# Optimized Gateway Placement for Interference Cancellation in Transmit-Only LPWA Networks
## 1 Introduction  
The sensor nodes (SNs) in a low-power wide area network (LPWAN) are often required to be low cost and low energy, while the LPWAN should provide reliable communication and wide area coverage. LPWANs are an important technology for the Internet of Things (IoT) [1]. Several existing LPWAN solutions, such as the non-cellular systems of the SigFox [2], LoRa [3] and cellular narrow band IoT (NB-IoT) system of 3 GPP [4], are being promoted. LPWAN application areas include smart cities, precision agriculture, wearables, transport, utilities and environmental monitoring [5]. In this paper, we study the sensor network, in which the sensors have one-hop to the gateways (GWs), which is known as star network topology (Figure 1), and in particular, the preferred placements of the GWs, when the GWs are capable of interference cancellation (IC). Two of the main objectives in LPWAN design are to minimize power consumption on the sensors and minimize total system cost, including deployment, operation, maintenance, etc. Currently, most LPWANs are equipped with transceiver sensor radios. However, the receiver module of a transceiver often consumes more energy and is more costly than the transmitter [6; 7; 8]. Furthermore, many LPWAN applications contain hundreds or thousands of SNs, and have as their function to simply report sensed data to the server or cloud periodically and/or when an event is detected. Keeping the receiver turned off or removing it entirely not only saves the energy of receiver operation but also eliminates the energy overhead of medium access control (MAC) packets. Therefore, exploiting transmit only (TO) SNs in LPWAN can provide significant reduction in complexity, cost, and energy consumption [6; 7; 8]. The lack of receiver function in TO SNs has certain implications with regards to MAC. The TO SNs cannot perform carrier-sensing, as in the carrier sense multiple access (CSMA) systems, and data transmissions by these nodes are completely uncoordinated. This characteristic rules out the use of most existing MAC protocols such as IEEE 802.11 [9], B-Mac [10], S-Mac [11], and TSMP [12]. While ALOHA-based protocols are attractive for LPWANs because of their simplicity, lack of receiver rules out those protocols also, because acknowledgements cannot be received. Network time synchronization, which is the synchronization of the clocks on all the SNs in a network, is not possible for TO SNs, implying that time-division multiple access protocols cannot be supported. As in ALOHA-based protocols, collisions will be unavoidable in TO networks. Packet repetition provides reliability to TO SNs [13]. Advanced signal processing at the GWs allows most of the burden of TO channel conflict resolution to be shifted to the GWs, which simplifies the hardware and functionality of the SNs and drastically reduces the energy consumption in the SNs. To resolve the collisions, the GWs can perform capture and IC. Capture is the decoding of a packet despite interference. IC is the well-known process of subtracting the effects of a decoded packet from the stored soft samples of the received waveform, so that an underlying weaker packet may be decoded. Practical IC does not achieve perfect subtraction and the residual error power causes interference on the weaker packet. Many authors model the residual power from imperfect IC as a simple fraction of the power of the packet being canceled (e.g., [14]). This paper shows that this model of IC residual error implies quite particular preferred locations for the GWs. The TO LPWA networks referred to in this paper, as illustrated in Figure 1, adopt a multi-gateway architecture, i.e., data packets are sent over wireless links from SNs to GWs, where the packets are decoded. Then, the GWs forward the packets to a server or the cloud via the Internet. We assume the GWs will coordinate data reception to reduce packet losses and maximize channel efficiency by providing diversity against fading and IC to mitigate packet collisions. Every SN is within a single hop of one or more GWs.