Emitter signals modulation recognition based on discriminative projection and collaborative representation

IET Radar, Sonar & NavigationVolume 14, Issue 5 p. 782-791 Research ArticleFree Access Emitter signals modulation recognition based on discriminative projection and collaborative representation Dongjin Li, Corresponding Author Dongjin Li li_dong_jin@163.com orcid.org/0000-0002-7675-1340 People's Liberation Air Force Early Warning Academy, Wuhan, 430019 People's Republic of ChinaSearch for more papers by this authorRuijuan Yang, Ruijuan Yang People's Liberation Air Force Early Warning Academy, Wuhan, 430019 People's Republic of ChinaSearch for more papers by this authorRuijie Dong, Ruijie Dong People's Liberation Air Force Early Warning Academy, Wuhan, 430019 People's Republic of ChinaSearch for more papers by this authorJiajun Zuo, Jiajun Zuo People's Liberation Air Force Early Warning Academy, Wuhan, 430019 People's Republic of ChinaSearch for more papers by this author Dongjin Li, Corresponding Author Dongjin Li li_dong_jin@163.com orcid.org/0000-0002-7675-1340 People's Liberation Air Force Early Warning Academy, Wuhan, 430019 People's Republic of ChinaSearch for more papers by this authorRuijuan Yang, Ruijuan Yang People's Liberation Air Force Early Warning Academy, Wuhan, 430019 People's Republic of ChinaSearch for more papers by this authorRuijie Dong, Ruijie Dong People's Liberation Air Force Early Warning Academy, Wuhan, 430019 People's Republic of ChinaSearch for more papers by this authorJiajun Zuo, Jiajun Zuo People's Liberation Air Force Early Warning Academy, Wuhan, 430019 People's Republic of ChinaSearch for more papers by this author First published: 02 March 2020 https://doi.org/10.1049/iet-rsn.2019.0550AboutSectionsPDF 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 To enhance the modulation recognition performance of emitter signals under low signal-to-noise ratio (SNR), a recognition system based on secondary time–frequency distribution, discriminative projection, and collaborative representation is proposed. Firstly, a novel time–frequency processing method, including sparse-domain noise reduction and secondary feature extraction, is proposed to reduce noise interference and information redundancy in time–frequency images. In this way, secondary time–frequency distribution with high stability and detailed representation is obtained. Then, the classifier based on discriminative projection and collaborative representation was designed to enhance the ability of low-dimensional representation and between-class discrimination, which optimised using the mini-batch random gradient descent method. As shown in the simulation, the overall average recognition success rate of this system aiming at eight types of emitter signals reaches 95.6% at the SNR of −8 dB. Results of simulation and analysis indicate the superiority of the proposed classification system in terms of robustness, timeliness, and adaptability. 1 Introduction Fast and efficient emitter signals modulation recognition is the core functions required in the electronic warfare systems. Non-cooperative information obtained by efficient identification will directly influence the performance of subsequent tasks such as electronic countermeasures and detection. The development of emitter signal recognition technology depends on feature engineering and classifier models. With the development of signal processing and pattern recognition technology, non-linear feature transformation (fuzzy function, wavelet transformation etc.) and machine learning technology has been widely applied in this field and obtains a lot of achievements [1-6]. In recent years, as motivated by big data and strong computing capacity, the emitter signal recognition based on artificial intelligence (AI) technology has gradually become a hot topic. In [7], the transformed time–frequency domain feature was extracted through a short-time Fourier transform (STFT); recognition was completed through enhancement of the deep belief network, but the setting of the signal parameters was singular, and high-precision carrier frequency prior estimation was needed. In [8], the Choi-Williams distribution (CWD) was used to restrain cross-term interference of time–frequency feature, and the image noise reduction algorithm was used to enhance the robustness; then a convolution neural network (CNN) based on LeNet-5 was used to complete classification and recognition, but time–frequency structures of signals were quite different and could not reflect the generalisation ability. In [9-14], the intelligent recognition algorithm based on the deep learning network was used to obtain higher recognition performance. From the comprehensive perspective, conventional recognition methods of k-nearest neighbour (KNN) and support vector