Fairness consideration in the wireless resource scheduling is important for enhancing the quality of user experience, despite the consequent throughput loss. This paper analyzes the associated penalty in obtaining a certain fairness criteria for multiple antenna broadcast channels. We define a fairness penalty as the achievable sum-rate difference in the regime of high SNR. We show that the penalty for the max-product fair scheduling criterion is negligible and derive the penalty for the max-min fair scheduling criterion. We analyze ergodic behaviors for the Rayleigh-fading channel both when the average SNRs are homogeneous (identical) and when the SNRs are heterogeneous (different). For the homogeneous case, it is shown that the penalty diminishes as the number of transmit antennas increases. For the heterogeneous case, there is an inevitable bias term which is associated with the users' SNR distribution.
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