Pipelined architectures for the LMS adaptive Volterra filter

In this paper, efficient pipelined architectures for Least Mean Square (LMS) adaptive filtering and system identification of discrete-time Volterra models is presented. First, the multichannel embedding is adopted for the transformation of the discrete-time Volterra model to an equivalent multi-input single output format. Then, the LMS algorithm with delayed coefficients adaptation is applied, for the identification of the model parameters. The adaptation delay introduced in the computational flow of the adaptive scheme, allows for a pipelined implementation, however, the convergence and tracking properties of the algorithm are affected. Proper correction terms are subsequently introduced that compensate the adaptation delay and give results identical to the original LMS algorithm, subject to a latency delay.