Andreas Bollig

Dictionary-based reconstruction of the cyclic autocorrelation via ℓ 1 -minimization for cyclostationary spectrum sensing

One of the main enablers of dynamic spectrum access is fast and reliable spectrum sensing. Acquiring the occupation status of a spectral band can be accomplished in different ways, one of which is called cyclostationary spectrum sensing. The aforementioned method exploits the prior knowledge of periodicities inherent in most man-made signals for the purpose of detecting their presence in a set of sample data. One prerequisite for the detection is the knowledge of the signals cyclic autocorrelation (CA), which can be estimated from a finite amount of time-domain samples. This work introduces a new method for estimating the CA using a very small amount of time-domain samples, i.e. a short observation time. This is accomplished by modeling the desired CA vector using a custom dictionary describing its known properties and recovering it by solving a convex optimization problem.

Distributed sensing of a slowly time-varying sparse spectrum using matrix completion

In this paper, we consider the problem of sensing a frequency spectrum in a distributed manner using as few measurements as possible while still guaranteeing a low detection error. To achieve this goal we use the newly developed technique of matrix completion which enables to recover a low rank matrix from a small subset of its entries. We model the sensed bandwidth at different cognitive radios as a spectrum matrix. It has been shown that in many cases the spectrum used by a primary user is underutilized. Therefore the spectrum matrix often has a low rank structure. By taking few measurements at several cognitive radios and reconstructing the matrix at a fusion center, we can dramatically reduce the required number of samples to reconstruct the utilization of the bandwidth. This is a key enabler for efficient and reliable spectrum reuse.

Compressive energy detection for blind coarse wideband sensing: Comparative performance study

Wideband signal acquisition and spectrum sensing play a crucial role in a number of applications. In this work we discuss the task of blind spectrum sensing of frequency-sparse wideband signals sampled at sub-Nyquist rates. We show how in a generic sub-Nyquist sampling framework the results of the support recovery can be directly used for coarse multichannel energy detection. We numerically study the performance of the proposed compressive energy detector and compare it with that of the related approaches. Our results demonstrate that it outperforms its closest counterpart that operates on the recovered power spectral density and provides a comparable performance to the Nyquist-rate energy detector in the high SNRs.

Analytical test statistic distributions of the MMME eigenvalue-based detector for spectrum sensing

We present an analytical derivation of the probability density functions (PDFs) of the maximum-minus-minimum eigenvalue (MMME) detector for the special case of two cooperating secondary users (SUs) in a spectrum sensing scenario. For this we employ a simple additive white Gaussian noise (AWGN) model, where in general K cooperating SUs are monitoring the wireless spectrum to determine the presence of a single primary user, which transmits phase shift keying (PSK) modulated signals. The sample covariance matrix is aWishart matrix under both the noise only and the signal plus noise hypothesis under this model. For K = 2, we derive the exact PDFs for the MMME detector under both hypotheses for a finite number of samples N taken. Then, we compare the performance of the MMME detector and the maximum-minimum eigenvalue (MME) detector aided by exact PDFs available in the literature for this model. Finally, we analyze the noise power uncertainty tolerance margin of the MMME detector under which it shows superior performance to the MME detector.

MMME and DME: Two new eigenvalue-based detectors for spectrum sensing in cognitive radio

Cognitive radio and dynamic spectrum access (DSA) promise to ease the scarcity of radio spectrum, which is growing more acute as the demand for wireless connectivity increases. One of the key ingredients of a reliable and efficient DSA system is spectrum sensing, i.e., the act of checking a spectral resources occupancy state before opportunistically accessing it. To this end, the present work proposes two new eigenvalue-based detectors, the Maximum-Minus-Minimum-Eigenvalue (MMME) detector and the Difference-of-Means-of-Eigenvalues (DME) detector, both of which exploit the properties of the eigenvalues of the covariance matrix of a received signal, which is contaminated with i.i.d. noise. We explain the intuition behind the new detectors, investigate the choice of the DME detectors parameter and assess their performance in comparison to other covariance-based detectors.

Exact quickest spectrum sensing algorithms for eigenvalue-based change detection

We study a collaborative quickest detection scheme that uses a function of the eigenvalues of the sample covariance matrix for a spectrum sensing system with a fusion center. A simple model consisting of one potentially present primary user (PU), which utilizes phase shift keying (PSK), and the standard additive white Gaussian noise (AWGN) assumption is considered. Here, for both detection hypothesis, the sample covariance matrix follows a Wishart distribution. For K = 2 collaborating secondary users (SUs), the probability distribution function (PDF) of the maximum-minimum eigenvalue (MME) test statistic can be derived analytically under both hypotheses, allowing us to develop exact quickest detection algorithms for known and unknown SNR. We analyze the two types of change detection problems in spectrum sensing, i.e., the channel becoming free when it was occupied before and vice versa. Performance evaluation is done by evaluating bounds and by comparing the presented quickest detection algorithms with the traditional block detection scheme.

Joint Sparse Spectrum Reconstruction and Information Fusion via L1-Minimization

This paper considers the problem of sensing a sparsely occupied wideband spectrum utilizing a set of geographically distributed sensing nodes as well as a fusion center. Exchange of measurement data between the sensing nodes and the fusion center takes up parts of the precious radio spectrum and thus, methods for diminishing the minimum amount of measurements still ensuring a reliable reconstruction of the spectrum at the fusion center are needed. To this end we propose two approaches in the form of convex optimization problems to tackle the problem. The first approach applies classic compressive sampling, while the second approach improves the optimization problem, so that all measurements which have been acquired in a distributed manner can be taken into consideration in a single spectrum recovery operation. This makes it possible, to exploit the inherent diversity gain. The presented approaches to efficient distributed spectrum sensing enable reliable dynamic spectrum access.