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Active Reconfigurable Intelligent Surface Enhanced Spectrum Sensing for Cognitive Radio Networks

Jungang Ge, Ying-Chang Liang, Sumei Sun, Yonghong Zeng, Zhidong Bai

TL;DR

This work addresses the challenge of reliable spectrum sensing in opportunistic cognitive radio when the primary signal is weak by introducing an active RIS to boost the desired PU signal and suppress interference. The authors formulate the sensing problem as maximizing the largest population eigenvalue, equivalently $p_0 \mathbf{h}_0^H \mathbf{R}^{-1} \mathbf{h}_0$, under a false-alarm constraint, and solve it via a WMMSE-based Reflecting Coefficient Matrix (RCM) optimization that iteratively updates auxiliary variables and the RIS coefficients. They derive both active- and passive-RIS optimization schemes, with explicit steps for the active case, including the MMSE-based solution and alternative MF/ZF strategies, and they analyze the RIS power-budget trade-offs using a spiked-model framework and Tracy-Widom thresholding. Simulation results show that active RIS can outperform passive RIS when interference is weak, while the passive RIS may be more power-efficient in strong-interference settings due to the larger number of passive elements under the same budget. Overall, the paper provides a principled optimization framework for RIS-enhanced spectrum sensing and offers practical insights into when to deploy active versus passive RIS configurations.

Abstract

In opportunistic cognitive radio networks, when the primary signal is very weak compared to the background noise, the secondary user requires long sensing time to achieve a reliable spectrum sensing performance, leading to little remaining time for the secondary transmission. To tackle this issue, we propose an active reconfigurable intelligent surface (RIS) assisted spectrum sensing system, where the received signal strength from the interested primary user can be enhanced and underlying interference within the background noise can be mitigated as well. In comparison with the passive RIS, the active RIS can not only adapt the phase shift of each reflecting element but also amplify the incident signals. Notably, we study the reflecting coefficient matrix (RCM) optimization problem to improve the detection probability given a maximum tolerable false alarm probability and limited sensing time. Then, we show that the formulated problem can be equivalently transformed to a weighted mean square error minimization problem using the principle of the well-known weighted minimum mean square error (WMMSE) algorithm, and an iterative optimization approach is proposed to obtain the optimal RCM. In addition, to fairly compare passive RIS and active RIS, we study the required power budget of the RIS to achieve a target detection probability under a special case where the direct links are neglected and the RIS-related channels are line-of-sight. Via extensive simulations, the effectiveness of the WMMSE-based RCM optimization approach is demonstrated. Furthermore, the results reveal that the active RIS can outperform the passive RIS when the underlying interference within the background noise is relatively weak, whereas the passive RIS performs better in strong interference scenarios because the same power budget can support a vast number of passive reflecting elements for interference mitigation.

Active Reconfigurable Intelligent Surface Enhanced Spectrum Sensing for Cognitive Radio Networks

TL;DR

This work addresses the challenge of reliable spectrum sensing in opportunistic cognitive radio when the primary signal is weak by introducing an active RIS to boost the desired PU signal and suppress interference. The authors formulate the sensing problem as maximizing the largest population eigenvalue, equivalently , under a false-alarm constraint, and solve it via a WMMSE-based Reflecting Coefficient Matrix (RCM) optimization that iteratively updates auxiliary variables and the RIS coefficients. They derive both active- and passive-RIS optimization schemes, with explicit steps for the active case, including the MMSE-based solution and alternative MF/ZF strategies, and they analyze the RIS power-budget trade-offs using a spiked-model framework and Tracy-Widom thresholding. Simulation results show that active RIS can outperform passive RIS when interference is weak, while the passive RIS may be more power-efficient in strong-interference settings due to the larger number of passive elements under the same budget. Overall, the paper provides a principled optimization framework for RIS-enhanced spectrum sensing and offers practical insights into when to deploy active versus passive RIS configurations.

Abstract

In opportunistic cognitive radio networks, when the primary signal is very weak compared to the background noise, the secondary user requires long sensing time to achieve a reliable spectrum sensing performance, leading to little remaining time for the secondary transmission. To tackle this issue, we propose an active reconfigurable intelligent surface (RIS) assisted spectrum sensing system, where the received signal strength from the interested primary user can be enhanced and underlying interference within the background noise can be mitigated as well. In comparison with the passive RIS, the active RIS can not only adapt the phase shift of each reflecting element but also amplify the incident signals. Notably, we study the reflecting coefficient matrix (RCM) optimization problem to improve the detection probability given a maximum tolerable false alarm probability and limited sensing time. Then, we show that the formulated problem can be equivalently transformed to a weighted mean square error minimization problem using the principle of the well-known weighted minimum mean square error (WMMSE) algorithm, and an iterative optimization approach is proposed to obtain the optimal RCM. In addition, to fairly compare passive RIS and active RIS, we study the required power budget of the RIS to achieve a target detection probability under a special case where the direct links are neglected and the RIS-related channels are line-of-sight. Via extensive simulations, the effectiveness of the WMMSE-based RCM optimization approach is demonstrated. Furthermore, the results reveal that the active RIS can outperform the passive RIS when the underlying interference within the background noise is relatively weak, whereas the passive RIS performs better in strong interference scenarios because the same power budget can support a vast number of passive reflecting elements for interference mitigation.
Paper Structure (14 sections, 2 theorems, 75 equations, 7 figures, 2 algorithms)

This paper contains 14 sections, 2 theorems, 75 equations, 7 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Active RIS Assisted Spectrum Sensing System
  3. Signal Model
  4. MED with Whitened Signal Samples
  5. Power Consumption Model of Active RIS
  6. Problem Formulation
  7. Reflecting Coefficient Matrix Optimization
  8. WMMSE-based RCM Optimization for Active RIS
  9. WMMSE-based RCM Optimization for Passive RIS
  10. How much power budget is required to realize a given target detection probability?
  11. With Negligible Interferers
  12. With Non-negligible Interferers
  13. Simulation Results
  14. Conclusions

Key Result

Lemma 1

Given two matrices $\mathbf{A}\in\mathbb{C}^{n\times p}$, $\mathbf{B}\in\mathbb{C}^{p\times l}$, let $\mathbf{N}$ be a positive definite matrix, we have where $\mathbf{E}(\mathbf{\Gamma}, \mathbf{B})$ is defined as $\mathbf{\Gamma}\in\mathbb{C}^{n\times l}$ and $\mathbf{\Omega}\in\mathbb{C}^{l\times l}$ are two auxiliary matrices with $\mathbf{\Omega}$ a positive definite matrix. Moreover, the o

Figures (7)

  • Figure 1: The considered active RIS assisted spectrum sensing system.
  • Figure 2: The performance gains of the active RIS and passive RIS on the detection probability.
  • Figure 3: The required power budget to realize a target detection probability of $0.9$ for different $T$'s under the case with negligible interferers.
  • Figure 4: The required power budget to realize a target detection probability for different $T$'s under the case with non-negligible interferers.
  • Figure 5: The required power budget to realize a target detection probability of $P_{d}=0.9$ for different active probabilities of the interferers.
  • ...and 2 more figures

Theorems & Definitions (2)

  • Lemma 1: Principle of the WMMSE framework
  • Lemma 2