Energy-efficient power allocation for training-based multiple-input multiple-output system with and without feedback

In this study, the authors discuss energy-efficient power allocation for training-based multiple-input multiple-output (MIMO) system with and without feedback. Firstly, they consider the non-feedback MIMO system, where data power is equally allocated to transmit antennas. With pilot power fixed, the energy efficiency (EE)-optimal data power is derived based on the pseudo-concavity of the EE expression. When data power and pilot power are both variable, a convergent alternating optimisation algorithm is proposed to obtain EE-suboptimal data power and pilot power. Then, they consider the feedback MIMO system where data power is water-filling allocated to transmit antennas. Although the effective transmit antennas number at this scenario is discrete, they propose an algorithm to calculate it and its corresponding EE-optimal data power with pilot power fixed. When data power and pilot power are both variable, a similar convergent alternating optimisation algorithm is given. The numerical results demonstrate the EE performance of the training-based MIMO system with and without feedback. The impacts of multi-antennas configuration, circuit power and block length are also shown and analysed.