Based on a recently proposed L1-distance fairness measure, an achievable tradeoff between sum rate and fairness of multiple-input multiple-output (MIMO) downlink communications is provided in this thesis. Two communication schemes for MIMO broadcast channel (BC), the dirty paper coding (DPC) scheme and successive zero-forcing DPC (SZFDPC) scheme, are considered in this thesis. We propose an algorithm to find the achievable tradeoff of DPC scheme, and compare it to the optimal tradeoff of SZFDPC scheme. Simulation results show that the DPC scheme has a better sum rate-fairness tradeoff performance than SZFDPC.