Modulation Classification Based on Fourth-Order Cumulants of Superposed Signal in NOMA Systems

In this paper, we study the automatic modulation classification in a non-orthogonal multiple access system. To mitigate the effect of interference, a likelihood-based algorithm and a fourth-order cumulant-based algorithm are proposed. Different from the maximum likelihood classifier for a single signal without interference, a likelihood function of the far and near users' signals is derived. Then, a marginal probability for the far user is obtained by using the Bayesian formula. Hence, the modulation type can be determined by maximizing the marginal probability. The high computational complexity of the likelihood-based algorithm renders it impractical; accordingly, it serves as a theoretical performance bound. On the other hand, we construct a feature vector through the estimated fourth-order cumulants of the received signal including the superposed signal and noise. For each modulation pair, using the mean and covariance matrix of the estimated feature vector, its probability density function can be obtained. Then, the key is to calculate the mean and covariance matrix of the estimated feature vector. To solve this problem, the moments of the superposed signal are derived. Therefore, modulation classification can be performed by maximizing the probability density function. Extensive simulations verify that the two proposed algorithms perform well under a wide range of signal-to-noise ratios and observation lengths.