# Performance of Narrow Band Wide Area Networks with Gateway Diversity
## 1 Introduction  
Low-Power Wide-Area Networks (LPWAN) enable the Internet of Things (IoT) applications and hardware, such as smart meters, supply chain and logistics trackers, smart home/city sensors for automation, agricultural sensors, retail store sensors, asset/pet trackers, parking sensors, environmental sensors, healthcare sensors, safety and security sensors, remote controls, etc. The majority of the aforementioned IoT applications require battery operation with very low application data rate requirements, making long-range and low-power consuming modulation and coding schemes a viable choice. The use of low bandwidths and sub-GHz carrier frequencies, along with using constant envelope modulations in turn, reduces the hardware cost of the IoT sensors significantly, allowing wide adoption [1, 2, 3]. The sensors should be designed with battery operation in mind and hence very low bandwidths, such as 125 kHz, 250 kHz, and 500 kHz that are typically used with constant envelope modulation schemes. For example, the LoRa modulation has been a very popular choice as it can work under noise, thanks to the processing gain provided by the chirped spread spectrum (CSS) technique. The aforementioned processing gain per bit allows the LoRa modulation at the PHY layer to achieve very good sensitivity levels. This increases the range of the wireless link at the cost of increased airtime with increasing processing gain, resulting in lower bitrates along with susceptibility to channel variations due to mobility. Gateways (GWs) are hardware entities that have access to the internet/cloud that are the building blocks of the LPWAN. They typically have access to wall power or solar power and do not operate on a battery. Furthermore, they can be installed outside of homes or garages, allowing them to reach a better coverage area. Hence, GWs are typically more sophisticated and more powerful than end-nodes, allowing them to process data from multiple sensors. End-nodes refer to the HW sensors that operate on a battery. They rely on a GW to access the cloud to send sensory data. The Uplink (UL) refers to the traffic initiatedby an end-node that is received by a GW. Similarly, Downlink (DL) refers to the traffic sent by a GW to end-nodes. Typically, the UL is the bottleneck in such WAN as multiple end-nodes have to content for successful transmission to the nearest GW and suffer from collisions. Furthermore, it is easier to establish coordination among GWs (for DL) with high-bandwidth cloud links. The operation of the LPWAN network is depicted in Figure 1 as an example. The sensor (as an end-node (EN)) is trying to access a GW, e.g., smart metering purposes, which requires very low bitrates such as 2 kbps. It can access the cloud via the closest neighbor's GW or via the user's own GW which may not necessarily have the closest proximity to the sensor. This is referred to as GW diversity, where multiple GWs can pick up an ENs packet and pass it on to the cloud server for being sent to the application layer. In the later sections of this paper, the simulation results show the benefits of such GW diversity. In [4], the authors study the performance of LPWAN with message replication and multiple receive antennas. The authors provide an optimum number of message copies for different data rates and show improvements with time and antenna diversity in the UL. In [5], the authors perform experimental results for UL with GW diversity in an urban area. The coverage is defined as distances to the GW where at least one packet was received successfully out of many packets. However, this causes the Packet Success Rate (PSR) target to be set to only 1% at the declared range if only one packet was received out of one hundred, which does not provide a stable link. Hence, such an assumption causes overpromising results for range as it does not consider maintaining a reliable PSR per link. In this paper, the coverage area is defined for a given PSR target.