Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Elements Allocation for Joint Active and Passive IRS Aided Wireless Communications: A Rate-Maximization Perspective

Chaoying Huang, Wen Chen, Qingqing Wu, Nan Cheng

TL;DR

This work studies the rate-maximization problem for a joint AIRS-PIRS wireless link under a fixed total element budget, considering two transmission orders: TAPR (Tx→AIRS→PIRS→Rx) and TPAR (Tx→PIRS→AIRS→Rx). By formulating convexified optimization problems and applying alternating optimization for 3D placements and element allocations, the authors derive both exact and closed-form near-optimal solutions, revealing that the passive surface should receive more elements and that the received SNR scales cubically with the total element count when the AIRS-PIRS distance is large, i.e., an $O(M^3)$ scaling. The analysis shows TAPR generally outperforms TPAR under practical amplification budgets, and both schemes outperform benchmark IRS configurations (single/double PIRS, hybrid IRS) in rate performance. The results offer design guidelines for jointly deploying AIRS and PIRS under budget constraints in 3D space, with potential extensions to energy efficiency and IoT deployments.

Abstract

Unlike previous works that focused solely on passive intelligent reflecting surface (PIRS) or active IRS (AIRS), a novel joint AIRS and PIRS architecture has been developed to flexibly utilize their combined advantages in mitigating multiplicative path loss cost-effectively. In this paper, we consider the AIRS-PIRS jointly aided wireless point-to-point communication system with two different deployment schemes in three-dimensional (3D) space. To balance the trade-off between the square-order beamforming gain of PIRS and the unique power amplification gain of AIRS, we optimize the elements allocation and beamforming design of the two IRSs under various practical constraints from a rate-maximization perspective. Moreover, we derive a series of element-related closed-form analytical expressions and compare the performance of the two schemes. Our analysis shows that in both schemes, PIRS should be allocated more elements than AIRS, and the received signal-to-noise ratio (SNR) increases asymptotically with the cube of the number of reflecting elements, when the distance between AIRS and PIRS is sufficiently large. Last, simulation results validate our analysis and indicate that both schemes can achieve superior rate performance over various benchmarks.

Elements Allocation for Joint Active and Passive IRS Aided Wireless Communications: A Rate-Maximization Perspective

TL;DR

This work studies the rate-maximization problem for a joint AIRS-PIRS wireless link under a fixed total element budget, considering two transmission orders: TAPR (Tx→AIRS→PIRS→Rx) and TPAR (Tx→PIRS→AIRS→Rx). By formulating convexified optimization problems and applying alternating optimization for 3D placements and element allocations, the authors derive both exact and closed-form near-optimal solutions, revealing that the passive surface should receive more elements and that the received SNR scales cubically with the total element count when the AIRS-PIRS distance is large, i.e., an scaling. The analysis shows TAPR generally outperforms TPAR under practical amplification budgets, and both schemes outperform benchmark IRS configurations (single/double PIRS, hybrid IRS) in rate performance. The results offer design guidelines for jointly deploying AIRS and PIRS under budget constraints in 3D space, with potential extensions to energy efficiency and IoT deployments.

Abstract

Unlike previous works that focused solely on passive intelligent reflecting surface (PIRS) or active IRS (AIRS), a novel joint AIRS and PIRS architecture has been developed to flexibly utilize their combined advantages in mitigating multiplicative path loss cost-effectively. In this paper, we consider the AIRS-PIRS jointly aided wireless point-to-point communication system with two different deployment schemes in three-dimensional (3D) space. To balance the trade-off between the square-order beamforming gain of PIRS and the unique power amplification gain of AIRS, we optimize the elements allocation and beamforming design of the two IRSs under various practical constraints from a rate-maximization perspective. Moreover, we derive a series of element-related closed-form analytical expressions and compare the performance of the two schemes. Our analysis shows that in both schemes, PIRS should be allocated more elements than AIRS, and the received signal-to-noise ratio (SNR) increases asymptotically with the cube of the number of reflecting elements, when the distance between AIRS and PIRS is sufficiently large. Last, simulation results validate our analysis and indicate that both schemes can achieve superior rate performance over various benchmarks.
Paper Structure (13 sections, 6 theorems, 25 equations, 3 figures)

This paper contains 13 sections, 6 theorems, 25 equations, 3 figures.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. TAPR Transmission Scheme
  4. System Model
  5. Problem Formulation
  6. TPAR Transmission Scheme
  7. Low-Complexity Allocation Design and Performance Analysis
  8. Suboptimal Solutions
  9. TAPR Scheme
  10. TPAR Scheme
  11. TAPR Versus TPAR
  12. Simulation Results
  13. Conclusion

Key Result

Lemma 1

We have $(C_{2}^{\mathrm{AP}}+C_{3}^{\mathrm{AP}})/x_{\mathrm{act}}x_{\mathrm{pas}}^{2} \! \gg\! C_{1}^{\mathrm{AP}}/x_{\mathrm{act}}$ and $C_{1}^{\mathrm{PA}}/x_{\mathrm{act}}x_{\mathrm{pas}}^{2} \!\gg \!C_{2}^{\mathrm{PA}}/x_{\mathrm{act}}x_{\mathrm{pas}}^{2}+C_{3}^{\mathrm{PA}}/x_{\mathrm{act}}$

Figures (3)

  • Figure 1: The A-IRS and B-IRS jointly aided wireless communication system.
  • Figure 2: Effect of the total budget on elements allocation and achievable rate.
  • Figure 3: Rate comparison of joint AIRS-PIRS with benchmark systems.

Theorems & Definitions (6)

  • Lemma 1
  • Lemma 2
  • Proposition 1
  • Lemma 3
  • Proposition 2
  • Proposition 3