  In this work, we consider the downlink of a multi-cell multiple-input
multiple-output (MIMO) system and find the jointly optimal number of base
station (BS) antennas and transmission powers that minimize the power
consumption while satisfying each user's effective
signal-to-interference-and-noise-ratio (SINR) constraint and the BSs' power
constraints. Different from prior work, we consider a power consumption model
that takes both transmitted and hardware-consumed power into account. We
formulate the joint optimization problem for both single-cell and multi-cell
systems. Closed-form expressions for the optimal number of BS antennas and
transmission powers are derived for the single-cell case. The analysis for the
multi-cell case reveals that increasing the number of BS antennas in any cell
always improves the performance of the overall system in terms of both
feasibility and total radiated power. A key contribution of this work is to
show that the joint optimization problem can be relaxed as a geometric
programming problem that can be solved efficiently. The solution can be
utilized in practice to turn on and off antennas depending on the traffic load
variations. Substantial power savings are demonstrated by simulation.
