# An Energy-Efficient Game-Theory-Based Spectrum Decision Scheme for Cognitive Radio Sensor Networks
## 3 Energy-Efficient Game-Theory-Based Spectrum Decision
### CRSN Settings  
The EGSD scheme is proposed for CRSNs where there is a number of sensor nodes placed randomly in an area of interest and a sink located at the center of the area. The CRSN is able to access three spectrum bands: television (TV), ISM 2.4 GHz, and ISM 5 GHz. The TV band consists of 30 channels [46], with the first channel being the common control channel. The CRSN operations, management and transmission activities, are performed in frames. A frame is equal to 2 s, and it is divided into 111 time slots where each time slot equals 18 ms [47] and the last time slot is equal to 20 ms. The CRSN is located in a populated city where the incumbent users of the TV band (herein PU) exist. The PU model is as follows: The maximum number of PUs is predetermined, however the number of PUs at a certain time is not fixed. The PUs can be either active or passive. A PU is active when it transmits or receives a data transmission; otherwise, it is passive. A passive PU can become active, and vice versa. PUs can change their operating channel and move their location while they are active. The licensed and unlicensed channel models are as follows: the sensor nodes perform spectrum sensing in licensed channels, and they obtain information on whether the channel is vacant. The unlicensed channel may be occupied by other wireless networks. Thus, we model the unlicensed channel in terms of peak interferences. The peak interferences take place on a certain channel, and they affect up to two adjacent channels. When a sensor node selects an unlicensed channel with high interference, the probability of transmission failure is higher, whereas when it uses a licensed channel, the transmission success is guaranteed unless the total number of sensor nodes transmitting on that channel is higher than a certain threshold. If the number of total sensor nodes transmit-ting on a licensed channel exceeds the threshold, then the probability of transmission failure increases with the number of channel occupants. We define one licensed channel as the common control channel (CCC). The CCC is used exclusively to transmit control packets, and the channel's occupant threshold is higher than the threshold for other licensed channels. Each sensor node is equipped with one CR transceiver; thus, it is able to tune in one channel at a time. Meanwhile, the sink has two CR transceivers, in which one transceiver is always tuning in the CCC and another can switch its channel. The sink has a constant power supply and higher computation capability. It can broadcast its control packets on the CCC so that every sensor node can receive them. Fundamentally, enabled by the CR's reconfiguration ability, the sensor nodes are also able to transmit to the sink directly. However, direct transmission is not favorable because long-distance transmission requires high energy consumption. We designed the EGSD scheme for CRSNs to suit environmental maintenance systems that require periodic data collection. The EGSD scheme has two operation modes: coordination mode (C mode) and data transmission mode (D mode). A frame can be in either C mode or D mode. In C mode, coordination activities take most parts of the frame, whereas in D mode, environment-sensing data collections are encouraged. Both modes consist of the same modules: spectrum sensing, spectrum decision, and data transmission module. The duration of spectrum sensing module (\(t_{ss}\)) is maximized in C mode to support full spectrum sensing, and it is minimized in D mode where only partial spectrum sensing is performed. On the other hand, the duration of data transmission module (\(t_{dt}\)) is maximized in D mode. The duration of the spectrum decision module (\(t_{sd}\)) for both modes is the same (see Figure 1). The operation mode of the initial frame is C mode, and the operation mode of the following frames is decided by the sink. The last time slot in each frame is allocated to sensor nodes to report to the sink whether they require C mode or not through the CCC.