In this paper, convergence properties of the LMS, LMF, and LVCMS algorithms are investigated under the assumption of the uncorrelated Gaussian input data. By treating these algorithms as special cases of more general algorithm family, unified results on these algorithms are obtained. First the upper bound on the step size parameter is obtained. Second, an expression for misadjustment is obtained. These theoretical results confirm earlier LMS works. Further, the results explain why the LMS and LVCMS algorithms are experiencing difficulties with plant noise having heavier tailed densities. Simulation results agree with theoretical expectation closely for various plant noise statistics.