machines (SVM) based on machine learning have a certain intelligence level [15-20], while the feature stability can be enhanced by technologies such as non-linear feature transformation, but the adaptability and timeliness to complicated environments must be improved. In addition, the AI recognition algorithm reduces the influences of artificial factors and depends more on the network depth and sample capacity, but its advantages are difficult to be reflected when the sample capacity is insufficient. In actual application, sample capacity always can hardly satisfy the demands for deep learning under the causes such as insufficiency in intercepted samples. Besides, requirements for timeliness and accuracy can hardly be satisfied with conventional algorithms, so a more efficient recognition algorithm is required. Based on this, the paper makes combined design from perspectives of feature engineering and classifiers. The feature stability and classifier complexity are fully considered. In the feature engineering part, problems such as non-stability and noise pollution caused by complicated electromagnetic environments are mainly solved. In the classifier portion, we use another popular and efficient representation learning paradigm called dictionary learning. The goal was to learn an empirical basis from the data. The sparse representation-based classifier (SRC) has been widely applied in fields such as cognitive radio, computer vision, and image processing [21]. In [22], the emitter signal recognition based on sparse theory was discussed, but the form was relatively simple, and l0-norm regular constraint is subject to the limit in sparsity. In [23], l1-norm regular constraint was used to optimise the sparse representation structure and enhance robustness, but the computing was relatively complicated. In [24], the idea of collaborative representation was introduced, while a collaborative representation classification (CRC) method was proposed with the l2-norm regular constraint. In [25], it was introduced into the field of emitter signals recognition. On this basis, through the introduction of various types of optimisation discriminant items, a series of reinforced classification algorithms such as label consistent K-SVD speaking, feature engineering emphasises feature stability, while the classifier focuses on recognition capacity and timeliness [26-30]. The l2-norm regular constraint has high timeliness and can make full use of samples for fitting, which is more targeted than sparse representation forms. Hence, the idea of collaborative representation was used for classifier design. Meanwhile, conventional collaborative representation classifier only considers the influences of regular constraints and reconstruction error. The paper further introduces the ideas of discriminative projection [31, 32], which realise between-class differences enhancement and feature linear dimension reduction. In this paper, an emitter signal modulation recognition system based on secondary time–frequency distribution (STFD), discriminative projection, and collaborative representation is exploited. It aims to improve the recognition success rate (RSR) and timeliness. The paper is organised as follows. Section 2 introduces the emitter signals modulation recognition system and signal model. Section 3 explains the algorithm for feature extraction. Section 4 describes the details of the novel recognition method, including the classification model and optimisation method. In Section 5, we perform performance analysis under experimental comparisons. Finally, Section 6 draws the conclusions. 2 System overview Fig. 1 shows the whole framework of the modulation recognition method for emitter signals proposed in this work. The system comprises feature extraction, discriminative projection, and collaborative representation-based classification (DP-CRC). Firstly, feature extraction is performed through STFT. Pre-processing is completed through noise reduction and STFD to ensure the stability of the new feature. Secondly, the model of dictionary classification based on low-dimensional (LD) representations is optimised with supervised learning. Then, the discriminative projection matrix and the dictionary would be saved for the unsupervised testing and the performance verification of the system. Fig. 1Open in figure viewerPowerPoint Emitter signals modulation recognition system based on STFD and DP-CRC The emitter signals considered in our work include single carrier frequency modulation (SCFM), binary frequency shift keying (BFSK), quadrature frequency shift keying (QFSK), binary phase shift keying (BPSK), quadrature phase shift keying (QPSK), non-linear frequency modulation (NLFM), linear frequency modulation (LFM), polyphase codes modulation (Frank) [7]. In the Gaussian white noise environment, the intercepted single-pulse sampling sequence model is given by (1) where k is an integer, A is amplitude, is the initial frequency, is the instantaneous phase, is the initial phase, is Gaussian white noise. The for LFM can be described as , where B is bandwidth and is pulse width. The for NLFM can be described as , where and are modulation parameters. The phase state of Frank satisfies , where M is Frank code's order. The differences between emitter signals are concentrated in . 