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Jointly Optimal RIS Placement and Power Allocation for Underlay D2D Communications: An Outage Probability Minimization Approach

Sarbani Ghose, Deepak Mishra, Santi P. Maity, George C. Alexandropoulos

TL;DR

The paper addresses OP minimization for RIS-enabled underlaid D2D communications in cognitive networks, deriving a closed-form OP under Rayleigh fading with a direct DS-DU link and RIS assistance. It develops a CLT-based SINR analysis and an equivalent optimization by approximating the OP and moments, enabling decoupled optimization of RIS placement and DS power for parallel and elliptical RIS topologies. The proposed jointly optimal design shows substantial gains over benchmarks (up to 44% improvement) and provides practical guidelines for RIS deployment and power control in D2D-cognitive settings. The work lays a foundation for extending to multiple D2D pairs, richer BS precoding, and secrecy considerations in RIS-assisted networks.

Abstract

In this paper, we study underlay device-to-device (D2D) communication systems empowered by a reconfigurable intelligent surface (RIS) for cognitive cellular networks. Considering Rayleigh fading channels and the general case where there exist both the direct and RIS-enabled D2D channels, the outage probability (OP) of the D2D communication link is presented in closed-form. Next, for the considered RIS-empowered underlaid D2D system, we frame an OP minimization problem. We target the joint optimization of the transmit power at the D2D source and the RIS placement, under constraints on the transmit power at the D2D source and on the limited interference imposed on the cellular user for two RIS deployment topologies. Due to the coupled optimization variables, the formulated optimization problem is extremely intractable. We propose an equivalent transformation which we are able to solve analytically. In the transformed problem, an expression for the average value of the signal-to-interference-noise ratio (SINR) at the D2D receiver is derived in closed-form. Our theoretical derivations are corroborated through simulation results, and various system design insights are deduced. It is indicatively showcased that the proposed RIS-empowered underlaid D2D system design outperforms the benchmark semi-adaptive optimal power and optimal distance schemes, offering $44\%$ and $20\%$ performance improvement, respectively.

Jointly Optimal RIS Placement and Power Allocation for Underlay D2D Communications: An Outage Probability Minimization Approach

TL;DR

The paper addresses OP minimization for RIS-enabled underlaid D2D communications in cognitive networks, deriving a closed-form OP under Rayleigh fading with a direct DS-DU link and RIS assistance. It develops a CLT-based SINR analysis and an equivalent optimization by approximating the OP and moments, enabling decoupled optimization of RIS placement and DS power for parallel and elliptical RIS topologies. The proposed jointly optimal design shows substantial gains over benchmarks (up to 44% improvement) and provides practical guidelines for RIS deployment and power control in D2D-cognitive settings. The work lays a foundation for extending to multiple D2D pairs, richer BS precoding, and secrecy considerations in RIS-assisted networks.

Abstract

In this paper, we study underlay device-to-device (D2D) communication systems empowered by a reconfigurable intelligent surface (RIS) for cognitive cellular networks. Considering Rayleigh fading channels and the general case where there exist both the direct and RIS-enabled D2D channels, the outage probability (OP) of the D2D communication link is presented in closed-form. Next, for the considered RIS-empowered underlaid D2D system, we frame an OP minimization problem. We target the joint optimization of the transmit power at the D2D source and the RIS placement, under constraints on the transmit power at the D2D source and on the limited interference imposed on the cellular user for two RIS deployment topologies. Due to the coupled optimization variables, the formulated optimization problem is extremely intractable. We propose an equivalent transformation which we are able to solve analytically. In the transformed problem, an expression for the average value of the signal-to-interference-noise ratio (SINR) at the D2D receiver is derived in closed-form. Our theoretical derivations are corroborated through simulation results, and various system design insights are deduced. It is indicatively showcased that the proposed RIS-empowered underlaid D2D system design outperforms the benchmark semi-adaptive optimal power and optimal distance schemes, offering and performance improvement, respectively.
Paper Structure (28 sections, 5 theorems, 55 equations, 11 figures, 1 table)

This paper contains 28 sections, 5 theorems, 55 equations, 11 figures, 1 table.

Table of Contents

  1. Introduction
  2. State-of-the Art
  3. Motivation and Contributions
  4. Organization and Notation
  5. System and Channel Models
  6. Network Topology and Access Protocol
  7. Parallel
  8. Elliptical
  9. RIS and Channel Models
  10. Received Signal and SINR Modeling
  11. Outage Probability Analysis
  12. Distribution of the SINRs
  13. Outage Probability (OP)
  14. The Case of the Absence of the Direct Link
  15. Proposed Optimization Framework
  16. ...and 13 more sections

Key Result

Lemma 1

The function $\Gamma_{\mathrm{d}}(\cdot)$ in eq_snr_DU_fin is unimodal, hence, using Jensen's inequality, we can write $\mathbb{E}[\Gamma_{\mathrm{d}}(\cdot)]\ge \Gamma_{\mathrm{d}}(\mathbb{E}[\cdot])$. An approximation of the expected value of $\Gamma_{\rm d}$ is given in expression eq_d2d_snr_2ndo

Figures (11)

  • Figure 1: The RIS-empowered underlay D2D communication system model under consideration.
  • Figure 2: The topology of the simulated RIS-aided underlaid D2D communication system.
  • Figure 3: The values of $\widehat{\Gamma}_{\rm d}$ as a function of $\bar{\gamma}_{\rm s}$ in dB considering an RIS with $N$={10, 20, 40, 80} tunable reflecting elements.
  • Figure 4: The values of $\Gamma_{\mathrm{d}}$ and $\Gamma_{\mathrm{d}}^{\star}$ as a function of $N$.
  • Figure 5: The mean and variance of the Gumbel-distributed random variable $\gamma_{\rm v}$ as functions of the number $M$ of BS antennas for different values of $\alpha_{\rm bd}$ in dB.
  • ...and 6 more figures

Theorems & Definitions (11)

  • Remark 1: Absence of the Direct Link
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Lemma 4
  • proof
  • Corollary 1
  • ...and 1 more