Multiantenna spectrum sensing for Cognitive Radio: overcoming noise uncertainty

Abstract

Abstract-Spectrum sensing is a key ingredient of the dynamic spectrum access paradigm, but it needs powerful detectors operating at SNRs well below the decodability levels of primary signals. Noise uncertainty poses a significant challenge to the development of such schemes, requiring some degree of diversity (spatial, temporal, or in distribution) for identifiability of the noise level. Multiantenna detectors exploit spatial independence of receiver thermal noise. We review this class of schemes and propose a novel detector trading off performance and complexity. However, most of these methods assume that the noise power, though unknown, is the same at all antennas. As it turns out, calibration errors have a substantial impact on these detectors. Another novel detector is proposed, based on an approximation to the Generalized Likelihood Ratio, outperforming previous schemes for uncalibrated multiantenna receivers.

Scaled Largest Eigenvalue Detection for Stationary Time-Series

“…We 1 Please note that the usual ML sample covariance matrix estimate for multivariate Gaussian signals [10], typically used in multiantenna scenarios, does not apply here since we consider a time-series scenario and do not assume that the received samples follow a Gaussian distribution. 2 As a result, please note that even if the time-series samples follow a Gaussian distribution, neither of the following estimators for Σx are ML.…”

“…Such approaches make it difficult to derive the statistical distribution of the estimated covariance matrix and for this reason, we will instead use more naive (but tractable) estimation techniques 2 . More specifically, we may use either of the following two approximations.…”

“…SLE statistic Γ. IfΣ x is Toeplitz, its entries are entirely determined by the vectorς, whose statistical distribution is linked to the input signal x(n) via equation (2). If we suppose that the noise samples are i.i.d complex Gaussian distributed, v(n) ∼ CN (0, σ 2 n ), the vectorς is composed of quadratic forms of Gaussian random variables, which can be approximated using Chi-squared distributions as shown in [14].…”

“…through its eigenvalues do exist [2], [3], [4], [5], we focus our attention on the Scaled Largest Eigenvalue (SLE) detector whose test statistic is given by the ratio of the largest eigenvalue to the trace (or equivalently, the sum of its eigenvalues) of the sample covariance matrixΣ x .…”

“…When the received signal is a sequence of i.i.d multivariate Gaussian vectors and the signal to be detected possesses a rank-one covariance matrix, this detector has been derived as a sufficient statistic for the Generalized Log-Likelihood Ratio Test (GLRT) [2]. It has also been shown to maximize the SNR among all the statistics that linearly combine the received samples [6].…”