A Novel Widely Linear Quaternion Multiband-Structured Subband Adaptive Filter Algorithm

A novel widely-linear quaternion multiband-structured subband adaptive filter (WL-QMSAF) algorithm is proposed for further enhancing the convergence rate of estimation error when input signals are greatly correlated in the quaternion domain. Using the derivative rule in GHR-calculus, the WL-QMSAF algorithm is developed on the basis of the principle of minimum fluctuations. The proposed WL-QMSAF algorithm decomposes the input signal into multiple parallel channels to promote more effective signal processing. Since quaternion widely linear model is able to describe complete second-order statistics of input signal, the proposed algorithm can effectively process both Q-proper and Q-improper signals. In addition, the analysis of mean-square steady state for the WL-QMSAF algorithm is performed according to the principle of energy conservation. Finally, numerical simulations are conducted on circular data as well as noncircular data to support the steady-state analysis of mean-square error as well as validate the effectiveness of the proposed WL-QMSAF algorithm.