Compressive Covariance Sampling for Spectrum Sensing (CoCoSa)

尽管大部分获得许可的频段未得到充分利用，但可用的无线电频谱已成为一种稀缺资源。在认知无线电的框架内，已经开发出更有效地利用可用频谱的方法。关键思想是让未经许可的无线电访问免费的频谱资源，只要它们能够确保不干扰许可的使用。实现可靠的许可用户检测并因此能够安全地二次利用的方法被称为频谱感知。手头的问题是在非常低信噪比(SNR)的情况下检测信号。已经提出了多种方法，其中一些利用了通信信号中固有的随机特征的存在，例如信号的协方差矩阵的性质。然而，为了可靠地检测通信信号的特征随机特征，必须处理大量的测量数据，为此，我们的目标是开发从大幅减少的样本数量中检测许可发射机的方法和算法。应分析不同类型的协方差估计的误差性能，并开发新的检测器。特别是，我们将对在其结构的现实假设下进行精确协方差估计所需的最小样本数进行严格的数学分析。通常，独立地处理协方差矩阵的估计和用于二元假设检验(信道空闲或占用)的检验统计量的选择。通过互锁估计和检测方法以及相关的测试统计，由于预期的合作，我们有望获得新的见解。具体地说，我们计划开发定制的稀疏尺子，用于无损恢复不同信号类型的协方差矩阵。此外，我们将从理论上分析在不同误差保证下估计协方差矩阵所需的样本数。只有通过穷举搜索才能找到最小稀疏标尺。为了解决这个问题并获得实时能力，我们将开发智能搜索启发式算法。此外，我们打算通过寻找新的测试统计数据来改进已知的检测器。由于对测试统计参数的更好估计会导致检测性能的提高，因此很大一部分合作努力将放在这个主题上。将导出基于信号协方差矩阵的测试统计的估计参数的误差界。这将导致更有效的测试统计。作为最后一步，我们将在软件无线电测试床上实现这些新方法，以评估它们在现实世界中的性能。

The available radio spectrum has become a scarce resource despite the fact that large parts of the licensed spectral bands are underutilized. Approaches to make more efficient use of the available spectrum have been developed within the framework of cognitive radio.The key idea is to let unlicensed radios access free spectral resources as long as they can ensure not to interfere with licensed usage. The methods enabling reliable licensed user detection, and thus safe secondary utilization, go by the name of spectrum sensing.The problem at hand is the detection of signals in very low signal to noise ratio (SNR) regimes. Multiple approaches have been put forward, some of which exploit the presence of inherent stochastic features in communication signals, e.g., properties of a signal's covariance matrix. However, to detect characteristic stochastic features of communication signals reliably, a large amount of measurement data has to be processed.To this end, we aim at developing methods and algorithms for licensed transmitter detection from a drastically reduced number of samples. Different types of covariance estimation shall be analyzed with respect to their error performance, and new detectors are to be developed. In particular, we will make a rigorous mathematical analysis on the minimal number of samples required for accurate covariance estimation under realistic assumptions on its structure. Typically, estimation of the covariance matrix and the choice of a test statistic for the binary hypothesis test (channel free or occupied) are treated independently. By interlocking estimation and detection approaches and associated test statistics new insights are to be expected due to the intended cooperation.In concrete terms, we plan on developing customized sparse rulers for the lossless recovery of the covariance matrix of different signal types. Furthermore, we will theoretically analyze the number of samples necessary for estimating a covariance matrix under different error guarantees. Finding a minimal sparse ruler can only be accomplished by exhaustive search. To tackle this problem and to attain real-time capability, we will develop smart search heuristics. Moreover, we intend to improve upon known detectors by finding new test statistics. Since better estimation of test statistic parameters leads to improved detection performance, a large part of the cooperative effort will be placed on this topic. Error bounds for the estimated parameters of the test statistics based on the signal covariance matrix will be derived. This will lead to more effective test statistics. As a final step, we will implement the new methods on a software defined radio testbed in order to evaluate their performance in the real world.