Noise variance estimation for signal and noise subspace models

A noise variance estimator in complex-valued models with unknown signal subspace is proposed. Highlighted is that the conventional, maximum likelihood based, way of estimating the noise variance in this setting is highly biased, especially in low sample support and/or low SNR scenarios. The proposed estimator is derived by exploiting that the distribution of the sample covariance eigenvalues can be derived in closed form. By imposing the signal subspace structure, i.e., the multiplicity of the noise eigenvalue, the estimate is found through optimization of the considered likelihood. Simulations show that the presented approach, although slightly biased, improves on standard techniques.