Spectrum sensing based on adversarial transfer learning

IET CommunicationsVolume 16, Issue 17 p. 2059-2069 ORIGINAL RESEARCHOpen Access Spectrum sensing based on adversarial transfer learning Jiawu Miao, Jiawu Miao orcid.org/0000-0001-6602-8784 School of information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing, People's Republic of ChinaSearch for more papers by this authorYuebo Li, Yuebo Li School of information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing, People's Republic of ChinaSearch for more papers by this authorXiaojun Jing, Corresponding Author Xiaojun Jing jxiaojun@bupt.edu.cn School of information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing, People's Republic of China Correspondence Xiaojun Jing, Beijing University of Posts and Telecommunications, No.10, Xitucheng Road, Haidian District, Beijing, People's Republic of China Email: jxiaojun@bupt.edu.cnSearch for more papers by this authorFangpei Zhang, Fangpei Zhang Information Science Academy of China Electronics Technology Group Corporation, Beijing, People's Republic of ChinaSearch for more papers by this authorJunsheng Mu, Junsheng Mu School of information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing, People's Republic of ChinaSearch for more papers by this author Jiawu Miao, Jiawu Miao orcid.org/0000-0001-6602-8784 School of information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing, People's Republic of ChinaSearch for more papers by this authorYuebo Li, Yuebo Li School of information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing, People's Republic of ChinaSearch for more papers by this authorXiaojun Jing, Corresponding Author Xiaojun Jing jxiaojun@bupt.edu.cn School of information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing, People's Republic of China Correspondence Xiaojun Jing, Beijing University of Posts and Telecommunications, No.10, Xitucheng Road, Haidian District, Beijing, People's Republic of China Email: jxiaojun@bupt.edu.cnSearch for more papers by this authorFangpei Zhang, Fangpei Zhang Information Science Academy of China Electronics Technology Group Corporation, Beijing, People's Republic of ChinaSearch for more papers by this authorJunsheng Mu, Junsheng Mu School of information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing, People's Republic of ChinaSearch for more papers by this author First published: 16 July 2022 https://doi.org/10.1049/cmu2.12459AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract Recently, deep learning (DL) based spectrum sensing (SS) has drawn much attention due to its better capacity of feature extraction and superb performance. However, the model robustness of the DL based scheme is limited by reason of the dynamic radio environment, leading to the floating of sensing performance. Motivated by this, adversarial transfer learning is applied to SS here, where the model is pre-trained at the central node firstly and fine-tuned at the local nodes. More specifically, a 2D dataset of the observed signal is constructed under various signal-to-noise-ratio (SNRs) and a convolution neural network (CNN) model is designed. Then a part of samples with various SNRs in the constructed dataset are employed to pre-train the proposed CNN model. After that, the pre-trained CNN model is distributed to local nodes with different SNRs and the pre-trained CNN model is fine-tuned. The proposed CNN model is pre-trained based on the samples under various SNRs, resulting in its stronger adaptability at the local node. The simulation experiments validate the effectiveness of the proposed scheme. 