Steady-state MSE convergence of LMS adaptive filters with deterministic reference inputs with applications to biomedical signals

In this paper, we analyze the steady-state mean square error (MSE) converge nce of the LMS algorithm when deterministic functions are used as reference inputs. A particular adaptive linear combiner is presented where the refer ence inputs are any set of orthogonal basis functions-the adaptive orthogon al linear combiner (AOLC). Several authors have applied this structure alwa ys considering in the analysis a time-average behavior over one signal occu rrence, In this paper, we make a more precise analysis using the determinis tic nature of the reference inputs and their time-variant correlation matri x. Two different situations are considered in the analysis: orthogonal comp lete expansions and incomplete expansions, The steady-state misadjustment i s calculated using two different procedures with equivalent results: the cl assical one (analyzing the transient behavior of the MSE) and as the residu al noise at the output of the equivalent time-variant transfer function of the system. The latter procedure allows a very simple formalism being valid for colored noise as well. The derived expressions for steady-state misadj ustment are contrasted with experimental results in electrocardiographic (E CG) signals, giving exact concordance for any value of the step size.