How Much Impedance Bandwidth Does an LTE or 5G NR Antenna Need? Closed-Form OFDM Link Penalties for Resonant Antennas

Hussain, Mohammed Khaire

doi:10.26706/ijceae.7.5.20261002

Abstract

Antenna papers often declare a design fit for LTE or 5G NR when its −10 dB reflection bandwidth covers the band, but the cost to an orthogonal frequency-division multiplexing (OFDM) link is rarely quantified. This paper derives that cost for resonant antennas. Each subcarrier sees a power transfer of 1 − |Γ|², and the link penalty depends only on the ratio r of occupied bandwidth to −10 dB impedance bandwidth and on the channel offset from resonance. Under Rayleigh fading, the required-SNR penalty is 10log₁₀(1 + r²/27) for one antenna and 10log₁₀(1 + 2r²/27 + r⁴/405) for a transmit–receive pair, independent of the modulation order.

Simulations of LTE 20 MHz and NR 100 MHz links in EPA, EVA and ETU channels with QPSK–64QAM and least-squares pilot estimation agree with the analysis within the 95% confidence interval in all 84 cases, and estimation changes it by at most 0.16 dB. A channel filling the −10 dB band costs 0.32 dB. A 0.5 dB budget allows r ≤ 1.25, which for NR 100 MHz at 3.55 GHz means Q ≤ 30 and a radius of at least 4.5 mm. Double tuning helps at equal antenna Q but is worse at equal −10 dB bandwidth when r > 1.27.

Keywords

OFDM LTE 5G NR antenna bandwidth quality factor impedance mismatch link-level simulation

