In echo cancellation, proper control of stepsize and regularization parameters of the normalized least mean squares (NLMS) can improve the overall performance of the system. The filter update equation for NLMS is

(1) 
where μ(n) is the variable stepsize and ε(n) is the variable regularization. The main goals of these control parameters and of any adaptive algorithm is to increase the convergence speed, minimizing the system distance and decrease the divergence rate in the presence of noise. Analysis of how these parameters affect the performance of the adaptive algorithm reveals how these parameters can be made time variable to achieve these goals, and thus greatly improve the overall performance of an echo canceller.
Adaptive filter theory shows us the relationship the stepsize and regularization parameters have on the misadjustment, and the convergence speed of the echo cancellation system. For example, the convergence speed is

(2) 
where Τ_{max}, is the maximum time constant and λ_{min} is the minimum eigenvalue of the autocorrelation matrix R. As we can observe from (2) is that convergence speed is inversely proportional to the stepsize. The misadjustment is described as
M = μTr(R)  (3) 
where M is the misadjustment and Tr(R) is the trace of the autocorrelation matrix. This shows that the misadjustment is proportional to the stepsize. The translation of these results for the regularization parameter results in reversing the proportionality. Combining the results of (2) and (3), results in an engineering tradeoff between convergence speed and the system distance. Therefore, for initial convergence or readaptation, the stepsize should be close to one and the regularization should be close to zero, and as the misadjustment approaches zero, the stepsize should approach zero and the regularization should approach infinity. In acoustic echo cancellation (AEC), the ability to vary the stepsize (or lower the regularization value) is an important characteristic for environments in which the echo path is timevarying.
In addition to controlling the convergence speed and misadjustment, the stepsize and regularization parameters can be used to control the influence of noise into the system. This noise includes the presence of the nearend talker and/or local background noise. As discussed in the DoubleTalk Detection in Echo Cancellation, when significant levels of nearend and farend signals are present simultaneously, adaptation needs to be frozen in order to prevent divergence. Therefore, an optimal stepsize parameter should be decreased by the presence of noise. To put this result together from the results of the previous paragraph, the optimal stepsize parameter should be
where
is the expectation value of the residual error power, and
is expectation value of the noise power. As one can observe, when the residual error signal is large, the stepsize will be close to one, and when the presence of local noise is large, the stepsize is close to zero. This scaling is important in handsfree communication systems set in environments with large levels of background noise, such as drivethru’s and factory settings.