WSSUS信道中RLS算法的跟踪性能
Tracking performance of RLS algorithms in WSSUS channels
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中文总结 AI 辅助
该研究针对WSSUS信道，分析指数RLS、SRLS等算法的跟踪性能，推导MSD通用公式并推广到带延迟RLS及SRLS-L算法，其分析结果与数值仿真匹配良好。
中文摘要 AI 辅助
自适应算法广泛应用于线性时变系统的估计，例如通信信道。其跟踪性能取决于噪声水平、时变特性和算法参数。优化这些参数并预测算法性能是一项重要任务。本文提出一种方法，用于分析递归最小二乘（RLS）自适应算法在信道中的跟踪性能，这类信道的时变特性由具有功率谱密度（PSD）的广义平稳不相关散射（WSSUS）随机过程描述。本文聚焦于指数RLS算法和滑动窗口RLS（SRLS）算法，根据PSD的谱矩获得了作为跟踪性能度量的均方偏差（MSD）的通用公式。作为示例，针对具有均匀、Jakes'和自回归PSD的随机过程对这些公式进行了具体化。这些结果进一步推广到带延迟的RLS算法（例如处理延迟或非因果自适应RLS算法中引入的延迟），以及使用勒让德多项式近似信道时变特性的SRLS-L算法。数值示例表明，分析得到的MSD与仿真结果匹配良好。
英文摘要
Adaptive algorithms are widely used for estimation of linear time-varying systems, such as communication channels. Their tracking performance depends on the level of noise, characteristics of time variations, and the algorithm parameters. Optimizing these parameters and predicting the algorithm performance is an important task. In this paper, we present an approach for analysing the tracking performance of recursive least squares (RLS) adaptive algorithms in channels with time variations described as wide-sense stationary uncorrelated scattering (WSSUS) random processes characterised by a power spectral density (PSD). We focus on exponential RLS and sliding-window RLS (SRLS) algorithms, for which general formulas for the mean square deviation (MSD) as a measure of the tracking performance are obtained in terms of spectral moments of the PSD. As examples, they are specified for random processes with uniform, Jakes' and autoregressive PSDs. These results are further generalized to RLS algorithms with delays, e.g. processing delays or delays introduced in non-causal adaptive RLS algorithms, and to the SRLS-L algorithm with approximation of channel time variations using Legendre polynomials. Numerical examples show good match between the analytical MSD and simulation results.
