# Detection of Transmission State of Multiple Wireless Sources: A Statistical Mechanics Approach
## 1 Introduction  
Dynamic spectrum sensing has emerged as an important approach to deal with spectrum scarcity, which is caused by the deployment of many IoT-enabled devices [1], where secondary users/devices monitor a given spectrum band to determine the presence (or absence) of active (licensed) sources, whose state is dynamic and intermittent in time. This method guarantees that subsequent usage of the spectrum by secondary opportunistic users does not result in significant interference with the primary source communications and vice versa. The above is a particular paradigm of a Cognitive Radio (CR)-enabled IoT network [2], which injects high-level intelligence into IoT networks and assists sensor nodes in using the available spectrum without interfering with the primary sources. In addition, it improves the whole system throughput compared to traditional homogeneous network topologies [3] (i.e., classical cellular, ad hoc), and as a promising enabler communication technology for the IoT, it attains the levels of performance and efficiency required by future wireless communications. The identification of emitting sensors in the context of a Cognitive Radio-enabled IoT network is of paramount importance. Apart from the enhanced spectrum efficiency, where the identification of emitting sources can assist in efficiently utilizing the available spectrum by avoiding interference and allocating frequency bands to different IoT devices, it improves the coexistence and compatibility of various devices and systems in the same environment, such as Wi-Fi, Bluetooth, Zigbee, and other wireless technologies [4]. Thus, identifying the emitting sources allows Cognitive Radio systems to determine which devices are using which frequencies or channels, enabling them to select available andinterference-free channels for their own communication. From a network security perspective, the identification of emitting sources also allows for the detection of unauthorized or malicious devices in the network, revealing potential security threats or unauthorized access points [5]. Last, by identifying the emitting sources, network operators can gain insights into the utilization of the radio spectrum. This information can be used for network planning, optimization, and resource management and assist network operators in designing efficient IoT deployments, identifying areas of congestion, and improving the overall network performance. In a Cognitive Radio-enabled IoT network deployment in a smart home environment, such as the one depicted in Figure 1 the primary sources can be the devices or systems designed to send data or information within the network. These devices can be Wi-Fi Access Points, which provide wireless connectivity within the smart home network and act as primary sources of radio signals for data transmission. Zigbee or Z-Wave hubs are also systems that are commonly used for smart home automation and control, communicating with various Zigbee or Z-Wave devices such as smart lights, thermostats, door locks, etc. Bluetooth-enabled devices, such as smartphones, smart speakers, wearables, etc., are also included in the long list of devices within a smart home network. On the other hand, secondary sources can potentially include wireless security cameras or surveillance systems, which may operate in frequency bands that overlap with Wi-Fi or other IoT protocols, leading to interference. The detection and localization of primary sources can be accomplished by taking advantage of radio environment maps (REM) [6]. REMs are integrated databases that provide multi-domain environmental information regarding all devices that are capable of transmitting and/or receiving radio signals. The location information and power levels of primary sources are typical examples of stored information. However, since the state of these sources is intermittent and typically changes without notice at different times of the day, it is important to come up with algorithms that are able to periodically update the transmission states of the sources.