Online Large Margin Semi-supervised Algorithm for Automatic Classification of Digital Modulations Hamidreza Hosseinzadeh*, Farbod Razzazi**, and Afrooz Haghbin*** Department of Electrical and Computer Engineering, Islamic Azad University, Science & Research Branch, Tehran, Iran * hr.hosseinzadeh@srbiau.ac.ir ** razzazi@srbiau.ac.ir *** ahaghbin@gmail.com Abstract: Automatic classification of modulation type in detected signals is an intermediate step between signal detection and demodulation, and is also an essential task for an intelligent receiver in various civil and military applications. In this paper, we propose a semi-supervised online passive-aggressive classifier that uses self-training approach for AWGN channels with unknown or variable signal to noise ratios to classify the modulated signals. Simulation results shows that adding unlabeled input samples to the training set, improve the generalization capacity of the presented classifier. In addition to the online properties which are suitable for time variated systems, this algorithm requires less numbers of signal samples (thus is fast) to convergence to the correct answer and can be further to adapt to the input. The selection of appropriate features helps the general system to work for a set of initial sample of each class. The simulation results show that the employing this learning method increase the accuracy level. Keywords: Automatic modulation classification, Pattern recognition, Semi-supervised learning, Passive-aggressive classifier, Online learning. 1. INTRODUCTION During the age of wireless communications, it has often been assumed that receiver is aware of modulation type of transmitted signal. However, nowadays, there is a vast variety of applications that it is essential to detect and demodulate the signal without given priori information about the received signal. In such cases, unlike regular receivers in which the primitive information of the received signals, such as carrier frequencies, frequency bandwidth, bit rate, and modulation type, is available, there is no information available for the received signal, and the receiver is blind. In this case, an automatic modulation classifier (AMC) as an intermediate step helps the receiver employ the correct decoder in the receiver. AMC covers a wide range of applications including electronic warfare applications, intelligent services systems, spectrum monitoring, signal surveillance, interfere identification and cognitive radio applications. Generally, designing a modulation classifier substantially consists of two steps: pre-processing the received signal and choosing a proper classification algorithm. The pre-processing task might include noise reduction, carrier frequency estimation, and signal to noise ratio estimation and so on. Depending on the classification algorithm in the second step, the pre-processing tasks should be provided. The focus of this study is on the second step. Regarding to the second step, the classification algorithms may be divided into two major categories: decision theory based approaches and feature matching based approaches [1-2]. The former approach is based on the received signal likelihood function and the decision-making is based on the comparison of the likelihood function with a threshold ratio. The complexity of this approach is usually high. In addition, this approach does not perform well when the sampled signal has random phase offsets, timing offsets, or timing jitters. In contrast, the latter approach usually extracts one or more features form the received signal and the decision-making is performed based on their measured values by using a trainable classification algorithms. The calculation complexity of this approach is lower than the first approach. Our proposed algorithm is categorized in the second approach. Feature matching based systems involve two main subsystems; the feature extraction subsystem and the classifier subsystem. In the former, one or several features are extracted from the received signal, and in the latter, the membership of signal to each class is determined. This study proposes a new online semi-supervised large margin classifier using classic state of the art features. Therefore, the contribution of the paper is concentrated on the second subsystem. From the published works in automatic modulation classification, it appears clear that unfortunately, most of the proposed AMC algorithms are evaluated on stationary, aware case which is far away from realistic conditions. In contrast, most of AMC applications should be utilized in variable, non-stationary environments and AMC algorithms should be both fast and robust to follow the environments variability. In addition, all of the mentioned previous studies rely on the availability of large labeled datasets to train the classifier they assume to have a large set of labeled training samples which again is not applicable in most AMC applications, need to deal with both labeled and unlabeled data simultaneously. Training the classifier using both labeled and unlabeled samples is called semi-supervised learning [3-4]. One of semi-supervised classification models is self-training. Self-training models is characterized by the fact that the learning process uses its own predictions to teach itself [3]. In this paper, we propose a self-training large margin method for modulation classification applications. The algorithm is developed based on passive-aggressive online algorithm [5] to train the semi-supervised classifier and determine the modulated signal type.
