Comparisons of one and two adaptation gain complex PtNLMS algorithms

Learning curves of the complex proportionate-type normalized least mean square (CPtNLMS), simplified CPtNLMS, and one-gain CPtNLMS algorithms are compared for different complex input signals and complex impulse responses. Cases when the algorithms show different behaviors are presented. In addition the water-filling algorithm for optimal adaptation gain allocation is extended from real-valued signals to complex-valued signals. In fact, two complex water-filling algorithms are derived, namely, the complex water-filling with one gain for coefficient real and imaginary parts and the complex water-filling algorithm with separate gains for coefficient real and imaginary parts.