# Beacon Success Rate versus Gateway Density in Sub-GHz Sensor Networks
### Contributions of the Paper  
This section provides the motivation and introduction to the contributions of this paper. The previously mentioned works explore various aspects of improving MAC efficiency within IoT systems. In adaptive schemes, difficulties emerge in link adaptation via dynamically changing Modulation and Coding Scheme (MCS) or in formulating scheduling decisions based on link quality. Such difficulties are especially relevant in scenarios where Channel State Information (CSI) might not be readily accessible. This constraint is particularly notable in low-bitrate IoT systems characterized by extended airtimes, heightened protocol latencies, and operation in unlicensed bands, making the Channel State Information (CSI) obsolete by the time it is available for decision making. To address these challenges, this study takes a different approach by focusing on fixed bit-rate strategy and employing simple periodic beaconing alongside TSCH. The aim is to simplify the protocol and to reduce the overhead, especially for low-bitrate End Nodes (ENs). While this simplification mitigates certain complexities, it introduces challenges related to intra-network interference and its impact on latency, which are thoroughly analyzed in this paper.  
The findings in this study indicate that enhancing beacon success rates can be achieved by implementing larger beacon intervals and increasing the number of channels. Introducing GW diversity proves advantageous in reducing beacon acquisition latency and expanding the coverage area [2]. In urban settings, the abundance of GWs enhances the potential for Gateway diversity. Despite a potential increase in DL beacon collision rates, the significant benefits of spatial diversity become apparent. Each GW plays a role in subdividing the path-loss into smaller segments, thereby improving the overall network performance. Furthermore, the strategic use of larger beacon intervals proves advantageous in augmenting network capacity by reducing beacon collision rates. This emphasizes the significance of strategically utilizing GW diversity and fine-tuning beacon intervals to optimize network performance in urban environments. Additionally, this paper introduces a co-channel interference model that dynamically considers partial overlaps from other co-channel interferers. This model takes into account the relative power of these interferers compared to the desired signal, providing a comprehensive understanding of interference dynamics in the network. As a result, it offers insights into the fine-tuning of various system parameters. The model is used to derive the relationship between beacon collisions and packet loss rates. The paper presents guidance on the selection of GFSK modulation parameters for low bit-rate and narrow-bandwidth IoT applications.  
This paper is organized as follows. In Section 2, the system model regarding the channel access scheme, interference, and path-loss models is presented. Section 3 presents the PHY layer model with GFSK modulation parameters specifically tailored for narrowband IoT sensors. Such parameters have not been previously explored, making it of significant importance for narrowband devices. The theoretical analysis of the beacon collision probability versus network size is presented in Section 4. The simulator architecture is presented in Section 5. Finally, the numerical simulation results of the collision probability versus network density are presented in Section 6 with the PHY and Medium Access Control (MAC) layer models. The conclusions from this study are presented in Section 7.