A Novel Online Censoring-Based Generalized Complex-Valued Kernel Least Mean Square

The generalized complex-valued kernel least mean square (gCKLMS) has shown superior performance in modeling circular and noncircular complex-valued nonlinear signals by leveraging both kernel and pseudo-kernel functions. However, its applicability to large-scale or real-time scenarios is hindered by the exponential increase in computational complexity caused by the growing number of kernel coefficients over iterations. To overcome this challenge, we first propose the online censoring (OC)-based gCKLMS (OC-gCKLMS), which integrates the OC strategy into the gCKLMS framework. The OC selectively retains informative input data and its corresponding kernel and pseudo-kernel coefficients by exploiting data redundancy and then incorporates them into the update process. This significantly reduces computational burden without compromising performance. Then, we theoretically analyze the mean square convergence of the OC-gCKLMS. Finally, the elegant properties of the OC-gCKLMS are validated through simulations on three benchmark problems.