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Active RIS Versus Passive RIS: Which Is Superior with the Same Power Budget?
Kangda Zhi, Cunhua Pan, Hong Ren, Kok Keong Chai, Maged Elkashlan
TL;DR
The paper asks whether active or passive RIS is better when both share the same overall power budget. It derives the active-RIS power allocation and theoretically and numerically compares the systems, finding active RIS superior when the budget is sufficient and the element count is not very large.
Problem
Existing comparisons did not theoretically analyze active and passive RISs under the same overall power budget, despite active RIS requiring amplifier power.
Method
The paper derives the optimal power allocation between BS transmit power and active-RIS output power, then analyzes parameter effects and compares achievable performance.
Results
Active RIS is superior when the power budget is sufficient and N is not very large, whereas passive RIS performs better for small budgets or very large N.
Takeaways & Limitations
Active RIS can achieve a high achievable rate with a small number of elements under an adequate power budget.
Abstract
from arXiv · showhide
This letter theoretically compares the active reconfigurable intelligent surface (RIS)-aided system with the passive RIS-aided system. For fair comparison, we consider that these two systems have the same overall power budget that can be used at both the base station (BS) and the RIS. For active RIS, we first derive the optimal power allocation between the BS's transmit signal power and RIS's output signal power. We also analyze the impact of various system parameters on the optimal power allocation ratio. Then, we compare the performance between the active RIS and the passive RIS, which demonstrates that the active RIS would be superior if the power budget is not very small and the number of RIS elements is not very large.
I. INTRODUCTION
Passive RIS avoids nearly all additional power but suffers double path-loss, motivating active RIS with amplification. This letter compares both under the same overall power budget and analyzes when each is superior.
- Passive RIS enhances signals through phase adjustment and constructive superposition while requiring nearly zero additional power.
- Double path-loss across the BS-RIS and RIS-user paths weakens passive RIS signals, motivating active RIS amplification.
- Active RIS requires additional amplifier power, so prior superiority comparisons did not impose the same overall power budget.
- The study fairly compares active and passive RISs, derives active-RIS power allocation, and analyzes parameter effects and performance differences.
II. SYSTEM MODEL
The model considers a SISO RIS-assisted system with N elements, blocked direct transmission, and LoS reflected channels. Active RIS uses common amplification and introduces component noise and hardware power consumption.
- The system is SISO, uses an RIS with N elements, and blocks the direct BS-user channel for comparison.
- The reflected channels are modeled with LoS paths and distance-dependent path-loss factors determined by distances and path-loss exponents.
- At d_sr = d_rd = 100 m with α_sr = α_rd = 2, each hop has a small channel gain, producing approximately −140 dB product path-loss.
- For passive RIS, each element has ρ_n = 1; active RIS permits ρ_n > 1 and assumes a common amplification factor ρ.
- Active RIS adds thermal noise from its components, while receiver noise is modeled separately.
- Overall power consumption includes BS transmit power, active-RIS output signal power, phase-shift switch and control power, and per-element DC biasing power.
III. ACTIVE RIS VERSUS PASSIVE RIS
Without a shared budget, active RIS can exceed passive RIS under conditions involving amplification and noise. A fair comparison therefore constrains both systems to the same overall power budget.
- Active RIS achieves higher SNR than passive RIS when amplification satisfies ρ^2 > 1 under the stated channel and noise condition.
- The comparison imposes equal overall power consumption, Q^act = Q^pas, because active-RIS superiority is otherwise non-trivial to assess fairly.
A. Problem Formulation with the Same Power Budget
With a common total budget Q_tot, the active-RIS problem allocates remaining power between the BS and active RIS while accounting for hardware consumption. The allocation is optimized through amplification-dependent SNR conditions.
- The common total budget is defined as Q^act = Q^pas = Q_tot.
- After hardware consumption, the remaining quantity C is available for allocation between the BS and active RIS.
- When C ≤ 0, the active-RIS BS transmit power and SNR are both zero, so analysis focuses on C > 0.
- The optimization determines the active RIS output power allocation and uses the fact that active-RIS SNR increases with amplification.
- The formulation recognizes that BS power and active-RIS power must be jointly optimized rather than fixed independently.
