Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Molecular Absorption-Aware User Assignment, Spectrum, and Power Allocation in Dense THz Networks with Multi-Connectivity

Mohammad Amin Saeidi, Hina Tabassum, Mehrazin Alizadeh

TL;DR

The work addresses maximizing the sum-rate in dense THz networks by jointly optimizing user associations, sub-band counts and allocations within a transmission window, edge-band widths, and power, while accounting for molecular absorption, beam squint, blockage, hardware impairment, and imperfect CSI. It introduces a convex absorption coefficient approximation and edge-band determination, enabling a beam-squint-aware lower bound on the number of sub-bands, S. The optimization is split into a unimodular LP-based joint association/sub-band assignment and a FP/ADMM-based power allocation, solved iteratively with convergence guarantees. Numerical results show substantial gains from multi-connectivity and show robustness to THz-specific impairments, offering practical insights into base-station density, edge-band design, and hardware limitations for future 6G THz networks.

Abstract

This paper develops a unified framework to maximize the network sum-rate in a multi-user, multi-BS downlink terahertz (THz) network by optimizing user associations, number and bandwidth of sub-bands in a THz transmission window (TW), bandwidth of leading and trailing edge-bands in a TW, sub-band assignment, and power allocations. The proposed framework incorporates multi-connectivity and captures the impact of molecular absorption coefficient variations in a TW, beam-squint, molecular absorption noise, and link blockages. To make the problem tractable, we first propose a convex approximation of the molecular absorption coefficient using curve fitting in a TW, determine the feasible bandwidths of the leading and trailing edge-bands, and then derive closed-form optimal solution for the number of sub-bands considering beam-squint constraints. We then decompose joint user associations, sub-band assignment, and power allocation problem into two sub-problems, i.e., \textbf{(i)} joint user association and sub-band assignment, and \textbf{(ii)} power allocation. To solve the former problem, we analytically prove the unimodularity of the constraint matrix which enables us to relax the integer constraint without loss of optimality. To solve power allocation sub-problem, a fractional programming (FP)-based centralized solution as well as an alternating direction method of multipliers (ADMM)-based light-weight distributed solution is proposed. The overall problem is then solved using alternating optimization until convergence. Complexity analysis of the algorithms and numerical convergence are presented. Numerical findings validate the effectiveness of the proposed algorithms and extract useful insights about the interplay of the density of base stations (BSs), Average order of multi-connectivity (AOM), molecular absorption, {hardware impairment}, {imperfect CSI}, and link blockages.

Molecular Absorption-Aware User Assignment, Spectrum, and Power Allocation in Dense THz Networks with Multi-Connectivity

TL;DR

The work addresses maximizing the sum-rate in dense THz networks by jointly optimizing user associations, sub-band counts and allocations within a transmission window, edge-band widths, and power, while accounting for molecular absorption, beam squint, blockage, hardware impairment, and imperfect CSI. It introduces a convex absorption coefficient approximation and edge-band determination, enabling a beam-squint-aware lower bound on the number of sub-bands, S. The optimization is split into a unimodular LP-based joint association/sub-band assignment and a FP/ADMM-based power allocation, solved iteratively with convergence guarantees. Numerical results show substantial gains from multi-connectivity and show robustness to THz-specific impairments, offering practical insights into base-station density, edge-band design, and hardware limitations for future 6G THz networks.

Abstract

This paper develops a unified framework to maximize the network sum-rate in a multi-user, multi-BS downlink terahertz (THz) network by optimizing user associations, number and bandwidth of sub-bands in a THz transmission window (TW), bandwidth of leading and trailing edge-bands in a TW, sub-band assignment, and power allocations. The proposed framework incorporates multi-connectivity and captures the impact of molecular absorption coefficient variations in a TW, beam-squint, molecular absorption noise, and link blockages. To make the problem tractable, we first propose a convex approximation of the molecular absorption coefficient using curve fitting in a TW, determine the feasible bandwidths of the leading and trailing edge-bands, and then derive closed-form optimal solution for the number of sub-bands considering beam-squint constraints. We then decompose joint user associations, sub-band assignment, and power allocation problem into two sub-problems, i.e., \textbf{(i)} joint user association and sub-band assignment, and \textbf{(ii)} power allocation. To solve the former problem, we analytically prove the unimodularity of the constraint matrix which enables us to relax the integer constraint without loss of optimality. To solve power allocation sub-problem, a fractional programming (FP)-based centralized solution as well as an alternating direction method of multipliers (ADMM)-based light-weight distributed solution is proposed. The overall problem is then solved using alternating optimization until convergence. Complexity analysis of the algorithms and numerical convergence are presented. Numerical findings validate the effectiveness of the proposed algorithms and extract useful insights about the interplay of the density of base stations (BSs), Average order of multi-connectivity (AOM), molecular absorption, {hardware impairment}, {imperfect CSI}, and link blockages.
Paper Structure (39 sections, 5 theorems, 58 equations, 12 figures, 3 tables, 3 algorithms)

This paper contains 39 sections, 5 theorems, 58 equations, 12 figures, 3 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Works
  3. Contributions
  4. System Model and Assumptions
  5. Downlink Transmission Model
  6. Beam Squint Consideration and THz Channel Model
  7. THz SINR Model and Blockage-Aware Rate Model
  8. Problem Formulation, Constraints, and Transformations
  9. Problem Formulation
  10. Molecular Absorption Coefficient
  11. Convexifying the Molecular Absorption Coefficient
  12. Leading and Trailing Edge Bands of the TW
  13. Bound on the Number of THz Sub-bands with Beam-Squint
  14. Transformation of the Objective Function
  15. Proposed Algorithm for WSR Maximization in a Multi-Cell THz Network
  16. ...and 24 more sections

Key Result

Lemma 1

For a given power allocation and user association, the objective function in $\mathcal{P}_1$, i.e., $\sum\limits_{b \in \mathcal{B}} \sum\limits_{n \in \mathcal{N}} \sum\limits_{s \in \mathcal{S}} R_{b,s,n}$ is a decreasing function of the total number of sub-bands, $S$. Therefore, the lower bound o

Figures (12)

  • Figure 1: System model illustrating BSs and users in the presence of randomly distributed blockers.
  • Figure 2: Graphical illustration of $\mathbf{T}^{(2)}$ and $\mathbf{T}^{(3)}$.
  • Figure 3: Varying antennas' directionality on (a) network sum-rate (b) average multi-connectivity order. $\Gamma^L_n=1$, $B=6$, $N=12$.
  • Figure 4: (a) System sum-rate (b) AOM vs number of BSs, $\Gamma^L_n=1$, $q=0.2$, $N=12$.
  • Figure 5: Network sum-rate vs molecular absorption coefficient, $\Gamma^L_n=1$, $B=6$, $N=12$.
  • ...and 7 more figures

Theorems & Definitions (13)

  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Definition 1: Totally Unimodular Matrix (TUM)
  • Theorem 1
  • proof
  • Definition 2: Operations that Preserve Unimodularity
  • Definition 3
  • Lemma 3
  • ...and 3 more