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NCR vs. Passive/Active RIS: How Much NCR Amplification is Required to Beat RIS?

Özlem Tuğfe Demir, Ozan Alp Topal, Cicek Cavdar, Emil Björnson

Abstract

This paper investigates the fundamental tradeoff between reconfigurable intelligent surfaces (RISs) and network-controlled repeaters (NCRs) in terms of achievable signal-to-noise ratio (SNR). Considering an uplink system with a multi-antenna base station (BS) and a single-antenna user equipment (UE), we derive closed-form SNR expressions for passive RIS-, active RIS-, and NCR-assisted communication under line-of-sight propagation between the BS-RIS/NCR and RIS/NCR-UE. Both narrowband and wideband transmissions are analyzed, with and without the presence of a direct BS--UE link. Our analysis reveals a key structural difference: while the SNR achieved with RISs grows unboundedly with the number of RIS elements, the SNR provided by an NCR is fundamentally limited by the UE--repeater channel due to noise amplification. Nevertheless, we show that NCRs can outperform both passive and active RISs when deployed close to the UE, provided that sufficient amplification is available. Numerical results based on realistic path loss models quantify the amplification levels required for NCRs to outperform RISs across different deployment geometries and system dimensions. These findings provide clear design guidelines for the practical integration of RISs and NCRs in future wireless networks.

NCR vs. Passive/Active RIS: How Much NCR Amplification is Required to Beat RIS?

Abstract

This paper investigates the fundamental tradeoff between reconfigurable intelligent surfaces (RISs) and network-controlled repeaters (NCRs) in terms of achievable signal-to-noise ratio (SNR). Considering an uplink system with a multi-antenna base station (BS) and a single-antenna user equipment (UE), we derive closed-form SNR expressions for passive RIS-, active RIS-, and NCR-assisted communication under line-of-sight propagation between the BS-RIS/NCR and RIS/NCR-UE. Both narrowband and wideband transmissions are analyzed, with and without the presence of a direct BS--UE link. Our analysis reveals a key structural difference: while the SNR achieved with RISs grows unboundedly with the number of RIS elements, the SNR provided by an NCR is fundamentally limited by the UE--repeater channel due to noise amplification. Nevertheless, we show that NCRs can outperform both passive and active RISs when deployed close to the UE, provided that sufficient amplification is available. Numerical results based on realistic path loss models quantify the amplification levels required for NCRs to outperform RISs across different deployment geometries and system dimensions. These findings provide clear design guidelines for the practical integration of RISs and NCRs in future wireless networks.
Paper Structure (20 sections, 1 theorem, 72 equations, 10 figures)

This paper contains 20 sections, 1 theorem, 72 equations, 10 figures.

Table of Contents

  1. Introduction
  2. System and Channel Model
  3. Passive RIS-assisted communication
  4. Active RIS-assisted communication
  5. NCR-assisted communication
  6. Comparison between passive/active RIS and NCR
  7. Comparison between passive RIS and NCR
  8. Comparison between active RIS and NCR
  9. Comparison When the Direct Path is Included
  10. Passive RIS-assisted communication
  11. Active RIS-assisted communication
  12. NCR-assisted communication
  13. Comparison between passive RIS and NCR
  14. Comparison between active RIS and NCR
  15. Wideband Case
  16. ...and 5 more sections

Key Result

Theorem 1

The SNR in eq:SNR-complicated-activeRIS2 is maximized when all RIS amplitude gains are identical, i.e., $|\psi_{{\rm A},n}| = \alpha_{\rm A\text{-}RIS}$ for all $n$, under the maximum amplitude constraint $\alpha_{\rm A-RIS}\leq \alpha_{\rm A-RIS, max}$. Under this configuration, the SNR can be expr where Moreover, the optimal amplitude is given by where

Figures (10)

  • Figure 1: The required amplification gain $\alpha_{\rm NCR}$ of the repeater to outperform the passive RIS in terms of the distance between the NCR/RIS and BS.
  • Figure 2: The SNR obtained with passive RIS and NCR in terms of the distance between the NCR/RIS and BS.
  • Figure 3: The required amplification gain $\alpha_{\rm NCR}$ of the repeater to outperform the active RIS in terms of the distance between the repeater/RIS and BS.
  • Figure 4: The SNR obtained with active RIS and NCR in terms of the distance between the NCR/RIS and BS.
  • Figure 5: The SNR obtained with passive/active RIS and NCR in terms of the horizontal position of the RIS/NCR.
  • ...and 5 more figures

Theorems & Definitions (3)

  • Theorem 1
  • proof
  • Remark 1