In this paper, a novel nonlinear Volterra equalizer is presented. We define a framework for nonlinear second-order Volterra models, which is applicable to different applications in engineering. We use this framework to define the channel and to model the equalizer. We then solve the minimum mean-square error (MMSE) problem explicitly for the tandem connection of the two second-order Volterra systems. Optimal solutions for a simplified, linear version of the MMSE equalizer are also presented. The novel equalizer was tested when applied to a nonlinear ultra-wideband transmitted reference receiver front end. As a comparison, a least mean squares (LMS) equalizer with a training sequence has been used to verify the performance of the newly proposed equalizer. The simulation results show that the LMS equalizer is only able to attain the proposed MMSE equalizer after very long training, which might not be desirable in a communication system.