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

TL;DR

This paper introduces a new analytical framework for modeling the sum of squared extended $ ext{eta}$-$ ext{mu}$ and $ ext{kappa}$-$ ext{mu}$ random variables, enabling efficient performance analysis of future wireless systems in FR3 and sub-THz bands.

Contribution

It develops a novel, tractable representation for sums of squared extended $ ext{eta}$-$ ext{mu}$ and $ ext{kappa}$-$ ext{mu}$ RVs, facilitating system performance analysis in advanced frequency bands.

Findings

Derived new PDFs and CDFs for the models.

Analyzed outage and error probabilities for various modulations.

Demonstrated computational efficiency for massive MIMO systems.

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.