Simulation and Performance Analysis of Time-Modulated Array Beamforming

Abstract

Phased-array beamforming steers a beam electronically toward a Low Earth Orbit (LEO) satellite, but the phase shifter needed at every element makes the hardware costly, power-hungry, and difficult to scale for a compact Non-Terrestrial Network (NTN) user terminal. A conventional binary Time-Modulated Array (TMA) removes the phase shifter by switching each element ON/OFF in time, but its coarse two-state control caps achievable sidelobe level (SLL) and wastes radiated power in unwanted harmonics. This work develops a tri-state (+1, 0, ?1) TMA for 5G New Radio (NR) NTN downlink terminals, in which each element is driven by an independent positive and negative pulse within a shared switching period. Closed-form harmonic coefficients are derived for the tri-state switching function and combined with the array steering vector to synthesise the first-harmonic radiation pattern. A Quadratic Programming Optimization (QPO) routine, warm-started with Chebyshev tapering, jointly minimises sidelobe level and half-power beamwidth (HPBW), while an Alternating Direction Method of Multipliers (ADMM) framework, realised as a Bartlett spatial-matched-filter coarse-to-fine search, adaptively tracks the satellite\'s direction of arrival (DoA). Simulated on a multi-element ULA driven by a realistic 5G NR OFDM waveform, the developed design reduces the sidelobe level from approximately ?13 dB to ?26 dB while improving output SINR and maintaining accurate beam tracking, with a beam pattern nearly indistinguishable from the ideal-DoA case, all at a considerably lower relative hardware cost than a fully phase-shifter-based array.

Introduction

This study presents a Tri-State Time-Modulated Array (TMA) beamforming framework for 5G Non-Terrestrial Networks (NTNs), particularly for Low Earth Orbit (LEO) satellite communication systems. Modern wireless applications such as IoT, autonomous systems, smart cities, and remote healthcare require highly efficient and reliable communication networks. While 5G networks use technologies such as massive MIMO, millimetre-wave communication, and beamforming, conventional phased-array systems face challenges due to high cost, power consumption, hardware complexity, and calibration requirements, especially for portable satellite terminals.

To overcome these limitations, the research explores Time-Modulated Arrays (TMAs), which replace expensive RF phase shifters with high-speed switches. Conventional binary TMAs provide low-cost beamforming but suffer from poor sidelobe suppression and limited excitation control. The proposed tri-state TMA approach introduces three switching states: positive (+1), zero (0), and negative (−1), providing improved control over element excitation while maintaining low hardware complexity. This enables better beam steering, sidelobe reduction, and the possibility of generating multiple beams using harmonic components.

The proposed framework integrates a complete communication-level simulation pipeline based on a realistic 5G NR OFDM NTN downlink waveform at 1.55 GHz L-band frequency. Unlike previous studies that mainly evaluate radiation patterns, this work combines signal generation, beamforming optimization, adaptive tracking, and communication performance evaluation.

Main Contributions

The study contributes:

1. A realistic 5G NR OFDM-based NTN simulation framework for evaluating TMA beamforming.
2. Mathematical derivation of tri-state switching functions and harmonic coefficients.
3. A Quadratic Programming Optimization (QPO) technique with Chebyshev amplitude tapering to improve sidelobe performance.
4. An ADMM-based adaptive DoA tracking algorithm using Bartlett spatial matched filtering for continuous satellite tracking.
5. A complete evaluation framework considering Side Lobe Level (SLL), Half Power Beam Width (HPBW), gain, SINR, BER, and EVM, along with comparisons of hardware complexity and power consumption.

Literature Review Summary

Previous research established the foundations of GAN-like harmonic beamforming concepts and adaptive array processing. Lema et al. introduced tri-state TMA concepts for NTN terminals and demonstrated improvements in sidelobe suppression and hardware efficiency. Kummer et al. provided theoretical analysis of harmonic generation in TMAs. Array theory and adaptive beamforming principles from Balanis and Van Trees support the steering-vector and DoA estimation methods used in this work. Boyd et al.’s ADMM optimization framework motivates adaptive tracking, while 3GPP Release-17 standards provide the foundation for the simulated NTN waveform.

Existing studies highlight that phased arrays provide excellent steering capability but have high hardware costs, while traditional TMAs are inexpensive but have limited beam quality. This research addresses this gap by combining tri-state switching, optimization algorithms, realistic waveforms, and communication-level analysis.