3 Feature extraction and pre-processing In this section, STFT is used to get the initial 2D feature. Noise reduction and secondary distribution feature extraction are used to reduce noise interference and information redundancy. Noise reduction is completed based on the time–frequency domain sparsity. The secondary distribution feature is extracted through the optimisation of a projection subspace. 3.1 Short-time Fourier transform STFT has a stable representation capacity for time–frequency structure and has high timeliness. The discrete domain STFT can be expressed as (2) where m and n refer to indexes of time and frequency. N is the Fourier transform length, is the conjugation of Hamming window function with a length of . The time–frequency distribution images of STFT are shown in Fig. 2. All types have good 2D time–frequency structures, together with sparsity and different degrees of information redundancy. Specifically, dispersion degrees of time–frequency components of BFSK and QFSK signals are relatively high. SCFM, BPSK, and QPSK are narrowband signals which have low differences under low signal-to-noise ratio (SNR). In addition, LFM and NLFM are similar in signal structures. Fig. 2Open in figure viewerPowerPoint Time–frequency distribution of eight type signals (a) SCFM, BFSK, BPSK, and QFSK, (b) QPSK, LFM, NLFM, and Frank 3.2 Noise reduction Processes shown in Fig. 3 are utilised to extract the STFD feature. First, resize the original time–frequency signal into using the bicubic interpolation algorithm [33]. Then a filter coefficient matrix is established with the initial value . Each column signals corresponds to the local frequency-domain feature with sparsity. The normalisation processing is conducted by column (3) Then, calculate the coefficient by applying the following sparse representation: (4) where the is coefficient enhancement function and . Due to the fast convergence of the coefficient enhancement function, formulas (3) and (4) are repeated twice to complete the optimisation. Then the time–frequency signal is updated as , where is Hadamard product. Fig. 3Open in figure viewerPowerPoint Processes of feature extraction and pre-processing (SNR = −5 dB) 3.3 Secondary time–frequency distribution Redundant information does not provide gain for modulation identification and affects the recognition performance to a certain extent. Hence, the quantisation function is introduced for a quantitative description of redundancy information. The slide window detection mechanism is used for optimisation. In this way, the position of signal subspace or marginal frequency distribution is obtained, and information redundancy is reduced. The frequency-domain projection of the time–frequency signal reflects the spectral distribution and the energy difference of the marginal frequency distribution. The weight coefficients of the frequency domain are defined by (5) where m and n refer to indexes of time and frequency. Then, the weighting coefficients are normalised. Based on the continuity of the signal distribution, a sliding window detection mechanism is introduced, and the detection result is expressed by (6) where is the unit rectangular window with a width of , is the window index, is the in-window index and . Then the weight coefficient is vectorised by , where is the ith row of . Similarly, the time-domain projection of the time–frequency signal reflects its continuity and proportion of state. The binary representation of time–frequency distribution is initialised by , and binary quantification with a zero-crossing mean threshold is expressed by (7) Then, perform slide window detection on binarised time–frequency data, and binary pixels in the window are expressed as follows: (8) where is a cumulative state. is a smooth filtered pixel, which represents the existence ( while ) or non-existence ( while ) state of the signal in the window of at each. The duty ratio can be expressed as (9) where is the duty ratio of the signal in the window at the index position of the frequency domain. The duty ratio is 1 when the whole signal subspace contained in the window, and the duty ratio is 0 when the window contains only the noise subspace. Then, the duty ratio is vectorised by , where is the ith row of . On this basis, the marginal frequency distribution is defined as (10) Here, the redundant information can be reduced by intercepting the corresponding signal subspace in the time–frequency space. The upper and lower limits of the marginal frequency distribution are expressed as and , respectively, where and . The secondary distribution data is . In order to avoid 'curse of dimensionality' and the output format differences, the bicubic interpolation algorithm is used to standardise secondary distribution data. Therefore, the STFD data is uniformly output as . 