Energy Efficiency Analysis of Active RIS-enhanced Wireless Network under Power-Sum Constraint

Recently, as a green wireless technology, active reconfigurable intelligent surface (RIS) attracts numerous research activities due to its amplifying ability to combat the double-fading effect compared to passive one. How about its energy efficiency (EE) over passive one? Below, the EE of active RIS-aided wireless network in Rayleigh fading channels is analyzed. Using the law of large numbers, EE is derived as a function of five factors: power allocation factor, the number (N) of RIS elements, the total power, the noise variances at RIS and at user. To evaluate each factor's impact, the simple EE function for the concerning factor is given with others fixed. To assess the impact of N on EE, we establish an equation with the EE of active RIS equaling that of passive one, and three methods, bisection, Newton's method, and simulated annealing, are designed to find the roots of this equation. Simulation results show that as N tends to medium-scale or large-scale, the asymptotic performance formula is consistent with the exact EE expression well. As N varies from small-scale to large-scale, the active RIS intersects passive one at some point. When N< N_0, active RIS performs better than passive one in terms of EE. Otherwise, there is a converse conclusion.