Quantized Compressive Spectrum Sensing (QuaCoSS)

频谱感测旨在检测无线电频谱中的未占用频带，以便使未授权（次要）用户能够在这些频带上机会性地通信。目标是增加次级用户的通信速率，而不对许可（主要）用户产生干扰。然而，这需要监控非常大的带宽，使得以奈奎斯特速率采样可能导致不可接受的大量样本。众所周知，频谱感测中使用的一些测试统计量具有稀疏性，即，频谱已经被示出为稀疏地占据，并且人造信号的循环谱是稀疏的。通过利用这种稀疏性，可以使用压缩感测技术而不是传统的香农-奈奎斯特采样，以便显著减少样本的数量，同时仍然确保对未占用频带的可靠检测。在实际应用中，样本在交换之前必须先进行量化，本计画旨在探讨压缩感知中量化对频谱感知的影响。我们将探讨一位量化的极端情况，其中仅保留测量的符号，以及多位量化方案。一个特别的重点放在结构化的随机测量，如随机部分傅立叶矩阵，这是高度相关的实际应用。虽然关于量化压缩感知的初步理论结果可用于高斯随机测量矩阵，但到目前为止，结构化随机矩阵在这方面仍然完全未被探索。此外，我们计划调查量化压缩频谱感知的实际应用中的两个开放的基本问题。首先，给定一个固定的比特预算的通信，我们将调查的权衡有关的量化分辨率和测量的次用户，以达到最佳的检测性能。其次，我们将分析占用决策频率和每个决策可用的比特预算之间的权衡，以最大限度地减少浪费的传输机会。Mathar的研究小组将致力于量化压缩感知算法的开发，实现和仿真及其在频谱感知方面的应用。Rauhut和Dirksen研究小组的重点将是量化压缩感知的理论分析，目的是推导出严格的误差保证和所需测量次数的严格界限。这两个小组的相互作用预计将是至关重要的，以实现量化压缩频谱感知的理解和实际实施的重大进展。

Spectrum sensing aims at detecting non-occupied frequency bands in the radio spectrum in order to enable unlicensed (secondary) users to opportunistically communicate over these bands. The goal is to increase communication rates for the secondary users without creating interference for licensed (primary) users. However, this demands to monitor a very large bandwidth so that sampling at the Nyquist rate may result in unacceptably large amount of samples. It is well-known that some of the test statistics used in spectrum sensing feature sparsity, i.e., the frequency spectrum has been shown to be sparsely occupied and the cyclic spectra of man-made signals are sparse. By exploiting this sparsity, one may use compressed sensing techniques instead of traditional Shannon-Nyquist sampling in order to significantly reduce the number of samples, while still ensuring reliable detection of non-occupied bands. In practice, samples have to be quantized before exchanging these.This project aims to explore the effect of quantization in compressed sensing on spectrum sensing. We will explore both the extreme case of one-bit quantization, where only the sign of a measurement is retained, as well as multi-bit quantization schemes. A particular focus is put on structured random measurements such as the random partial Fourier matrix, which are highly relevant in practical applications. While initial theoretical results on quantized compressed sensing are available for Gaussian random measurement matrices, structured random matrices remain completely unexplored in this context up to now. Moreover, we plan to investigate two open fundamental problems in the practical application of quantized compressive spectrum sensing. Firstly, given a fixed bit-budget for communication we will investigate the tradeoff concerning the quantization resolution and the number of measurements taken by secondary users in order to achieve optimal detection performance. Secondly, we will analyze the tradeoff between the occupancy decision frequency and the bit-budget available per decision in order to minimize wasted transmission opportunities.The research group of Mathar will dedicate its efforts to the development, implementation and simulation of quantized compressed sensing algorithms and their application in the spectrum sensing context. The focus of the research group of Rauhut and Dirksen will be on the theoretical analysis of quantized compressed sensing with the aim of deriving rigorous error guarantees and sharp bounds on the required number of measurements. The interaction of the two groups is expected to be crucial for achieving significant progress on the understanding and practical implementation of quantized compressive spectrum sensing.