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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