On the Use of the Sparse Property of the Cyclic Autocorrelation Function to Blindly Estimate the Cyclostationarity
Abstract
Based on the sparse property of the Cyclic Autocorrelation Function (CAF) in the cyclic frequency domain, we propose in this paper a new blind estimator using compressed sensing, which better estimates the Cyclic Autocorrelation Function at a given delay compared to the classical non blind estimator when using the same number of samples. Two metrics are used to evaluate this estimation: the Mean Square Error of type one and that of type two (MSE1 and MSE2). The first metric compares the estimated Cyclic Autocorrelation Vector (CAV) which is a particular vector of the CAF for a fixed delay , with the theoretical reference vector obtained using the CAF. The second metric compares the value of the estimated cyclic frequency with the theoretical one. Simulation results show lower MSE1 and MSE2 for the new proposed estimator compared to the classical one under the same conditions, from the simplest scenario to the more realistic one that uses a filter at the transmission side, a reception noise, and fading channel.