<p>Because of bandwidth limitation and high data rate demands, wireless devices dedicated to the Internet of Things ask for high spectral efficiency as well as energy-efficient devices powered by battery with limited resources. To address the trade-off between spectral and energy efficiencies, numerous studies use simplified models of energy consumption for point-to-point communication. More advanced energy models do exist though they are rarely used, especially not for this specific trade-off. Previous works analyze the total consumed energy per transmitted bit for a M-QAM source through an AWGN channel and provide an optimal spectral efficiency minimizing this consumption. As a first approach in this work, we propose to extend this analysis to a Rayleigh fading channel when considering a M-QAM input source. In a second stage, a more advanced energy model, based on a hardware-dependent power amplifier power, is integrated into the previous analysis for both AWGN and Rayleigh fading channels. Computer simulations demonstrate that the proposed energy consumption model provides a valuable analysis of the trade-off between spectral and energy efficiencies. The effectiveness of the proposed approach is proved through several analysis.</p>