Digital Modulated Signal Dataset Labeled Samples Sequential unlabeled Samples Test Evaluation Modulation Type Initial General Training Train Parameters High Confidence No Ignore Sample for Training Yes Adaptation Figure 1. The overall block diagram of proposed classifier The rest of the paper is organized as follows: in section 2, we present the proposed architecture and adaptation algorithm. This section also reviews the online passive-aggressive learning algorithms as the basis of the proposed architecture. Section 3 provides a description of employed test bench and discusses on simulation results. Finally, section 4 concludes the paper and comments on how this algorithm can be further expanded. 2. PROPOSED CLASSIFIER ARCHITECTURE 2.1 Online Passive-Aggressive Classifier Passive-Aggressive (PA) algorithm [5] is a maximum margin based learning algorithm, which has been mainly used in on-line learning. Online PA algorithm, on one hand, modifies the current classifier in order to correctly classify the current example by updating the weight vector from to ; and on the other hand, the new classifier should be as close as possible to the current classifier, where is a kernel function and is bias. Our idea for modulations classification was based on the PA algorithm, and we pursued both above ideas at the same time. The vector is initialized to. In round, the new weight vector was determined by solving the following optimization problem, where. Furthermore, is instantaneous loss which is defined by * +. In this study, the concept of PA algorithm was used to deal with the semi-supervised learning problem. To do so, we should add the term into the function of standard support vector machine (SVM) which converts the following optimization equation [6]: (1) (2), - where is the weight vector that produced by using only labeled data. The optimization criterion is formulated as follow: (3), - where is a weight parameter which used to have a trade-off between maximizing the mentioned margin and generating a new classifier close to original classifier [6]. Terms denote the inner product of two vectors. In the case of multiclass classification, the algorithm prediction is a vector in where each element in the vector corresponds to score assigned to the respective label. These score calculations, have been devised in [7]. The prediction of the PA algorithm is set to be the label with the highest score. 2.2 Proposed Classifier In this section, we propose a self-training architecture using online passive-aggressive algorithm so that the classification result of each sample would be determined and evaluated at the time of occurrence. The diagram of our classifier is shown in Fig. 1. In our self-training algorithm, the classifier is first trained with the labeled samples and the obtained result is used to classify the unlabeled input samples that have been entered one by one. Thus, the unlabeled input samples that are predicted with high confidence score is collected to augment into the labeled samples gradually. The classifier is retrained using this new labeled sample and can be adapted. The result is used to classify the next unlabeled samples every time. This procedure is repeated until the last unlabeled sample is entered. Referring to the simulation results, it is clear that this classifier will converge with a few unlabeled samples. The simulation results show that the system accuracy is almost the same as the overall system accuracy after entering the 2 th sample.
