Sphericity minimum description length: Asymptotic performance under unknown noise variance

This paper revisits the model order selection problem in the context of second-order spectrum sensing in cognitive radio. Taking advantage of the recent interest on the generalized likelihood ratio (GLR), the asymptotic performance of the minimum description length (MDL) rule under unknown noise variance is addressed. In particular, by exploiting the asymptotically Chi-squared distribution of the GLR, a complete characterization of the error probability is reported, instead of approximating only the missed-detection probability as done in the literature.