Energy Efficiency Scaling Law for MIMO Broadcasting Channels

This letter investigates the energy efficiency (EE) scaling law for the broadcasting channels (BC) with many users, in which the non-ideal transmit independent power consumption is taken into account. We first consider the single antenna case with $K$ users, and derive that the EE scales as $\frac{{\log }_2\ln K}{\alpha }$ when $\alpha >0$ and ${\log }_{2}K$ when $\alpha = 0$,where$\alpha$ is the normalized transmit independent power. After that, we extend it to the general MIMO BC case with a $M$-antenna transmitter and $K$ users each with $N$ antennas. The scaling law becomes $\frac{{M \log_2 \ln NK}}{\alpha}$when$\alpha > 0$and$ \log_2 NK$when$\alpha = 0$.