We consider the downlink multi-user multi-cell massive MIMO systems, assuming that the number of antennas at base station (BS) and the number of users are large. Our system model accounts for channel estimation, pilot contamination, and uniformly random user location distribution. We derive the approximation of area spectral efficiency (ASE) with regularized zero-forcing (RZF) precoding technique which are proven to be accurate via simulation results. With a realistic power consumption model considering not only transmit power but also the fundamental power for operating the circuit at transmitter and receiver, we analyze the performance of area energy efficiency (AEE). Finally, based on the proposed power consumption model, we determine the optimal number of antennas at BS aimed at maximizing AEE when transmit power is given.
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