On the optimum energy efficiency for flat-fading channels with rate-dependent circuit power: Time invariant case

This paper investigates the optimum energy efficiency (EE) and the corresponding spectral efficiency (SE) for a communication link over a flat-fading channel. The EE is evaluated by the total energy consumption for transmitting per message bit (TEPB). The link´s circuit power is modeled as ρ+φ(R)Watt, where ρ > 0 is the rate-independent part and φ(R) is a (not necessarily strictly) increasing and convex function of the bit rate R ≥ 0. The TEPB is proven to be a strictly quasiconvex function of the SE. Using this key property, the tradeoff between the TEPB and the SE is studied analytically. After that, the impact of system parameters on the optimum TEPB and SE are investigated for the general model as well as three special-case models of φ(R). Limits of the minimum TEPB and the optimum SE are also derived when either ρ or the channel power gain varies. A polynomial-complexity algorithm is also developed with the bisection method to find the optimum SE. The theoretical analysis is corroborated by numerical experiments.