This paper investigates the impact of certain signal properties or information on the Statistical Resolution Limit (SRL), We consider at first the gain obtained when knowing fully or partially the transmitted signal in a cooperative scheme. After that, we consider some ’weaker’ information relative to signal’s properties (non-circularity and cyclo-stationarity) and show how they affect the SRL in different scenarios and in particular w.r.t the signal’s statistical dependency. Simulation results are provided to illustrate the concluding remarks and observations made out of this study.