## 4 Discussion
### Normalized Time-Averaged Gain  
The CDFs in Figure 5 compare the \(G_{m}^{N,K}\) values for parameter configurations that correspond to those shown in Figure 4. Increasing the BS antenna count \(N\) decreases the normalized time-averaged gain for all studied schemes, with other parameters fixed. Two factors are contributing to this effect. First, the normalization coefficient in (12) is proportional to \(N\), which counteracts the increase in the absolute array gain. Second, with larger \(N\) the BS is capable of producing narrower beams, which are less likely to interlap in the DOD region within the cell, reducing the maximum of the average taken according to (11). Decreasing the connection time \(T\) also decreases the time averaged gain, that is, \(G_{m}^{N,K}(T=60\,\mathrm{s})>G_{m}^{N,K}(T=10\,\mathrm{s})>G_{m}^{N,K}(T=1\, \mathrm{s})\) for any fixed \(m\), \(N\) or \(K\). This observation is explained by the fact that the more independent UE sets are served in the averaging time-span \(T_{avg}\) (or, equivalently, the less the \(T\) value is), the closer \(G_{m}^{N,K}\) approaches the normalized average of instantaneous array patterns \(A(\theta,\varphi,\mathbf{t})\) over the cell. Conversely, in the limit of a single UE served with \(T=T_{avg}\), as follows from (10), (11), (12), the time-averaged gain is the instantaneous BS pattern maximum. In this case, the CB beamforming realizes the maximum theoretical gain \(G_{max}\) for the codebook directions coinciding with the maxima of the BS antenna element's individual pattern. This can be seen by substituting \(\mathbf{t}=\mathbf{b}_{k}\) into (10), assuming that the beam center DOD satisfies \((\theta_{k},\varphi_{k})=\arg\max_{\theta,\varphi}[A_{dip}]\). When only a single UE is connected at a time (\(K=1\), shown in black in Figure 5), CB, MRT, and ZF show very similar distributions of the normalized gain. In fact, as can be seen from (3) in the degenerate case of \(K=1\), the matrix inverse of \(\mathbf{H}\mathbf{H}^{H}\) becomes a reciprocal of a squared channel coefficient magnitude. The ZF and MRT formulations are then equivalent, with appropriately chosen normalization coefficients \(\alpha\) in (3). The minor discrepancy in Table 1 between the MRT and ZF (\(<\)1%) for \(K=1\) is due to the numerical round-off error propagation. The difference between \(G_{MRT}^{N,1}\) and \(G_{CB}^{N,1}\), gradually increases with increasing \(N\) and decreasing \(T\). Both \(G_{MRT}^{4,1}\) and \(G_{CB}^{4,1}\) are decreasing monotonously from around 0.85 for \(T=60\) s to around 0.66 for for \(T=1\) s (see Table 1). At \(N=100\), \(G_{m}^{N,1}\) drops rapidly to around a half of that (\(\simeq\)0.42 for CB) for \(T=60\) s, around a third (\(\simeq\)0.22 for MRT) for \(T\simeq 10\) s, and less than a quarter (\(\simeq\)0.15 for MRT) for \(T=1\) s.  
Increasing the number of simultaneously served UEs \(K\) was found to decrease \(G_{MRT}^{N,K}\) and \(G_{ZF}^{N,K}\) for any fixed \(N\) and \(T\). Increasing \(K\) decreased \(G_{CB}^{N,K}\) only for larger BS arrays (\(N\geq 16\)) for \(T=60\) s and led to its increase with any \(N\) for shorter connection time values. For \(N=4\), the CB time-averaged gain closely approached the theoretical maximum for any \(T\) and \(K\geq 5\) (\(G_{CB}^{N,K}\geq 0.9\)). This indicates that smaller BS antenna arrays implementing CB beamforming offer little to no benefit in terms of human EMF exposure reduction. In a realistic usage scenario, we take \(T\simeq 10\) s [6]. If the BS is equipped with 64 antenna elements, \(p^{95}\) of \(G_{CB}^{64,K}\) is just above 0.2 (around 7 dB reduction) for any \(K\). This is in agreement with the results in [7] obtained with a similar configuration in the outdoor macrocell environment. Direct comparison with [6] is not possible, as in that case the UE count was varied during the averaging time. Increasing the averaging time \(T\) to 60 s increases the 95 th percentile of \(G_{m}^{64,5}\) to 0.35 (4.6 dB) for CB, 0.30 (5.2 dB) for MRT, and 0.21 (6.8 dB) for ZF.