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This paper investigates the optimum energy efficiency (EE) and thecorresponding spectral efficiency (SE) for a communication link operating overa flat-fading channel. The EE is evaluated by the total energy consumption fortransmitting per message bit. Three channel cases are considered, namely staticchannel with channel state information available at transmitter (CSIT),fast-varying (FV) channel with channel distribution information available attransmitter (CDIT), and FV channel with CSIT. A general circuit power model isconsidered. For all the three channel cases, the tradeoff between the EE and SEis studied. It is shown that the EE improves strictly as the SE increases from0 to the optimum SE, and then strictly degrades as the SE increases beyond theoptimum SE. The impact of {\kappa}, {\rho} and other system parameters on theoptimum EE and corresponding SE is investigated to obtain insight.Some of theimportant and interesting results for all the channel cases include: (1) when{\kappa} increases the SE corresponding to the optimum EE should keep unchangedif {\phi}(R) = R, but reduced if {\phi}(R) is strictly convex of R; (2) whenthe rate-independent circuit power {\rho} increases, the SE corresponding tothe optimum EE has to be increased. A polynomial-complexity algorithm isdeveloped with the bisection method to find the optimum SE. The insight iscorroborated and the optimum EE for the three cases are compared by simulationresults.

On the Optimum Energy Efficiency for Flat-fading Channels with Rate-dependent Circuit Power