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IRS Configuration Techniques for Ultra Wideband Signals and THz Communications

Alberto Tarable, Laura Dossi, Giuseppe Virone, Alessandro Nordio

TL;DR

This paper tackles configuring IRSs for THz communications in the presence of ultra-wideband signals (up to 50% relative bandwidth), addressing beam squint and large-bandwidth effects. It develops a realistic system model, derives a tight end-to-end rate upper bound, and proposes multiple suboptimal IRS configuration techniques ranging from UCQP-based solvers to narrowband-inspired solutions. The work analyzes performance under rank-1 and rank-2 PSD scenarios, provides complexity assessments, and offers design rules that connect geometry, bandwidth, and IRS operation. The results demonstrate that simple NB-central solutions can be near-optimal for modest bandwidths, while robust methods like Max-eig phase deliver strong performance with manageable complexity in wideband THz-UWB IRS-aided systems, informing practical 6G implementations.

Abstract

Motivated by the challenges of future 6G communications where terahertz (THz) frequencies, intelligent reflective surfaces (IRSs) and ultra-wideband (UWB) signals coexist, we analyse and propose a set of efficient techniques for configuring the IRS when the signal bandwidth is a significant fraction of the central frequency (up to 50%). To the best of our knowledge this is the first time that IRS configuration techniques are analyzed for such huge bandwidths. In our work we take into account for the channel model, the power spectral density of the signal reflected by the IRS and the network geometry. We evaluate the proposed solutions in terms of achievable rate and compare it against an upper bound we derived. Our results hint rules for designing IRS-aided communication systems and allow to draw conclusions on the trade-off between performance and complexity required for configuring the IRS.

IRS Configuration Techniques for Ultra Wideband Signals and THz Communications

TL;DR

This paper tackles configuring IRSs for THz communications in the presence of ultra-wideband signals (up to 50% relative bandwidth), addressing beam squint and large-bandwidth effects. It develops a realistic system model, derives a tight end-to-end rate upper bound, and proposes multiple suboptimal IRS configuration techniques ranging from UCQP-based solvers to narrowband-inspired solutions. The work analyzes performance under rank-1 and rank-2 PSD scenarios, provides complexity assessments, and offers design rules that connect geometry, bandwidth, and IRS operation. The results demonstrate that simple NB-central solutions can be near-optimal for modest bandwidths, while robust methods like Max-eig phase deliver strong performance with manageable complexity in wideband THz-UWB IRS-aided systems, informing practical 6G implementations.

Abstract

Motivated by the challenges of future 6G communications where terahertz (THz) frequencies, intelligent reflective surfaces (IRSs) and ultra-wideband (UWB) signals coexist, we analyse and propose a set of efficient techniques for configuring the IRS when the signal bandwidth is a significant fraction of the central frequency (up to 50%). To the best of our knowledge this is the first time that IRS configuration techniques are analyzed for such huge bandwidths. In our work we take into account for the channel model, the power spectral density of the signal reflected by the IRS and the network geometry. We evaluate the proposed solutions in terms of achievable rate and compare it against an upper bound we derived. Our results hint rules for designing IRS-aided communication systems and allow to draw conclusions on the trade-off between performance and complexity required for configuring the IRS.
Paper Structure (28 sections, 5 theorems, 41 equations, 10 figures)

This paper contains 28 sections, 5 theorems, 41 equations, 10 figures.

Table of Contents

  1. INTRODUCTION
  2. Contributions of this work
  3. Related works
  4. Mathematical notation
  5. System model and problem formulation
  6. IRS model
  7. Overall system model
  8. Rate optimization problem
  9. Upper bound to the end-to-end communication rate
  10. Sub-optimal IRS configuration techniques
  11. Numerical algorithms solving UCQP problems
  12. A heuristic solution based on eigenvalue decomposition
  13. A family of solutions inspired by narrowband signals
  14. Small BS and UE array size
  15. Small BS and UE array size and discrete signal spectrum
  16. ...and 13 more sections

Key Result

Proposition 1

For $M_1\ge M_2$ and $L \ge M_2$, the maximum rate can be upper-bounded as where $N_0$ is the noise power spectral density, $\boldsymbol{\gamma}=[\gamma_1,\ldots,\gamma_L]^{\mathsf{T}}$, $\gamma_{\ell}={\rm e}^{{\rm j} \theta_{\ell}}$, for $\ell=1,\ldots,L$. The coefficients $B_m$ are defined as being $r_Q(f)$ any upper bound to the rank of the matrix ${\bf H}(f,\boldsymbol{\theta}) {\bf G}(f) {

Figures (10)

  • Figure 1: Representation of a communication network where a BS and a UE communicate by exploiting an IRS. The LoS link between BS and UE is unavailable due to an obstacle. Channel multipath components are due to the presence of a small number of reflectors.
  • Figure 2: Geometry of the simulated wireless communication network. The IRS is attached to a wall which also acts as a reflector. The IRS has square shape and is composed of $L=L_s^2$ elements.
  • Figure 3: Power spectral density profile of the signal transmitted by the $k$-th beam: (a) the entire available bandwidth is dedicated to a single user and (b) only some sub-bands are assigned to the UE.
  • Figure 4: Rate, $R$, versus $B_w$, as $\phi_{\rm UE}$ varies, for $K=1$, $M_1=16$, $P^{\rm tx}=22$ dBm, $L=64 \times 64$ and $\phi_{\rm BS}=45^\circ$. The BS implements single carrier UWB communication with "Adapted beamforming".
  • Figure 5: Rate $R$ versus $B_w$, for $K=1$, $M_1=16$, $L=64\times 64$, $\phi_{\rm BS}=45^\circ$, $\phi_{\rm UE}=30^\circ$, $P^{tx}_{1,s}=22$ dBm, "equal power loading" among sub-bands, and "Adapted beamforming" at the BS. The signal power spectral density is organized as in Figure \ref{['fig:Gf']}(b) with $N_1=2$. The effects of multipath and shadowing are not taken into account.
  • ...and 5 more figures

Theorems & Definitions (8)

  • Remark 1
  • Proposition 1
  • Proposition 2
  • Remark 2
  • Proposition 3
  • Proposition 4
  • Proposition 5
  • Remark 3