1 INTRODUCTION With the in-depth integration of artificial intelligence (AI), Internet of Things (IoT) and wireless communications, wireless devices are growing exponentially, resulting in an increasing shortage of spectrum resources [1-3]. According to the report of Federal Communications Commission (FCC), the spectrum utilization of current registered frequency bands is very low [4]. To alleviate the issue of spectrum shortage, the improvement of spectrum efficiency seems a significant direction. As an effective way to improve spectrum utilization, Cognitive Radio (CR) has drawn much attention in recent years [5]. The main principle of CR is opportunistic spectrum access for the secondary user (SU) when the primary (registered) user (SU) is idle for some a moment. Once PU returns, SU will stop communication immediately and release current spectrum resources. In consequence, to periodically monitor the status of the observed bands is a particularly vital task, named spectrum sensing (SS). Usually, the performance of SS is evaluated by false alarm probability and detection probability [6]. A lower false alarm probability denotes a higher system throughput while a higher detection probability signifies a better capability to protect PUs. In fact, every SS scheme is a tradeoff between false alarm probability and detection probability [7]. In the literature, plenty of classical SS schemes have been proposed with their respective advantages and disadvantages, including energy detection (ED) [8], matched filter detection [9] and Cyclostationary feature detector (CFD) [10]. However, the required optimization parameters increase exponentially in this era of information explosion, leading to the inadaptability of the model-driven SS schemes. In this context, the AI technology brings novel insights for SS by learning the necessary hiding rules from massive data and making a decision based on the obtained rules thereafter [11]. Essentially, SS is a process of binary classification for machine learning (ML) based SS schemes. [12] proposed an algorithm through K-Means and Gaussian mixture model, and applied it to ED, which not only improved the detection performance, but also avoided the threshold derivation process caused by noise uncertainty in traditional ED. A SS algorithm was proposed based on the hidden semi-Markov model [13]. The model introduced a new parameter to represent the duration of the state on the basis of the hidden Markov model, which can obtain a more accurate prior estimation, and a better detection accuracy as a consequence. Recently, deep learning (DL) based SS model has also been widely applied to SS due to its strong ability to extract hidden features [14-16]. At present, various DL models have been considered for SS, such as convolution neural networks (CNN) [17], recurrent neural network (RNN) [18] or long short-term memory (LSTM) [11]. A single-user multi-antenna SS system was proposed in [19]. According to the similarity between the covariance matrix of the signal and the image, the test statistics was extracted from the covariance matrix of the received signal and then a decision was made by the CNN network. In [20], CNN was applied to the automatic classification of modulation modes for communication signals. In [21], the signal classification was conducted by the constructed 2D CNN network by the input of 1D observed signal. Although the DL based SS schemes have the superior sensing performance, there are still many challenges that need to be solved urgently. Currently, the DL based SS models are trained based on the fixed data distribution. However, the radio environment is time-varying. As a result, a large recognition error may occur for the trained SS model, especially in time-varying channels. To improve the robustness of DL based SS, transfer learning was firstly applied to SS in [22], where both cases of no labelled and few-sample conditions were considered. The main motivation of the work in [22] was to make the local trained models applicable to different communication settings, such as the sensing capacity transfer from QPSK signals to additive white Gaussian noise (AWGN) signals. However, the same type of observed signals at different sensing nodes may differ respectively due to the corresponding radio environment, resulting in performance fluctuation for the