If the power amplifiers have a peak output power of about 20 dBm each, and are built using the most advanced techniques available today, the total power dissipation in such a panel will be 3 to 4 W. This already assumes the use of data converters with limited bit depths, since research shows that we may need less resolution to deliver the same signal integrity to the receiver when using multiple antenna elements than when using a single antenna. However, the data converters still need to run at high speed to handle large signal bandwidths. The power amplifies account for about 75% of total dissipation when transmitting, since the efficiency at mm-wave frequencies is very low.
There are techniques, such as Doherty circuit architectures and envelope-tracking schemes, to improve PA efficiency, but they need elaborate digital pre-distortion, which itself consumes power, to achieve acceptable spurious signal levels. At some point, the benefits of these techniques are outweighed by the energy cost of implementing them, and there is no net gain. This 4x4 array example is very close to that cross-over point, so there is little point in applying such energy-saving PA architectures. Even in case of a simple, pretty linear class AB amplifier some kind of energy-efficient linearization will be required anyhow. Fortunately massive MIMO systems will probably use TDD and the power amplifiers are only on part of the time.
In our example design, then, between 3 and 4 W of heat is being generated on a panel of 400 mm2. We want to cool it passively, for cost, energy consumption (in the fan), and reliability reasons. We can do this with an aluminum plate with cooling ribs, which has a cooling capacity of about 60 W/m2K. Assuming an ambient temperature of 60ºC (think of a basestation on a Middle Eastern rooftop in summer) and a temperature of 100ºC at the connection between the antenna panel and the transceiver chips, a quick calculation shows that we can cool 0.25 W/cm2 – or about a quarter of what the array needs. To dissipate the full 3.5 W will take a cooling panel of about 1400 mm2.
One way to fix this issue is to build a panel of the right size to cool the electronics, and then have it drive a separate, smaller antenna array panel. This may work for a 4x4 element array, but is impractical for arrays with tens or hundreds of antennas.