References

C. A. Balanis, Antenna Theory: Analysis and Design, 4th ed. Hoboken, NJ, USA: Wiley, 2016.
D. M. Pozar, Microwave Engineering, 4th ed. Hoboken, NJ, USA: Wiley, 2012.
S. Sesia, I. Toufik, and M. Baker, Eds., LTE – The UMTS Long Term Evolution: From Theory to Practice, 2nd ed. Chichester, U.K.: Wiley, 2011.
3GPP, “Evolved Universal Terrestrial Radio Access (E-UTRA); User Equipment (UE) radio transmission and reception,” TS 36.101, Annex B (propagation conditions). 3GPP TS 36.101 V18.10.0 (ETSI TS 136 101 V18.10.0), Release 18, Jul. 2025.
E. Dahlman, S. Parkvall, and J. Sköld, 5G NR: The Next Generation Wireless Access Technology, 2nd ed. London, U.K.: Academic Press, 2020.
3GPP, “NR; User Equipment (UE) radio transmission and reception; Part 1: Range 1 Standalone,” TS 38.101-1, Tables 5.2-1 and 5.3.2-1. 3GPP TS 38.101-1 V18.13.0 (ETSI TS 138 101-1 V18.13.0), Release 18, Apr. 2026.
L. J. Chu, “Physical limitations of omni-directional antennas,” Journal of Applied Physics, vol. 19, no. 12, pp. 1163–1175, 1948, doi: 10.1063/1.1715038.
H. A. Wheeler, “Fundamental limitations of small antennas,” Proceedings of the IRE, vol. 35, no. 12, pp. 1479–1484, 1947, doi: 10.1109/JRPROC.1947.226199.
J. S. McLean, “A re-examination of the fundamental limits on the radiation Q of electrically small antennas,” IEEE Transactions on Antennas and Propagation, vol. 44, no. 5, pp. 672–676, 1996, doi: 10.1109/8.496253.
A. D. Yaghjian and S. R. Best, “Impedance, bandwidth, and Q of antennas,” IEEE Transactions on Antennas and Propagation, vol. 53, no. 4, pp. 1298–1324, 2005, doi: 10.1109/TAP.2005.844443.
A. L. Challoob, “Data transfer in smart grids: Leveraging MIMO-OFDM for enhanced communication,” International Journal of Computational and Electronics Aspects in Engineering, vol. 5, no. 4, pp. 154–164, 2024, doi: 10.26706/ijceae.5.4.20241104.
A. A. Salih, “Improved security and handover technique in (4G) LTE,” International Journal of Computational and Electronics Aspects in Engineering, vol. 3, no. 4, pp. 76–83, 2022, doi: 10.26706/ijceae.3.4.2211616.
R. M. Fano, “Theoretical limitations on the broadband matching of arbitrary impedances,” Journal of the Franklin Institute, vol. 249, no. 1, pp. 57–83, 1950, doi: 10.1016/0016-0032(50)90006-8.
H. W. Bode, Network Analysis and Feedback Amplifier Design. Princeton, NJ, USA: Van Nostrand, 1945.
V. Shyianov, M. Akrout, F. Bellili, A. Mezghani, and R. W. Heath, “Achievable rate with antenna size constraint: Shannon meets Chu and Bode,” IEEE Transactions on Communications, vol. 70, no. 3, pp. 2010–2024, 2022, doi: 10.1109/TCOMM.2021.3099842.
N. V. Deshpande, M. R. Castellanos, S. R. Khosravirad, J. Du, H. Viswanathan, and R. W. Heath, “A generalization of the achievable rate of a MISO system using Bode-Fano wideband matching theory,” IEEE Transactions on Wireless Communications, vol. 23, no. 10, pp. 13313–13329, 2024, doi: 10.1109/TWC.2024.3400793.
B. Tadele, V. Shyianov, F. Bellili, and A. Mezghani, “Channel estimation for multicarrier systems with tightly-coupled broadband arrays,” arXiv:2304.07440, 2023, doi: 10.48550/arXiv.2304.07440.
G. P. Gibiino, A. M. Angelotti, A. Santarelli, and P. A. Traverso, “Error vector magnitude measurement for power amplifiers under wideband load impedance mismatch: System-level analysis and VNA-based implementation,” Measurement, vol. 187, Art. no. 110254, 2022, doi: 10.1016/j.measurement.2021.110254.
A. Ortiz, G. Fleta, J. Navarro, F. Ferrero, A. Andújar, and J. Anguera, “On the antenna impedance mismatch over the radiated power in IoT devices,” Electronics, vol. 15, no. 9, Art. no. 1948, 2026, doi: 10.3390/electronics15091948.
Kaelus Inc., “EVM degradation in LTE systems by RF filtering,” White Paper, 2017.
G. A. Mavridis, D. E. Anagnostou, and M. T. Chryssomallis, “Evaluation of the quality factor, Q, of electrically small microstrip-patch antennas [Wireless Corner],” IEEE Antennas and Propagation Magazine, vol. 53, no. 4, pp. 216–224, 2011, doi: 10.1109/MAP.2011.6097329.
A. Goldsmith, Wireless Communications. Cambridge, U.K.: Cambridge University Press, 2005, doi: 10.1017/CBO9780511841224.
K. Cho and D. Yoon, “On the general BER expression of one- and two-dimensional amplitude modulations,” IEEE Transactions on Communications, vol. 50, no. 7, pp. 1074–1080, 2002, doi: 10.1109/TCOMM.2002.800818.
S. Coleri, M. Ergen, A. Puri, and A. Bahai, “Channel estimation techniques based on pilot arrangement in OFDM systems,” IEEE Transactions on Broadcasting, vol. 48, no. 3, pp. 223–229, 2002, doi: 10.1109/TBC.2002.804034.
J.-J. van de Beek, O. Edfors, M. Sandell, S. K. Wilson, and P. O. Börjesson, “On channel estimation in OFDM systems,” in Proc. IEEE 45th Vehicular Technology Conference, vol. 2, 1995, pp. 815–819, doi: 10.1109/VETEC.1995.504981.
R. A. Hussein, “Performance analysis of RIS-assisted SISO systems under different small scale fading channels,” International Journal of Computational and Electronics Aspects in Engineering, vol. 7, no. 4, pp. 437–449, 2026, doi: 10.26706/ijceae.7.4.20260810.
E. Becker, “A review on STBC design with two transmit antennas,” International Journal of Computational and Electronics Aspects in Engineering, vol. 4, no. 4, pp. 127–133, 2023, doi: 10.26706/ijceae.4.4.20231105.
K. Swain and M. K. Sahoo, “FPGA implementation of LMS algorithm used in adaptive equalizer,” International Journal of Computational and Electronics Aspects in Engineering, vol. 1, no. 1, pp. 45–51, 2014.
3GPP, “Evolved Universal Terrestrial Radio Access (E-UTRA); Physical channels and modulation,” TS 36.211, Sec. 6.10.1.2. 3GPP TS 36.211 V18.0.2 (ETSI TS 136 211 V18.0.2), Release 18, Aug. 2025.
3GPP, “NR; Physical channels and modulation,” TS 38.211, Sec. 7.4.1.1.2. 3GPP TS 38.211 V18.8.0 (ETSI TS 138 211 V18.8.0), Release 18, Feb. 2026.
B. Efron and R. J. Tibshirani, An Introduction to the Bootstrap. New York, NY, USA: Chapman & Hall, 1993.
A. L. K. Attaby, G. A. Alhaddad, and S. Kadhim, “Modern permutation decoding methods: Energy efficiency, cognitive maps and innovative algorithms in telecommunications,” International Journal of Computational and Electronics Aspects in Engineering, vol. 7, no. 1, pp. 91–99, 2026, doi: 10.26706/ijceae.7.1.20260110.
H. A. Mutar and I. R. N. ALRubeei, “AI-driven power optimization in 6G networks: A comprehensive review,” International Journal of Computational and Electronics Aspects in Engineering, vol. 7, no. 1, pp. 45–57, 2026, doi: 10.26706/ijceae.7.1.20260104.

