EAGER: Feedback optimization of dynamic nonlinear signal processing systems

该研究将探讨一种新的方法来设计非线性信号处理系统，利用有效的真实的时间实现的频率加权最小二乘优化与信号值的约束：一个修改的经典维纳滤波器设置，其中优化的信号最小化二次频域积分，其样本被限制到一个给定的紧凑集。特别地，这种优化是由峰功率比降低中的应用激发的，其中优化的输出信号必须尽可能接近输入，同时满足频谱屏蔽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量化的，而其时域样本被限制为有限集。此外，拟议的研究旨在建立一个高品质的线性有限脉冲响应滤波器，一个无处不在的数字信号处理单元的元素，容易消耗大量的资源，在FPGA和ASIC实现的复杂性降低的分析基础。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决方案是滤波器设计中的一个公认的基本思想。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。在约束频率加权二次优化的情况下，在这个建议中进行研究，最优性的分析条件是众所周知的，但在一个令人沮丧的形式，一个无限的非线性方程组相对于一个无限数量的变量。建议的研究是基于最近的观察支持的期望，在合理的假设下，从输入到最佳输出的动态映射将具有指数衰减记忆，而且，将近似非常准确的一类基于反馈的真实的时间算法。该提案旨在建立一个非因果版本的鲁棒性分析机制，以量化和评估非线性动态系统的指数稳定性，其中当前输出样本同等程度地依赖于过去和未来的输入，并提供高质量的真实的时间实现这样的系统。拟议的工作有可能提供一个从根本上新的一类实用的非-具有上级性能的线性信号处理算法。它还将通过将其一些基本工具扩展到由信号处理应用激励的非因果系统来增强反馈控制的鲁棒性分析理论。本提案中的应用问题是由开发用于下一代通信设备的数字信号处理算法的当前需求激发的，最重要的是，涉及无线电中的数字信号调节的那些（蜂窝塔基站、WiFi集线器等）。如果成功，拟议的研究将成为降低常见数字信号处理单元功耗和占用空间的因素。它还可能影响通信标准的编写方式，确保轻松获得许多常见信号处理任务的高效高性能实现。因此，该项目可能有助于加强学术界和工业界之间的伙伴关系，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.