Frequency of Samples class 1.5 1 1.5 class 3.5 1 1.5 class 5.5 1 1.5 class 7.5 1 1.5 class 9.5 1 1.5 Confidence Value class 2.5 1 1.5 class 4.5 1 1.5 class 6.5 1 1.5 class 8.5 1 1.5 class 1.5 1 1.5 Confidence Value Figure 2. The histogram of distance to decision boundary for different classes after depicted the 3 th sample in =4 db 2.3 Proposed Confidence measures In a semi-supervised learning algorithm, the system may miss the accuracy or even the convergence unless the new labeled data is reliable. Here, we have introduced a new algorithm to select the confident samples. In the used PA algorithm, the confident and reliable samples are the samples where the value of classification equation for these samples is positive for predicted class and negative for all rest classes. By using predicted unlabeled samples which is occurred gradually, we have determined the histogram of the value of classification equation for each target class. This histogram is updated iteratively during the entering time interval of each sample. Finally, if the input sample lies in the 9% of the above predicted unlabeled samples and has confident score then it will be chosen as high confidence sample. Since, relative frequency of predicted unlabeled samples in each recognized class are not the same, we have considered a threshold for each recognized classes. It should be noted that the procedure is blind regarding the real label of the sample. The predicted class is used to update the target class threshold. The histogram of the distance to decision boundary for different classes in = 4 db after depicted 3 th sample for each class has been shown in Fig. 2. 3. EXPERIMENTS AND RESULTS 3.1 Evaluation Benchmarks According to the increasing expansion of digital systems and the trend towards digital telecommunication instead of analog telecommunication, today mostly the digital signals are put to use. Considering the changes in message parameters, there are four general digital signal types, M-ASK, M-PSK, M-FSK and M-QAM [8]. The modulation techniques of digital input signals in this paper are considered to be: FSK2, FSK4, ASK2, ASK4, PSK2, PSK4, PSK8, QAM16, QAM32, and QAM64. To simplify the indication, these signals are substituted with S 1, S 2, S 3, S 4, S 5, S 6, S 7, S 8, S 9 and S 1, respectively. The radial basis function (RBF) was employed for this experiment as the kernel function of PA classifier. A grid search technique was used to find the optimal values of kernel parameters. In practice, the standard method to determine the best value for parameters γ and c is through the grid search method. We have used using cross-validation method to evaluate classifier generalization performance. The performances of the algorithms are compared based on the classification accuracy. Classification accuracy of each experiment is computed as the ratio of the number of samples correctly classified to the total number of samples. In this study, the performance evaluation of the classifiers is performed on the unseen samples to test the generalization capacity of the classifier. Classification accuracy assessments of different classes have been provided by the confusion matrix and accuracy matrix in percentage. Here we assumed that the carrier frequency has been correctly estimated before or it has been known. Therefore, we only considered complex baseband signals. In addition, it was assumed that the simulated signals were bandwidth limited. The additive white Gaussian noise was added according to s in 4, 8, and 12 db. Each signal type has realizations which are generated randomly for every trial to ensure that the results will be independent of the considered input samples. There are labeled samples and unlabeled samples. 