Study of the Convergence Behavior of the Complex Kernel Least Mean Square Algorithm

作者：Paul Thomas K^*; Ogunfunmi Tokunbo

来源：IEEE Transactions on Neural Networks and Learning Systems, 2013, 24(9): 1349-1363.

DOI：10.1109/TNNLS.2013.2256367

• Adaptive filters
• complex kernel least mean square
• complexified
• Gaussian kernel
• mean-square error
• steady-state analysis

The complex kernel least mean square (CKLMS) algorithm is recently derived and allows for online kernel adaptive learning for complex data. Kernel adaptive methods can be used in finding solutions for neural network and machine learning applications. The derivation of CKLMS involved the development of a modified Wirtinger calculus for Hilbert spaces to obtain the cost function gradient. We analyze the convergence of the CKLMS with different kernel forms for complex data. The expressions obtained enable us to generate theory-predicted mean-square error curves considering the circularity of the complex input signals and their effect on nonlinear learning. Simulations are used for verifying the analysis results.

• 出版日期2013-9