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Opportunistic User Scheduling for Secure RIS-aided Wireless Communications

Burhan Wafai, Sarbani Ghose, Chinmoy Kundu, Ankit Dubey, Mark F. Flanagan

TL;DR

This work tackles secure RIS-aided wireless communications with multiple users and eavesdroppers by proposing two opportunistic scheduling schemes: SS when eavesdropper CSI is unavailable and OS when CSI is available. It derives approximate closed-form SOP expressions and tight high-SNR approximations, incorporating a realistic path-loss model and CLT-based fading for the RIS-enabled links. The analysis reveals SOP saturation at high SNR, with exponential decay in $N$ for SS and in $MN$ for OS, and demonstrates that RIS can outperform DF relays when the element count is sufficiently large, with frequency-dependent thresholds. Numerical results validate the theory and highlight practical design guidelines for RIS element budgeting, placement, and scheduling strategy in secure multi-user networks.

Abstract

In this paper, we provide expressions for the secrecy outage probability (SOP) for suboptimal and optimal opportunistic scheduling schemes in a reconfigurable intelligent surface (RIS) aided {single antenna} system with multiple eavesdroppers in approximate closed form. A suboptimal scheduling (SS) scheme is analyzed, which is used when the channel state information (CSI) of the eavesdropping links is unavailable, and the optimal scheduling (OS) scheme is also analyzed, which is used when the global CSI is available. For each scheme, we provide a simplified expression for the SOP in the high signal-to-noise ratio (SNR) regime to demonstrate its behavior as a function of the key system parameters. At high SNR, the SOP saturates to a constant level which decreases exponentially with the number of RIS elements in the SS scheme and with the product of the number of RIS elements and the number of users in the OS scheme. We also show that the derived SOP of the SS scheme can directly provide the SOP for the best antenna-user pair scheduling scheme in a multiple antenna system. We compare the performance of the opportunistic user scheduling schemes with that of a non-orthogonal multiple access (NOMA) based scheduling scheme which chooses a pair of users in each time slot for scheduling and we show that the opportunistic schemes outperform the NOMA-based scheme. We also derive a closed-form expression for the SOP of a decode-and-forward (DF) relay-aided scheduling scheme in order to compare it with that of the RIS-aided system. It is found that the RIS-aided system outperforms the relay-aided systems when the number of RIS elements is sufficiently large. An increased number of RIS elements is required to outperform the relay-aided system at higher operating frequencies.

Opportunistic User Scheduling for Secure RIS-aided Wireless Communications

TL;DR

This work tackles secure RIS-aided wireless communications with multiple users and eavesdroppers by proposing two opportunistic scheduling schemes: SS when eavesdropper CSI is unavailable and OS when CSI is available. It derives approximate closed-form SOP expressions and tight high-SNR approximations, incorporating a realistic path-loss model and CLT-based fading for the RIS-enabled links. The analysis reveals SOP saturation at high SNR, with exponential decay in for SS and in for OS, and demonstrates that RIS can outperform DF relays when the element count is sufficiently large, with frequency-dependent thresholds. Numerical results validate the theory and highlight practical design guidelines for RIS element budgeting, placement, and scheduling strategy in secure multi-user networks.

Abstract

In this paper, we provide expressions for the secrecy outage probability (SOP) for suboptimal and optimal opportunistic scheduling schemes in a reconfigurable intelligent surface (RIS) aided {single antenna} system with multiple eavesdroppers in approximate closed form. A suboptimal scheduling (SS) scheme is analyzed, which is used when the channel state information (CSI) of the eavesdropping links is unavailable, and the optimal scheduling (OS) scheme is also analyzed, which is used when the global CSI is available. For each scheme, we provide a simplified expression for the SOP in the high signal-to-noise ratio (SNR) regime to demonstrate its behavior as a function of the key system parameters. At high SNR, the SOP saturates to a constant level which decreases exponentially with the number of RIS elements in the SS scheme and with the product of the number of RIS elements and the number of users in the OS scheme. We also show that the derived SOP of the SS scheme can directly provide the SOP for the best antenna-user pair scheduling scheme in a multiple antenna system. We compare the performance of the opportunistic user scheduling schemes with that of a non-orthogonal multiple access (NOMA) based scheduling scheme which chooses a pair of users in each time slot for scheduling and we show that the opportunistic schemes outperform the NOMA-based scheme. We also derive a closed-form expression for the SOP of a decode-and-forward (DF) relay-aided scheduling scheme in order to compare it with that of the RIS-aided system. It is found that the RIS-aided system outperforms the relay-aided systems when the number of RIS elements is sufficiently large. An increased number of RIS elements is required to outperform the relay-aided system at higher operating frequencies.
Paper Structure (18 sections, 2 theorems, 43 equations, 5 figures)

