  In this paper, a new family of proportionate normalized least mean square
(PNLMS) adaptive algorithms that improve the performance of identifying
block-sparse systems is proposed. The main proposed algorithm, called
block-sparse PNLMS (BS-PNLMS), is based on the optimization of a mixed l2,1
norm of the adaptive filter coefficients. It is demonstrated that both the NLMS
and the traditional PNLMS are special cases of BS-PNLMS. Meanwhile, a
block-sparse improved PNLMS (BS-IPNLMS) is also derived for both sparse and
dispersive impulse responses. Simulation results demonstrate that the proposed
BS-PNLMS and BS-IPNLMS algorithms outperformed the NLMS, PNLMS and IPNLMS
algorithms with only a modest increase in computational complexity.
