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Large system transient analysis of adaptive least squares filtering

机译：自适应最小二乘滤波的大系统瞬态分析

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摘要

The performance of adaptive least squares (LS) filtering is analyzed for the suppression of multiple-access interference. Both full-rank LS filters and reduced-rank LS filters, which reside in a lower dimensional Krylov space, are considered with training, and without training but with known signature for the desired user. We compute the large system limit of output signal-to-interference-plus-noise ratio (SINR) as a function of normalized observations, load, and noise level. Specifically, the number of users K, the degrees of freedom N, and the number of training symbols or observations i all tend to infinity with fixed ratios K/N and i/N. Our results account for an arbitrary power distribution over the users, data windowing (e.g., recursive LS (RLS) with exponential windowing), and initial diagonal loading of the covariance matrix to prevent ill-conditioning. Numerical results show that the large system analysis accurately predicts the simulated convergence performance of the algorithms considered with moderate degrees of freedom (typically N=32). Given a fixed, short training length, the relative performance of full- and reduced-rank filters depends on the selected rank and diagonal loading. With an optimized diagonal loading factor, the performance of full- and reduced-rank filters are similar. However, full-rank performance is generally much more sensitive to the choice of diagonal loading factor than reduced-rank performance.
机译：分析了自适应最小二乘（LS）滤波的性能，以抑制多址干扰。驻留在较低维Krylov空间中的全秩LS滤波器和降阶LS滤波器都经过培训，没有经过培训，但具有所需用户的已知签名，因此被认为是必需的。我们根据归一化观测值，负载和噪声水平来计算输出信噪比（SINR）的较大系统限制。具体地，用户的数量K，自由度N以及训练符号或观察的数量i都倾向于以固定比率K / N和i / N无穷大。我们的结果说明了用户上的任意功率分布，数据窗口化（例如具有指数窗口化的递归LS（RLS））以及协方差矩阵的初始对角线加载以防止不良情况。数值结果表明，大型系统分析可以准确地预测具有中等自由度（通常为N = 32）的算法的仿真收敛性能。给定一个固定的，短的训练长度，全秩和低秩滤波器的相对性能取决于所选的秩和对角线负载。通过优化的对角线加载因子，全秩滤波器和降秩滤波器的性能相似。但是，与降低秩的性能相比，完全秩的性能通常对对角线加载因子的选择更为敏感。

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