3.2 Feature Extraction Feature extraction is the determinant part of a pattern recognition system whose aim is to reveal the distinctive properties of an object to be recognized. Here, a suitable set of features was considered as a combination of high order moments, high order cumulants and instantaneous characteristics of digital signal types. In the rest of this section, the employed features are briefly described. Instantaneous features will demonstrate to be suitable for the signals which contain instantaneous phase or instantaneous frequency [9]. In this work, the instantaneous features for classification were selected from the suggested features by Azzouz and Nandi [1-11]. These features were derived from the instantaneous properties of the received signals. Therefore, these features called as instantaneous features. The instantaneous key features used for this identification algorithm are derived from the instantaneous amplitude and the instantaneous frequency of the signal under consideration. Based on the considered signals, some of these key features are used to generate the input data set of the classifier in this paper. The first feature is the maximum value of the power spectral density of the normalized-centered instantaneous amplitude of the intercepted signal which is formulated as follows:. ( ) / (4) where is the number of the sample in the range and is value of centralized normalized instantaneous amplitude and it is defined by
a( i) acn ( i) an( i) 1, an ( i) (5) ma and is the average value of instantaneous amplitude over one frame, i.e. 1 ma N s N s i1 a( i) This feature is designed to discriminate between constant envelope (CE) signals and non-ce signals. The second feature is the standard deviation of the absolute value of the normalized-centered instantaneous amplitude of a signal which is formulated as follows: (6) C 84 3 2 2 1 BPSK 4PSK 8PSK 16QAM 32QAM 64QAM 2 N s N s 1 2 1 aa acn i acn i (7) N s N 1 s i i1 This feature is originally designed to discriminate between ASK2 and ASK4 signals. The third feature is the standard deviation of absolute value of normalized-centered instantaneous frequency over non-weak segments of the intercepted signal which is calculated as: af 2 1 2 1 fcn ( i) fcn ( i) L L a cn i at acn i at (8) where is the centralized normalized instantaneous frequency that is defined as (9) In this equation, is the bit rate. is a preset threshold value to detect non-weak samples; because instantaneous frequency is very noise sensitive. In this paper, the detection threshold of non-weak samples is chosen as.this feature is designed to discriminate between FSK signals. The fourth key feature is the statistical moments. The moment of a random variable may be defined as follow, - (1) where p is called the moment order and s * stands for complex conjugate of s. The fifth key feature is cumulants which is the most widely used feature in this area. The symbolism for pth order of cumulants is similar to that of the pth order moment., - (11) The mentioned expression have (p-q) terms s, and q terms s *. Cumulants may be expressed in term of moments as, - [ ] 1 (12) 5 1 15 2 25 3 Figure 3. Variation of c 84 in different s where the summation index is over all partitions for the set of indices, and q is the number of elements in a given partition [12]. Based on trial and error method, we selected the proper higher order moment and cumulants with empirically high performance. Unfortunately, these characteristics are highly noise dependent. Therefore, a strategy must be devised to decrease the effect of this dependency, as far as possible. Fig. 3 shows the amount of C 84 cumulant changes in different s for the selected modulations set. The figure shows that the selected features are depended on. 3.3 Performance Evaluation of PA algorithm In the first step, the performance of offline and online maximum margin classifiers in batch mode, based on the classification accuracy, were assessed. Comparing the PA algorithm with the classic offline algorithms (e.g. SVM), it can be concluded that their results are close to each other. In fact, they are two different problem solving methods which both pursue a similar goal. These results are presented in TABLE I. According to TABLE I, it could be observed that SVM could well be replaced by PA in online learning mode. 3.4 Performance Evaluation of proposed classifier In this section, we evaluated the performance of our classifier at different s via simulation. TABLE II shows the classification rates of proposed Classifier in 4, 8 and 12 db s. TABLE I. COMPARISON OF PA AND SVM ALGORITHMS BASED ON CLASSIFICATION ACCURACY Offline SVM Offline PA db 84.18 85.6 4 db 97.36 97.21 8 db 99.85 99.84 12 db
