## 2 System Model  
Consider the setting illustrated in Figure 1, which involves \(N\) wireless devices, each operating a Radio Access Technology (RAT) drawn from a set of \(M\) distinct RAT types, and a single receiver, tasked with monitoring device spectrum activity. Denote the devices by \(d_{mm}\), where \(n=1,\ldots,N\) is an index reflecting a unique usage context that includes user activity patterns and application data profiles, and by \(m=1,\ldots,M\) the RAT-type label. When in transmission mode, \(d_{nm}\) emits an _unconverted_ version of a base-band time-varying signal \(s_{nm}(t)\) by Radio Frequency (RF) with a given carrier frequency. The signal \(s_{nm}(t)\) contains payload data formatted into RAT-defined packets, and its bandwidth and center frequency determine the spectrum band of operation, which can be fixed or dynamically determined as is the case with the unlicensed shared operation. A typical implementation of the receiver uses software-defined radios (SDRs), which are available off-the-shelf or custom-made [5] for applications including radio-environment maps (REMs) that characterize spatio-temporal spectrum access patterns and provide a useful tool for enforcing access policies by identifying violations. Assuming that there is no interference and that the receiver is tuned to the same spectrum band as the emitter, the _downconverted_ received signal is denoted as \(r(s_{nm})\) and can be modeled as  
\[r(s_{nm})=H(s_{nm})+G(s_{nm}), \tag{1}\]  
where \(G(s_{nm})\) denotes the additive white Gaussian noise (AWGN), and \(H(s_{nm})\) other physical and user-induced degradation present in the wireless communication link between \(d_{nm}\) and the receiver: it may include multipath, shadowing and non-line-of-sight (NLOS), mobility-induced Doppler effects, and specific Signal-to-Noise Ratio (SNR) conditions. Upon reception, \(r(s_{nm})\) is converted to a spectrogram by applying the Short-Time Fourier Transform (STFT) [57]. We selected the spectrogram mainly because it is one of the most general and commonly-used time-frequency representations. The model and the methodology we employ can be extended to other representations, e.g., to spectrogram's functions, such as the power spectrum transform and other custom time-frequency representations. Let us denote by \(\mathcal{R}(s_{nm})\in\mathbb{C}^{N_{f}\times N_{t}}\) the matrix of complex values representing the the STFT of the received signal \(r(s_{nm})\), with matrix elements \(\mathcal{R}(s_{nm})(\tau,\omega)\), where \(\tau\) and \(\omega\) denote values of the discretized time and frequency, respectively, while \(N_{f}\) and \(N_{t}\) denote the number of points sampled along the frequency dimension and time dimension, respectively. If we denote by \(i\in[1,N_{f}]\) and \(j\in[1,N_{t}]\), respectively, the index of the time and of frequency discretized values, the elements (pixels) of the \(N_{f}\times N_{t}\) matrix are denoted by \([\mathcal{R}(s_{nm})]_{ij}\). Figure 1: Emitter classification system model. The real valued spectrogram \(R(s_{nm})\in\mathbb{R}^{N_{f}\times N_{t}}\) of the received signal is obtained by calculating pixel-by-pixel the norm of the corresponding complex number in the spectrogram \(\mathcal{R}(s_{nm})\), i.e.,  
\[[R(s_{nm})]_{ij}\equiv|[\mathcal{R}(s_{nm})]_{ij}|\]  
Summarizing the relationships between the defined quantities we have  
\[s_{nm}(t)\xrightarrow{H+\mathcal{G}}r(s_{nm}(t))\xrightarrow{STFT}\mathcal{R }(s_{nm})\in\mathbb{C}^{N_{f}\times N_{t}}\xrightarrow{norm}R(s_{nm})\in \mathbb{R}^{N_{f}\times N_{t}}\]  
The chain of transformations applied to \(r(s_{nm}(t))\) can be applied to the original transmitted signal \(s_{nm}(t)\).