In this paper, we consider the scheduling problem where data packets from K input-flows need to be delivered to K corresponding wireless receivers over a heterogeneous wireless channel. Our objective is to design a wireless scheduler that achieves good throughput and fairness performance while minimizing the buffer requirement at each wireless receiver. This is a challenging problem due to the unique characteristics of the wireless channel. We propose a novel idea of exploiting both the long-term and short-term error behavior of the wireless channel in the scheduler design. In addition to typical first-order Quality of Service (QoS) metrics such as throughput and average delay, our performance analysis of the scheduler permits the evaluation of higher-order metrics, which are needed to evaluate the buffer requirement. We show that variants of the proposed scheduler can achieve high overall throughput or fairness as well as low buffer requirement when compared to other wireless schedulers that either make use only of the instantaneous channel state or are channel-state independent in a heterogenous channel.