4 Discriminative projection and collaborative representation based classification analysis In this section, we designed the classifier of DP-CRC. Timeliness and stable feature representation capacity of a classifier model are emphasised. An objective function is constructed with the Fisher criterion. Optimisation is realised with the mini-batch stochastic gradient descent (MSGD) method of dynamic increment constraints [34]. 4.1 Objective function The general model for dictionary learning can be described as the following optimisation problem: (11) where is the dictionary, is a regularisation parameter, are the parameters of optimisation mode, while corresponding l1-norm sparse representation and corresponding l2-norm collaborative representation. In order to enhance the timeliness, was set in the paper. Meanwhile, learning appropriate LD representations of data plays a critical role as a pre-processing procedure for the success of discrimination learning algorithms, because of its parsimony on computations. Hence, the discriminative projection matrix was introduced to realise dimension reduction mapping from the N-dimensional feature space to the N1-dimensional feature space. Through limiting of orthogonality of the projection matrix, the Euclidean distance of the original space can be maintained. The encoding coefficient of the corresponding DP-CRC is expressed as (12) where is a testing sample, is an encoding coefficient, K is the number of dictionary atoms, N is the initial feature dimension with the corresponding dictionary expression of . Suppose that we have L distinct classes of subjects, is the sub-dictionary of ith class, and . The encoding coefficient can be calculated as (13) Then, the reconstruction residual and classification results can be calculated as (14) Define as the reconstruction error when correctly classified, and as the minimum error term among misclassification errors. Types c and d correspond to the correct class and the nearest misclassification can be expressed as (15) where is the training sample of ith class. The difference and recognition capacity of dictionary atoms can be enhanced through enlargement of differences in types c and d. In order to enhance the recognition ability, with the Fisher criterion and the deep learning ideas as the reference [26, 27, 34], a secondary objective function is introduced for the optimal solution of discriminative projection and dictionary atoms. The objective function of our method can be expressed as follows: (16) where is a quantisation function, is a jth training sample of ith class, is batch size of training set, and is the random sample size of ith class. In the above formula, the batched computing idea is adopted for optimisation with MSGD to ensure a more stable gradient update direction. The quantitative function is used for gradient update. The sigmoid function with bounded output and the slope parameter is selected, namely Sβ(x) = 1/(1 + eβ (1−x)). The intra-class and nearest between-class difference quantisation function is defined as (17) where critical value is , and corresponding is 1. In addition, there are mainly two cases: (1) while , correct classification to class c can be realised, and the wrong classification probability is reduced; (2) while , signals can be easily misclassified into class d. The MSGD method helps to correct the error. 4.2 Optimisation Gradient computation is conducted for the loss function , wherein the gradient of and are expressed as (18) where is the partial derivative of . is defined as . Influences of on the gradient are neglected, the partial derivative is (19) The gradient descent directions for updating the projection and dictionary can be expressed as follows: (20) Denote that and . and are momentum factor, and are learning rates. When the batch learning strategy is used, the gradient averaging is conducted to the formula (18). Hence, the learning rate varies with the batch parameters. Learning rates in case that and , and is the initial learning rate. The specific optimisation scheme is described as follows. Algorithm 1.The DP-CRC algorithm based on MSGDInput: Dictionary learning parameters of , , and ; MSGD parameters of , , , , , and B.Initialisation: Initialise dictionary by SVD algorithm. Initialise discriminative projection as Gaussian random projection. Set iteration t = 1.Repeat: Randomly dividing the training set into NUM batches. for i = 1: NUM Solve the encoding coefficient by formula (13), get the nearest misclassification category d by the formula (15). Update and by formula (18) and (19). Update and by the formula (20). Apply an orthogonal transform to . Normalise dictionary atoms by column. end for Set t = t + 1. Until convergence Output: and . 