# Effective Energy Efficiency under Delay–Outage Probability Constraints and ℱ-Composite Fading

## TL;DR

This paper studies energy efficiency in 6G networks for IoT devices, considering channel fading and quality of service constraints.

## Contribution

The paper introduces a new model for evaluating effective energy efficiency under F-composite fading and QoS constraints in 6G networks.

## Key findings

- The EEE is quasiconcave, showing a trade-off between transmit power and rate.
- A PSO algorithm is used to solve power and rate allocation problems for maximizing EEE.
- The impact of line-of-sight and shadowing parameters on EEE is analyzed.

## Abstract

The paradigm of the Next Generation cellular network (6G) and beyond is machine-type communications (MTCs), where numerous Internet of Things (IoT) devices operate autonomously without human intervention over wireless channels. IoT’s autonomous and energy-intensive characteristics highlight effective energy efficiency (EEE) as a crucial key performance indicator (KPI) of 6G. However, there is a lack of investigation on the EEE of random arrival traffic, which is the underlying platform for MTCs. In this work, we explore the distinct characteristics of F-composite fading channels, which specify the combined impact of multipath fading and shadowing. Furthermore, we evaluate the EEE over such fading under a finite blocklength regime and QoS constraints where IoT applications generate constant and sporadic traffic. We consider a point-to-point buffer-aided communication system model, where (1) an uplink transmission under a finite blocklength regime is examined; (2) we make realistic assumptions regarding the perfect channel state information (CSI) available at the receiver, and the channel is characterized by the F-composite fading model; and (3) due to its effectiveness and tractability, application data are found to have an average arrival rate calculated using Markovian sources models. To this end, we derive an exact closed-form expression for outage probability and the effective rate, which provides an accurate approximation for our analysis. Moreover, we determine the arrival and required service rates that satisfy the QoS constraints by applying effective bandwidth and capacity theories. The EEE is shown to be quasiconcave, with a trade-off between the transmit power and the rate for maximising the EEE. Measuring the impact of transmission power or rate individually is quite complex, but this complexity is further intensified when both variables are considered simultaneously. Thus, we formulate power allocation (PA) and rate allocation (RA) optimisation problems individually and jointly to maximise the EEE under a QoS constraint and solve such a problem numerically through a particle swarm optimization (PSO) algorithm. Finally, we examine the EEE performance in the context of line-of-sight and shadowing parameters.