#### Energy Efficiency Scaling Law for MIMO Broadcasting Channels

##### Jie Xu, Ling Qiu

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 $\alpha = 0$.

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