TABLE II. CLASSIFICATION RATE OF PROPOSED CLASSIFIER IN DIFFERENT S (%) TABLE IV. CONFIDENCE THRESHOLDS FOR EACH RECOGNIZED CLASS IN DIFFERENT S AFTER DEPICTED THE 3 TH SAMPLE 4 db 8 db 12 db S 1 S 2 S 3 99.4 S 4 97.4 S 5 S 6 S 7 98.4 S 8 55.3 94.9 S 9 95.9 S 1 89.7 88.9 Mean 93.61 98.38 From the mentioned results in TABLE II, it can be deduced that the performance of classifier in different are generally good. This fact is because of the samples that are used to train the classifier have a high confidence. However, the performance is slightly degraded in lower s. This indicates that these features may not be able to tolerate high noise. As a sample, the confusion matrix is presented at =4 db to analyze in the confusion of different classes. These results are presented in TABLE III. As it is mentioned in the previous section, a confidence threshold should be determined to collect a well confident sample when it occurs. The values of confidence thresholds for each predicted class, may be right or wrong, in different s after depicted 3 th sample are presented in TABLE IV. As it is observed in Table IV, the confidence threshold has very low levels for =12 db. In this case, all of the samples have high confidence and there is no need to apply the confidence threshold. Furthermore, this results show that it is capable to converge to the correct answer with a few samples. In TABLE V, the accuracy of first 2 samples is compared with the final system accuracy. TABLE III. CONFUSION MATRIX OF PROPOSED ALGORITHM IN = 4 DB (%) S 1 S 2 S 3 S 4 S 5 S 6 S 7 S 8 S 9 S 1 S 1 S 2 S 3 99.9.1 S 4 3.3 96.7 S 5 S 6 S 7 S 8 92.8 7.2 S 9.6.3 98.9.2 S 1 25.8.3 73.9 4 db 8 db 12 db S 1.2.879 1.241 S 2.133.785 1.113 S 3.4.3.2 S 4.2.4.112 S 5.117.9.14 S 6.194.682.899 S 7.57.778 1.4696 S 8.111.669.8271 S 9.28.797.8252 S 1.96.685.773 As it is observed in TABLE V, on average, the accuracy after depicted the 2 th samples is 98% of final accuracy after showing the last sample. This means that the system is able to work with a few samples. 3.5 Performance Comparison In this section, to quantify the effect of our algorithm for semi-supervised learning, we compared it with other classifiers. We generate a set of samples and their labels based on considered digital modulation and then evaluate the effect of different classifiers on it. First, the accuracies which obtained from the proposed classifier were compared to that of the system that was trained by the PA algorithm with the labeled data in the matched. Then, semi-supervised PA is compared to supervised PA, to evaluate the effect of unlabeled samples. In addition, for the confidence evaluation, the proposed algorithm is performed in the no confidence mode. The results are indicated in TABLE VI. As it is observed in TABLE VI, all of the evaluated algorithms have similar performance in noise-free mode. Simulation results show that by reducing, the proposed algorithm generally has good performance and its accuracy is close to the analysis in matched. Comparing semi-supervised PA in confidence mode (proposed classifier) to semi-supervised PA in non-confidence mode indicate that the 62.42% number of errors are reduced with applying confidence. TABLE V. EVALUATING SYSTEM PERFORMANCE WITH A FEW SAMPLES (%) Accuracy after showing 2 th sample Accuracy after showing the last sample 4 db 92.5 93.61 8 db 98 98.38 12 db
TABLE VI. PERFORMANCE COMPARISON (%) Proposed Classifier P.A. training with the matched Proposed Classifier without confidence 4 db 93.61 97.21 87.51 8 db 98.38 99.84 9 12 db 99.97 Noise-free 3.6 Comparison with previous works Finally, the accuracies which were obtained from proposed classifier was compared to important previous papers [12-16]. Direct comparison with other works is difficult, because on one hand the candidate modulations are often not the same and on the other hand, the parameters of the classifiers which take into account are not the same. However, we simulated some of the algorithms under the same conditions. In comparison among the existing works, the proposed classifier has many advantages. This classifier can recognize the considered digital signals even at low s for AWGN channels with unknown or variable s. Simulation results in TABLE VI are the evidences of this issue. While in the most existing works, training performs in matched. Simulation result show that the performance of proposed classifier is close to the classifiers which trained in the matched. In addition, this classifier is online semi-supervised classification method which is proper for a time variated applications. The performance comparison of the proposed classifier and important previous works in low is shown in TABLE VII. As it is observed in TABLE VII, our proposed classifier despite of unawareness and real-time nature has an accuracy which is comparable with previous aware algorithms. 