Transmission over wireless fading channels under quality of service (QoS) constraints is studied when only the receiver has perfect channel side information. Being unaware of the channel conditions, transmitter is assumed to send the information at a fixed rate. Under these assumptions, a two-state (ON-OFF) transmission model is adopted, where information is transmitted reliably at a fixed rate in the ON state while no reliable transmission occurs in the OFF state. QoS limitations are imposed as constraints on buffer violation probabilities, and effective capacity formulation is used to identify the maximum arrival rate that a wireless channel can sustain while satisfying statistical QoS constraints. Energy efficiency is investigated by obtaining the minimum bit energy and wideband slope expressions in both low-power and wideband regimes. The increased energy requirements due to the presence of QoS constraints are quantified. Comparisons with variable-rate/fixed-power and variable-rate/variable-power cases are given. Overall, an energy-delay tradeoff for fixed-rate transmission systems is provided.