaluate the performance of the proposed EBT-based adaptive beamforming in the MNF field. In the simulations, an 11-element ULA with half-wavelength spacing is adopted, and the desired signal and two interferences are located at (15°, 30 m), (−25°, 1000 m), and (35°, 15 m), respectively, with an interference-to-noise ratio of 20 dB and 200 Monte Carlo trials. These experiments include the beamformer performance, the impact of L-BFGS-B parameter selection (number of starting points and maximum iterations) on the algorithm performance, and the impact of the attenuation coefficient on it. The results show that the proposed algorithm maintains stable mainlobe gain in the direction of the desired signal, while forming deep nulls in the direction of interference, which greatly suppresses interference (Fig.1). Under MNF field conditions, the existing near-field and far-field algorithms are mismatched with this scenario and suffer from significant performance degradation when processing the array-received data. In contrast, the proposed algorithm can effectively solve the problem of beamformer performance degradation caused by the aforementioned coupling situation. Meanwhile, under the condition of high input signal-to-noise ratio (SNR), the difference between the output signal-to-interference-plus-noise ratio (SINR) of the proposed algorithm and the theoretical optimal value is less than 1 dB (Fig.2, Fig.3). Moreover, the output SINR value of the proposed algorithm is much higher than that of other algorithms under different snapshot numbers and approaches the optimal upper bound. In the simulation analysis of L-BFGS-B parameter and attenuation coefficient selection, the proposed algorithm can ensure that the output SINR value remains relatively stable under reasonable parameter selection and close to the theoretical optimal value (Fig.4, Fig.5). Overall, the proposed algorithm can effectively solve the problem of beamformer performance degradation caused by the aforementioned coupling situation and outperforms the compared beamforming algorithms. Conclusions This paper addresses the performance degradation of beamformers in MNF field scenarios caused by unknown and coupled source position parameters. A robust adaptive beamforming algorithm using EBT is proposed. The method first estimates the source response vector set via the multi-start L-BFGS-B optimization strategy to handle parameter coupling. It then reconstructs the interference-plus-noise covariance matrix through the EBT method, eliminating the desired signal component and avoiding direct noise power estimation. Finally, the corrected steering vector and the optimal weight vector are derived. Simulation results demonstrate that the proposed algorithm effectively maintains mainlobe gain towards the desired signal while forming deep nulls at interference directions, significantly suppressing interference. The proposed algorithm achieves an output SINR close to the theoretical optimum, especially under high input SNR, and outperforms the compared far-field or near-field algorithms. The performance remains robust across different snapshot numbers and parameter selections. Therefore, the EBT-based algorithm provides an effective solution for robust adaptive beamforming in complex MNF field environments, enhancing system reliability in modern communication and sensing applications.

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