Certain blind channel estimation techniques allow the identification of the channel up to a scale or phase factor. This results in singularity of the Fisher information matrix (FIM). The Cramer-Rao bound, which is the inverse of the FIM, is then not defined. To regularize the estimation problem, one can impose constraints on the parameters. In general, many sets of constraints are possible but are not always relevant. We propose a constrained CRB, the pseudo-inverse of the FIM, which gives, for a minimum number of constraints, the lowest bound on the mean squared estimation error.