Improved convergence analysis of stochastic gradient adaptive filters using the sign algorithm

Transient analysis of adaptive filters with error nonlinearities

“…Analyses that are based on this technique fail to accurately describe the adaptive filter performance for large values of the error, e.g., at early stages of adaptation. b) Restricted classes of nonlinearities (e.g., [8]- [14]). Here, the analysis is restricted to particular classes of algorithms such as the sign-LMS algorithm, the least-mean mixed-norm (LMMN) algorithm, the least-mean fourth (LMF) algorithm, and error saturation nonlinearities.…”

“…This assumption was shown in [16] to be valid asymptotically. More accurate is the assumption that the residual error is Gaussian [4], [10] or that its conditional value is [8], [9]. By central limit arguments, this assumption is justified for long adaptive filters [4], [10].…”

“…d) Restricted class of inputs. It is common to assume that the input sequence is white and/or has a Gaussian distribution (e.g., [4], [6], [8]- [12], [20]- [22]). e) Independence assumption.…”

“…f) Gaussian noise. Noise is sometimes restricted to be iid Gaussian as in [4], [8], [15], and [24], although Gaussianity is not as common as the previous assumptions. Surprisingly perhaps, the iid assumption on the noise is almost indispensable, even for the analysis of the simplest of adaptive algorithms.…”

Robust Hammerstein Adaptive Filtering under Maximum Correntropy Criterion

“…In addition, the noise is often restricted to be zero-mean, identically distributed [33][34][35]. As discussed in [44,45], the assumption (B) is reasonable for long adaptive filters. Since ep(n) is the a priori error when only the nonlinear part is adapted while the linear filter is fixed, we have the approximation w * ≈ w(n) such that w(n) is asymptotically uncorrelated with f 2 (e(n)).…”