Accurate channel estimation is essential for broadband wirelesscommunications. As wireless channels often exhibit sparse structure, theadaptive sparse channel estimation algorithms based on normalized least meansquare (NLMS) have been proposed, e.g., the zero-attracting NLMS (ZA-NLMS)algorithm and reweighted zero-attracting NLMS (RZA-NLMS). In these NLMS-basedalgorithms, the step size used to iteratively update the channel estimate is acritical parameter to control the estimation accuracy and the convergence speed(so the computational cost). However, invariable step-size (ISS) is usuallyused in conventional algorithms, which leads to provide performance loss or/andlow convergence speed as well as high computational cost. To solve theseproblems, based on the observation that large step size is preferred for fastconvergence while small step size is preferred for accurate estimation, wepropose to replace the ISS by variable step size (VSS) in conventionalNLMS-based algorithms to improve the adaptive sparse channel estimation interms of bit error rate (BER) and mean square error (MSE) metrics. The proposedVSS-ZA-NLMS and VSS-RZA-NLMS algorithms adopt VSS, which can be adaptive to theestimation error in each iteration, i.e., large step size is used in the caseof large estimation error to accelerate the convergence speed, while small stepsize is used when the estimation error is small to improve the steady-stateestimation accuracy. Simulation results are provided to validate theeffectiveness of the proposed scheme.
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