5 Simulation and discussion In this section, the efficiency of the proposed system is verified by experimental comparison, which mainly consists of three parts: firstly, the DP-CRC parameters are analysed; secondly, the recognition performance and computational complexity of the proposed method are displayed and compared with other approaches; thirdly, the system performance of the robustness and adaptive capacity to environment are analysed. The specific simulation environment built on a machine with Intel (R) Core (TM) CPU i5-M480 running at 2267 MHz; 6 GB RAM, Windows 7 (64bit) running MATLAB R2018b. The simulation experiments were carried out using the eight types of emitter signals described in Section 2. The signal parameters are set as follows: the carrier frequency of SCFM, BPSK, and QPSK range from 5 to 40 MHz, the carrier frequency of LFM, NLFM, and Frank range from 5 to 25 MHz; BFSK's basis frequency varies from 5 to 20 MHz, and hopping frequency ranges from 5 to 20 MHz, QFSK's basis frequency and hopping frequency all range from 5 to 10 MHz; the encoding sequence of BPSK and BFSK randomly select from {7,11,13} Barker codes, the encoding sequence of QFSK and QPSK select '1,3,2,4,3,2,3,4,3,1,2' or '4,1,3,2,1,4,1,3,2,3,4'; the bandwidth of LFM ranges from 10 to 20 MHz; the NLFM's parameters () range from 5 to 10 MHz. The code order (M) of Frank is a random value between 5 and 8. The parameters of each signal are different, and the carrier frequency is uniform and random distributed. The testing environment is as follows: sampling frequency is 200 MHz; sampling duration is 10 μs; all the samples were generated according to the parameter distribution and feature processing processes; recognition results were averaged ten times; the datasets were generated under SNR that varies from −12 to 10 dB with a step of 1 dB. Under each SNR, there are 200 signal samples for each class, with the sample capacity of 36,800. The training set is constituted of 20 samples randomly selected from each class under each SNR. The sample capacity is 3680. The rest is the testing dataset. 5.1 Setting of parameters In the pre-processing phase, different-scale window combination modes were selected for coefficient optimisation. Corresponding window widths are 50 and 10. Window weighting coefficients are 2/3 and 1/3. In order to reduce the distortion of detailed features, the standard output dimension of the STFD feature is 60 × 60, with the corresponding vector-based feature dimension of 3600. The regular parameter () in the DP-CRC algorithm is 0.01. Ending condition: iteration error is smaller than 0.001 or the maximum number of iterations reaches 10. In MSGD, momentum factors ( and ) are 0.5. Corresponding parameters: , , , and . The dimension reduction parameter is 300. The number of atoms is the same in each sub-dictionary, namely . The influences of different parameters on performance are analysed as follows. 5.1.1 Influences of slope value Smoothness degree and gradient weight of the quantisation function can be flexibly adjusted by the slope value (). With the smaller , the gradient varies more smoothly, while the convergence is slower. With the larger , the gradient value is more considerable around the critical value, and the convergence is quicker. However, the gradient decreases quickly in parts remote from the critical value and can easily fall into a soft saturated area. During batched training, the probability of falling to the soft saturated area can be reduced effectively by the average gradient mode. Hence, performance is excellent under . Based on a comprehensive consideration of timeliness and recognition performance, was selected in the paper. 