NSF/ENG/ECCS-BSF: Sensing and Estimation under Energy and Communication Constraints

当今普遍存在的许多复杂的电子设备都是通过数字信号处理（DSP）实现的，该数字信号处理将与物理世界相关联的模拟信号转换到数字域。摩尔定律允许用小型、低成本、高能效的数字硬件来处理和传送这种数字化信号。 然而，关于模拟数据的采样、量化、通信和重构在保真度和总体能耗方面的性能限制和权衡的基本问题仍然是开放的。更好地理解这些性能限制和权衡将大大增强模拟传感器数据的收集、处理和通信能力，超越现有技术水平。这些能力对于健康和保健、安全、节能基础设施和智能城市等新兴传感器网络应用尤其重要。其中许多低成本低能量模拟传感器将收集大量数据并将其传输到远程位置进行处理。拟议的研究将调查之间的相互作用，采样，量化，通信和模拟信号的存储器约束，通信约束和能量约束下的重建。 建议的工作的目标是开发一个基本的率失真理论的采样，量化和模拟数据的重建受到这些约束。具体的香农理论限制的组合采样和源编码的性能-数字化仪的采样率和量化精度之间的失真方面的权衡将被调查。此外，在模拟数据的重建从一个序列的样本的最佳保真度将被导出。将确定在能量约束下通信的基本限制，其中模拟传感器必须在有限能量约束下传输和通信其数据。所使用的方法将从香农容量，率失真理论，联合信源信道编码和分离，采样，估计和统计的先前工作。特别是，在扩展现有的率失真理论的结果，将子奈奎斯特采样，联合信源信道编码技术应用于采样的模拟数据传输的速率受限的信道将开发。能量约束将被纳入信息理论模型的基础上计算能量沿着最近的结果有限块长度码和最小能量每比特容量。

Many of the sophisticated electronic devices ubiquitous today have been enabled by digital signal processing (DSP) that converts the analog signals associated with the physical world to the digital domain. Moore's law allows such digitized signals to be processed and communicated with small, low-cost energy-efficient digital hardware. Yet fundamental questions regarding the performance limits and tradeoffs associated with the sampling, quantization, communication, and reconstruction of analog data with respect to both fidelity and overall energy consumption remain open. Better understanding of these performance limits and tradeoffs will significant enhance capabilities for collection, processing, and communication of analog sensor data beyond the current state of the art. These capabilities are particularly acute for emerging sensor network applications in health and wellness, security, energy-efficient infrastructures, and smart cities, where many low-cost low-energy analog sensors will be collecting large amounts of data and transmitting it to remote locations for processing. The proposed research will investigate the interplay between sampling, quantization, communication and reconstruction of analog signals under memory constraints, communication constraints, and energy constraints. The goal of the proposed work is to develop a fundamental rate-distortion theory for the sampling, quantization, and reconstruction of analog data subject to these constraints. Specific Shannon-theoretical limits for the performance of combined sampling and source coding - the tradeoff between the digitizer's sampling rate and quantization precision in terms of distortion will be investigated. In addition, the optimal fidelity in the reconstruction of analog data from a sequence of samples will be derived. Fundamental limits on communication under energy constraints, where an analog sensor must digitize and communication its data under finite energy constraints, will be determined. Methods used will draw from prior work in Shannon capacity, rate-distortion theory, joint source-channel coding and separation, sampling, estimation, and statistics. In particular, after extending existing results on rate-distortion theory to incorporate sub-Nyquist sampling, joint source-channel coding techniques applied to the sampled analog data transmitted over a rate-limited channel will be developed. Energy constraints will be incorporated based on information-theoretic models for computation energy along with recent results on finite-block-length codes and minimum energy-per-bit capacity.