Robust Recognition of Digital Modulations of Rectangular and Root-Raised-Cosine Pulse Trains
Open AccessThis work establishes a framework to distinguish continuous-phase frequency shift keying modulation from quadrature amplitude modulation and phase shift keying modulations in two scenarios. In the first scenario, we assume that the central frequencies of linear modulations are different from that of frequency shift keying modulation. In the second scenario instead the central frequencies of linear modulations and that of frequency shift keying modulations are the same after frequency down-conversion. For the first scenario, we propose a simple and robust feature to distinguish continuous-phase frequency shift keying from quadrature amplitude and phase shift keying modulations. The feature is based on theproduct of two consecutive signal values and on time averagingof the imaginary parts of the product. First, binary frequency shift keying signal is separated from the linear modulations using a method that we propose. Initially, the conditionalprobability density functions of the feature given the modulation type are determined. In order to overcome the complexity of calculating the probability density functions, the centrallimit theorem for strictly stationary $m$-dependent sequences isused to obtain Gaussian approximations. After calculating theprobability density functions the thresholds are determinedbased on the minimization of the total probability ofmisclassification. Since the minimum probability of misclassification threshold results are valid for special cases requiring knowledge of many parameters, we resort to usage of support vector machines for classification. 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 lower oversampling of symbols than what is found in other approaches. There is no assumption or prior knowledge about the central frequencies of the signals in the second scenario. In this case we use three simple features for separation. The features are based on sample mean and sample variance of the real and 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. In both the scenarios, effectiveness of the feature(s) for signal separation by the proposed minimum error probability classifier as well as the support vector machines is tested in the joint presence 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 methods are compared to the wavelet based classifier that uses support vector machines for modulation separation. Furthermore, in this work we present and analyze a set of features based on approximate entropy that identifies the order of continuous-phase frequency shift keyings in the joint presence of fast fading, carrier offset, asynchronous sampling and symbol intervals, and additive white Gaussian noise. The set of distinguishing features are classified by support vector machines. 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 and initial symbol phase (timing offset).
- All rights reserved
Notice to Authors
If you are the author of this work and you have any questions about the information on this page, please use the Contact form to get in touch with us.