Summary: ON THE SELECTION OF OPTIMAL NONLINEARITIES FOR STOCHASTIC
GRADIENT ADAPTIVE ALGORITHMS
TAREQY. AL-NAFFOURI~,ALIH. SAYED2, AND THOMASKAILATH'
'Electrical Engineering Department
Stanford University, CA 94305
2Electrical Engineering Department
University of California, Los Angeles, CA 90095
This paper derives an expression for the optimal error
nonlinearity in adaptive filter design. Using an energy
conservation relation, and some typical assumptions,
the choice of the error function is optimized by min-
imizing the mean-square deviation subject to a fixed
rate of convergence. The resulting optimal choice is
shown to subsume earlier results as special cases.
LMS 4 2 )