Convergence rate limitations in certain frequency-domain adaptive filters

It is shown that the transport delay present in the feedback path of a frequency-domain adaptive filter consisting of the combination of a CMA (constant modulus algorithm) with a transmultiplexer reduces the filter's maximum attainable convergence rate. An upper bound for the convergence rate is developed in terms of the amount of group delay and hardware pipeline delay present in the adaptive system under analysis. These limitations are shown to be fundamental in nature. They relate directly to the amount of spectral resolution desired in the adaptive filter and not to the particular nonlinear error function employed.<>