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In this paper we consider the performance of Volterra filters in canceling the severe nonlinear amplitude and phase distortions caused by traveling wave tube (TWT) high power amplifiers (HPAs, TWTAs) typically used on many legacy satellite communication systems. The nonlinear nature of Volterra filters would seem to make them a natural choice for canceling intersymbol interference (ISI) resulting from these distortions. Preliminary results of simulation studies using QPSK with up to 5th-order adaptive Volterra kernels filter are presented. The practical aspect of this work is that we would like to achieve good performance while reducing computational complexity, ultimately making efficient implementation on an FPGA feasible. It was found that an LMS adaptive Volterra filter offered significant ISI reduction only at relatively high SNRs (~25 dB), while at lower (and more typical) SNRs, improvement was only marginal, as noise tended to dominate the LMS algorithm. Adding a 5th-order Volterra kernel to the linear and 3rd-order LMS kernels offered negligible improvement in performance over the linear and 3rd-order kernels alone.