Online Hybrid Likelihood Based Modulation Classification Using Multiple Sensors

Hybrid likelihood-based approaches equipped with the expectation-maximization (EM) algorithm have received attention in the modulation classification literature during recent years. Despite their superior classification performance, these methods, which rely on iterative batch (offline) processing of the measurements, are not particularly suitable for practical applications due to their high computational demand. In this paper, two online methods that facilitate close to optimal classification performance with reduced computational complexity are employed for modulation classification over unknown nonidentical flat block-fading additive white Gaussian noise channels using multiple sensors. The presented algorithms rely on Titterington's and Cappé's online versions of the EM algorithm that are derived from stochastic approximations of the E- and M-steps of the standard EM algorithm. Unlike the batch method, where the a posteriori probabilities for all the transmitted symbols are updated based on the current set of channel estimates, only the a posteriori probability for the most recently transmitted symbol is computed at each symbol interval and this information is employed to estimate the parameters in a sequential manner. Since the a posteriori probabilities corresponding to the previous symbols are not updated at a given iteration, the computational demand is significantly reduced in comparison with the offline variants. Furthermore, the Polyak-Ruppert averaging is employed to improve the convergence speed. Numerical examples are provided to corroborate the effectiveness of the proposed online EM-based classifiers.