System Model and Methodology

The proposed system consists of several stages:

1. 5G NR NTN Signal Generation
   • A realistic OFDM-based downlink waveform is generated at an L-band carrier frequency of 1.55 GHz.
   • The RF signal is obtained by up-converting the complex baseband waveform.
2. Array Signal Model
   • A Uniform Linear Array (ULA) receives the satellite signal.
   • The received signal consists of the desired waveform, steering vector, and noise components.
   • The steering vector is used for beamforming, DoA estimation, and tracking.
3. Binary TMA Analysis
   • Conventional binary switching uses ON/OFF states controlled by switching duration and timing.
   • Fourier-series analysis determines harmonic coefficients responsible for beam formation.
   • Limited control over excitation results in higher sidelobe levels.
4. Tri-State TMA Beamforming
   • Each antenna element uses positive, negative, and zero excitation states.
   • Two independent switching pulses provide additional control over amplitude and phase.
   • The derived harmonic coefficient improves beamforming flexibility compared with binary TMA.
5. Optimization and Adaptive Tracking
   • QPO optimization combined with Chebyshev tapering reduces sidelobe levels and improves beam quality.
   • ADMM-based tracking with Bartlett spatial matched filtering enables continuous adjustment of the beam direction as LEO satellites move.

Overall Summary

The proposed Tri-State Time-Modulated Array Beamforming System provides a low-complexity alternative to conventional phased arrays for 5G NTN applications. By combining tri-state switching, harmonic beam utilization, optimization algorithms, and adaptive DoA tracking, the system improves sidelobe suppression, beam steering accuracy, and communication reliability while reducing hardware complexity, power consumption, and cost. The framework demonstrates the potential of TMAs as an efficient solution for future portable satellite communication terminals in 5G and 6G networks.

Conclusion

This paper developed a tri-state Time-Modulated Array formulation for 5G NR NTN user terminals, deriving closed-form tri-state harmonic coefficients, combining QPO-based sidelobe/beamwidth optimisation with Chebyshev-tapering warm starts, and implementing an ADMM-based Bartlett DoA tracker. Simulated on a 16-element ULA driven by a realistic 5G NR OFDM waveform, the resulting design pushed SLL from about ?13 dB to about ?26 dB past the 3GPP-consistent ?25 dB target at a gain cost of only around 0.3 dB, while SINR improved by more than 4 dB and DoA tracking remained closely aligned with the ideal case. Together with a cost/power advantage over conventional phased-array and digital beamforming that widens as more beams are required, these results support tri-state TMA beamforming as a workable, lower-complexity, lower-power alternative to phased arrays for NTN terminals. Future work will target real-time adaptive switching-parameter tuning, evaluation under realistic channel impairments (atmospheric attenuation, Doppler shift, RF switch loss, mutual coupling), and multi-user harmonic-diversity multibeam scaling for 6G/ISAC deployments. More broadly, the results support the view that the sidelobe and harmonic-utilisation limits historically associated with time-modulated arrays stem from under-parameterised switching control rather than the switching principle itself: given enough degrees of freedom a third excitation state, an independently placed negative pulse, and a jointly solved SLL/HPBW objective a TMA can approach phased-array-like pattern quality while retaining switch-based hardware\'s cost and power advantage.

References

[1] G. G. Lema, E. Lagunas, M. R. Bhavani Shankar, and J. Grotz, \"Time Modulated Arrays Beamforming for Non-Terrestrial Network User Terminal,\" IEEE Open Journal of the Communications Society, vol. 6, pp. 271–288, 2025. [2] W. H. Kummer, A. Villeneuve, T. S. Fong, and F. G. Terrio, \"Ultra-Low Sidelobes from Time-Modulated Arrays,\" IEEE Transactions on Antennas and Propagation, vol. 11, no. 6, pp. 633–639, 1963. [3] C. A. Balanis, Antenna Theory: Analysis and Design, 4th ed. Hoboken, NJ, USA: John Wiley & Sons, 2016. [4] H. L. Van Trees, Optimum Array Processing, Part IV of Detection, Estimation, and Modulation Theory. New York, NY, USA: Wiley, 2002. [5] S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, \"Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers,\" Foundations and Trends in Machine Learning, vol. 3, no. 1, pp. 1–122, 2011. [6] 3GPP TS 38.211, NR; Physical Channels and Modulation, Release 17, 2023. [7] 3GPP TS 38.300, NR; Overall Description; Stage-2, Release 17, 2023. [8] M. M. Azari et al., \"Evolution of Non-Terrestrial Networks From 5G to 6G: A Survey,\" IEEE Communications Surveys & Tutorials, vol. 24, no. 4, pp. 2633–2672, 2022.

Copyright

Copyright © 2026 Chandanagiri Bhavani, Dr. M Madhavi Latha. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.