volume | PIER Journals

Abstract

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 (d_U ≲ d_R/2, where d_R = 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 d^NF_min; 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 (SAR_1D ≥ SAR_FF ≥ SAR_2D). (3) A closed-form NF phase-taper Δϕ_n recovering up to 0.4 bit/s/Hz SAR-constrained spectral efficiency (SCSE) at d_U = 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 (d_eff = 1.1d_U), 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 d_U ≥ 0.5 m. Validated over 5 × 10³ Monte Carlo (MC) trials at 3.5 GHz (N = 64, P_max = 200 mW): d^NF_min = 0.727 m¹ vs. d^FF_min = 0.498 m - far-field models underestimate the required safety exclusion radius by 46%, risking ICNIRP 2020 non-compliance.

1. Wu, Qingqing and Rui Zhang, "Towards smart and reconfigurable environment: Intelligent reflecting surface aided wireless network," IEEE Communications Magazine, Vol. 58, No. 1, 106-112, Jan. 2020.
doi:10.1109/mcom.001.1900107 Google Scholar

2. Di Renzo, Marco, Alessio Zappone, Merouane Debbah, Mohamed-Slim Alouini, Chau Yuen, Julien De Rosny, and Sergei Tretyakov, "Smart radio environments empowered by reconfigurable intelligent surfaces: How it works, state of research, and the road ahead," IEEE Journal on Selected Areas in Communications, Vol. 38, No. 11, 2450-2525, Nov. 2020.
doi:10.1109/jsac.2020.3007211 Google Scholar

3. International Commission on Non-Ionizing Radiation Protection (ICNIRP) "Guidelines for limiting exposure to electromagnetic fields (100 kHz to 300 GHz)," Health Physics, Vol. 118, No. 5, 483-524, May 2020.
doi:10.1097/HP.0000000000001210 Google Scholar

4. Zhang, Juping, Gan Zheng, Ioannis Krikidis, and Rui Zhang, "Specific absorption rate-aware beamforming in MISO downlink SWIPT systems," IEEE Transactions on Communications, Vol. 68, No. 2, 1312-1326, Feb. 2020.
doi:10.1109/tcomm.2019.2956522 Google Scholar

5. Zappone, Alessio and Marco Di Renzo, "Energy efficiency optimization of reconfigurable intelligent surfaces with electromagnetic field exposure constraints," IEEE Signal Processing Letters, Vol. 29, 1447-1451, 2022.
doi:10.1109/lsp.2022.3181532 Google Scholar

6. Balanis, Constantine A., Antenna Theory: Analysis and Design, Wiley, Hoboken, NJ, 2005.

7. Sherman, J., "Properties of focused apertures in the Fresnel region," IRE Transactions on Antennas and Propagation, Vol. 10, No. 4, 399-408, Jul. 1962.
doi:10.1109/tap.1962.1137900 Google Scholar

8. Aerts, Sam, Kenneth Deprez, Leen Verloock, Robert G. Olsen, Luc Martens, Phung Tran, and Wout Joseph, "RF-EMF exposure near 5G NR small cells," Sensors, Vol. 23, No. 6, 3145, Mar. 2023.
doi:10.3390/s23063145 Google Scholar

9. Hasgall, P., et al. "IT’IS Foundation Database for Thermal and Electromagnetic Parameters of Biological Tissues," ver. 4.1, IT’IS Foundation, Zurich, Switzerland, 2022.

10. 3GPP, , User equipment (UE) radio transmission and reception; Part 1: Range 1 standalone, Sep..
doi:2022

11. 3GPP, , Study on channel model for frequencies from 0.5 to 100 GHz, Mar. 2022.

12. Aerts, Sam, Leen Verloock, Matthias Van Den Bossche, Davide Colombi, Luc Martens, and Christer Törnevik, "In-situ measurement methodology for the assessment of 5G NR massive MIMO base station exposure at sub-6 GHz frequencies," IEEE Access, Vol. 7, 184658-184667, 2019.
doi:10.1109/access.2019.2961225 Google Scholar

13. Björnson, Emil, Özgecan Özdogan, and Erik G. Larsson, "Intelligent reflecting surface versus decode-and-forward: How large surfaces are needed to beat relaying?," IEEE Wireless Communications Letters, Vol. 9, No. 2, 244-248, Feb. 2020.
doi:10.1109/lwc.2019.2950624 Google Scholar