5.1.2 Influences of learning rates Learning rate is an important parameter that can influence the recognition performance. and were selected, and the performance is shown in Fig. 4. Under different SNR, the optimum recognition rate could be reached when , and the recognition performance tended to decrease when . Comprehensive comparison results show that recognition performance was greatly influenced by the learning rate parameter, with the fluctuation range of about 15% at−12 dB. The performance was good under and . The overall performance was optimal when and . Fig. 4Open in figure viewerPowerPoint Effect of learning rates on RSR under different SNR (a) SNR = − 12 dB, (b) SNR = −10 dB, (c) SNR = −8 dB 5.1.3 Influences of batch size Stability and effectiveness of gradient updates can be ensured by batch data differences of the batch computation mode. In addition, uncertainty in gradient direction and computation cost generated from the introduction of small sample computation can be avoided. Batch computation is accelerated through matrix computation. Different batch parameters were used for testing. The recognition performance (overall average RSR) did not vary a lot under different batch parameters. The computation complexity decreased with the increase of B. Specific performance parameters are shown in Table 1. Results show that mainly the model optimisation timeliness was influenced by the parameter. Under a large overall sample capacity, B can be appropriately increased. B shall not be too large when the sample capacity decreases. is selected for subsequent processing. Table 1. Effect of parameters B on training time and RSR B 100 200 300 400 500 time, s 362.78 256.89 182.72 163.38 118.73 RSR, % 95.72 95.70 95.72 95.77 95.79 5.1.4 Influences of atoms and dimensions Intra-class representation and between-class identification ability in sub-dictionaries depend jointly on dictionary atoms and dimension reduction parameters. Through the rational reduction of the number of dictionary atoms and dimension reduction parameters, the feature redundancy and computation complexity can be reduced. and were selected for testing. Recognition performance corresponding to different parameters is shown in Fig. 5. Comprehensively speaking, the performance was stable under , and the convergence performance was good under small ; with the increase of , the convergence got worse gradually, while the upper limit of performance could hardly be realised when . When , the dictionary is over-complete with a lot of redundant atoms. After dimension reduction, the correlation between redundant atoms and sub-dictionaries is large and the recognition performance is reduced on the contrary. Through the further increase of , the computation cost significantly increased, while the recognition rate did not increase obviously. Hence, in order to enhance intra-class recognition, the number of dictionary atoms shall not be too large. and were selected for comparison. The corresponding performance was optimal when and . The number of dictionary atoms is associated with different applications. In applications such as face recognition, more dictionary atoms are required. Fig. 5Open in figure viewerPowerPoint Influences of dictionary atoms and feature dimensions on RSR (a) , (b) , (c) , (d) Except for influences on the recognition rate, the dimension reduction parameter and dictionary atoms can directly influence timeliness of recognition. Training time and testing time corresponding to different parameters are shown in Table 2. Comparison results show that the computation complexity mainly depends on the number of parameters included in P and D, and is positively related to the dimension reduction parameter and number of dictionary atoms. Based on comprehensive consideration of recognition performance and computation complexity, the dimension reduction parameter and the number of dictionary atoms were set as and . Table 2. Computational complexity comparison of different parameters (training time/testing time, unit: s) N1 K0 50 100 200 50 41.31/1.51 78.29/2.18 247.06/5.15 100 52.88/5.05 102.39/6.51 291.57/8.45 200 81.95/11.50 148.78/11.65 380.21/17.21 300 118.7/13.8 212.75/14.62 458.47/26.98 400 161.4/19.4 256.66/24.28 590.12/33.60 500 199.3/26.6 316.86/28.98 714.72/35.18 5.2 Method performance comparison 5.2.1 Feature extraction comparison The feature extraction algorithm affects recognition performance to some extent. Therefore, the quantitative effects of feature processing methods at different stages on performance are analysed and compared with the feature extraction methods in [7, 8]. In [7], the energy cumulant short-time Fourier transform (EC-STFT) feature is extracted by frequency domain projection; in [8], the time–frequency image (TFI) feature is extracted by time–frequency transforming, TFI clipping, binary processing and noise removing, and so on. When compared with the TFI feature, STFT instead of CWD is used to obtain the initial feature. Here, the feature after STFT and noise reduction processing is recorded as DSTFT. Recognition results are shown in Fig. 6, which shows that the STFD feature is more stable. The EC-STFT feature only retains one-dimensional frequency domain components, which are sensitive to carrier frequency randomness and intra-pulse parameter randomness; so the generalisation ability is poor. On the contrary, 2D time–frequency features retain more details. The STFT-TFI feature is stable at high SNR, but the image denoising algorithm is difficult to adapt to a