Power Reduction Factor Modeling and Directional Power Control for EMF Compliance of Massive MIMO Base Stations

Abstract

Modern cellular radio base stations (RBS) employ beamforming to dynamically
steer radio frequency (RF) energy toward active users. This adaptive transmission
produces significant angular and temporal variations in the equivalent isotropically radiated power (EIRP). To account for these variations, electromagnetic
field (EMF) compliance assessment of RBSs rely on the usage of the EIRP envelope together with a power reduction factor (PRF). The EIRP envelope is given
in each direction by the maximum EIRP considering all beams supported by the
RBS. However, each beam will be used only for a fraction of time which is lower
than the averaging time associated with the EMF limits, typically 6 or 30 minutes.
PRF are therefore derived to obtain a more accurate estimate of the time-averaged
EIRP contributing to the RF EMF exposure in a certain direction.
This thesis presents a generalized method to compute PRF for beamforming
array antennas. The method combines precoding matrix indicator (PMI)-based
beam-usage probabilities with Monte Carlo simulation to evaluate time-averaged
exposure under full traffic load conditions. The proposed approach is validated by
reproducing published results for an 8-column antenna array, resulting in a PRF
of 29%, which is close to that from the previous studies [32%], it is subsequently
applied to a 16-column antenna (PRF = 16%).
In some countries, the use of PRF for EMF compliance assessments is subject
to the availability of RBS software features to monitor and/or control the timeaveraged EIRP. A previously developed feature divides the RBS coverage area into
8 horizontal segments and it ensures that the time-averaged EIRP in each segment
is not exceeding the PRF based threshold.
For existing power controllers employing cell-wide power back-off, we identify
the segmentation that maximizes aggregated output power while ensuring that the
set threshold is not exceeded in any of the segments. Using this metric, we show
that 8 horizontal segments are optimal for an 8-column array and 16 horizontal
segments are optimal for a 16-column array, using the PRF based threshold.
Then we introduce a per-segment controller that selectively reduces power only
in segments approaching the threshold, allowing maximum power transmission in
the other segments. Results from Monte Carlo simulations show that the persegment controller better preserves service in the directions not approaching the
threshold and improves aggregated performance metrics, at the cost of higher
implementation complexity and reduced performance in segments where power reduction is triggered.

Popular Abstract

Imagine a cellphone tower as a really smart flashlight, not just a boring old lantern.
Instead of shining light everywhere, it directs energy where is needed, improving
the performance towards active users making their connections more efficient. As
a result of this technology, known as beamforming, the tower’s transmitted power
is constantly changing from direction to direction and moment to moment. This
variability needs to be accounted for when assessing EMF compliance of base
stations with the existing regulatory requirements.
This thesis boils all that messy behavior down to one practical number: the
power reduction factor (PRF). PRF is the fraction of an antenna’s maximum power
that reflects the realistic time-averaged exposure, accounting for the beam-steering.
In plain terms, it’s the “adjustment factor” you apply to avoid overestimating how
much energy is actually being sent in any given direction over time.
The thesis tested its recipe by reproducing earlier results for an 8-column
antenna getting a PRF of 29% (close to previously reported value of 32%) and
extended the idea to a 16-column antenna calculating a PRF of 16%.
Beyond calculating PRF, this thesis also addresses how towers can actively
control their power output. Many regulators require towers to have software features in place to monitor and/or self-regulate output power. This is done by
checking the time-averaged power in slices of the service area, it is like cutting the
coverage pizza into slices. The author considered two ways to do this:
• A simple one-size-fits-all back-off: reduce power in all slices so every direction is below predefined threshold levels. It’s easy but wastes capacity in
directions that were already compliant. They found that dividing the coverage into 8 and 16 slices for the 8 and 16 column antenna respectively yielded
optimal balance between performance and computational intensity.
• A smarter per-segment controller: only pull back power in the slices that
would otherwise exceed limits, leaving other slices unaffected. This keeps
service better where it’s already compliant but is more complex to build and
can cause extended local drops where reductions are triggered.
The simulations show the smarter controller keeps more of the network’s performance intact overall, at the price of complexity and unevenness. In plain terms:
tailored, slice-by-slice control is like dimming only the overly bright parts of a stage
light instead of lowering the whole rig, you keep the show looking better, but the lighting system has to be smarter, and dimmed sectors may take longer to return
to full brightness.

• author: Chowdhury, Samin Ahmed
• supervisor: Mats Gustafsson
• organization: Department of Electrical and Information Technology
• course: EITM01 20252
• year: 2025
• type: H2 - Master's Degree (Two Years)
• subject: Technology and Engineering
• keywords: 5G, 6G, beamforming, radio base station, EMF compliance, power reduction factor, directional power control
• report number: LU/LTH-EIT 2025-1103
• language: English
• id: 9216036
• date added to LUP: 2025-12-10 12:09:31
• date last changed: 2025-12-10 12:09:31