In this paper we analyze the performance of random beamforming schemes in a multi-user Gaussian broadcast channel. Each user will have N > 1 receive antennas allowing optimal combining to be performed. To notify the transmitter of its current channel state, each user feeds back their SINR after LMMSE combining. Two feedback schemes are analyzed. The first scheme allows each user to feedback the post-processed SINR for each of the random transmit beams. To analyze this scheme, the distribution of the post-processed SINR is found. The second scheme attempts to limit feedback by allowing each user to feedback only the largest observed post-processed SINR and the index of the associated transmit beam. Using the Fr´echet bounds, the throughput of the reduce feedback scheme is bounded and shown to have the same asymptotic scaling properties as the first scheme. Empirically, it is observed that as the number of users in the system increases, the reduced feedback scheme approaches the throughput of the scheme without thresholding.