This paper reports a solution to a linear blind equalizer used in communication systems under the effect of two factors: i) An unknown linear inter symbol interference and ii) the impulsive noise satisfying the $\alpha$ -stable distribution. First, a constellation matching error-based cost function associated with the linear equalizer is designed to effectively compensate for the inter symbol interference and suppress the influence of the impulsive noise. Second, an improved form of the proposed cost function is derived through the finite alphabet property of information symbols. The theoretical analysis shows that the improved cost function significantly reduces the local minima and converges more stably in high-order modulation systems. Furthermore, based on the special structure of the designed cost function, a modified Newton scheme is constructed to quickly minimize it, and then the corresponding optimal blind equalizer can be obtained. Finally, computer simulations are presented to demonstrate the robust equalization performance and fast convergence of the novel algorithm under both impulsive and Gaussian noise environments.

中文翻译：

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$\alpha$-稳定噪声下盲均衡的鲁棒决策导向算法

本文报告了在两个因素影响下用于通信系统的线性盲均衡器的解决方案：i) 未知的线性符号间干扰和 ii) 脉冲噪声满足 $\alpha$ - 稳定的分布。首先，设计了与线性均衡器相关联的星座匹配误差代价函数，以有效补偿符号间干扰并抑制脉冲噪声的影响。其次，通过信息符号的有限字母属性推导出所提出的成本函数的改进形式。理论分析表明，改进的代价函数显着降低了局部最小值，在高阶调制系统中收敛更稳定。此外，基于所设计的代价函数的特殊结构，构造了一个改进的牛顿方案，使其快速最小化，从而得到相应的最优盲均衡器。最后，