Journal of Radio Electronics. eISSN 1684-1719. 2026. №6

Full text in Russian (pdf)

DOI: https://doi.org/10.30898/1684-1719.2026.6.10

Vector-Based Electrodynamic Model of External Passive Intermodulation
in the Near Field of FDD Massive MIMO Antenna Arrays

V.V. Nesterenko¹, S.A. Krikunov², V.A. Lyashev¹

¹Moscow Institute of Physics and Technology, (National Research University),
141701, Russia, Moscow Region, Dolgoprudny, Institutskiy per., 9

²Skolkovo Institute of Science and Technology,
1121205, Russia, Moscow, Bolshoy Blvd., bld. 30

The paper was received June 2, 2026.

Abstract. External passive intermodulation produced by passive nonlinear objects near a base station antenna is a primary mechanism that limits receiver sensitivity in frequency-division-duplex massive multiple-input multiple-output systems. Existing analytical models typically rely on the far-field assumption, treating the interfering scatterer as a point illuminated by a locally plane wave. This approximation fails when the scatterer sits within the radiating near field of a metre-scale antenna array, a regime that is common in both industrial deployments and anechoic-chamber measurements. The present work introduces a rigorous physical model of intermodulation generation that preserves the spherical phase front and the per-element amplitude taper across the array aperture. The model is built on a coordinate-free vector projection of the finite-length-dipole equations, which gives the radiated field directly in the global Cartesian frame and removes the rotation matrices that are otherwise required for arbitrarily oriented elements. To isolate the contribution of each physical macro-effect, an ablation study is performed in which the spherical phase and the aperture amplitude taper are switched off in turn. The model is validated against anechoic-chamber measurements on a sixteen-port array across five scenarios that span two source strengths, two distances and three lateral offsets. The proposed approach reproduces the measured power profile across the beam-scanning sweep with a root-mean-square error below two decibels for the weak source and locates the main beam without error in every scenario. Dropping the spherical-phase term shifts the predicted main lobe and inflates the predicted side lobes, while dropping the aperture taper distorts the profile whenever the source is off the array axis. The model is suitable as a digital twin for the design and benchmarking of spatial intermodulation cancellation algorithms.

Key words: passive intermodulation; external PIM; near field; Fresnel zone; antenna array; massive MIMO; frequency-division duplex; digital twin; vector projection method; ablation analysis; beamforming; finite-length dipole.

Corresponding author: Nesterenko Vladislav Vitalievich, nesterenko.vv@phystech.edu

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For citation:

Nesterenko V.V., Krikunov S.A., Lyashev V.A. Vector-based electrodynamic model of external passive intermodulation in the near field of FDD Massive MIMO antenna arrays. // Journal of Radio Electronics. – 2026. – №. 6. https://doi.org/10.30898/1684-1719.2026.6.10 (In Russian)