Based on recent results that link sparsity hypotheses and robust statistics, a new noise variance estimator for application to communication electronic support is derived in this contribution. Numerical simulations indicate that the proposed estimator clearly outperforms the median absolute deviation measure. They also highlight the benefits of this new estimator for CFAR detection and show that it can be implemented in systems with high spectral scanning rate. The Matlab code corresponding to the proposed estimator is available at http://perso.telecom-bretagne.eu/pastor/software.