# Beacon Success Rate versus Gateway Density in Sub-GHz Sensor Networks
### Introduction to IEEE 802.15.4 Specification  
In this section, a brief introduction to Institute of Electrical and Electronics Engineers (IEEE)-802.15.4 standard is provided.  
The IEEE-802.15.4 standard provides specifications for the physical layer (PHY) and medium access control (MAC) sublayers, specifically tailored for wireless connectivity at low data rates involving fixed, portable, and mobile devices with either no battery or stringent battery consumption constraints. Numerous investigations explore the connectivity performance of diverse PHYs delineated in the IEEE802.15.4g (2012) amendment to the IEEE802.15.4 (2003) standard. This amendment introduces 31 PHYs specifically designed for Smart-metering Utility Network (SUN) applications, grouped into three modulation families: Frequency Shift Keying (FSK), Offset Quadrature Phase-Shift Keying (O-QPSK), and Orthogonal Frequency Division Multiplexing (OFDM) [13]. With data rates ranging from 25 kbps to 800 kbps, these PHYs function across two frequency bands: 2.4 GHz and sub-GHz [1].  
The various PHY specifications outlined in the standard accommodate devices operating in diverse geographic regions [1]. In summary, the specification is designed for short-, medium-, and long-range communication with low data rates, low power consumption, and low complexity. In this paper, Gaussian Frequency Shift Keying (GFSK) modulation with a data rate of 50 kbps is assumed for 802.15.4-based networks, particularly for Narrowband IoT (NB-IoT) applications. This choice is motivated by various factors presented, as follows.  
* Low Power Consumption: GFSK modulation is known for its energy efficiency, making it suitable for low-power devices and battery-operated sensors. In NB-IoT applications, where devices may need to operate on battery power for extended periods, minimizing energy consumption is crucial.
* Spectral Efficiency: GFSK modulation ensures the effective use of the frequency spectrum by allowing data transmission in a comparatively narrow bandwidth. This efficiency is achieved via the integrated Gaussian Pulse Shaping filter. This becomes particularly significant in situations where the available frequency spectrum is constrained, a common occurrence in IoT deployments. Moreover, GFSK modulation, being a constant envelope modulation, avoids issues of spectral regrowth caused by Power Amplifier Nonlinearities.
* Moderate-Range Communication: The GFSK modulation with a narrow bandwidth is designed for moderate-range communication, typically within a few hundred meters. This makes it suitable for applications where devices are located in close proximity to a building, such as home automation, industrial monitoring, or healthcare settings.
* Cost-Effective Implementation: GFSK modulation's simplicity facilitates cost-effective radio transceivers, making it an appealing choice in cost-sensitive IoT deployments.
* Compatibility with the IEEE-802.15.4 Standard: GFSK modulation with a data rate of 50 kbps aligns with the specifications of the 802.15.4 standard. This ensures interoperability between devices from different manufacturers that adhere to the same standard, fostering a more open and scalable IoT ecosystem.
* Suitability for Low-Data-Rate Applications: The 50 kbps data rate is well-suited for many IoT applications where the focus is on transmitting small amounts of data intermittently. Examples include sensor data, control signals, and sensor status updates.  
In summary, the choice of 802.15.4-based GFSK modulation with a 50 kbps data rate in NB-IoT networks is driven by the need for low power consumption, spectral efficiency, and suitability for medium-range, low-data-rate communication in cost-sensitive IoT applications.