  Accurate channel estimation is essential for broadband wireless
communications. As wireless channels often exhibit sparse structure, the
adaptive sparse channel estimation algorithms based on normalized least mean
square (NLMS) have been proposed, e.g., the zero-attracting NLMS (ZA-NLMS)
algorithm and reweighted zero-attracting NLMS (RZA-NLMS). In these NLMS-based
algorithms, the step size used to iteratively update the channel estimate is a
critical parameter to control the estimation accuracy and the convergence speed
(so the computational cost). However, invariable step-size (ISS) is usually
used in conventional algorithms, which leads to provide performance loss or/and
low convergence speed as well as high computational cost. To solve these
problems, based on the observation that large step size is preferred for fast
convergence while small step size is preferred for accurate estimation, we
propose to replace the ISS by variable step size (VSS) in conventional
NLMS-based algorithms to improve the adaptive sparse channel estimation in
terms of bit error rate (BER) and mean square error (MSE) metrics. The proposed
VSS-ZA-NLMS and VSS-RZA-NLMS algorithms adopt VSS, which can be adaptive to the
estimation error in each iteration, i.e., large step size is used in the case
of large estimation error to accelerate the convergence speed, while small step
size is used when the estimation error is small to improve the steady-state
estimation accuracy. Simulation results are provided to validate the
effectiveness of the proposed scheme.
