The least-mean-square (LMS) is promising in a system whose signal statistics are time-varying, and it is preferred in adaptive digital predistortion techniques. In a nonlinear memory system, it is found that the high nonlinearity, the finite sampling rate and the finite number of digits will introduce colored noise that is dependent on signals. In this paper, the long-term stability of the conventional LMS in the presence of signal-dependent noise is analyzed using perturbation analysis. It is revealed that the cumulative effect of the signal-dependent noise may lead to a divergence of the conventional LMS, and a properly selected leaky coefficient is needed to suppress the divergence. Unfortunately, the compensation performance may be harmed by enlarging the leaky coefficient. To address this problem, a modified LMS (MLMS) algorithm is proposed. By adjusting the updating strategy in the iterations, the long-term stability of the algorithm is guaranteed, without harming the linearization performance. Numerical simulations verify that the MLMS outperforms the conventional LMS both in stability and compensation performance.

中文翻译：

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用于消除非线性记忆效应的修正 LMS 算法的稳定性

最小均方 (LMS) 在信号统计随时间变化的系统中很有前景，并且在自适应数字预失真技术中是首选。在非线性存储系统中，发现高非线性、有限采样率和有限位数会引入依赖于信号的有色噪声。在本文中，使用扰动分析分析了传统 LMS 在存在信号相关噪声的情况下的长期稳定性。It is revealed that the cumulative effect of the signal-dependent noise may lead to a divergence of the conventional LMS, and a properly selected leaky coefficient is needed to suppress the divergence. 不幸的是，增大泄漏系数可能会损害补偿性能。为了解决这个问题，提出了一种改进的 LMS (MLMS) 算法。通过在迭代中调整更新策略，保证了算法的长期稳定性，同时不损害线性化性能。数值模拟验证了 MLMS 在稳定性和补偿性能方面均优于传统 LMS。