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Correntropy-Based Adaptive Filtering of Noncircular Complex Data

Real world complex-valued signals typically exhibit rotation-dependent distributions (noncircularity), and significant performance gains in learning algorithms can be obtained by accounting for information beyond the standard second-order noncircularity (impropriety). To this end, we introduce a new closed form definition of complex correntropy which is general enough to cater for both circular and noncircular distributions in complex data, and serves as a basis for a novel cost function for widely linear adaptive filtering, termed the maximum improper complex corren-tropy criterion (MICCC). A stochastic gradient adaptive filtering algorithm is developed based on the MICCC, and its standard and complementary convergence and stability analyses are conducted with respect to both the circularity of the estimation error and the kernel size in the underlying Parzen estimator. Performance advantages over the strictly linear correntropy algorithm (MCCC) and the mean square error based complex least mean square (CLMS) and augmented CLMS (ACLMS) are demonstrated through analysis and simulations.