[1] C. A. Balanis, Antenna Theory: Analysis and Design, 4th ed. Hoboken, NJ, USA: Wiley, 2016.

[2] D. M. Pozar, Microwave Engineering, 4th ed. Hoboken, NJ, USA: Wiley, 2012.

[3] S. Sesia, I. Toufik, and M. Baker, Eds., LTE – The UMTS Long Term Evolution: From Theory to Practice, 2nd ed. Chichester, U.K.: Wiley, 2011.

[4] 3GPP, “Evolved Universal Terrestrial Radio Access (E-UTRA); User Equipment (UE) radio transmission and reception,” TS 36.101, Annex B (propagation conditions). 3GPP TS 36.101 V18.10.0 (ETSI TS 136 101 V18.10.0), Release 18, Jul. 2025.

[5] E. Dahlman, S. Parkvall, and J. Sköld, 5G NR: The Next Generation Wireless Access Technology, 2nd ed. London, U.K.: Academic Press, 2020.

[6] 3GPP, “NR; User Equipment (UE) radio transmission and reception; Part 1: Range 1 Standalone,” TS 38.101-1, Tables 5.2-1 and 5.3.2-1. 3GPP TS 38.101-1 V18.13.0 (ETSI TS 138 101-1 V18.13.0), Release 18, Apr. 2026.

[7] L. J. Chu, “Physical limitations of omni-directional antennas,” Journal of Applied Physics, vol. 19, no. 12, pp. 1163–1175, 1948, doi: 10.1063/1.1715038.

[8] H. A. Wheeler, “Fundamental limitations of small antennas,” Proceedings of the IRE, vol. 35, no. 12, pp. 1479–1484, 1947, doi: 10.1109/JRPROC.1947.226199.

[9] J. S. McLean, “A re-examination of the fundamental limits on the radiation Q of electrically small antennas,” IEEE Transactions on Antennas and Propagation, vol. 44, no. 5, pp. 672–676, 1996, doi: 10.1109/8.496253.

[10] A. D. Yaghjian and S. R. Best, “Impedance, bandwidth, and Q of antennas,” IEEE Transactions on Antennas and Propagation, vol. 53, no. 4, pp. 1298–1324, 2005, doi: 10.1109/TAP.2005.844443.

[11] A. L. Challoob, “Data transfer in smart grids: Leveraging MIMO-OFDM for enhanced communication,” International Journal of Computational and Electronics Aspects in Engineering, vol. 5, no. 4, pp. 154–164, 2024, doi: 10.26706/ijceae.5.4.20241104.

[12] A. A. Salih, “Improved security and handover technique in (4G) LTE,” International Journal of Computational and Electronics Aspects in Engineering, vol. 3, no. 4, pp. 76–83, 2022, doi: 10.26706/ijceae.3.4.2211616.

[13] R. M. Fano, “Theoretical limitations on the broadband matching of arbitrary impedances,” Journal of the Franklin Institute, vol. 249, no. 1, pp. 57–83, 1950, doi: 10.1016/0016-0032(50)90006-8.

[14] H. W. Bode, Network Analysis and Feedback Amplifier Design. Princeton, NJ, USA: Van Nostrand, 1945.

[15] V. Shyianov, M. Akrout, F. Bellili, A. Mezghani, and R. W. Heath, “Achievable rate with antenna size constraint: Shannon meets Chu and Bode,” IEEE Transactions on Communications, vol. 70, no. 3, pp. 2010–2024, 2022, doi: 10.1109/TCOMM.2021.3099842.

[16] N. V. Deshpande, M. R. Castellanos, S. R. Khosravirad, J. Du, H. Viswanathan, and R. W. Heath, “A generalization of the achievable rate of a MISO system using Bode-Fano wideband matching theory,” IEEE Transactions on Wireless Communications, vol. 23, no. 10, pp. 13313–13329, 2024, doi: 10.1109/TWC.2024.3400793.