This paper contains 18 sections, 2 theorems, 43 equations, 5 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. User Scheduling without Eavesdroppers' CSI
  4. User Scheduling with Eavesdroppers'CSI
  5. SOP in the high-SNR regime
  6. Single-User Scenario
  7. User Scheduling without Eavesdroppers' CSI
  8. User Scheduling with Eavesdroppers' CSI
  9. DF Relay-aided Scheduling
  10. Numerical Results
  11. Comparison of SE, ME, SS, and OS schemes
  12. Comparison of opportunistic user scheduling with NOMA-based scheduling
  13. Comparison of RIS-aided and DF relay-aided systems
  14. Conclusion
  15. The solution of $\mathcal{J}_{+}^{(\boldsymbol{k},l)}((\sigma^{(\boldsymbol{k})}_{\text{U}})^2)$ given by (\ref{['eq_I1_prime_subopt_ext']})
  16. ...and 3 more sections

Key Result

Theorem 1

An approximate closed-form expression for the SOP of the SS scheme is given by where $\mathcal{S}_m$ is the set of integer vectors $\boldsymbol{k}=[k_1, k_2, k_3]$ such that $k_{i}\in\{0 ,\ldots, m\}$ for each $i\in\{1 ,2, 3\}$ and $\sum_{i=1}^3k_i=m$, $\binom{m}{\boldsymbol{k}}= \frac{m!}{ k_1!k_2!k_{3}!}$, $\sigma^{(\boldsymbol{k})}_{\text{U}}= \frac{\sigma_{\text{U}}}{\sqrt{\sum

Figures (5)

  • Figure 1: An RIS-aided system with multiple users and multiple eavesdroppers.
  • Figure 2: SOP vs. $P/N_0$ by varying $N=\{512, 1024\}$ when $f=2$ GHz, $\{(M, L)\}=\{(1,1), (1, 10), (10,10)\}$, $\delta_{\text{SU}}=900$ m, $\delta_{\text{SE}}=300$ m, and $\delta_{\text{SR}} = \delta_{\text{RS}} = \delta_{\text{RU}} = \delta_{\text{RE}} = 200$ m.
  • Figure 3: Comparison of opportunistic scheduling and NOMA-based scheduling by varying $N=\{512, 1024\}$ when $f=2$ GHz, $\{(M, L)\}=\{ (10,10)\}$, $\delta_{\text{SU}}=900$ m, $\delta_{\text{SE}}=300$ m, and $\delta_{\text{SR}} = \delta_{\text{RS}} = \delta_{\text{RU}} = \delta_{\text{RE}} = 200$ m.
  • Figure 4: SOP vs. $N$ for the RIS and DF relay-aided systems by varying $f=\{1,2\}$ GHz when $P/N_0=20$ dB, $M=10$, $L=3$, $\delta_{\text{SR}}=40$ m, $\delta_{\text{SU}}=200$ m, $\delta_{\text{SE}}=125$ m, $\delta_{\text{RS}} = \delta_{\text{RU}} = \delta_{\text{RE}} = 30$ m, and $\upsilon = 3$.
  • Figure 5: SOP vs. $\delta_{\text{SE}}$ for the RIS and DF relay-aided systems when $f=2$ GHz, $N =64$, $M=10$, $L=3$, $\delta_{\text{SR}}=50$ m, $\delta_{\text{RS}}=\delta_{\text{RU}}=70$ m, $\delta_{\text{RE}}=20$ m, and $\upsilon=3$.

Theorems & Definitions (15)

  • Theorem 1
  • proof
  • Corollary 1
  • proof
  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Remark 5
  • Remark 6
  • ...and 5 more