# Towards Harmonious Coexistence in the Unlicensed Spectrum: Rational Cooperation of Operators
## 2 Multi-RAT Systems in the Unlicensed Spectrum
### Payoffs of LTE and WiFi Networks  
Although WiFi networks cannot be considered as a player in this game because they have only one strategy, we consider payoffs of WiFi networks depending on the behaviors of LTE operators. Before formulating a game, we first generalize payoffs of both LTE and WiFi operators as follows.  
\(U_{s}\) is the payoff when a single network exploits one channel of the unlicensed spectrum and has a successful transmission in a given time period. If \(U_{s}\) is considered as the channel capacity of a certain network, it depends on radio access technology (RAT), inherent RF performance, the number of users, scheduling methods, and geographical conditions. We also denote \(U_{s}^{LTE}\) and \(U_{s}^{WiFi}\) as payoffs of LTE and WiFi networks, respectively.  
\(U_{sh}\) is the payoff that all networks harmoniously share the co-channel of the unlicensed spectrum by using CCA. The exact values of \(U_{sh}\) for multi-RATs are different because of CCA schemes and scheduling methods configured by a certain network. Regardless of networks' characteristics, \(U_{s}>U_{sh}\) generally holds because \(U_{sh}\) results from multi-RATs coexisting in the co-channel of the unlicensed spectrum. In the sharing scenario, \(U_{sh}^{LTE}\) and \(U_{sh}^{WiFi}\) are payoffs of LTE and WiFi networks, respectively and usually \(U_{sh}^{LTE}>U_{sh}^{WiFi}\) holds based on experiments [14]. The reason is that as soon as the LBT procedure is used by an operator, LTE users can access the unlicensed spectrum by centralized LTE scheduling, which has significantly higher spectral efficiency than the DCF mechanism [14].  
\(U_{f}\) is the payoff that two LTE operators fail to transmit data by causing severe unknown interference to each other when they use the co-channel of the unlicensed spectrum at the same time. Although this undesirable case may provide a weak communication link between users and an operator, no operators want to encounter low throughput with unreliable transmission. In addition, there is a possibility that imperfect sensing of new arrival networks induces the hidden node problem such that multi-RATs networks interfere each other spatially and temporally. To focus on the behavior of LTE operators, herein, we assume that all systems are capable of perfect sensing under the CCA procedure.  
\(U_{w}\) is the payoff when LTE and WiFi networks wait for the next transmission opportunity. In this case, both networks cannot utilize the unlicensed spectrum based on its CCA result even if they have full of buffer data to transmit. Here, note that the term CCA includes CSMA/CA as well as many LBT schemes such as carrier-sensing adaptive transmission (CSAT), LBT with duty cycle, and LBT with random back-off [14]. Moreover, the value of \(U_{w}\) can be zero in terms of channel capacity when the network is idle in the unlicensed spectrum. However, for high-quality real-time traffic such as voice and video streaming applications, mobile subscribers are extremely delay-sensitive such that the potential revenue loss due to frequent and/or long delay is considered as an opportunity cost to LTE operators, and thus \(U_{w}\) can be negative.