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 $\frac{\log_2 \ln K}α$ when $α> 0$ and $\log_2 K$ when $α= 0$, where $α$ 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 $\frac{M \log_2 \ln NK}α$ when $α> 0$ and $\log_2 NK$ when $α= 0$.

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