B. Optimal Power Allocation
The optimal active-RIS power allocation depends on the total budget, RIS size, noise conditions, and RIS placement. Increasing the budget generally raises both BS and RIS powers, while parameter-dependent priorities determine how additional power should be split.
- Equal BS and RIS power allocation is optimal when the RIS is located midway between the BS and user.
- As receiver noise vanishes, larger RIS power is preferred; as RIS noise dominates, increasing BS power more effectively improves the SNR.Increasing ρ is ineffective in the latter regime because it also amplifies RIS noise.
- As Qtot increases, the optimal powers allocated to both the BS and active RIS increase; as N increases, both powers decrease.Unequal allocation of increased budget sacrifices performance.
- When σ2_rd is larger, more power should be allocated to the BS because BS power reduces the impact of RIS noise.
- When σ2_sr is larger, more power should be allocated to the active RIS, increasing ρ and reducing receiver-noise impact.
- When the RIS is near the BS, allocate more power to the RIS; when it is near the user, allocate more power to the BS.The received signal at the RIS is stronger when the RIS is closer to the BS, requiring more RIS power to amplify it for a given ρ.
C. SNR Comparison
The SNR comparison identifies regimes where passive or active RIS performs better under the same power budget, while linking the outcome to RIS size, path loss, noise, and allocation.
- For sufficiently large N, active RIS can suffer from severe amplified noise, making passive RIS preferable.
- The N required for active RIS superiority may be very large because the RIS-user path-loss value h^2_rd is small.
- Passive RIS performs better for low power budgets, whereas active RIS performs better when the power budget is sufficient.
- When N is not very large and Qtot is not very small, active RIS can outperform passive RIS by compensating double path-loss attenuation with RIS gain.
IV. SIMULATION RESULTS
The simulations validate the theoretical allocation analysis and compare active and passive RIS performance under varying element counts and total power budgets. Active RIS is favored with sufficient power and moderate element counts, while passive RIS performs better in the low-power or very-large-array regimes.
- Rate versus N: Active RIS outperforms passive RIS when N is not very large because amplification strengthens the signal attenuated during the first hop.For very large N, amplifier power consumption and active-RIS thermal noise reduce the active system's rate.
- Rate versus power budget Qtot: Passive RIS performs better for small power budgets, whereas active RIS is superior when the power budget is sufficient.As Qtot increases, equal allocation becomes less effective because the optimal BS-to-active-RIS allocation ratio must be adjusted.
V. CONCLUSION
The conclusion summarizes a fair same-power-budget comparison between active and passive RIS and the derivation of active-RIS power allocation. It also identifies how the optimal allocation is obtained and how the systems' relative performance depends on system conditions.
- V. CONCLUSION: The paper derives the optimal power allocation ratio between the BS and active RIS under the same overall power budget.The comparison then uses the derived allocation to discuss when active or passive RIS performs better.
- V. CONCLUSION: The optimal allocation is obtained by analyzing the first-order derivative of γact with respect to P act_BS and locating a root within (0, C).The relevant root is selected from the roots of f1(P act_BS).
- V. CONCLUSION: When f1(P act_BS) is linear and f1(C/2) = 0, the optimal BS power allocation is P act_BS = C/2.The derivative analysis establishes the maximizing solution at this point.
APPENDIX B
Appendix B analyzes how the relevant function changes with C and uses this behavior to establish the dependence of the allocation-related result on total power and RIS size.
- APPENDIX B: The function's monotonicity with respect to C determines the direction of the allocation-related dependence.The derivative analysis distinguishes increasing and decreasing cases according to the system parameters.
- APPENDIX B: Because C increases with Qtot but decreases with N, the derived result increases with total power budget and decreases with RIS element count.This conclusion follows directly from the stated dependence of C.
APPENDIX D
Appendix D studies the sign and monotonicity of f4(C), showing that its behavior changes with RIS size and determines whether the BS-power allocation initially rises or ultimately falls.
- APPENDIX D: The appendix establishes that f4(C) is a decreasing function in the relevant case.The derivative is negative for the stated condition.
- APPENDIX D: For sufficiently large N, f4(C) is positive under the stated threshold condition.The derivative contains one negative and one positive term, so the sign depends on N.
- APPENDIX D: Otherwise, f4(C) decreases from the positive value f4(0) to the negative value f4(∞).This sign change means the active-RIS BS power allocation first increases and then decreases.