Energy Efficiency Analysis of Discrete Phase-Shifted Active RIS Enhanced Communication Systems
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摘要: 有源可重构智能表面(Reconfigurable Intelligent Surface, RIS)通过集成射频放大器可提升系统性能，但同时引入放大噪声与能耗挑战。此外，基站对RIS的高精度数字调相会带来较大的通信开销。鉴于此，该文研究离散有源RIS增强通信系统的能效性能。首先，基于大数定律与泰勒展开，推导了用户处能效损失及近似损失表达式。其次，结合费拉里法与朗伯W函数，获得了使能效最大化的功率分配因子与RIS元件数的近似最优解。最后，基于朗伯W函数揭示了RIS处与用户处能效关系。仿真表明：当总功率$ {P}_{\text{t}}=1 $ W，RIS元件数$ N=256 $时，3至4比特离散移相器可逼近连续移相性能；所求功率分配因子与RIS元件数的近似最优解与精确最优解误差极小；用户处能效随RIS处能效的增加呈先上升后下降至零的趋势。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 than0.0265 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. -
表 1 主要符号表
符号 符号含义 符号 符号含义 $ N $ 有源RIS元件数 $ {\phi }_{\text{d}} $ 基站到用户直达信道的相位 $ k $ 离散移相器量化比特数 $ \Omega $ 离散移相器的可选相位集合 $ B $ 系统传输带宽 $ p(n) $ 第$ n $个RIS元件的放大反射系数 $ g $ 基站与有源RIS间的信道 $ \lambda $ 有源RIS反射元件的统一放大系数 $ {h}^{\text{H}} $ 有源RIS与用户间的信道 $ {P}_{\text{t}} $ 系统总功率 $ {h}_{\text{d}} $ 基站与用户间直达信道 $ \beta $ 基站与有源RIS之间的功率分配因子 $ {L}_{g} $ 基站到RIS的路径损耗 $ {P}_{\text{RIS}} $ 有源RIS的总功耗 $ {L}_{h} $ RIS到用户的路径损耗 $ {P}_{\text{tot}} $ 系统总功耗 $ {L}_{\text{d}} $ $ {\phi }_{h}(n) $基站到用户直达链路的路径损耗 $ {P}_{\text{c,n}} $ 单个有源RIS反射元件的静态功耗 $ {\alpha }_{g} $ 基站到RIS链路瑞利分布参数 $ {P}_{\text{0,RIS}} $ RIS额外静态功耗 $ {\alpha }_{h} $ RIS到用户链路瑞利分布参数 $ {P}_{0} $ 系统除RIS外其他设备的静态功耗 $ {\alpha }_{\text{d}} $ 基站到用户直达链路瑞利分布参数 $ {P}_{\text{c}} $ 系统常量静态功耗总和 $ {\phi }_{g}(n) $ 基站到第$ n $个RIS元件信道的相位 $ \sigma _{\text{r}}^{2} $ RIS处噪声功率 $ {\phi }_{h}(n) $ 第$ n $个RIS元件到用户信道的相位 $ \sigma _{\text{u}}^{2} $ 用户处噪声功率 $ {\phi }_{p}(n) $ 第$ n $个RIS元件的反射相位 $ {\gamma }_{\text{RIS}} $ RIS处信噪比 $ {\phi }_{\text{pi}}(n) $ 第$ n $个RIS元件的理想连续反射相位 $ {\gamma }_{\text{u}} $ 用户处信噪比 $ \Delta {\phi }_{p}(n) $ 第$ n $个RIS元件的相位量化误差项 $ {\tilde{\gamma }}_{\text{u}} $ 考虑相位量化误差后的用户处信噪比 
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