Blind Adaptive Fractionally-Spaced Linear Equalizer Behavior

这项研究的中心主题是对无记忆误差函数(或Bussgang)型盲均衡算法的行为进行更全面的理论描述，特别是在实践中使用的有限长度、分数间隔、高阶(非恒定模数、非均匀分布)信源星座、(确定性和随机)相关信源时间序列和适度信道噪声的CMA。最初的目标是具有相关(或周期)源的分数间隔CMA的行为，这在实践中似乎能够导致不当行为。除了自适应系统分析中流行的平均理论工具外，我们还计划使用基于拓扑学、代数几何(特别是伯恩斯坦定理、松弛方法和莫尔斯理论)的分析工具，这些工具通常与自适应滤波器的研究不相关。最终目的是将扩展的理论转换为步长、长度、分数间隔、初始化选择和故障恢复技巧的情况相关设计指南，以便将CMA用作高数据吞吐量应用的启动方案(随后切换到决策方向)。我们计划将我们对恒模算法的分析进展转化为无记忆误差函数类的其他盲均衡器算法的分数间隔实现(包括对恒模算法的改进)，对于这些算法，实际操作数据可以像对恒模算法一样在工业上获得。我们还计划利用我们对CMA的行为洞察，帮助提供与竞争方案(如符号间隔判决反馈均衡器和基于分数间隔均衡的单输入、多输出模型的二阶相关统计的类似复杂性算法)的实际操作数据的公平比较。

The central theme of this research is the development of a fuller theoretical description of the behavior of memoryless-error- function (or Bussgang) type blind equalization algorithms, in particular CMA, as used in practice with finite-length, fractional spacing, higher-order (non-constant modulus, non-uniformly distributed) source constellations, (deterministic and stochastic) correlated source time series, and modest channel noise. The initial target is the behavior of fractionally-spaced CMA with a correlated (or periodic) source, which appears capable of causing misbehavior in practice. We plan to use analytical tools from topologically based, algebraic-geometry (in particular Bernstein's theorem, relaxation methods, and Morse theory) non typically associated with the study of adaptive filters in addition to averaging theory tools popular in adaptive systems analysis. The ultimate intent is to convert an expanded theory into situation dependent design guidelines for stepsize, length, fractional- spacing, initialization selection, and failure recovery tricks for the use of CMA as a start-up scheme (with a subsequent switch to decision-direction) for high data throughput applications. We plan to translate our analytical advances on CMA to fractionally-spaced realizations of other blind equalizer algorithms of the memoryless error function class (including refinements to CMA), for which actual operating data can be obtained industrially as for CMA. We also plan to use our behavior insights into CMA to help provide fair comparisons on actual operating data to competing schemes such as symbol-spaced decision feedback equalizers and similar complexity algorithms based on second-order correlation statistics of single-input, multiple- output models of fractionally-spaced equalization.