## 3 System Model
The diversity in the number of antennas arises due to the inherent variations among different UEs. Based on the scenario assumptions, NPi is subject to the following constraints:  
\[N_{P_{i}}\in\{1,2,4\},\;i=1,2,\ldots,n \tag{3}\]  
The multi-port reception by Alice can lead to inter-port interference during the UE's transmission, thus requiring the UE to perform pre-coding during the UL transmission process. In Equation (1), for the sake of simplicity, the pre-coding matrix is included in \(\mathbf{H}\). To improve computational efficiency, it is assumed that Alice employs a linear receiver, and the inter-port interference is mitigated by the Zero Forcing (ZF) receiver through channel estimation [28]. The method is based on:  
\[\mathbf{W}_{a}=\frac{1}{\sqrt{\rho_{i}}}(\widehat{\mathbf{H}}^{H}\widehat{ \mathbf{H}})^{-1}\widehat{\mathbf{H}}^{H} \tag{4}\]  
where \(\mathbf{W}_{a}\) is the weight matrix of Alice's linear receiver, which is used to calculate the receiver output by weighting the signal \(\mathbf{y}\), and \(\mathbf{W}_{a}\in\mathbb{C}^{N_{b}\times N_{a}}\). \(\widehat{\mathbf{H}}\) is the channel response matrix, and \(\mathbf{W}_{a}\) is the channel response matrix. The interference between the two signals is modeled by the interference between the two signals. The interference between the two signals is modeled by the interference between the two signals. matrix obtained by [PERSON] through channel estimation based on SRS signal values. The notation \(\widehat{\mathbf{H}}^{H}\) denotes the Hermitian transpose of the complex matrix \(\widehat{\mathbf{H}}\). By utilizing Equations (1) and (4), the output \(\mathbf{z}\) of the ZF receiver can be calculated as:  
\[\mathbf{z}=\mathbf{W}_{a}\mathbf{y}=\mathbf{x}+\frac{1}{\sqrt{\rho_{i}}}( \widehat{\mathbf{H}}^{H}\widehat{\mathbf{H}})^{-1}\widehat{\mathbf{H}}^{H} \mathbf{N} \tag{5}\]  
Alice can continuously collect channel information reported by each UE, enabling reciprocity-based TDD transmission and device authentication. Let \(\mathbf{V_{alice}}\) represent the feature vector composed of the features collected by Alice from different UE. Then, \(\mathbf{V_{alice}}\) can be represented as:  
\[\mathbf{V_{alice}}=[\mathbf{V_{1}},\mathbf{V_{2}},\dots,\mathbf{V_{n}}]^{T} \tag{6}\]  
According to the assumption, the system consists of one legitimate UE and \(n-1\) malicious UEs. \(\mathbf{V_{i}}\) of UE \(i\) can be expressed as:  
\[\mathbf{V_{i}}=[\widehat{\mathbf{H}}_{i}^{1},\dots,\widehat{\mathbf{H}}_{i}^{ N_{Fi}}]^{T},\;i=1,2,\dots,n \tag{7}\]  
Vector \(\mathbf{V_{i}}\) extracted by [PERSON] is stored as three-dimensional complex vector in this model, and \(\mathbf{V_{i}}\in\mathbb{C}^{N_{Hi}\times N_{Hi}\times N_{Hi}}\). After the training phase, [PERSON] continues to collect feature vectors, which are then fed into the trained DTRN for authentication to determine whether a UE is legitimate. If the UE is deemed legitimate, [PERSON] grants network access, otherwise, the network directly rejects the user's access. In addition, physical environment between [PERSON] and Bob remains stable, although there are location differences between Bob and Eve. Therefore, the presence of multiple antennas and multipath fading results in Bob's physical layer features containing specific information that exhibits independence [29; 30], which can serve as authentication evidence.