Automatic classification of linear modulations using multiple receivers in the presence of symbol timing uncertainty

Modulation classification of signals collected from multiple receivers over additive white Gaussian noise channels is considered. It is assumed that the channel between the transmitter and each receiver is subject to unknown flat block fading and symbol timing uncertainty. Following the hybrid likelihood framework, the likelihood function of the waveforms observed at the receivers is marginalised over the distribution of the transmitted symbol sequence. Then, the parameter estimates obtained by the particle swarm optimisation technique are substituted into the average likelihood expression in order to compute the test statistic for each assumed modulation scheme. A classification decision is declared in favour of the modulation scheme with the highest overall likelihood score. Numerical examples are provided to evaluate the performance of the proposed classifier as a function of the average received signal-to-noise ratio for different number of receivers and varying quality of the initial parameter estimates.