Spectral-Energy Efficiency Tradeoff in Relay-Aided Massive MIMO Cellular Networks With Pilot Contamination

This paper concerns with a relay-aided massive multiple input multiple output (MIMO) cellular network. The exact closed-form expressions of both spectral efficiency (SE) and energy efficiency (EE) are obtained for downlink single-cell multi-user multi-relay massive MIMO transmission in the pilot-contaminated regime, where the number of users is larger than the pilot sequence length. Based on the theoretical results of SE and EE, we investigate the effects of some system parameters [such as number of antennas at the base station (BS), transmit power at the BS, and transmit power of each relay station (RS)] on system performance, and achieve the tradeoff between SE and EE by power control. Specifically, the tradeoff problem is solved by joint optimization over transmit power $P$ of the BS and transmit power $p_{r}$ of each RS, so as to maximize EE while satisfying the SE requirement. With the proposition that EE function is strictly quasi-concave with either $P$ or $p_{r}$ , we propose two optimization methods: 1-D searching and alternate optimization. Comparatively, the former achieves a better performance, while the latter has a lower complexity. Simulation results validate the effectiveness of the two methods.