trained DL models, especially in spatial SS scenarios. Motivated by the mentioned above, the transfer learning is applied to SS in this paper transferring the sensing capacity of the same type of the observed signal under the spatial SS conditions, where the local observed signal with various signal-to-noise ratios (SNRs) are collected to the central node and the proposed CNN model is trained in advance at the central node. Then the trained model is distributed to local nodes and the trained model is fine-tuned according to the received data of local node. The fine-tuned model is applicable to time-varying radio environment and therefore a better sensing accuracy can be obtained. The simulation experiments validate the effectiveness of the proposed scheme. Note that this paper considers the issue of SS with multiple sensing nodes in a non-cooperative manner. The local observed signal with different SNRs is sent to the central node for the cooperative pre-training of the proposed CNN model. However, the fine-tuned CNN models at each local node based on the pre-trained model are deployed for the same observed spectrum band in different sensing spaces. As a result, this paper mainly aims at performing the task of SS in an independent manner and the transfer learning based cooperative SS will be exploited in the future work. The main contributions and the primary work of this paper are concluded as follows: (1) The 2D dataset of the observed signal is constructed under various SNRs. A CNN model is trained according to the constructed dataset. (2) The adversarial transfer learning is considered for the local node, where the trained model with various SNRs is fine-tuned with some a SNR at the local node. To the best knowledge of the authors, the proposed scheme can obtain a superb sensing performance in few-shot conditions. (3) The sensing performance of the proposed scheme is compared with the CNN model without transfer learning, ED and improved ED (IED). The corresponding detection probability comparisons are made under different SNRs for the fixed false alarm probability. The rest of this paper is organized as follows. Section 2 reviews the related work, including transfer learning and CNN based SS schemes. The system model is provided in Section 3. In addition, the experiments and discussions are exhibited and analyzed in Section 4. Finally, Section 5 concludes this paper. 2 RELATED WORK 2.1 Transfer learning With the emergence of various machine learning (ML) application scenarios, the existing supervised learning requires a lot of tagging data. However, to tag data is a boring and costly task. Transfer learning can effectively solve this issue and it has attracted increasing attention in consequence. The main motivation of transfer learning is to transfer the parameters of the trained model (pre-training model) to a new model to help the training of the new model. Considering that most of the data or tasks are relevant, the parameter sharing of the pre-training model can speed up and optimize the learning efficiency of the model to be trained. For transfer learning, there are two important concepts, domain and task, D = χ , P ( X ) , \begin{equation}D = \left\{ {\chi ,P(X)} \right\}{\rm{,}}\end{equation} (1)where χ denotes feature space and P ( X ) $P(X)$ denotes marginal probability distribution. In addition, X = { x 1 , K , x n } ∈ χ $X = \{ {{x}_1,K,{x}_n} \} \in \chi $ .y signifies the label space and f() is the target prediction function. According to [23], transfer learning contains the following categories. To improve domain adaptation of classical neural network architectures, domain-adversarial neural network (DANN) was proposed in [24], as it is shown in Figures 1 and 2. From Figure 2, DANN consists of three modules: feature extractor, label predictor and domain classifier. In the process of training, for the tagged data from the source domain, the network constantly minimizes the loss of all data and label predictors