Herein, we consider asymptotic performance analysis of eigenvalue-based blind Spectrum Sensing (SS) techniques for large-scale Cognitive Radio (CR) networks using Random Matrix Theory (RMT). Different methods such as Scaled Largest Value (SLE), Standard Condition Number (SCN), John's detection and Spherical Test (ST) based detection are considered. The asymptotic sensing bounds for John's detection and ST based detection techniques are derived under a noise only hypothesis for sensing the presence of Primary Users (PUs). These asymptotic bounds are then used as thresholds for the SS decision and their performance is compared with other techniques in terms of probability of correct detection under both hypotheses. It is noted that the SLE detector is the best for a range of scenarios, followed by JD, SCN, ST. Furthermore, it is shown that noise correlation significantly degrades the performance of ST and JD detectors in practical scenarios.