  Constant gain least-mean-squares (LMS) algorithms have a wide range of
applications in trajectory tracking problems, but the formal convergence of LMS
in mean square is not yet fully established. This work provides an upper bound
on the constant gain that guarantees a bounded mean-squared error of LMS for a
general design vector. These results highlight the role of the fourth-order
moment of the design vector. Numerical examples demonstrate the applicability
of this upper bound in setting a constant gain in LMS, while existing criteria
may fail. We also provide the associated error bound, which can be applied to
design vectors with linearly dependent elements.
