## 2 System Model  
Why is security necessary in wireless sensor networks (WSNs)? Due to the broadcast nature of the transmission medium, wireless sensors are vulnerable. Another vulnerability is that nodes are often placed in a hostile or dangerous environment, and they are not physically safe. Most of the threats and attacks against security in WSNs are almost similar to their wired counterparts, while some are exacerbated with the inclusion of wireless connectivity. Attacks on WSNs can be classified as follows:  
1. Attacks against security mechanisms;
2. Attacks against basic mechanisms (such as routing mechanisms). In many applications, the data obtained by the sensing nodes need to be authentic. A false or malicious node could intercept private information in the absence of proper security or could send false messages to nodes in the network. In this paper, we considered a dense WSN, used as a smart environmental monitoring system, where \(N\) low-complexity sensing nodes are distributed on an area \(\mathcal{A}\) and communicate with a sink node. The considered IoT network is based on a classical star-topology network, where the sink node coordinates the sensor devices distributed around it (Figure 1). Sensor nodes are supposed to be devices with low-resource (i.e., computation, memory and energy), performing simple tasks that monitor some physical parameters (e.g., humidity, gas, water level, vibration, pressure, etc.) and transmitting them to the coordinator. Hence, sensor devices are equipped with a low-power microcontroller with an integrated radio transceiver equipped with a single antenna and a sensor interface. Differently, the coordinator is a higher-powerful device with mode complex functionalities. Indeed, the sink node has in charge the management of the access and communication in the network (e.g., access and resource management, authentication, channel estimation, etc.) and could also perform processing of received data. The coordinator is supposed to have more computing and memory resources and always be connected to a power source. The transceiver is equipped with multiple antennas so that the spatial information can be exploited in the network. The proposed WF authentication method is based on PHY-channel features; hence, we have to resort to a suitable channel model. In particular, we consider the 802.11 ac(tm) (TGac) multipath fading channel [34]. This is a system level model, which can describe an arbitrary number of propagation environment realizations for single or multiple radio links for all the defined scenarios, with one mathematical framework by different parameter sets. The TGac channel model follows a stochastic channel modeling approach, as the channel parameters are determined stochastically, based on statistical distributions extracted from channel measurements. This model is frequently used for indoor area wireless communication systems operating in a 5 GHz spectrum with a bandwidth up to 160 MHz. In this paper, we  
Figure 1: WSN with sink node responsible for the security of the system. selected the Model-D scenario [35] that represents the propagation conditions in a typical large indoor open environment, with mobility (0-5 km/h). More in detail, we assume that the transmitting/receiving nodes are in fixed positions, but we consider a certain time variability to take into account the scatterers' movement in the area. The 802.11 acTM model represents a multiple input multiple output (MIMO) channel, with \(M\) transmitting and \(Q\) receiving antennas. However, we focus on the particular case with \(M=1\); hence, we focus on a SIMO (single input multiple output) system. Indeed, we consider low-complexity IoT sensor nodes, equipped with a single antenna.