to mobility, changing environment, and multipath fading caused by the constructive and destructive superimposition of the multipath signal components [@book]. These random changes in the received signal strength lead to variations in the instantaneous data rates that can be supported by the channel. In addition, mobile wireless systems can only be equipped with limited energy resources, and hence energy efficient operation is a crucial requirement in most cases.

To measure and compare the energy efficiencies of different systems and transmission schemes, one can choose as a metric the energy required to reliably send one bit of information. Information-theoretic studies show that energy-per-bit requirement is generally minimized, and hence the energy efficiency is maximized, if the system operates at low signal-to-noise ratio (${{\text{\footnotesize{SNR}}}}$) levels and hence in the low-power or wideband regimes. Recently, Verdú in [@sergio] has determined the minimum bit energy required for reliable communication over a general class of channels, and studied of the spectral efficiency–bit energy tradeoff in the wideband regime while also providing novel tools that are useful for analysis at low ${{\text{\footnotesize{SNR}}}}$s. In many wireless communication systems, in addition to energy-efficient operation, satisfying certain quality of service (QoS) requirements is of paramount importance in providing acceptable 