Blind Adaptive Fractionally-Spaced Linear Equalizer Behavior

本研究的中心主题是对无记忆误差函数的行为进行更全面的理论描述（或Bussgang）型盲均衡算法，特别是CMA，如在实践中使用的有限长度、分数间隔、高阶（非恒定模量，非均匀分布）源星座，（确定性和随机性）相关源时间序列和适度信道噪声。 初始目标是具有相关（或周期）源的分数间隔CMA的行为，这似乎能够在实践中引起错误行为。 我们计划使用拓扑为基础的分析工具，代数几何（特别是伯恩斯坦的定理，松弛方法，和莫尔斯理论）非通常与自适应滤波器的研究，除了平均理论工具流行的自适应系统分析。 最终的目的是将扩展的理论转换成用于步长、长度、分数间隔、初始化选择和故障恢复技巧的情况相关的设计准则，用于将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CMA的分析进展转化为无记忆误差函数类（包括CMA的改进）的其他盲均衡器算法的分数间隔实现，可以在工业上获得CMA的实际操作数据。 我们还计划使用我们对CMA的行为洞察来帮助提供对实际操作数据与竞争方案的公平比较，例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度算法。

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.