Robust Test Statistic for Cooperative Spectrum Sensing Based on the Gerschgorin Circle Theorem

The Gerschgorin circle theorem was recently applied to build two detectors for the purpose of spectrum sensing in cognitive radio applications, the so-called Gerschgorin radius-based and the Gerschgorin disk-based detectors. However, the corresponding test statistics do not exhibit the constant false alarm rate (CFAR) property and are not robust against dynamical noise, the situation in which nonuniform noise levels fluctuate over time. In this paper, a novel and simple detector for cooperative or multi-antenna spectrum sensing is proposed. The test statistic is the ratio between the sum of the Gerschgorin radii and the sum of the Gerschgorin centers relative to the covariance matrix of the signal received from one or more transmitters. It is named Gerschgorin radii and centers ratio (GRCR) detector. The GRCR exhibits the CFAR property and is robust against nonuniform and dynamical noise and received signal powers, yet being able to detect time-uncorrelated or time-correlated transmitted signals over additive Gaussian noise and fading channels.