14. Zhang, Haiyang, Nir Shlezinger, Francesco Guidi, Davide Dardari, Mohammadreza F. Imani, and Yonina C. Eldar, "Beam focusing for near-field multiuser MIMO communications," IEEE Transactions on Wireless Communications, Vol. 21, No. 9, 7476-7490, Sep. 2022.
doi:10.1109/twc.2022.3158894 Google Scholar

15. Wu, Qingqing, Shuowen Zhang, Beixiong Zheng, Changsheng You, and Rui Zhang, "Intelligent reflecting surface-aided wireless communications: A tutorial," IEEE Transactions on Communications, Vol. 69, No. 5, 3313-3351, May 2021.
doi:10.1109/tcomm.2021.3051897 Google Scholar

16. IEEE, "IEEE standard for safety levels with respect to human exposure to electric, magnetic, and electromagnetic fields, 0 Hz to 300 GHz," IEEE Std C95.1-2019, Oct. 2019.
doi:10.1109/IEEESTD.2019.8859679

17. International Electrotechnical Commission (IEC), "Determination of RF field strength, power density and SAR in the vicinity of radiocommunication base stations for the purpose of evaluating human exposure," IEC 62232:2022 (supersedes IEC 62232:2017), Geneva, Switzerland, 2022.

18. Kuster, N. and Q. Balzano, "Energy absorption mechanism by biological bodies in the near field of dipole antennas above 300 MHz," IEEE Transactions on Vehicular Technology, Vol. 41, No. 1, 17-23, Feb. 1992.
doi:10.1109/25.120141 Google Scholar

19. Selvan, Krishnasamy T. and Ramakrishna Janaswamy, "Fraunhofer and Fresnel distances: Unified derivation for aperture antennas," IEEE Antennas and Propagation Magazine, Vol. 59, No. 4, 12-15, Aug. 2017.
doi:10.1109/map.2017.2706648 Google Scholar

20. Björnson, Emil and Luca Sanguinetti, "Power scaling laws and near-field behaviors of massive MIMO and intelligent reflecting surfaces," IEEE Open Journal of the Communications Society, Vol. 1, 1306-1324, Sep. 2020.
doi:10.1109/ojcoms.2020.3020925 Google Scholar

21. Wu, Qingqing and Rui Zhang, "Beamforming optimization for wireless network aided by intelligent reflecting surface with discrete phase shifts," IEEE Transactions on Communications, Vol. 68, No. 3, 1838-1851, Mar. 2020.
doi:10.1109/tcomm.2019.2958916 Google Scholar

22. Cui, Mingyao and Linglong Dai, "Channel estimation for extremely large-scale MIMO: Far-field or near-field?," IEEE Transactions on Communications, Vol. 70, No. 4, 2663-2677, Apr. 2022.
doi:10.1109/tcomm.2022.3146400 Google Scholar

23. Yang, Songjie, Chenfei Xie, Wanting Lyu, Boyu Ning, Zhongpei Zhang, and Chau Yuen, "Near-field channel estimation for extremely large-scale reconfigurable intelligent surface (XL-RIS)-aided wideband mmWave systems," IEEE Journal on Selected Areas in Communications, Vol. 42, No. 6, 1567-1582, Jun. 2024.
doi:10.1109/jsac.2024.3389120 Google Scholar

24. Ibraiwish, Hussam, Ahmed Elzanaty, Yazan H. Al-Badarneh, and Mohamed-Slim Alouini, "EMF-aware cellular networks in RIS-assisted environments," IEEE Communications Letters, Vol. 26, No. 1, 123-127, Jan. 2022.
doi:10.1109/lcomm.2021.3120688 Google Scholar

25. Di, Boya, Hongliang Zhang, Lingyang Song, Yonghui Li, Zhu Han, and H. Vincent Poor, "Hybrid beamforming for reconfigurable intelligent surface based multi-user communications: Achievable rates with limited discrete phase shifts," IEEE Journal on Selected Areas in Communications, Vol. 38, No. 8, 1809-1822, Aug. 2020.
doi:10.1109/jsac.2020.3000813 Google Scholar

26. Cao, Xiaomin, Mohammadali Mohammadi, Hien Quoc Ngo, Hyundong Shin, and Michail Matthaiou, "RIS-assisted XL-MIMO for near-field and far-field communications," IEEE Transactions on Wireless Communications, Vol. 25, 5320-5338, 2025.
doi:10.1109/twc.2025.3617656 Google Scholar

Dr. Sohel Rana

Prof. Nagendranath

Prof. Shaik Md. Rafee

Dr. Venkata Krishnamoorthy

Dr. Ravi Sankar

Dr. Tukaram Shep

Dr. Kiranmayi Sridhara