An Accurate Closed-Form Approximation of the Energy Efficiency-Spectral Efficiency Trade-off over the MIMO Rayleigh Fading Channel

Energy efficiency (EE) is gradually becoming one of the key criteria, along with the spectral efficiency (SE), for evaluating communication system performances. However, minimizing the energy-per-bit consumption while maximizing the SE are conflicting objectives and, thus, the main criterion for designing efficient communication systems will become the trade-off between SE and EE. The EE-SE trade-off for the multi-input multi-output (MIMO) Rayleigh fading channel has been accurately approximated in the past but only in the low-SE regime. In this paper, we propose a novel and more generic closed-form approximation of this EE-SE trade-off which exhibits a greater accuracy for a wider range of SE values and antenna configurations. Our expression, which can easily be used for evaluating and comparing the EE-SE trade-off of MIMO communication systems, has been utilized in this paper for analyzing the impact of using multiple antennas on the EE and the EE gain of MIMO in comparison with single-input single-output (SISO) system. Our results indicate that EE can be improved predominantly through receive diversity in the very low-SE regime and that MIMO is far more energy efficient than SISO at high SE over the Rayleigh fading channel