Energy Efficiency Analysis of Discrete Phase-Shifted Active RIS Enhanced Communication Systems

SHU Feng; LIN Zhiyuan; ZHENG Weihai; WANG Yan; JIANG Hao; WANG Jiangzhou

doi:10.11999/JEIT260462

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SHU Feng, LIN Zhiyuan, ZHENG Weihai, WANG Yan, JIANG Hao, WANG Jiangzhou. Energy Efficiency Analysis of Discrete Phase-Shifted Active RIS Enhanced Communication Systems[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT260462

Citation:

SHU Feng, LIN Zhiyuan, ZHENG Weihai, WANG Yan, JIANG Hao, WANG Jiangzhou. Energy Efficiency Analysis of Discrete Phase-Shifted Active RIS Enhanced Communication Systems[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT260462

Citation:

SHU Feng, LIN Zhiyuan, ZHENG Weihai, WANG Yan, JIANG Hao, WANG Jiangzhou. Energy Efficiency Analysis of Discrete Phase-Shifted Active RIS Enhanced Communication Systems[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT260462

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Energy Efficiency Analysis of Discrete Phase-Shifted Active RIS Enhanced Communication Systems

doi: 10.11999/JEIT260462 cstr: 32379.14.JEIT260462

SHU Feng^{1, 2
,
,},
LIN Zhiyuan¹,
ZHENG Weihai³,
WANG Yan¹,
JIANG Hao^{4, 5},
WANG Jiangzhou⁵

1.
School of Information and Communication Engineering, Hainan University, Haikou 570228, China
2.
School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
3.
China Mobile Group Hainan Co., Ltd., Haikou 571250, China
4.
School of Artificial Intelligence, Nanjing University of Information Science and Technology, Nanjing 210044, China
5.
National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, China

Funds: The National Natural Science Foundation of China (U22A2002), Hainan Provincial Natural Science Foundation of China (626ZD0993, 526QN0542, 626QN0553), Hainan Province Science and Technology Special Fund (ZDYF2024GXJS292)

Received Date: 2026-04-16
Accepted Date: 2026-07-13
Rev Recd Date: 2026-07-13

Available Online: 2026-07-23

Abstract

Abstract

Objective Active Reconfigurable Intelligent Surface (RIS) enhances wireless communication performance by integrating radio frequency amplifiers to mitigate the multiplicative fading inherent to passive RIS. However, amplification noise and additional power consumption are introduced. Furthermore, high-precision digital phase control at the base station incurs considerable communication overhead. Employing low-precision phase shifters is therefore an effective approach for practical RIS deployment. Therefore, characterizing the Energy Efficiency (EE) performance of active RIS-assisted communication systems and quantifying the effect of finite-bit phase quantization errors on EE are essential for system design and practical implementation. To this end, a discrete phase-shifted active RIS-assisted communication system over Rayleigh fading channels is investigated. The EE loss caused by phase quantization errors is analyzed, approximate optimal solutions for the power allocation factor and the number of RIS elements that maximize EE are derived, and the relationship between RIS EE and user EE is established, providing theoretical guidance for the practical deployment of active RIS. Methods Based on the law of large numbers and Taylor series expansion, closed-form expressions for the user EE loss and its approximation are derived. The effects of system parameters on EE are investigated by expressing EE as explicit univariate functions. Ferrari’s method and the Lambert W function are then employed to derive approximate optimal solutions for the power allocation factor and the number of RIS elements that maximize EE. Finally, the relationship between RIS EE and user EE is established using the law of large numbers and the Lambert W function. Results and Discussions User EE is expressed as a function of six parameters: the number of quantization bit ($ k $), power allocation factor ($ \beta $), the number of RIS elements ($ N $), the total power sum of base station and active RIS ($ {P}_{\text{t}} $), the noise at active RIS ($ \sigma _{\text{r}}^{2} $), and the noise at user ($ \sigma _{\text{u}}^{2} $). First, the EE loss decreases as $ k $ increases. When $ k $=3, the difference between the approximate EE loss and the lossless case is less than 0.026 8 Mbit/J, while the difference between the EE loss and the lossless case is less than 0.026 5 Mbit/J (Fig. 3). Therefore, 3- to 4-bit discrete phase shifters achieve performance close to that of continuous phase shifters. Second, user EE exhibits a unimodal dependence on both $ \beta $ and $ N $. The approximate optimal solution for $ \beta $ differs from the exact optimal solution obtained by the Dinkelbach algorithm by less than 0.01 (Fig. 4), whereas the approximate and exact optimal solutions for $ N $ are identical (Fig. 5), demonstrating the high accuracy of the proposed approximations. Third, user EE exhibits a unimodal trend as $ {P}_{\text{t}} $ increases. Higher phase quantization precision produces a higher EE peak while requiring a lower optimal $ {P}_{\text{t}} $ to achieve the maximum EE (Fig. 6). In addition, user EE decreases as both $ \sigma _{\text{r}}^{2} $ and $ \sigma _{\text{u}}^{2} $ increase. User EE is more sensitive to the amplification noise introduced at the RIS, indicating that reducing the RIS noise power yields a greater EE improvement (Fig. 7). Finally, user EE first increases and then decreases sharply to zero as RIS EE increases. The signal-to-noise ratio at the RIS is identified as the key factor governing the relationship between RIS EE and user EE (Fig. 8). Conclusions The EE performance of active RIS-assisted wireless networks employing discrete phase shifters over Rayleigh fading channels is investigated. First, closed-form expressions are derived for the user EE in the lossless case, the lossy case, and the approximate-loss case. Simulation results demonstrate that 3- to 4-bit discrete phase shifters closely approach the performance of continuous phase shifters. Next, explicit functions describing the effects of key system parameters on user EE are established. Ferrari’s method and the Lambert W function are employed to derive approximate optimal solutions for the power allocation factor and the number of RIS elements that maximize EE, and both exhibit negligible errors relative to the exact solutions. Finally, the relationship between RIS EE and user EE is established, demonstrating that user EE initially increases and subsequently decreases to zero as RIS EE increases.
- Active Reconfigurable Intelligent Surface (RIS),
- Energy Efficiency (EE),
- Phase quantization error,
- Power allocation,
- Law of large numbers

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References(19)

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