Digital LMS adaptation of analog filters without gradient information

The least mean square (LMS) algorithm has practical problems in the analog domain mainly due to DC offset effects. If digital LMS adaptation is used, a digitizer (analog-to-digital converter or comparator) is required for each gradient signal as well as the filter output. Furthermore, in some cases the state signals are not available anywhere in the analog signal path necessitating additional analog filters. Here, techniques for digitally estimating the gradient signals required for the LMS adaptation of analog filters are described. The techniques are free from DC offset effects and do not require access to the filter's internal state signals. Digitizers are required only on the input and error signal. The convergence rate and misadjustment are identical to traditional LMS adaptation, but an additional matrix multiplication is required for each iteration. Hence, analog circuit complexity is reduced but digital circuit complexity is increased with no change in overall performance making it an attractive option for mixed-signal integrated systems in digital CMOS. Signed and subsampled variations of the adaptive algorithm can provide a further reduction in analog and digital circuit complexity, but with a slower convergence rate. Theoretical analyses, behavioral simulations, and experimental results from an integrated filter are all presented.