p范数约束漏损LMS算法用于稀疏系统辨识
p Norm Constraint Leaky LMS Algorithm for Sparse System Identification
AI总结：
本文提出一种引入p范数惩罚的改进漏损LMS算法，以增强稀疏系统辨识中的滤波性能，尤其在脉冲响应稀疏时表现更优。
摘要：
本文提出了一种新的漏损最小均方（leaky LMS，LLMS）算法，其中引入了范数惩罚以迫使解在系统辨识应用中保持稀疏性。由于标准LMS算法在输入高度相关时性能下降，因此提出了改进的LLMS算法，即Lp-LLMS算法，通过在LLMS的成本函数中引入p范数惩罚，从而在权重更新方程中实现收缩，从而在稀疏系统辨识设置中提高滤波器性能，特别是在脉冲响应稀疏时。仿真结果验证了所提算法在存在噪声输入信号时，能够提高稀疏系统设置中滤波器的性能。
英文摘要：
This paper proposes a new leaky least mean square (leaky LMS, LLMS) algorithm in which a norm penalty is introduced to force the solution to be sparse in the application of system identification. The leaky LMS algorithm is derived because the performance ofthe standard LMS algorithm deteriorates when the input is highly correlated. However, both ofthem do not take the sparsity information into account to yield better behaviors. As a modification ofthe LLMS algorithm, the proposed algorithm, named Lp-LLMS, incorporates a p norm penalty into the cost function ofthe LLMS to obtain a shrinkage in the weight update equation, which then enhances the performance of the filter in system identification settings, especially when the impulse response is sparse. The simulation results verify that the proposed algorithm improves the performance ofthe filter in sparse system settings in the presence ofnoisy input signals.
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