4. CONCOLUSION Automatic modulations classification plays a significant role in civil and military applications. In this paper, a semi-supervised online passive-aggressive approach using a proposed self-training algorithm is presented to classify a relatively complete set of digital modulated signals. TABLE VII. Ref. Proposed classifier COMPARISON OF PROPOSED CLASSIFIERS WITH OTHER WORKS Considered signals (db) Accuracy (%) [1] ASK2, ASK4, PSK2, PSK4, FSK2, FSK4 1 9 [12] FSK2, FSK4, ASK2, ASK4, QAM8,PSK2, PSK4, QAM16, QAM64 4 96 [13] PSK4, PSK8, QAM16 5 9 [14] PAM4, BPSK, PSK8, PSK16 1 96 [15] BPSK, PSK8, PSK16, QAM4, QAM16, QAM64 12 9 [16] PSK8, PSK16, QAM4, QAM8,QAM16,QAM64 3 9 FSK2, FSK4, ASK2, ASK4, PSK2, PSK4, PSK8, QAM16 QAM32, QAM 64 4 93.61 It was shown that its performance, even in low s, is similar to the well trained system in the input signals. Simulation results show that the presented classifier is able to work with a few samples and is capable to converge to the correct answer with few samples. Furthermore, the evaluation of the set of unseen samples in the convergence point shows high accuracy. This classifier, in addition to the above mentioned advantage, has a rapid convergence behavior with low complexity. This feature can prepare the preliminaries for using the suggested classifier in cognitive radio systems; because in these systems, the immediate recognition of users modulation type is crucial. The effective online modulation classification in the presence of non-gaussian noise, such as fading and multipath channels, will be investigated in the future. REFERENCES [1] O. Dobre, A. Abdi, Y. Bar-Ness and W. Su, Survey of automatic modulation classification techniques: classical approaches and new trends, IET Commun., vol. 1, no. 2, pp. 137-156, Apr. 27. [2] H. C. Wu, M. Saquib, and Z. Yun, Novel automatic modulation classification using cumulant features for communications via multipath channels, IEEE Trans. Wireless Commun., vol. 7, no. 8, pp. 389-315, 28. [3] X. Zhu and A. B. Goldberg, Introduction to Semi-Supervised Learning, Morgan and Claypool Publishers, 29. [4] O. Chapelle, B. Scholkopf, A. Zien (Eds.), Semi-Supervised Learning, MIT Press, Cambridge, MA, 26. [5] K. Crammer, O. Dekel, J. Keshet, S. Shalev-shwartz, and Y. Singer, Online passive-aggressive algorithms, Journal of Machine Learning Research, vol. 7, pp. 551-585, 26. [6] C. C. Chang, Y. J. Lee and H. K. Pao, A Passive-Aggressive Algorithm for Semi-supervised Learning, in Proc. International Conf. on Technologies and Applications of Artificial Intelligence, pp. 335-341, 21. [7] K. Crammer and Y. Singer. A new family of online algorithms for category ranking. Jornal of Machine Learning Research, 3:125 158, 23a [8] J. G. Proakis Digital Communications, McGraw-Hill, New York, 21. [9] J. Lopatka and P. Macrej, Automatic modulation classification using statistical moments and a fuzzy classifier, in Proc. Of International Conference on Signal Processing (ICSP ), vol. 3, pp. 1-16, Aug 2. [1] E. E. Azzouz and A. K. Nandi, Automatic identification of digital modulation types, Signal Process, vol. 47, no. 1, pp.55-69, Nov. 1995. [11] E. E. Azzouz and A. K. Nandi, Algorithms for automatic modulation recognition of communication signals, IEEE Trans. Commun., vol. 46, no. 4, pp.431-436, 1998. [12] A. Ebrahimzadeh, Automatic recognition of radio signals using a hybrid intelligent technique, Expert Systems with Applications, vol. 37, no. 8, pp. 583-5812, Aug. 21. [13] B. G. Mobasseri, Digital modulation classification using constellation shape, Signal Process, vol. 8, no. 2, pp. 251-277, Aug 2. [14] A. Swami and B. M. Sadler, "Hierarchical digital modulation classification using cumulants," IEEE Trans. on Commun., Vol. 48, No. 3, pp. 416-429, March 2. [15] F. Wang and X. Wang, "Fast and Robust Modulation Classification via Kolmogorov-Smirnov Test," IEEE Trans. on Commun., Vol. 58, No. 8, pp. 2324-2332, Aug 21. [16] O. Azarmanesh and S. G. Bilen, "New Results on Two-Stage Novel Modulation Classification Technique for Cognitive Radio Application," in proc. IEEE MILCOM., 211, pp. 266-271.