Random beamforming with greedy scheduling policy in a heterogeneous setting is only fair as the number of transmit antennas M grows asymptotically. In practical systems with finite M and heterogeneous users having diverse large scale channel effects, in order to guarantee fairness among users and exploit multiuser diversity as well, an alternate scheduling policy is needed. In this paper, we leverage the cumulative distribution function based scheduling policy to achieve the two desired requirements and carry out both exact analysis and asymptotic analysis for systems employing random beamforming. The closed form sum rate with heterogeneous users is first derived by a recently proposed probability density function decomposition. We study individual scaling laws to examine the rate scaling for each individual user. Furthermore, asymptotic (in users) rate approximation is derived which tracks the exact performance well for small number of users.