We consider a time-division multiple access (TDMA) transmission scheme in MIMO broadcast channels. To cope with the fairness issue in heterogeneous networks with slow fading, an opportunistic scheduling algorithm based on the channel eigen-direction is investigated. In the system with sparse users, the mismatch between a random beamforming vector and the principle eigenvector of the channel incurs a throughput penalty. To reduce such a throughput loss, a multiple random beams selection (MRBS) scheme exploiting chordal distances is proposed. Two feedback schemes (unquantized or quantized chordal distances) are considered. The closed-form throughput expressions of the proposed schemes are derived.