Recursive techniques for the synthesis of a pth-order inverse of a Volterra system

A new recursive technique for the synthesis of a pth-order inverse of a Volterra system is presented. In such a method, the condition that the pth-order inverse be exactly of order p, as proposed by Schetzen, is relaxed. The choice of the residuals, that is the operators of the inverse whose order is higher than p, is done with the purpose of reducing the complexity of the synthesis scheme and of deriving a recursive procedure to build-up such an inverse. A comparison between the complexity of Schetzen's synthesis schemes and those obtained with our recursive procedure shows that the structures that we obtain are much less complex and easier to derive, and the increment of complexity related to the increase in order is much slower than in Schetzen's case. As an example of application, we use the proposed method in order to linearize a digital radio link in which the high-power amplifier is operated near saturation