# Energy Detection over Composite $\kappa-\mu$ Shadowed Fading Channels with Inverse Gaussian Distribution in Ultra mMTC Networks

## TL;DR

This paper derives new closed-form expressions for energy detection performance over complex fading channels in ultra mMTC networks, highlighting the importance of propagation paths over SNR.

## Contribution

It introduces novel mathematical expressions for detection probability over $ppa$-$mu$ shadowed channels using Inverse Gaussian distribution, with implications for 6G network design.

## Key findings

- Propagation paths significantly influence detection probability.
- Increasing SNR alone is less effective than optimizing placement and antenna alignment.
- First closed-form expression for average detection probability over these channels.

## Abstract

This paper investigates the characteristics of energy detection (ED) over composite $\kappa$-$\mu$ shadowed fading channels in ultra machine-type communication (mMTC) networks. We have derived the closed-form expressions of the probability density function (PDF) of signal-to-noise ratio (SNR) based on the Inverse Gaussian (\emph{IG}) distribution. By adopting novel integration and mathematical transformation techniques, we derive a truncation-based closed-form expression for the average detection probability for the first time. It can be observed from our simulations that the number of propagation paths has a more pronounced effect on average detection probability compared to average SNR, which is in contrast to earlier studies that focus on device-to-device networks. It suggests that for 6G mMTC network design, we should consider enhancing transmitter-receiver placement and antenna alignment strategies, rather than relying solely on increasing the device-to-device average SNR.