Beyond Diagonal IRS Assisted Ultra Massive THz Systems: A Low Resolution Approach

TL;DR

This paper addresses spectral efficiency optimization for downlink THz communication using a beyond-diagonal IRS (BD-IRS) under $1$-bit DAC constraints. It models the system with channels ${f H}$ and ${f g}$ and optimizes ${f v}$ and ${oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{}}}}}}}}}$ to maximize $ ext{SE} = ext{log}_2(1+oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{}}}}}})$ where $oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{}}}}}} = |({f H}^H oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{}}}}}} {f g})^H {f v}|^2/oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{}}}}}}$, under ${f v} rightarrow oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{}}}}}} ightarrow oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{}}}}} ext{ and } oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{}}}}} le P_{ ext{tot}}$. An alternating solution decouples into a CG-based low-resolution beamforming stage and an eigen-decomposition–guided discrete phase-shift stage, iterating until convergence. Results show BD-IRS yields substantial spectral-efficiency gains over diagonal-IRS configurations, with gains amplified by higher transmit power.

Abstract

The terahertz communications have the potential to revolutionize data transfer with unmatched speed and facilitate the development of new high-bandwidth applications. This paper studies the performance of downlink terahertz system assisted by beyond diagonal intelligent reconfigurable surface (BD-IRS). For enhanced energy efficiency and low cost, a joint precoding and BD-IRS phase shift design satisfying the $1$-bit resolution constraints to maximize the spectral efficiency is presented. The original problem is non-linear, NP-hard, and intricately coupled, and obtaining an optimal solution is challenging. To reduce the complexity, we first transform the optimization problem into two problems and then iteratively solve them to achieve an efficient solution. Numerical results demonstrate that the proposed approach for the BD-IRS assisted terahertz system significantly enhances the spectral efficiency compared to the conventional diagonal IRS assisted system.

Figures (3)

• Figure 1: Beyond diagonal IRS assisted THz communication, where we consider ${\bf H}\in\mathcal{C}^{M\times N}$ is the channel matrix between BS and BD-IRS, ${\bf g}\in\mathcal{C}^{M\times 1}$ is the channel vector between BD-IRS and user, and ${\bf v}\in\mathcal{C}^{N\times 1}$ is the effective transmitted signal.
• Figure 2: Convergence of the proposed algorithm, for $N=M=150$, $P_{tot}=10$ dBm.
• Figure 3: Number of antenna elements versus spectral efficiency of the system with different transmit power levels.