The computational complexity of nonlinear compensators based on the Volterra inverse

The performance of many analogue and digital signal processing systems is limited by nonlinear distortion mechanisms which can be modelled with a Volterra series. The nonlinear distortion can be compensated by the application of post (or pre)-distortion based on a Volterra inverse. The computational complexity associated with this type of compensation can be very high, particularly for systems with high nonlinearity order and long memory. We determine the 3rd and 5th order analytical Volterra inverses, and examine their associated computational complexity. We show how the analytical Volterra inverse can be used to determine the memory span of the kernels of an adaptive Volterra inverse, leading to computational complexity expressions. We then compare the computational complexity of the analytical and adaptive Volterra inverse. The results show that the analytical inverse has a much lower complexity than the adaptive inverse