## 2 Method
### Six-Minute Time-Averaged Gain (\(G_{\text{avg}}\))  
\(P_{\text{avg}}\) provides a measure of the total cell-wide time-averaged transmit power, but it does not provide information on its spatial distribution, which for a massive MIMO BS will vary over time depending on the beam selected for transmission. This was addressed by monitoring the BS antenna radiation patterns during operation. While 3 GPP allows for different beamforming schemes [14], the software running on the selected BSs at the time of the investigation supported single-user MIMO codebook-based beamforming with 8 CSI-RS ports. In this configuration, user equipment (UE) makes use of channel state information (CSI) reference signals (RS) transmitted from the BS to measure the radio channel quality. Based on this, the UE sends the CSI report, which contains a precoder matrix indicator (PMI), a rank indicator (RI), and some other indicators, to the BS. Then, the BS selects the corresponding beam(s) for downlink transmission of traffic data using the reported PMI and RI. The PMI and RI can be seen as a reference into a codebook of antenna precoding matrix (known  
Figure 1: Example of a six-minute time-averaged transmit power distribution (normalized) for a BS over a fifteen-minute interval. Each bar shows the number of samples falling into a specific range of values (100% would correspond to the BS operating at the maximum available power continuously for 6 minutes). The overlaying text represents the raw data as collected from the ENM, i.e., indicating that 966 samples of \(P_{\text{avg}}\) belonged to the 0–2.5% interval, 30 to 2.5–5%, 32 to 5–7.5%..304 to 22.5–25%. No samples in the example were obtained above the 22.5–25% interval.  
by both the BS and the UE) corresponding to a certain beam shape. The dynamic of the antenna radiation patterns was therefore studied by logging PMI and RI reported periodically to the BS by the UEs. As long as a UE is 'active' (i.e., receiving data from the BS), the BS will request PMI and RI reporting from it. Therefore, the time interval between consecutive reports collected in this study varied depending on the number of connected UEs with non-empty downlink transmit buffer (with a median value of 70 ms). For this study, a total number of about 13 million PMI and RI samples were collected in the 24 h.  
In Figure 2, antenna radiation patterns are shown as a function of the azimuth angle for a small subset of the available beam configurations (four out of sixteen patterns available for rank 1 transmission are displayed; transmission up to rank 4 was supported by the BSs [14]). For the 8 CSI-RS port codebook-based beamforming that was configured on the selected sites, only beam steering in the azimuth plane was supported (no vertical beam steering). A discussion about the effects of different beamforming implementations on the evaluation of the actual maximum exposure is provided in Section 4.  
The time-averaged gain, \(G_{\mathrm{avg}}\left(\varphi,\theta\right)\), was obtained by averaging the antenna radiation patterns corresponding to all PMI and RI reported by all 'active' UEs to the BS within every six-minute interval (a moving average was applied) over the 24 h. \(G_{\mathrm{avg}}\) was calculated at any time when a new CSI report was received. Those time intervals, for which no PMI and RI were reported, meaning that no data traffic was served by the BS or that the data logging had failed, were excluded from the analysis.