A complex adaptive delay filter

We propose an adaptive delay filter with complex coefficients for identifying an unknown system with complex sparse impulse response. The delay taps can not be determined by the conventional real adaptive delay filter, which evaluates the mean squared error with one constant gain in the system with complex coefficients. In the proposed method, a modified evaluation function, which consists of the mean squared error value with a complex constant gain and one with the conjugate value of the complex constant gain, is introduced in order to estimate the delay taps correctly. Using simulations we also clarify that the identification error is significantly reduced by means of the proposed complex adaptive delay filter.