CAREER: A Research, Education, and Technology Transfer Proposal in Statistical Signal Processing with Emphasis on Nonlinear System Identification

虽然线性近似和模型在分析中具有简单和易处理性，但大多数真实的生活问题都涉及非线性效应。 在信号处理和通信中，非线性系统在卫星链路、高速电话信道、功率放大器、磁记录和光记录系统中都有应用。 本研究旨在探索非线性系统的辨识、性能分析与缓解的新技术。 目标是使用最先进的统计信号处理工具来分析长期存在的问题，在非线性建模和应用，以电信问题。 目前的方法是采取一个新的眼光在传统的沃尔泰拉模型，并利用精心设计的循环平稳输入，导致在封闭形式的内核表达式与输入输出数据。 这样的解决方案将适用于任何阶数的有限记忆沃尔泰拉模型，即使在相对较短的数据记录下也能降低计算复杂性和噪声影响，并允许使用方差表达式进行分析性能评估。 研究人员计划使用从卫星链路接收的真实的数据模拟和测试由此产生的算法，其中放大器被驱动到非线性饱和区域。 她还在研究仅依赖于单个或多个传感器数据的盲非线性沃尔泰拉系统识别。 当没有训练输入时，或者当新的通信者加入多端口广播并且传输不能被中断以进行训练时，盲非线性信道估计和均衡的潜力是至关重要的。

While linear approximations and models possess simplicity and tractability in analysis, most real life problems entail nonlinear effects. Nonlinear system of current interest in signal processing and communications are encountered with satellite links, high-speed telephone channels, power amplifiers, magnetic and optical recording systems. This research is exploring novel techniques for identification, performance analysis, and mitigation of nonlinear systems. The goal is to use state-of-the-art statistical signal processing tools to analyze long-standing issues in nonlinear modeling and applications to tele- communications problems. The present approach is taking a fresh look at the traditional Volterra model and exploiting carefully designed cyclostationary inputs that result in closed-form kernel expressions with input-output data. Such solutions will apply to finite memory Volterra models of any order, reduce computational complexity and noise effects even with relatively short data records, and allow for analytical performance evaluation using variance expressions. The investigator plans to simulate and test the resulting algorithms using real data received from satellite links where amplifiers are driven to the nonlinear saturation region. She is also studying blind nonlinear Volterra system identification that relies on single or multi-sensor data only. The potential of blind nonlinear channel estimation and equalization is of paramount importance when no training inputs are available, or when new communicators join a multiport broadcast and transmission cannot be interrupted for training.