  A new family of block-sparse proportionate affine projection algorithms
(BS-PAPA) is proposed to improve the performance for block-sparse systems. This
is motivated by the recent block-sparse proportionate normalized least mean
square (BS-PNLMS) algorithm. It is demonstrated that the affine projection
algorithm (APA), proportionate APA (PAPA), BS-PNLMS and PNLMS are all special
cases of the proposed BS-PAPA algorithm. Meanwhile, an efficient implementation
of the proposed BS-PAPA and block-sparse memory PAPA (BS-MPAPA) are also
presented to reduce computational complexity. Simulation results demonstrate
that the proposed BS-PAPA and BS-MPAPA algorithms outperform the APA, PAPA and
MPAPA algorithms for block-sparse system identification in terms of both faster
convergence speed and better tracking ability.
