An equivalent gain for a multiplier with independent random inputs

This letter presents an extension of the Booton equivalent gain method to include a multiplier in a closed-loop system with random inputs. An equation is derived for the equivalent gain which minimizes the mean-squared-error between the output of the multiplier and a linear gain replacing the multiplier in one of the signal paths. A criterion is also suggested by which the validity of the approximation may be established for any particular case.