Trade-off between Spectral and Energy Efficiencies in a Fading Communication Link

Spectral efficiency (SE) is one of the key performance indicators of wireless communications, and energy efficiency (EE) is an urgent need to tackle the challenges raised by the high demands of wireless traffics and energy consumption. However, these two important design criteria conflict with each other and a careful study of their trade-off is mandatory for designing future wireless communication systems. In this paper, we introduce an optimization problem to maximize the ergodic SE of a point-to-point communication link with a constraint on its minimum ergodic EE. We prove that, at optimality, the constraint on minimum EE is met with equality, and use it to provide a closed-form expression for finding the optimal water-filling level in a Nakagami-m fading channel with integer values of m. We exploit this formulation to investigate the relationship between SE and EE as a function of circuit power, power amplifier (PA) efficiency and channel power gain. We observe that the SE and EE always contradict with each other, however, the trade-off curve is non-linear. The curve is steeper at the extremities as compared to the middle region. Hence, a small sacrifice in EE from its maximum value may map into a significant gain in SE. Our simulations show that this gain in SE is a decreasing function of the circuit power and channel power gain while an increasing function of the PA efficiency.