Family of adaptive algorithms based on second order Volterra filters for nonlinear acoustic echo cancellation: A technical survey

Acoustic echo arises when an audio signal is radiated in the real environment, resulting in the signal plus its attenuated, time delayed images. With time delay as the constraint, the prominence of the echo over communication channels is determined. Modern times have seen extensive research over the removal nonlinear echoes caused by portable communication systems and low cost audio equipment. Volterra filters employing adaptive algorithms have traditionally been a very important tool for nonlinear acoustic echo cancellation. This article presents a technical survey of the adaptive algorithms used in the design of a nonlinear equalizer modeled using a second order Volterra series expansion. In the initial sections, the problem of nonlinear echo cancellation is defined and a mathematical analysis of the Volterra series expansion is given. In further sections, a truncated version of the Volterra series which is called the second order Volterra filter is discussed. Finally, a detailed analysis has been carried out to determine the adaptive algorithm that is best in the business to solve the problem of nonlinear acoustic echo cancellation.