Mohammad Bari

Performance of the instantaneous frequency based classifier distinguishing BFSK from QAM and PSK modulations for asynchronous sampling and slow and fast fading

In this paper we propose a feature to distinguish frequency from amplitude-phase digital modulations. We compare the performance of the feature where every symbol is sampled more than once to that where every symbol is sampled only once. The feature is based on the product of two consecutive signal values and on time averaging of the imaginary part of the product if a symbol is sampled more than once. First, the conditional probability density functions of the feature given the present modulation are determined. The central limit theorem for strictly stationary m-dependent sequences is used to obtain Gaussian approximations. Then thresholds are determined based on the minimization of the total probability of misclassification. Following that, effects of fast and slow fading, and of the symbol period and delay being non-integer multiples of sampling period on the performance are studied. In the course of doing that, the proposed classifier is compared to the maximum likelihood classifier and the wavelet based classifier using support vector machine.

Simple Features for Separating CPFSK from QAM and PSK Modulations

In this letter we propose simple and robust features to distinguish continuous-phase frequency shift keying from quadrature amplitude modulation and phase shift keying modulations. The features are based on sample mean and sample variance of the imaginary part of the product of two consecutive complex signal values. Root raised cosine pulses are used to generate the linearly modulated signals. Support vector machines are employed to distinguish the signals. One benefit of using support vector machines is that it requires very few realizations for training. Moreover, no a priori information is required about carrier amplitude, carrier phase, carrier offset, symbol rate, pulse shape, initial symbol phase (timing offset) and channel impulse response. Effectiveness of the features and signal separation by support vector machines is tested by observing the joint effects of additive white Gaussian noise, carrier offset, lack of symbol and sampling synchronization, and either fast or slow fading. In the course of doing that, the proposed classifier is compared to the wavelet based classifier, equipped by support vector machines.

Distinguishing BFSK from QAM and PSK by sampling once per symbol

In this paper we propose a feature to distinguish FSK from QAM and PSK modulations. The feature is based on the imaginary part of product of two consecutive signal values where every symbol is sampled only once. Conditional probability density functions of the feature given the present modulation are determined. Central limit theorem for strictly stationary m-dependent sequences is used to obtain Gaussian approximations. Then the thresholds are determined based on the minimization of total probability of misclassification. Effects of AWGN, carrier offset and non-synchronized sampling on the performance are studied. Proposed classifier is compared to the maximum likelihood classifier.

Quickness of the instantaneous frequency based classifier distinguishing BFSK from QAM and PSK modulations

In this paper we study the quickness of a classifier based on simple feature that we have previously proposed to distinguish frequency from amplitude-phase digital modulations. The feature is based on the product of two consecutive signal values and on time averaging of the imaginary part of the product. First, the conditional probability density functions of the feature given the present modulation are determined. The central limit theorem for strictly stationary m-dependent sequences is used to obtain Gaussian approximations. Then thresholds are determined based on the minimization of the total probability of misclassification. Following that effects of carrier offsets, of fast fading, and of the symbol period and time delay being non-integer multiples of sampling period on the performance are studied. In the course of doing that, the proposed classifier is compared to the maximum likelihood classifier and the wavelet based classifier using support vector machine.

Identification of L-ary CPFSK in a fading channel using approximate entropy

In this paper we study approximate entropy as the feature to distinguish within the class of L-ary continuous-time FSK in the presence of correlated fast fading and additive white Gaussian noise. Support vector machines are employed to distinguish the signals. One benefit of using support vector machines is that they require very few realizations for training. Moreover, no a priori information is required about carrier amplitude, carrier phase, symbol rate and pulse shape. Performance of the approximate entropy feature classified by support vector machines is compared to the performance of wavelet-based feature classified by support vector machines.

Robust recognition of linear and nonlinear digital modulations of RRC pulse trains

In this paper we propose simple and robust features to distinguish continuous-phase frequency shift keying from quadrature amplitude and phase shift keying modulations. Robustness is tested in the presence of SNR estimation offset, block and correlated fast fading, lack of symbol and sampling synchronization, and carrier offset. The features are based on sample mean and sample variance of the imaginary part of the product of two consecutive complex signal values. Root raised cosine pulses are used to generate the linearly modulated signals. Root raised cosine as well as rectangular shaped instantaneous frequency pulses are used in designing the continuous-phase frequency shift keying signals. Support vector machines are employed to distinguish the signals. One benefit of using support vector machines is that it requires very few realizations for training. Moreover, no a priori information is required about carrier amplitude, carrier phase, carrier offset, symbol rate, pulse shape and initial symbol phase. Performance of the proposed feature is compared to the wavelet based feature that uses support vector machines for classification.

Distinguishing CPFSK from QAM and PSK Modulations

Digital modulation classification is important for many civilian as well as military applications. In this paper, we propose a simple and robust feature to distinguish continuous-phase FSK from QAM and PSK modulations. The feature is based on product of two consecutive signal values and on time averaging of imaginary part of the product. Conditional probability density functions of the feature given modulation type are determined. In order to overcome the complexity of calculating probability density functions, central limit theorem for strictly stationary m-dependent sequences is used to obtain Gaussian approximations. After calculating probability density functions, thresholds are determined based on minimization of total probability of misclassification. Since threshold-based results are valid for special cases requiring knowledge of some parameters, we resort to usage of support vector machines for classification, which require little training and no a priori information except for carrier frequency. Following that joint effects on the performance of carrier offset, fast fading, and non-synchronized sampling are studied in the presence of additive white Gaussian noise. For comparison purposes, rectangular pulse shape is used. To prove practical usefulness, not only the performance is analyzed for root-raised cosine pulses but also for quite less oversampling of symbols than what is found in other approaches. In the course of doing that, the performance is compared with wavelet-based feature that uses support vector machines for modulation separation.

Separation of signals consisting of amplitude and instantaneous frequency RRC pulses using SNR uniform training

This work presents sample mean and sample variance based features that distinguish continuous phase FSK from QAM and PSK modulations. Root raised cosine pulses are used for signal generation. Support vector machines are employed for signals separation. They are trained for only one value of SNR and used to classify the signals from a wide range of SNR. A priori information about carrier amplitude, carrier phase, carrier offset, roll-off factor and initial symbol phase is relaxed. Effectiveness of the method is tested by observing the joint effects of AWGN, carrier offset, lack of symbol and sampling synchronization, and fast fading.

Recognizing FM, BPSK and 16-QAM using supervised and unsupervised learning techniques

In this paper, we explore the use of supervised and unsupervised machine learning for signal classification in the joint presence of AWGN, carrier offset, asynchronous sampling and symbol intervals and correlated fast fading. Three simple features are studied to classify frequency modulation, binary phase shift keying and 16 point quadrature amplitude modulation. Support vector machines and self-organizing maps are used to classify the signals.

Order recognition of continuous-phase FSK

In this paper we study a set of distinguishing features based on approximate entropy. The set identifies the order of continuous-time frequency shift keyings in the joint presence of carrier offset, asynchronous sampling and symbol intervals, correlated fast fading and additive white Gaussian noise. Performance of the approximate-entropy-based features is compared to the performance of wavelet-based feature. For fair comparison of the features, both the approximate-entropy- based and wavelet-based features are classified by support vector machines. Major benefit of employing support vector machines is that they are able to train themselves using a very few realizations. Also, no a priori information is required about carrier phase, symbol rate and carrier amplitude.