Traditionally, the performance of blind SIMO channel estimates has been characterized in a deterministic fashion, by identifying those channel realizations that are not blindly identifiable. In this paper, we focus instead on the performance of Linear Equalizers for fading channels when they are based on blind channel estimates. Our analysis shows that with Zero Forcing Linear Equalizer (ZF-LE) at least one order of the diversity is lost depending on the way by which the scalar ambiguity that results from the blind channel estimation is resolved. However, in some Tx scenarios we are able to recover the diversity with MMSE-LE. Various Tx scenarios are considered in detail.