Methods For Modulation Classification Using Multiple Cumulants

Modulation classification is to identify the modulation format of a received signal automatically, a signal processing procedure between detection and demodulation. With the development of software-defined radio, adaptive modulation and cognitive radio, the civilian and military communication systems in future will use more flexible schemes for information transmitting and receiving. Modulation classification will make a key role in such intelligent communication systems. Compared with analog modulations, digital modulations have more advantages and are used more widely in commercial and military communications. The dissertation focuses on the modulation classification of digital communication signal and the research area includes the statistical model of cumulant feature, the estimation method of cumulant feature in multipath fading channels, the modulation classifier design with rejection ability and the distributed modulation classification method based on wireless sensor networks. The major contributions of this dissertation are listed as follows,1. The statistical model of a two-dimensional normalized fourth-order cumulant feature is analyzed under additive white Gaussian noise channel, the purpose of which is to determine the decision threshold or decision region for cumulant-based modulation classifier. It is derived that the two-dimensional feature asymptotically obeys joint Gaussian distribution. The mean and covariance matrix are theoretically derived too. In order to show the correctness of the proposition, a maximum likelihood classifier is formed in the two-dimensional feature domain according to the Baysian criterion. The average probability of correct classification of the binary class problem is theoretically determined, which is consistent with the result obtained by simulations, thus justifying the correctness of the proposed theoretical results.2. A fourth-order cumulant-based classifier with rejection ability is proposed to classify digital modulation formats under additive white Gaussian noise channel. It can reject the unknown modulation outside of the set of candidate modulations. Two normalized fourth-order cumulants are used to form the two-dimensional feature plane. The classification with rejection ability boils down to the segmentation problem of the feature plane with rejection region. A two-stage optimization is proposed to attain thesuboptimal solution of the problem. First, the greedy convexhull learning algorithm is used to determine the primary decision regions of all the candidate modulation formats from training sets. The primary decision regions have rejection ability but are always not mutually separate. Second, the alternative convexhull shrinkage algorithm is presented to separate the primary decision regions at small loss in the probability of correct classification(PCC). The simulation results show that besides desired rejection ability, the proposed classifier is competitive with two existing classifiers in PCC.3. A new estimator is proposed to estimate the fourth-order cumulant of transmitted symbol in a multipath fading channel with the help of the fourth-order cross-cumulants of the received symbols. The proposed estimator does not need the estimation of the multipath channel coefficients and is shown to be asymptotically unbiased. The impact of the channel order mismatch on the estimator is analyzed and it is proved that the estimator keeps unbiased in the case of the overestimation of the channel order. The simulated experiments are made to verify the cumulant-based classifier using the new estimator and the results show that it attains better performance for digital modulation classification than the two existing cumulant-based classifiers in a multipath channel.4. For the problem to classify amplitude-phase modulation formats under flat fading channels with non-Gaussian noise, it is proposed a likelihood-based distributed modulation classification method by utilizing wireless sensor networks. With the help of the spatial diversity of multiple receivers and the rotationally symmetric property of amplitude-phase constellations, it is concluded that the signals received at different sensors containing the same transmitted signal are statistical independent. Based on this result and the assumption that the non-Gaussian noise is modeled as the well-known Gaussian mixture distribution, a hybrid likelihood ratio test classifier is proposed in the context of wireless sensor networks. Since the maximum-likelihood estimates of the unknown parameters related to channel state information and Gaussian mixture distribution are required in the proposed classifier, a modified distributed expectation maximization algorithm is proposed to estimate the unknown parameters blindly. The Cramer-Rao lower bounds(CRLB) of the non-data aided estimates of the unknown parameters are derived for BPSK modulation format. The experimental results show that the proposed method offers performance gain over the state-of-the-art method using one receiver to classify amplitude-phase modulations under flat fading channels withnon-Gaussian noise.