The ANALYSIS OF BROADBAND MULTIPATH CHANNEL ESTIMATION ON A ZERO ATTRACTING PROPORTIONATE SYSTEM

Abstract

The proportionate normalized least mean square (PNLMS) algorithm, a popular tool for sparse system
identification, achieves fast initial convergence by assigning independent step sizes to the different taps,
each being proportional to the magnitude of the respective tap weight. However, once the active (i.e.,
non-zero) taps converge, the speed of convergence slows down as the effective step sizes for the inactive
(i.e., zero or near zero) taps become progressively less. In this paper, we try to improve upon both the
convergence speed and the steady state excess mean square error (EMSE) of the PNLMS algorithm, by
introducing a l1 norm (of the coefficients) penalty in the cost function which introduces a so-called zeroattractor term in the PNLMS weight update recursion. The zero attractor induces further shrinkage of the
coefficients, especially of those which correspond to the inactive taps and thus arrests the slowing down
of the convergence of the PNLMS algorithm, apart from bringing down the steady state EMSE. We have
also modified the cost function further generating a reweighted zero attractor which helps in confining the
“Zero Attraction” to the inactive taps only.