Complex-valued Normalized Maximum Versoria Criterion Algorithm for Widely Linear Adaptive Filter

The wide linear (WL) model promotes the application of the complex domain algorithms more extensive, controlling both the circular and the non-circular signals well. The WL complex least mean square (WL-CLMS) algorithm has been utilized in an assortment of filtering scenarios, and has achieved satisfactory results. However, the output of filter is usually interfered by non-Gaussian noise in the real world, leading to serious performance degradation of the WL-CLMS algorithm. By employing the maximum complex correntropy criterion (MCCC), previous work has presented the widely linear complex-valued estimated-input MCCC (WLC-EIMCCC) algorithm to solve impulsive noise. Nonetheless, the calculation cost of this algorithm is expensive due to the exponential operators, and its steady-state error still has room for improvements. In this work, the maximum complex Versoria criterion (MCVC) is defined according to the concept of complex correntropy. The WL-CMVC algorithm is put forward, of which the steady-state error is lower than the WL-MCCC algorithm. Besides, the normalized form is derived based on the WL-CMVC. Comparative experiments are carried out in system identification scenario wherein the unknown system is interfered with different background measurement noise. Simulation results verify that the proposed algorithms can achieve lower steady-state misadjustment than the WL-MCCC algorithm.