Complex colored water-filling algorithm for gain allocation in proportionate adaptive filtering

A complex colored water-filling algorithm is derived for gain allocation in proportionate-type NLMS filtering under the assumption that the input signal is Gaussian and the covariance and pseudo-covariance are known. The algorithm is derived by minimizing the mean square weight deviation at every time instance, where the weight deviation is defined as the difference between the unknown impulse response and the estimated impulse response at the current time. A single real-valued gain is used to simultaneously update both the real and imaginary parts of the estimated impulse response. The performance of the new algorithm is compared with the performance of several standard proportionate-type normalized least mean square algorithms for colored input.