A New Framework for the Sum of Squared $κ$-$μ$ RVs with Application to Sub-THz Systems

2025-08-08

AI Summary

Accurate modeling of received signal power in sub-terahertz (sub-THz) multi-antenna systems remains challenging, and existing κ–μ fading models lack closed-form expressions for the sum of squared independent identically distributed (i.i.d.) κ–μ random variables. Method: This paper establishes, for the first time, an exact analytical framework for the sum of squared i.i.d. κ–μ variates, deriving closed-form expressions for its probability density function (PDF) and cumulative distribution function (CDF). The framework ensures high computational efficiency, rapid convergence, and low truncation error. Integrated with maximum-ratio combining (MRC), it enables unified analysis of coverage probability and bit error rate. Results: Numerical evaluations confirm high accuracy and robustness across diverse channel parameters and antenna array sizes. To the best of our knowledge, this work provides the first analytically tractable and scalable theoretical tool for performance evaluation of sub-THz massive MIMO systems.

Technology Category

• Machine Learning: Evaluation and Analysis
• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Search and Optimization: Evaluation and Analysis

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

In this paper, we adopt the $κ$-$μ$ model to characterize the propagation in the sub-THz band. We develop a new exact representation of the sum of squared independent and identically distributed $κ$-$μ$ random variables, which can be used to express the power of the received signal in multi-antenna systems. Unlike existing ones, the proposed analytical framework is remarkably tractable and computationally efficient, and thus can be conveniently employed to analyze systems with massive antenna arrays. We derive novel expressions for the probability density function and cumulative distribution function, analyze their convergence and truncation error, and discuss the computational complexity and the implementation aspects. Moreover, we derive expressions for the coverage probability and bit error probability for coherent binary modulations. Lastly, we evaluate the performance of an uplink sub-THz system where a single-antenna user is served by a base station employing maximum ratio combining.

Problem

• Modeling sub-THz signal propagation using κ-μ distribution
• Developing tractable framework for sum of squared κ-μ random variables
• Analyzing performance of massive antenna arrays in sub-THz systems

Innovation

• New exact representation for sum of squared κ-μ RVs
• Tractable analytical framework for massive antenna arrays
• Derived novel PDF and CDF expressions with error analysis