from the source domain and target domain, as well as the loss of the domain discriminator. Then when testing the data, the feature extraction apparatus owns a higher domain tolerance and can deal with cross-domain data, leading to the rise of model robustness. FIGURE 1Open in figure viewerPowerPoint Transfer learning FIGURE 2Open in figure viewerPowerPoint DANN model [24] 2.2 CNN based SS As a branch of ML, DL has achieved a lot in the field of academia and industry in recent years, and it has become one of the driving skills of AI [30-33]. As a result, DL based wireless communication technology has been a hot topic, especially in terms of CR. CNN is widely used in image recognition and speech recognition due to its ability of feature extraction and the superb performance on classification accuracy compared with the traditional schemes. The essence of SS is a binary classification problem. In consequence, CNN based SS can take full advantage of the CNN module, resulting in the dramatic improvement on sensing performance. The classical CNN based SS schemes and their main contributions are concluded as follows in Table 1. TABLE 1. The classical CNN based SS schemes Index Tittle Contribution [26] Comparative analysis of various communication systems for intelligent sensing of spectrum: A novel approach towards Cognitive Radio Designing WDCS based on wavelet transform was proposed. [27] Intelligent sensing for automated spectrum assignment An intelligent distributed cooperative SS with centralized control was provided for automatic spectrum allocation based on dynamic spectrum management (DSM). [28] Intelligent cooperative spectrum sensing via hierarchical Dirichlet process in cognitive radio networks Intelligent cooperative SS algorithm was proposed based on non-parametric Bayesian learning model. [29] Intelligent channel assigning in CR-MANET based on spectrum sensing The problem of channel allocation was solved by fuzzy logic therein. [30] Intelligent sensing matrix setting in cognitive radio networks The optimal perception sequence is found for each SU without any prior knowledge or assumptions about the wireless environment based on the cooperation between the two neural networks. [31] Secure cooperative spectrum sensing and access against intelligent malicious behaviours A joint SS method was proposed, which optimally prevents intelligent malicious users (IMU) sensing tampering through AI. 3 SYSTEM MODEL Suppose that the number of the antennas at the receiver is M in a multi-antenna system and the number of signal sampling points is N. Then the time sampling sequence of the signal received by the i ( i = 1 , 2 , … , M ) $i(i = 1,2, \ldots ,M)$ antenna can be denoted as s i ( n ) ( n = 0 , 1 , … , N − 1 ) ${s}_i(n)(n = 0,1, \ldots ,N - 1)$ . Assume that the signal sequence of PU signal propagated through the channel is x i ( n ) ( n = 0 , 1 , … , N − 1 ) ${x}_i(n)(n = 0,1, \ldots ,N - 1)$ , and the noise sequence is n i ( n ) ( n = 0 , 1 , … , N − 1 ) ${n}_i(n)(n = 0,1, \ldots ,N - 1)$ . As SS is a binary classification problem, we can define two categories, L0 and L1, where L0 denotes that the received signal only contains the noise and L1 signifies the signal-plus-noise case. s i ( n ) ${s}_i(n)$ can be formulated as: s i ( n ) = n i ( n ) L 0 x i ( n ) + n i ( n ) L 1 , \begin{equation}{s}_i(n) = \left\{ { \def\eqcellsep{&}\begin{array}{@{}*{2}{c}@{}} {{n}_i(n)}&{{{\rm{L}}}_0}\\[4pt] {{x}_i(n) + {n}_i(n)}&{{{\rm{L}}}_1} \end{array} } \right.,\end{equation} (2) Then the received signal sequence of i th $i{\mathop{\rm th}\nolimits} $ branch antenna can be written as: S i = [ s i ( 0 ) , s i ( 1 ) , … , s i ( N − 1 ) ] . \begin{equation}{S}_i = [{s}_i(0),{s}_i(1), \ldots ,{s}_i(N - 1)].\end{equation} (3) Based on (3), the mean value s i − m e a n ${s}_{i - mean}$ of S i ${S}_i$ can be expressed as: s i − m e a n = 1 N ∑ n = 0 N − 1 s i ( n ) . \begin{equation}{s}_{i - mean} = \frac{1}{N}\sum_{n = 0}^{N - 1} {{s}_i(n)} {\rm{.