EAGER: Feedback optimization of dynamic nonlinear signal processing systems

这项研究将探索一种设计非线性信号处理系统的新方法，该方法利用具有信号值约束的频率加权最小二乘优化的有效实时实现：改进的经典维纳滤波器设置，其中优化的信号必须最小化二次频域积分，其样本限制在给定的紧致集内。特别是，这种优化是由峰值功率比降低中的应用所推动的，其中优化的输出信号必须尽可能接近输入，同时满足频谱掩码约束以及施加在其时域样本上的绝对值界限。另一个激励应用是最优量化，其中输出信号必须提供输入的最佳近似，如通过频率加权积分误差度量来量化，而其时域样本被限制在有限集合中。此外，本研究旨在为降低高品质线性有限冲激响应滤波器的复杂性奠定分析基础，线性有限冲激响应滤波器是数字信号处理单元中普遍存在的元件，在FPGA和ASIC实现中容易消耗大量资源。将信号处理系统的理想响应定义为根据系统输入指定的优化任务的解是滤波器设计中公认的基本思想。一个众所周知的例子是无约束频率加权二次优化的情况，其中最优解是由维纳滤波器实现的输入的线性函数。在本方案中要研究的约束频率加权二次优化的情况下，最优性的分析条件是众所周知的，但其形式是关于无穷多个变量的无穷多组非线性方程。所提出的研究是基于最近的观察，该观察支持这样的期望，即在合理的假设下，从输入到最优输出的动态映射将具有指数衰减的记忆，并且将被一类特定的基于反馈的实时算法非常精确地逼近。该方案旨在建立一个非因果版本的健壮性分析机制，量化和评估当前输出样本在同等程度上依赖于过去和未来输入的非线性动态系统的指数稳定性，并提供此类系统的高质量实时实现。所提出的工作有可能提供一类全新的具有优越性能的实用非线性信号处理算法。它还将通过将反馈控制的一些基本工具扩展到由信号处理应用驱动的非因果系统来增强反馈控制的稳健性分析理论。本提案中的应用问题是由于当前需要为下一代通信设备开发数字信号处理算法，最重要的是那些涉及无线电(蜂窝基站、WiFi集线器等)中的数字信号调理的通信设备。如果成功，这项拟议的研究将成为降低通用数字信号处理单元功耗和占地面积的一个因素。它还可能影响通信标准的编写方式，因为它确保了对许多常见信号处理任务的高效高性能实施的轻松访问。因此，该项目可能有助于增加学术界和工业界之间的合作伙伴关系，并提高美国的经济竞争力。

The proposed research will investigate a new approach to design of non-linear signal processing systems, utilizing efficient real time implementation of frequency weighted least square optimization with signal value constraints: a modified classical Wiener filter setup, in which the optimized signal has to minimizea quadratic frequency domain integral, subject to its samples being restricted to a given compact set. In particular, such optimization is motivated by applications in peak-to-power ratio reduction, where the optimized output signal has to be as close as possible to the input, while satisfying a spectral mask constraint, as well as an absolute value bound imposed on its time domain samples. Another motivating application is optimal quantization, where the output signal has to provide the best approximation of the input, as quantified by a frequency-weighted integral error measure, while its time domain samples are restricted to a finite set. In addition, the proposed research aims to establish an analytical foundation for complexity reduction of high quality linear finite impulse response filters, a ubiquitous element of digital signal processing units, prone to consume significant resources in FPGA and ASIC implementations. Defining the ideal response of a signal processing system as the solution of an optimization task specified in terms of system input is a well-established fundamental idea in filter design. A well-known example is the case of unconstrained frequency weighted quadratic optimization, where the optimal solution is a linear function of the input, implemented by the Wiener filter. In the case of constrained frequency weighted quadratic optimization, to be investigated in this proposal, analytical conditions of optimality are well known, but come in the discouraging form of an infinite set of non-linear equations with respect to an infinite number of variables. The proposed research is based on the recent observation supporting the expectation that, under reasonable assumptions, the dynamic mapping from the input to the optimal output will have exponentially fading memory, and, moreover, will be approximated extremely accurately by a specific class of feedback-based real time algorithms. The proposal intends to build a non-causal version of robustness analysis machinery, to quantify and assess exponential stability of nonlinear dynamical systems in which the current output sample depends in equal degree on the past and future inputs, and to provide high quality real time realizations of such systems.The proposed work has the potential to deliver a fundamentally new class of practical non-linear signal processing algorithms with superior performance. It will also enhance the theory of robustness analysis of feedback control by extending some of its basic tools to non-causal systems motivated by signal processing applications. The application problems in this proposal are motivated by the current needs of developing digital signal processing algorithms for the next generation of communication devices, most significantly, those involved in digital signal conditioning in radios (cell tower base stations, WiFi hubs, etc.) If successful, the proposed research will become a factor in reducing power consumption and footprint of common digital signal processing units. It may also affect the way communication standards are written, by ensuring easy access to efficient high performance implementation of a number of common signal processing tasks. Thus, the project may contribute to increased partnerships between academia and industry, and increase economic competitiveness of the US.