  To estimate multiple-input multiple-output (MIMO) channels, invariable
step-size normalized least mean square (ISSNLMS) algorithm was applied to
adaptive channel estimation (ACE). Since the MIMO channel is often described by
sparse channel model due to broadband signal transmission, such sparsity can be
exploited by adaptive sparse channel estimation (ASCE) methods using sparse
ISS-NLMS algorithms. It is well known that step-size is a critical parameter
which controls three aspects: algorithm stability, estimation performance and
computational cost. The previous approaches can exploit channel sparsity but
their step-sizes are keeping invariant which unable balances well the three
aspects and easily cause either estimation performance loss or instability. In
this paper, we propose two stable sparse variable step-size NLMS (VSS-NLMS)
algorithms to improve the accuracy of MIMO channel estimators. First, ASCE for
estimating MIMO channels is formulated in MIMO systems. Second, different
sparse penalties are introduced to VSS-NLMS algorithm for ASCE. In addition,
difference between sparse ISS-NLMS algorithms and sparse VSS-NLMS ones are
explained. At last, to verify the effectiveness of the proposed algorithms for
ASCE, several selected simulation results are shown to prove that the proposed
sparse VSS-NLMS algorithms can achieve better estimation performance than the
conventional methods via mean square error (MSE) and bit error rate (BER)
metrics.
