Complex dual channel estimation: Cost effective widely linear adaptive filtering

• MSE for estimating complex signals can be decomposed into 2 cost functions.
• Using separate estimators, we can minimize the 2 cost functions independently.
• This allows the necessary degrees of freedom while being computationally efficient.
• The CDC is a more efficient alternative to strictly and widely linear estimators.

Widely linear estimation for complex-valued data allows for a unified treatment of both second order circular (proper) and non-circular (improper) signals. We propose the complex dual channel (CDC) estimation technique as an alternative to widely linear estimation to both gain further insights into complex valued minimum mean square error (MMSE) estimation and to design computationally efficient adaptive filtering algorithms. This is achieved by finding two sets of optimal weights that minimize the mean square error (MSE) in estimating the real and imaginary parts of the signal independently. The concept is used in a stochastic gradient setting to design the dual channel complex least mean square (DC-CLMS). The analysis shows that any one of the sub-filters within the DC-CLMS can be used to estimate strictly linear models while the DC-CLMS is equivalent to widely linear estimation. This results in a reduction of computational complexity of complex-valued adaptive filters by a half, while providing enhanced physical insight and control over complex-valued estimation algorithms.