Energy Efficiency and Spectral Efficiency Tradeoff in Type-I ARQ Systems

The optimum energy efficient and spectral efficient designs for type-I automatic-repeat-request (ARQ) systems in Rayleigh flat fading channels are studied in this paper. Three optimum designs are considered: the first scheme maximizes the energy efficiency (EE), or equivalently, minimizes the total energy per information bit without considering the spectral efficiency (SE); the second scheme minimizes a new metric, the energy per information bit normalized by the SE; and the third scheme maximizes the EE under the constraint of a minimum SE. For given physical and link layer parameters, such as hardware power consumption, coding rate, modulation, bit rate, number of overhead bits, and communication distance, the three schemes are optimized with respect to the average transmission energy and the number of information bits per frame. The fundamental EE-SE tradeoff curve is analytically identified via the optimization of the third scheme, and it is shown that the optimum EE is quansiconcave in SE in a type-I ARQ system. The optimum solutions to the first two schemes are special operating points on the EE-SE tradeoff curve. Computer simulation results verify the analytical solutions.