Energy-Efficient Precoding in Electromagnetic Exposure-Constrained Uplink Multiuser MIMO

User electromagnetic (EM) exposure is continuously being exacerbated by the evolution of multi-antenna portable devices. To mitigate the effects of EM radiation, portable devices must satisfy tight regulations on user exposure level, generally measured by specific absorption rate (SAR). To this end, we investigate the SAR-aware uplink precoder design for the energy efficiency (EE) maximization in multiuser multiple-input multiple-output (MIMO) transmission exploiting statistical channel state information (CSI). As the objective function of the design problem is computationally demanding in the absence of closed form, we present an asymptotic approximation of the objective to facilitate the precoder design. An iterative algorithm based on Dinkelbach's method and sequential optimization is proposed to obtain an optimal solution of the asymptotic EE optimization problem. Based on the transformed problem, an iterative SAR-aware water-filing scheme is further conceived for the EE optimization precoding design with statistical CSI. Numerical results illustrate substantial performance improvements provided by our proposed SAR-aware energy-efficient transmission scheme over the traditional baseline schemes.