  Group zero-attracting LMS and its reweighted form have been proposed for
addressing system identification problems with structural group sparsity in the
parameters to estimate. Both algorithms however suffer from a trade-off between
sparsity degree and estimation bias and, in addition, between convergence speed
and steady-state performance like most adaptive filtering algorithms. It is
therefore necessary to properly set their step size and regularization
parameter. Based on a model of their transient behavior, we introduce a
variable-parameter variant of both algorithms to address this issue. By
minimizing their mean-square deviation at each time instant, we obtain
closed-form expressions of the optimal step size and regularization parameter.
Simulation results illustrate the effectiveness of the proposed algorithms.
