Sum of Squared Extended {eta}-{mu} and {kappa}-{mu} RVs: A New Framework Applied to FR3 and Sub-THz Systems

2025-02-04

AI Summary

This work addresses the challenges of inaccurate received power modeling and low analytical accuracy for multi-antenna systems operating in the FR3 and sub-terahertz (sub-THz) bands under generalized fading channels. To this end, we derive, for the first time, closed-form probability density function (PDF) and cumulative distribution function (CDF) expressions for the sum of squares of independent and identically distributed random variables under extended η–μ and κ–μ fading. The proposed analytical framework achieves high computational efficiency, low complexity, and rapid truncation convergence, enabling unified derivation of key performance metrics—including outage probability, coverage probability, bit error rate (BER), and symbol error probability (SEP)—in large-scale MIMO scenarios. Our results enable high-accuracy, low-overhead performance evaluation of FR3/sub-THz downlink transmissions under generalized fading, thereby providing both theoretical foundations and practical tools for 6G high-frequency system design and link budgeting.

Technology Category

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

Application Category

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

Abstract

The analysis of systems operating in future frequency ranges calls for a proper statistical channel characterization through generalized fading models. In this paper, we adopt the Extended {eta}-{mu} and {kappa}-{mu} models to characterize the propagation in FR3 and the sub-THz band, respectively. For these models, we develop a new exact representation of the sum of squared independent and identically distributed 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. For both the Extended {eta}-{mu} and {kappa}-{mu} distributions, we derive novel expressions for the probability density function and cumulative distribution function, we analyze their convergence and truncation error, and we discuss the computational complexity and implementation aspects. Moreover, we derive expressions for the outage and coverage probability, bit error probability for coherent binary modulations, and symbol error probability for M-ary phase-shift keying and quadrature amplitude modulation. Lastly, we provide an extensive performance evaluation of FR3 and sub-THz systems focusing on a downlink scenario where a single-antenna user is served by a base station employing maximum ratio transmission.

Problem

• Statistical channel characterization using generalized fading models
• Development of tractable analytical framework for multi-antenna systems
• Performance evaluation of FR3 and sub-THz communication systems

Innovation

• Extended η-μ and κ-μ models
• Exact sum of squared RVs
• Tractable analytical framework