Compressive Covariance Sampling for Spectrum Sensing (CoCoSa)

可用的无线电频谱已成为一种稀缺资源，尽管大部分许可的频谱频带未得到充分利用。在认知无线电的框架内，已经制定了更有效地利用现有频谱的方法。关键的想法是允许未授权的无线电访问免费的频谱资源，只要它们能确保不干扰已授权的使用。实现可靠的授权用户检测，从而实现安全的二次利用的方法被称为频谱感知。当前的问题是在非常低的信噪比（SNR）条件下检测信号。已经提出了多种方法，其中一些方法利用了通信信号中固有的随机特征，例如信号协方差矩阵的性质。然而，为了可靠地检测通信信号的特征随机特征，需要对大量的测量数据进行处理。为此，我们的目标是开发从大量减少的样本中检测许可发射机的方法和算法。分析不同类型的协方差估计的误差性能，开发新的检测器。特别是，我们将对在其结构的现实假设下准确协方差估计所需的最小样本数量进行严格的数学分析。通常，协方差矩阵的估计和二元假设检验（信道空闲或占用）的检验统计量的选择是独立处理的。通过联锁的估计和检测方法以及相关的测试统计，由于预期的合作，将期望获得新的见解。具体而言，我们计划开发定制的稀疏尺子，用于对不同信号类型的协方差矩阵进行无损恢复。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量。寻找最小稀疏标尺只能通过穷举搜索来完成。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。此外，我们打算通过寻找新的测试统计来改进已知的检测器。由于更好地估计测试统计参数可以提高检测性能，因此合作的大部分工作将放在这个主题上。基于信号协方差矩阵的测试统计估计参数的误差范围将被导出。这将导致更有效的测试统计。作为最后一步，我们将在软件定义的无线电测试台上实现新方法，以评估其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.