}}\end{equation} (4) The received signal S i − m ${S}_{i - m}$ after removing the mean s i − m e a n ${s}_{i - mean}$ can be reformulated as: S i − m = S i − s i − m e a n . \begin{equation}{S}_{i - m} = {S}_i - {s}_{i - mean}.\end{equation} (5) The time series matrix of the processed received signal can be denoted as: S = S 1 − m S 1 − m … S M − m = s 1 ( 0 ) − s 1 − m e a n … s 1 ( N ) − s 1 − m e a n s 2 ( 0 ) − s 2 − m e a n ⋱ s 2 ( N ) − s 2 − m e a n s M ( 0 ) − s M − m e a n … s M ( N ) − s M − m e a n . \begin{equation}S = \left[ { \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} {{S}_{1 - m}}\\[6pt] {{S}_{1 - m}}\\[6pt] \ldots \\[6pt] {{S}_{M - m}} \end{array} } \right] = \left[ {\left[ { \def\eqcellsep{&}\begin{array}{@{}*{3}{c}@{}} {{s}_1(0) - {s}_{1 - mean}}&\quad \ldots &\quad{{{\rm{s}}}_1(N) - {s}_{1 - mean}}\\[6pt] {{s}_2(0) - {s}_{2 - mean}}&\quad \ddots &\quad{{{\rm{s}}}_2(N) - {s}_{2 - mean}}\\[6pt] {{s}_M(0) - {s}_{M - mean}}&\quad \ldots &\quad{{{\rm{s}}}_M(N) - {s}_{M - mean}} \end{array} } \right]} \right].\end{equation} (6) Then, the corresponding covariance matrix R ( N ) $R(N)$ can be written as: R ( N ) = 1 N × S × S H , \begin{equation}R(N) = \frac{1}{N} \times S \times {S}^H{\rm{,}}\end{equation} (7)where S H ${S}^H$ denotes the conjugate transpose matrix of S. If S is a real matrix, then R ( N ) $R(N)$ can be denoted as: R ( N ) = 1 N × S × S H = 1 N × S × S T , \begin{equation}R(N) = \frac{1}{N} \times S \times {S}^H = \frac{1}{N} \times S \times {S}^T,\end{equation} (8)where S T ${S}^T$ denotes the transpose matrix of S. The system model of this paper is exhibited in Figure 3, where the OFDM signal received by multi-antenna receiving system after Rayleigh fading channel is regarded as the PU signal. Then the received signal is sampled and the corresponding covariance matrix is obtained. After that, the covariance matrix is converted into the true colour picture, forming the training set and the test set used here. FIGURE 3Open in figure viewerPowerPoint System model Assume that the process of converting to a true colour graph for R ( N ) $R(N)$ can be expressed as f ( R ( N ) ) $f( {R(N)} )$ and the operation process after the CNN module proposed in this paper can be denoted as Ψ [ f ( R ( N ) ) ] $\Psi [ {f( {R(N)} )} ]$ . Then the false alarm probability and the corresponding detection probability after the classifier of the CNN module can be formulated as: P f = P ( Ψ f R ( N ) > γ | L 0 ) , \begin{equation}{P}_f = P(\Psi \left[ {f\left( {R(N)} \right)} \right] > \gamma |{L}_0),\end{equation} (9) P d = P ( Ψ f R ( N ) > γ | L 1 ) , \begin{equation}{P}_d = P(\Psi \left[ {f\left( {R(N)} \right)} \right] > \gamma |{L}_1),\end{equation} (10)where γ denotes the sensing threshold fitted by the proposed CNN network. Note that the essence of this paper is to conduct SS by distinguishing the correlation between signals and that between noise. Ideally, the correlation between signals is obviously higher than that between noise. Covariance matrix seems a superb choice to characterize the correlation of the received signal. As a result, the covariance matrix of the observed signal is constructed by multi-antenna receiving system and the corresponding true colour pictures are obtained according to the covariance matrix. Meanwhile, CNN owns natural advantages for 2D image classification due to its capacity of local perception, parameter sharing and shift-invariance. By the reasons mentioned above, CNN is considered here, instead of LSTM. 4 PROPOSED SCHEMES 4.1 Dataset construction Here, the noise is superimposed on the OFDM signal after the Rayleigh fading channel, where the environment SNR varies from −10 to 4 dB with the step 1. The number of antennas is set as ten and the sampling covariance matrix is calculated by the real part and the imaginary part of the received signal (N = 10), respectively. As the result, the size of the sampling covariance matrix is 10 × 10 × 2. Usually, the channel of the true