Blind Adaptive Fractionally-Spaced Linear Equalizer Behavior

本研究的中心主题是发展对无记忆误差函数（或Bussgang）型盲均衡算法行为的更全面的理论描述，特别是CMA，在有限长度，分数间距，高阶（非恒定模量，非均匀分布）源星群，（确定性和随机）相关源时间序列和适度信道噪声的实践中使用。初始目标是具有相关（或周期性）源的分数间隔CMA的行为，这在实践中可能会导致不当行为。除了自适应系统分析中流行的平均理论工具外，我们计划使用基于拓扑的、代数几何的（特别是伯恩斯坦定理、松弛方法和莫尔斯理论）非典型地与自适应滤波器研究相关的分析工具。最终目的是将扩展的理论转换为基于情况的设计指南，用于步长、长度、分数间距、初始化选择和故障恢复技巧，以便将CMA用作高数据吞吐量应用程序的启动方案（随后切换到决策方向）。我们计划将我们在CMA上的分析进展转化为其他无记忆误差函数类的盲均衡器算法的分数间隔实现（包括对CMA的改进），这样就可以获得CMA的实际运行数据。我们还计划利用我们对CMA的行为洞察来帮助对实际操作数据与竞争方案（如符号间隔决策反馈均衡器和基于单输入多输出分数间隔均衡模型的二阶相关统计的类似复杂性算法）进行公平比较。

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.