Analog adaptive filtering based on a modified hopfield network

In the last few years analog adaptive filters have been a subject of active research because they have the ability to handle in real time much higher frequencies, with a smaller size and lower power consumption than their digital counterparts. During this time several analog adaptive filter algorithms have been reported in the literature, almost all of them use the continuous time version of the least mean square (LMS) algorithm. However the continuous time LMS algorithm presents the same limitations than its digital counterpart, when operates in noisy environments, although their convergence rate may be faster than the digital versions. This fact suggests the necessity to develop analog versions of recursive least square (RLS) algorithm, which is known to have a very low sensitivity to additive noise. However a direct implementation of the RLS in analog way would require a considerable effort. To overcome this problem, we propose an analog RLS algorithm in which the adaptive filter coefficients vector is estimated by using a fully connected network that resembles a Hopfield network. Theoretical and simulations results are given which show that the proposed and conventional RLS algorithms have quite similar convergence properties when they operate with the same sampling rate and signal-to-noise ratio. However, because of its analog realization form, the proposed algorithm can operate in real time with smaller sampling period than its digital counterpart, and then it can achieve a smaller misadjustment with a much better tracking ability than the conventional RLS algorithm.