colour graph is 3, therefore the third channel is set to zero matrix here. Note that the size of true colour graph is adjusted to 225 × 225 finally. Under each SNR considered here, two cases are considered, the signal-plus-noise case and the noise case, where 3000 samples are considered for each case. Consequently, the total number of the dataset is 45,000. The number of the training sets is 30,000 and the rest is for the test sets. The construction process of the dataset is shown in Figure 4. FIGURE 4Open in figure viewerPowerPoint The construction process of the dataset According to the operations in Figure 4, the dataset used here is constructed and the samples of the dataset are exhibited in Figure 5, where the case of L0 and the case of L1 are considered under each SNR condition. FIGURE 5Open in figure viewerPowerPoint The samples of the constructed dataset under various SNRs 4.2 Proposed CNN model The network structure of the proposed CNN model is shown in Figure 6 and the corresponding detailed parameters are exhibited in Table 2. From Figure 6 and Table 2, two convolutional layers are considered for the proposed model and the max pooling layer is followed by each convolution layer. After that, two fully connected layers are utilized to fuse the features from the convolution modules. FIGURE 6Open in figure viewerPowerPoint Proposed CNN model TABLE 2. The parameters of the proposed CNN model Type Filters Size Strides/Padding Conv1 /ReLu 10 5*5 1/Same Max-pooling1 None 2*2 1/Same Conv2 /ReLu 20 5*5 1/Same Max-pooling 2 None 2*2 1/Same Fully connected layers 1 /ReLu Out 50 Fully connected layers 2/Sigmoid Out 1 More specifically, the parameter settings of the model are inspired by the structure of Lenet-5 [34]. The convolution kernel size of the two convolution layers is 5 × 5 and the default sliding step is 1. In the first convolution layer, the number of channels for the input image is three, the number of channels for extracting feature graph is ten and the activation function is the rectified linear units (ReLU). In the second convolution layer, the number of channels for extracting the feature graph is 20, followed by random inactivation. The maximum pooling layer is considered with a sampling window of 2 × 2, where the activation function ReLu is considered for the first full connection layer and the sigmoid function is used for the second full connection layer. As described in the system model, R x ${R}_x$ is a real matrix with a dimension M × M × 3 $M \times M \times 3$ . Let R x ( i , j , τ ) ${R}_x(i,j,\tau )$ denote the element at position ( i , j ) $(i,j)$ of the τth dimension in R x ${R}_x$ . (1) Convolutional Layer C 1 : C 1 ${C}_1:{C}_1$ contains ten feature maps, and each feature map is gained by convolution operation. This paper picks a kernel size of 5 × 5 for all of the convolutions. Thus, C 1 ( i , j , τ ) = φ Re L U Σ k = 0 2 Σ i 0 = 0 4 Σ j 0 = 0 4 R x ( i + i 0 , j + j 0 , k ) K τ C 1 ( 5 − i 0 , 5 − j 0 , 2 − k ) ) , \begin{equation} \def\eqcellsep{&}\begin{array}{l} {C}_1 (i,j,\tau ) = {\varphi }_{{\mathop{\rm Re}\nolimits} LU}\left(\mathop \Sigma \limits_{k = 0}^2 \mathop \Sigma \limits_{{i}_0 = 0}^4 \mathop \Sigma \limits_{{j}_0 = 0}^4 {R}_x(i + {i}_0,j + {j}_0,k)\right)\\[9pt] \quad \quad \quad \quad \quad K_\tau ^{C1}(5 - {i}_0,5 - {j}_0,2 - k)), \end{array} \end{equation} (11) where C 1 ( i , j , τ ) ${C}_1(i,j,\tau )$ denotes the element at position ( i , j ) $(i,j)$ of the τth feature map in C1 layer, and K τ C 1 $K_\tau ^{C1}$ denotes the kernel of the τ − t h $\tau - th$ feature map in C1 layer. φ Re L U ( x ) = max ( 0 , x ) ${\varphi }_{{\mathop{\rm Re}\nolimits} LU}(x) = \max (0,x)$ signifies ReLu function, where max ( · ) $\max ( \cdot )$ denotes the maximum value, x is the independent variable of the function. (2) Pooling Layer s 1 : s 1 ${s}_1:{s}_1$ consists of ten feature maps, and each feature map is gained by Max-Pooling operation. So, S 1 ( i , j , τ ) = m a x ( C 1 ( 2 i − 1 , 2 j − 1 , τ ) , C 1 ( 2 i − 1 , 2 j , τ ) , C 1 ( 2 i , 2 j − 1 , τ ) , C 1 ( 2 i , 2 j , τ ) ) . \begin{equation} \def\eqcellsep{&}\begin{array}{l} {S}_1(i,j,\tau ) = max({C}_1(2i - 1,2j - 1,\tau ),{C}_1(2i - 1,2j,\tau ),\\[6pt] \quad \quad \quad \quad \quad \quad {C}_1(2i,2j - 1,\tau ),{C}_1(2i,2j,\tau )). \end{array} \end{equation} (12) (3) Convolutional Layer C 2 : C 2 ${C}_2:{C}_2$ contains 20 feature maps, and each feature map is gained by convolution operation. Thus, we have: C 2 ( i , j , τ ) = φ Re L U Σ k = 0 9 Σ i 0 = 0 4 Σ j 0 = 0 4 C 1 ( i + i 0 , j 0 , k ) K τ C 2 ( 5 − i 0 , 5 − j 0 , 9 = k ) . \begin{equation} \def\eqcellsep{&}\begin{array}{l} {C}_2(i,j,\tau ) = {\varphi }_{{\mathop{\rm Re}\nolimits} LU}\left(\mathop \Sigma \limits_{k = 0}^9 \mathop \Sigma \limits_{i0 = 0}^4 \mathop \Sigma \limits_{j0 = 0}^4 {C}_1(i + {i}_0,{j}_0,k)\right.\\[9pt] \left.K_\tau ^{C2}(5 - {i}_0,5 - {j}_0,9 = k)\right). \end{array} \end{equation} (13) (4) Pooling Layer s 2 : s 2 ${s}_2:{s}_2$ has 20 feature maps, and each feature map is gained by Max-Pooling operation. So, we have: S 1 ( i , j , τ ) = m a x ( C 2 ( 2 i − 1 , 2 j − 1 , τ ) , C 2 ( 2 i − 1 , 2 j , τ ) , C 2 ( 2 i , 2 j − 1 , τ ) , C 2 ( 2 i , 2 j , τ ) ) . \begin{equation} \def\eqcellsep{&}\begin{array}{l} {S}_1(i,j,\tau ) = max({C}_2(2i - 1,2j - 1,\tau ),{C}_2(2i - 1,2j,\tau ),\\[10pt] \quad \quad \quad \quad \quad {C}_2(2i,2j - 1,\tau ),{C}_2(2i,2j,\tau )). \end{array} \end{equation} (14) (5) Fully Connected Layer F 1 : F 1 ${F}_1:{F}_1$ is fully connected with s2, The number of neurons in F1 is set as 50. (6) Fully Connected Layer F2: because the spectrum sensing problem is a binary classification problem, F2 could output a probability value which represents the probability that the input sample belongs to L1. This probability value can be expressed as P L 1 ( R x ) ${P}_{{L}_1}({R}_x)$ . When P L 1 ( R x ) > 0.5 ${P}_{{L}_1}({R}_x) > 0.5$ , we think that R x ∈ L 1 ${R}_x \in {L}_1$ , otherwise R x ∈ L 0 ${R}_x \in {L}_0$ . In the process of model training, 1/3 of the training set is employed to pre-train the CNN model and then the pre-training CNN model is obtained in the central node. After that, the pre-training CNN model is distributed to local nodes, where the SNR of local nodes fluctuates at a specific value. Finally, the pre-training CNN model is fine-tuned at the local node according to the corresponding training samples. 5 EXPERIMENTS AND DISCUSSIONS In this section, the simulations are conducted to validate the effectiveness of the proposed schemes. In the simulations, the recognition accuracy of the local fine-tuned CNN model is obtained by the corresponding test samples. For convenience, four local nodes are considered in the experiments and the corresponding SNRs are at −6, −3, 0 and 3 dB. Three groups of experiments are conducted in the simulations. The performance comparisons are made between the proposed CNN model with transfer learning scheme and the proposed CNN model without transfer learning under various SNR conditions for the first group of the experiments. For the second group of the experiments, different proportions of the training set are considered for the proposed CNN model without transfer learning under various SNR conditions. In the third group of the simulations, the proposed CNN model with transfer learning is compared with the classical SS schemes, including ED and improved ED (IED) scheme. The performance comparisons are made between the proposed CNN model with transfer learning and the proposed CNN model without transfer learning under various SNR conditions in Figure 7. From Figure 7, the detection probability of the proposed CNN model with transfer learning is obviously higher than that of the proposed CNN model without transfer learning while the false alarm probability of the proposed CNN model with transfer learning is lower than the proposed CNN model with transfer learning. It states that the transfer learning is helpful to the