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)

Accepted Date: 2026-07-13
Rev Recd Date: 2026-07-13

Available Online: 2026-07-23

Abstract

Abstract

Objective Active Reconfigurable Intelligent Surface (RIS) can effectively overcome the multiplicative fading problem of passive RIS by integrating radio frequency amplifiers, significantly improving the performance of wireless communication systems. However, it also introduces amplification noise and increases power consumption. In addition, the high-precision digital phase control performed by base stations on RIS poses a challenge due to excessive communication overhead. Adopting low-precision phase shifters is a key approach to promoting the practical application of RIS. Therefore, deriving indicators that affect the energy efficiency (EE) performance of active RIS-assisted systems, as well as analyzing the impact of finite bit quantization errors on EE, have important guiding significance for future RIS system design and practical deployment. In view of this, a discrete active RIS-aided system model is proposed under Rayleigh fading channels, and the EE loss caused by phase quantization error is analyzed. The approximate optimal solution of the power allocation factor and the number of RIS elements that can achieve maximum EE is derived, and the relationship between EE at RIS and user is revealed, providing a theoretical basis for the practical engineering deployment of active RIS. Methods Based on the weak law of large numbers and Taylor series expansion, closed-form expressions for EE performance loss at user and corresponding approximate performance loss expression are derived. The impacts of system parameters on EE are investigated by formulating univariate functions. Combined with the Ferrari’s method and the Lambert W function, the approximate optimal solutions of the power allocation factor and the number of RIS elements for EE maximization are derived, respectively. By applying the weak law of large numbers and the Lambert W function, the relationship between EE at RIS and EE at user is revealed. Results and Discussions The expression of EE at user is derived to be a function of six factors: 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} $). Firstly, the EE performance loss decreases as $ k $ increases. When $ k $=3, the gap between the approximate performance loss and the without performance loss is less than 0.0268 Mbit/J, and the performance loss and the without performance loss is less than 0.0265 Mbit/J (Fig. 3). Therefore, discrete phase shifters with 3 to 4 bits can achieve extremely low performance loss.EE at user exhibits a unimodal characteristic with respect to both $ \beta $and $ N $. The approximate optimal solution of $ \beta $ for EE maximization has an error less than 0.01 compared with the exact optimal solution obtained by the Dinkelbach algorithm (Fig. 4), and there is no error between the approximate optimal solution and the exact optimal solution of $ N $ (Fig. 5), demonstrating the effectiveness of the two approximate models.EE at user first increases and then decreases with the increase of $ {P}_{\text{t}} $showing a unimodal variation. The higher the quantization precision, the larger the EE peak value, and the smaller the optimal $ {P}_{\text{t}} $ required to achieve the EE peak (Fig. 6). EE decreases with the increase of both $ \sigma _{\text{r}}^{2} $ and $ \sigma _{\text{u}}^{2} $. Moreover, EE at user is more susceptible to the amplification noise at RIS, and reducing the noise at RIS can achieve a more significant EE gain (Fig. 7). EE at user first increases and then drops sharply to zero with the increase of EE at active RIS, and the SNR at active RIS is the key factor determining the relationship between these two EE performances (Fig. 8). Conclusions The EE performance of active RIS assisted wireless networks with discrete phase shifters in Rayleigh fading channels is studied. Firstly, the expressions for the loss, no loss, and approximate loss of EE at active RIS and user are derived. Simulation results show that 3 to 4-bit discrete phase shifters can fully exploit the gain of RIS. Secondly, functions for each parameter of EE at user are constructed. Based on the Ferrari method and the Lambert W function, the approximate optimal solution of the power allocation factor and the number of RIS elements that can achieve maximum EE is derived. Simulation results showed that the error between the approximate optimal solution and the exact solution is minimal. Finally, the relationship between EE at RIS and EE at user is revealed, and the results show that EE at user first increases and then decreases to zero with the increases of EE at RIS.
- 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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