## 1 Introduction  
Adaptive filtering algorithms have been widely applied for multipath channel estimation, especially in broadband wireless systems [1; 2; 3; 4; 5; 6; 7], where the broadband signals are vulnerable to multipath fading as well as additive noises [8; 9; 10]. Hence, channel state information (CSI) is necessary for coherent demodulation [11]. Based on the classical Gaussian noise model, second-order statistics based least mean square (LMS) algorithm has been widely used to estimate channels due to its simplicity and robustness [1; 2]. However, the performance of LMS is usually degraded by impulsive noise [12], which is common in broadband wireless systems and can be described by the Gaussian mixture noise model (GMM) [13]. Thus, it is necessary to develop robust channel estimation algorithms in the presence of GMM impulsive noise. In [1], a standard sign least mean square (SLMS) algorithm was proposed to suppress impulsive noise. In [14], [PERSON] _et al._ proposed a sophisticated robust matched filtering algorithm in \(\ell_{p}\) -space to realize time delay estimation (TDE) and joint delay-Doppler estimation (JDDE) for target localization. On the other hand, wireless channels can be often modeled as sparse or cluster-sparse and hence many of channel coefficients are zero [15; 16; 17; 18; 19]. However, standard SLMS algorithm does not exploit sparse channel structure information, while some potential performance gain could be obtained by adopting advanced adaptive channel estimation algorithms.  
To exploit channel sparsity as well as to mitigate GMM impulsive noises, some state-of-the-art channel estimation algorithms using linear programming [20; 21] and Bayesian learning [22] have been investigated. However, these algorithms often have high computational complexity. It is well known that the fast channel estimation algorithm is one of important factors to design wireless communication systems. Hence, a fast adaptive sparse channel estimation algorithm, _i.e.,_ SLMS with reweighted L1-norm constraint (SLMS-RL1) algorithm was proposed in [23]. In our previous work, we focused on the convergence analysis without considering the reweighted factor selection, where the empirical parameter is set as \(\varepsilon=0.005\)[6]. However, the reweighted factor is one of critical parameters to balance estimation performance and sparsity exploitation. To this end, this paper proposes a Monte-Carlo (MC) based selection method to select suitable reweighted factor for SLMS-RL1 algorithm. Numerical simulations are provided to evaluate the performance of the SLMS-RL1 algorithm using the proposed reweighted factor.  
The rest of the paper is organized as follows. In Section 2, we introduce GMM noise model and review of SLMS-RL1 algorithm. By analyzing the convergence performance of LMS-RL1 algorithm, the important problem of the reweighted factor selection is point out. In Section 3, the MC-based selection method is proposed to select an appropriate reweighted factor for SLMS-RL1 algorithm. In Section 4, numerical simulations are provided to demonstrate the effectiveness of SLMS-RL1 with the proposed reweighted factor. Finally, Section 5 concludes this paper.