In this paper, we consider an underlay cognitive radio network where a large number of secondary users (SUs) can share the spectrum with a primary user (PU). We suppose that the cognitive base station (CBS) has multiple antennas and does not have the full channel state information (CSI) from SUs. We study the problem of SUs scheduling based on opportunistic beamforming. In order to reduce the feedback amount needed from SUs to CBS, we apply a multi-threshold mechanism to the signal to interference and noise ratio (SINR) feedback. The aim of our work is to determine analytically the optimal thresholds which reduce the number of SUs feeding back their SINR or the delay related to the average number of attempts (the average number of thresholds considered in the feedback process). To do this, we derive an accurate statistical characterization of the largest SINR for a particular user and we deduce upper bounds of the average number of SUs feeding back their SINR and of the average number of attempts.