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

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.