Previous studies on multiuser multiple-input multiple-output (MIMO) mostly assume a homogeneous signal-to-noise ratio (SNR), where each user has the same average SNR. However, real networks are more likely to feature heterogeneous SNRs (a random-valued average SNR). Motivated by this fact, we analyze a multiuser MIMO downlink with a zero-forcing (ZF) receiver in a heterogeneous SNR environment. A transmitter with Mantennas constructs M orthonormal beams and performs the SNR-based proportional fairness (S-PF) scheduling where data are transmitted to users each with the highest ratio of the SNR to the average SNR per beam. We develop a new analytical expression for the sum throughput of the multiuser MIMO system. Furthermore, simply modifying the expression provides the sum throughput for important special cases such as homogeneous SNR, max-rate scheduling, or high SNR. From the analysis, we obtain new insights (lemmas): i) S-PF scheduling maximizes the sum throughput in the homogeneous SNR and ii) under high SNR and a large number of users, S-PF scheduling yields the same multiuser diversity for both heterogeneous SNRs and homogeneous SNRs. Numerical simulation shows the interesting result that the sum throughput is not always proportional to M for a small number of users.