Near-Field SAR-Aware Power Control and Beamforming for Reconfigurable Intelligent Surfaces with Electromagnetic Safety Guarantees
Sohel Rana ,
Nagendranath ,
Shaik Md. Rafee ,
Venkata Krishnamoorthy ,
Ravi Sankar ,
Tukaram Shep and
Kiranmayi Sridhara
Existing electromagnetic (EM) safety analyses for reconfigurable intelligent surface (RIS) systems rely on the far-field equivalent plane-wave density (EPD) formula, which systematically underestimates tissue exposure when the user equipment (UE) operates in the radiating near-field (NF) zone (dU ≲ dR/2, where dR = 2D2/λ is the Rayleigh distance, and D = (N-1)λ/2 is the aperture length). This paper presents five analytically rigorous contributions to NF-aware power allocation and beamforming for RIS-assisted 5G/6G systems. (1) A conservative Fresnel-envelope correction factor κ(d,N) with a provable non-negative overestimation error ε(d,N) ≥ 0 (Propositions 1-2, Lemma 1). (2) Closed-form NF-corrected SAR power ceiling P∗NF and minimum exclusion radius dNFmin; the 1-D Fresnel bound is conservative for 2-D uniform planar arrays (UPAs) with a separability gap up to 13.2 dB, confirmed by exact 2-D spherical-wave summations (SAR1D ≥ SARFF ≥ SAR2D). (3) A closed-form NF phase-taper Δϕn recovering up to 0.4 bit/s/Hz SAR-constrained spectral efficiency (SCSE) at dU = 1 m (Proposition 3). (4) A two-stage NF-SAR alternating-optimisation (NF-SAR-AO) algorithm with O(N) per-iteration complexity, hard guard margin (deff = 1.1dU), and proved monotone convergence under line-of-sight (LOS) channels (Algorithm 1, Proposition 4). (5) 2-bit phase quantization incurring < 0.3 bit/s/Hz SCSE loss with 100% ICNIRP 2020 compliance for all dU ≥ 0.5 m. Validated over 5 × 103 Monte Carlo (MC) trials at 3.5 GHz (N = 64, Pmax = 200 mW): dNFmin = 0.727 m1 vs. dFFmin = 0.498 m - far-field models underestimate the required safety exclusion radius by 46%, risking ICNIRP 2020 non-compliance.