Various spectrum sensing approaches have been shown to suffer from a so-called signal-to-noise ratio (SNR)-wall, an SNR value below which a detector cannot perform robustly no matter how many observations are used. Up to now, the eigenvalue-based maximum-minimum-eigenvalue (MME) detector has been a notable exception. For instance, the model uncertainty of imperfect knowledge of the receiver noise power, which is known to be responsible for the energy detector's fundamental limits, does not adversely affect the maximum-minimum-eigenvalue (MME) detector's performance. While additive white Gaussian noise (AWGN) is a standard assumption in wireless communications, it is not a reasonable one for the maximum-minimum-eigenvalue (MME) detector. In fact, in this work, we prove that uncertainty in the amount of noise coloring does lead to an SNR wall for the maximum-minimum-eigenvalue (MME) detector. We derive a lower bound on this SNR wall and evaluate it for example scenarios. The findings are supported by numerical simulations.
Abstract-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.
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 resource's 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 detector's parameter and assess their performance in comparison to other covariancebased detectors.
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