# Joint Spreading Factor and Channel Assignment in Multi-Operator LoRaWAN Deployments
## 1 Introduction  
With an ever increasing demand for reliability within IoT deployments, and with the inevitable densification of internet of things (IoT) devices, concurrent approaches to spreading factor (SF) and channel assignment in Long Rage Wide Area Networks LoRaWAN networks no longer suffice. The low power, long range, and durable transmissions in LoRaWAN take place over the frequency channels of the unlicensed industrial, scientific, and medical (ISM) bands while using a spread-spectrum modulation. Six spreading factors that range from SF7 to SF12 are used. Transmissions that are on the same SFs and on the same frequency channels lead to collisions. The latter become inescapable with multiple LoRaWAN deployments cohabiting the same areas. A 1% duty cycle limitation, which was introduced to maintain fairness in the ISM band, does little to improve the reliability of LoRaWAN networks, while simultaneously limiting their scalability.  
In this paper, we aim to tackle the various problems facing the reliability and scalability of LoRaWAN via a joint SF and channel assignment proposal. We start by presenting an optimal formulation for the joint problem aimed at optimizing the throughput in a fair manner. Because of the complexity of the problem, and its unattainable requirement of a centralized solver in a multi-operator deployment, we choose to divide the problem into two: (a) an SF assignment subproblem and (b) a channel assignment subproblem. We use a non-cooperative game theory approach in order to portray each subproblem. The differentoperators are _competing, yet rational_, players of these games, and they each seek to maximize their own utility.  
For the SF assignment subproblem, we propose a semi-distributed best response algorithm aimed at finding the Nash equilibrium (NE) of the game. We additionally propose a heuristic to make it completely distributed.  
For the channel assignment subproblem, we show that our game possesses a weighted potential function and that, by extension, a pure NE exists and it can be reached via both best response and replicator dynamics. The game permits selecting the number of channels to be allocated to each operator, with its traffic being equally distributed on the channels it selects.  
We solve the decoupled problem for SF assignment first, and for channel assignment second. The joint algorithm can be semi-distributed (best response approaches) or completely distributed (learning approach). We describe our proposals and then compare them to the concurrent approach in SF and channel selection in LoRaWAN, which consists of adaptive data rate (ADR) for SF selection, along with random channel selection for each packet.  
The rest of this paper is structured, as follows: Section 2 describes the related works from the state-of-the-art and our contributions. In Section 3, we introduce our system model. We discuss our optimal formulation for SF and channel assignment in Section 4. Our game for SF assignment is detailed in Section 5, and its counterpart to channel assignment in Section 6. Section 7 presents the simulations and results. Finally, the paper is concluded with Section 8.