This paper studies the multiuser diversity with constellation selection based on a virtual representation of realistic Multiple Input Multiple Output (MIMO) correlated channels. To realize multiuser diversity in slow fading channels, random beamforming is adopted. Random beamforming matrix exploiting virtual channel representation is constructed, which can match the channel matrix of the desired user better. Simultaneously, adaptive coded modulation is applied to each sub-channel of the selected user to improve the system performance further.