1.

INTRODUCTION

Specific emitter identification (SEI) is the approach to identify wireless devices from corresponding radio frequency (RF) emissions¹. SEI is achievable due to the fact that the electronic circuits of different emitters possess unique characteristics, which are determined during the production and manufacturing processes². As these physical-layer characteristics are distinguishable indpendent of the content of signals, SEI has been extensively applied for wireless security in both military³ civilian fields⁴.

Recently, deep learning methods have shown superior performance for SEI. Neural networks including recurrent neural network (RNN) and convolutional neural network (CNN) are utilized. Long-short term memory (LSTM), a typical architecture of RNN, is adopted for SEI in References^5,6. CNNs are employed for SEI in References^7-11. Although deep learning methods have achieved superior performance for SEI if the training and testing data are received under the same condition, performance degrades when the testing data is received under a different condition. In particular, when the test data is received by a receiver different form the receiver of training data, the shifts of data distributions caused by receiver changing, which are also known as domain shifts, can influence the performance dramatically if not considered properly.

An approach based on deep adversarial neural network (DANN) is applied for cross-receiver SEI in this paper. DANN is an unsupervised domain adaptation method, which can mitigate domain shifts caused by different receivers. Furthermore, separated batch normalization (SepBN) is proposed to enhance the performance.

2.

PROBLEM FORMULATION

Assume there are K emitters {E₁,E₂,…,E_K} and M receivers {R₁,R₂,…,R_M}. The ideal equivalent baseband signal transmitted by the emitter is defined as s(t), then the signals emitted by E_k,k ∈ {1,2,…,K} and received by R_m,m ∈ {1,2,…,M} are formulated as:

where f_k (·) is a function denoting the characteristics of E_k, r_i(t) denotes the properties of R_m, and n(t) indicates additive white Gaussian noise. Samples are obtained by sampling from x(t):

where T is the sampling period.

The datasets collected by R_m are denoted as D_m = {(x₁,y₁),(x₂,y₂),…,(x_N,y_N)}, where N represents the number of samples, x_i is the ith signal sample and y_i is the corresponding label of emitter identity, i.e., y_j ∈ {E₁,E₂,…,E_K}. When samples of D_S, S ∈ {l,2,…,M} are used for training and samples of D_T, T ∈ {l,2,…,M},T ≠ S are used for testing, due to the different characteristics of R_S and R_T, samples of D_S and D_T are not independently and identically distributed. Therefore, a neural network trained on samples from one receiver can perform poorly on samples from another receiver.

3.

SEPBN-DANN

In this paper, a method named SepBN-DANN is proposed for cross-receiver SEI. The network architecture of SepBN-DANN is shown in Figure 1. SepBN-DANN is a transductive learning method, which utilizes training data with labels and unlabeled testing data. By aligning feature space of training data and testing data, SepBN-DANN learns receiver-invariant features so that performance of cross-receiver SEI can be improved.

Figure 1.

Network architecture of SepBN-DANN.

3.1

DANN

DANN¹² is a typical unsupervised domain adaptation method, which has been successfully applied for image classification¹², speaker recognition¹³ and SEI under varying frequency¹⁴. DANN is composed by three sub-networks, namely feature extractor, label classifier and domain discriminator, the parameters of which are denoted as Θ_F, Θ_C and Θ_D, respectively. The feature extractor seeks to learn features that are invariant for receivers and discriminative for emitter identities. Based on the outputs of the feature extractor, the label classifier identifies emitters of inputs, while the domain discriminator distinguishes receivers of inputs. While the feature extractor and the domain discriminator are trained in an adversarial manner to improve features’ invariance for receivers, the feature extractor and the label classifier are trained cooperatively so that the learnt features are discriminative for emitter identities. Therefore, the loss function of Θ_C is defined as the cross entropy between the outputs of the label classifier and emitter identities:

where 𝔼 denotes expectation, 𝕀(·) is the identity function, and ln(·) is the natural logarithm function, is the output of the label classifier, with representing the probability of the input belonging to E_k. Similarly, the loss function of Θ_D is defined as the cross entropy between the outputs of the domain discriminator and corresponding receivers:

where is the output of the domain discriminator, denoting the probability of the input belonging to R_S. Since the feature extractor is trained cooperatively with the label classifier, L_C is also the objective of the feature extractor. The feature extractor is trained adversarially with the domain discriminator, the adversarial loss function is defined as the cross entropy between the outputs of the domain discriminator and uniform distribution:

The total objective of Θ_F is:

where λ ~ [0,1] is a hyperparameter weighting the relative importance of L_A. During training, the three sub-networks are trained iteratively with corresponding objectives.

4.

EXPERIMENTS

To evaluate performance of the proposed approach for cross-receiver SEI, a dataset of 20 emitters and 2 receivers (R₁and R₂) is collected at 3 days (Day 1, Day 2 and Day 3). The parameters of emitters are kept the same and the parameters of receivers are identical. At each day, the number of samples for each emitter with each receiver is 1800. The proposed SepBN-DANN method is compared with DANN, which does not use SepBN, and vanilla CNN, which simply trains a convolutional neural network using training data for testing.

The accuracies of different methods for cross-receiver SEI at each day are shown in Table 1. SepBN-DANN achieves the highest accuracy under most conditions, which indicates the superiority of the proposed SepBN-DANN method. For CNN and DANN, the accuracies of cross-receiver SEI at Day1 are evidently lower than those at Day 2 and Day 3. This may be due to the fact that the signals collected by R₁ and R₂ at Day1 are more divergent. However, SepBN-DANN performs comparably at Day 1, demonstrating that SepBN-DANN is more stable.

Table 1.

Accuracy of cross-receiver SEI.

Features learned by different methods at Day 1 for R₁ → R₂ are visualized using t-SNE, as shown in Figure 2. Solid dots represent features of samples from R₁, while hollow dots represent features of samples from R₂. Different colors correspond to features of samples from different emitters. Since CNN does not take domain shifts into account, the learned features of R₂ are largely diverging from features of R₁, leading to poor performance. DANN partially mitigates the divergence of features between R₁ and R₂, and hence improves performance compared to CNN. By contrast, SepBN-DANN aligns the features of R₁ and R₂ to learn receiver-invariant features, so that desirable accuracy can be achieved.

Figure 2.

(a): Feature visualization of CNN; (b): Feature visualization of DANN; (c): Feature visualization of SepBN-DANN.

5.

CONCLUSION

In this paper, a method named SepBN-DANN is proposed for cross-receiver SEI. SepBN-DANN learns receiver-invariant features by aligning feature distributions of different receivers, and is more stable than conventional unsupervised domain adaptation method. Experimental results show that SepBN-DANN can improve accuracy substantially for cross-receiver SEI. Since SepBN-DANN only relies on the assumption that distributions of training and testing data are similar, the method may also be beneficial for other conditions, such as cross-channel and cross-modulation SEI. Like all other unsupervised domain adaptation methods, SepBN-DANN also suffers from the problem of negative transfer, i.e., signals of one emitter from source domain can be misaligned with signals of another emitter from target domain, which will be considered in future work.