[17] B. Tadele, V. Shyianov, F. Bellili, and A. Mezghani, “Channel estimation for multicarrier systems with tightly-coupled broadband arrays,” arXiv:2304.07440, 2023, doi: 10.48550/arXiv.2304.07440.

[18] G. P. Gibiino, A. M. Angelotti, A. Santarelli, and P. A. Traverso, “Error vector magnitude measurement for power amplifiers under wideband load impedance mismatch: System-level analysis and VNA-based implementation,” Measurement, vol. 187, Art. no. 110254, 2022, doi: 10.1016/j.measurement.2021.110254.

[19] A. Ortiz, G. Fleta, J. Navarro, F. Ferrero, A. Andújar, and J. Anguera, “On the antenna impedance mismatch over the radiated power in IoT devices,” Electronics, vol. 15, no. 9, Art. no. 1948, 2026, doi: 10.3390/electronics15091948.

[20] Kaelus Inc., “EVM degradation in LTE systems by RF filtering,” White Paper, 2017.

[21] G. A. Mavridis, D. E. Anagnostou, and M. T. Chryssomallis, “Evaluation of the quality factor, Q, of electrically small microstrip-patch antennas [Wireless Corner],” IEEE Antennas and Propagation Magazine, vol. 53, no. 4, pp. 216–224, 2011, doi: 10.1109/MAP.2011.6097329.

[22] A. Goldsmith, Wireless Communications. Cambridge, U.K.: Cambridge University Press, 2005, doi: 10.1017/CBO9780511841224.

[23] K. Cho and D. Yoon, “On the general BER expression of one- and two-dimensional amplitude modulations,” IEEE Transactions on Communications, vol. 50, no. 7, pp. 1074–1080, 2002, doi: 10.1109/TCOMM.2002.800818.

[24] S. Coleri, M. Ergen, A. Puri, and A. Bahai, “Channel estimation techniques based on pilot arrangement in OFDM systems,” IEEE Transactions on Broadcasting, vol. 48, no. 3, pp. 223–229, 2002, doi: 10.1109/TBC.2002.804034.

[25] J.-J. van de Beek, O. Edfors, M. Sandell, S. K. Wilson, and P. O. Börjesson, “On channel estimation in OFDM systems,” in Proc. IEEE 45th Vehicular Technology Conference, vol. 2, 1995, pp. 815–819, doi: 10.1109/VETEC.1995.504981.

[26] R. A. Hussein, “Performance analysis of RIS-assisted SISO systems under different small scale fading channels,” International Journal of Computational and Electronics Aspects in Engineering, vol. 7, no. 4, pp. 437–449, 2026, doi: 10.26706/ijceae.7.4.20260810.

[27] E. Becker, “A review on STBC design with two transmit antennas,” International Journal of Computational and Electronics Aspects in Engineering, vol. 4, no. 4, pp. 127–133, 2023, doi: 10.26706/ijceae.4.4.20231105.

[28] K. Swain and M. K. Sahoo, “FPGA implementation of LMS algorithm used in adaptive equalizer,” International Journal of Computational and Electronics Aspects in Engineering, vol. 1, no. 1, pp. 45–51, 2014.

[29] 3GPP, “Evolved Universal Terrestrial Radio Access (E-UTRA); Physical channels and modulation,” TS 36.211, Sec. 6.10.1.2. 3GPP TS 36.211 V18.0.2 (ETSI TS 136 211 V18.0.2), Release 18, Aug. 2025.

[30] 3GPP, “NR; Physical channels and modulation,” TS 38.211, Sec. 7.4.1.1.2. 3GPP TS 38.211 V18.8.0 (ETSI TS 138 211 V18.8.0), Release 18, Feb. 2026.

[31] B. Efron and R. J. Tibshirani, An Introduction to the Bootstrap. New York, NY, USA: Chapman & Hall, 1993.

[32] A. L. K. Attaby, G. A. Alhaddad, and S. Kadhim, “Modern permutation decoding methods: Energy efficiency, cognitive maps and innovative algorithms in telecommunications,” International Journal of Computational and Electronics Aspects in Engineering, vol. 7, no. 1, pp. 91–99, 2026, doi: 10.26706/ijceae.7.1.20260110.

[33] H. A. Mutar and I. R. N. ALRubeei, “AI-driven power optimization in 6G networks: A comprehensive review,” International Journal of Computational and Electronics Aspects in Engineering, vol. 7, no. 1, pp. 45–57, 2026, doi: 10.26706/ijceae.7.1.20260104.