## 4 Discussion
### Array Patterns for CB, MRT and ZF
In case the target UE resides in a shadow region (NLOS), several propagation paths typically contribute comparable amounts to the total received signal, e.g., if a UE is  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Scheme**} & \multicolumn{4}{c}{**CB**} & \multicolumn{4}{c}{**MRT**} & \multicolumn{4}{c}{**ZF**} \\ \hline \multirow{2}{*}{\(\mathbf{K}\)} & \multirow{2}{*}{\(\mathbf{N}\)} & \multirow{2}{*}{4} & \multirow{2}{*}{16} & \multirow{2}{*}{36} & \multirow{2}{*}{64} & \multirow{2}{*}{100} & \multirow{2}{*}{4} & \multirow{2}{*}{16} & \multirow{2}{*}{36} & \multirow{2}{*}{64} & \multirow{2}{*}{100} & \multirow{2}{*}{16} & \multirow{2}{*}{36} & \multirow{2}{*}{64} & \multirow{2}{*}{100} \\  & & & & & & & & & & & & & & & \\ \hline \multirow{2}{*}{\(\mathbf{\psi}\)} & 1 & 0.85 & 0.63 & 0.51 & 0.46 & 0.43 & 0.85 & 0.63 & 0.52 & 0.47 & 0.42 & 0.63 & 0.52 & 0.46 & 0.42 \\  & 2 & 0.92 & 0.58 & 0.44 & 0.37 & 0.33 & 0.79 & 0.53 & 0.42 & 0.35 & 0.31 & 0.44 & 0.37 & 0.32 & 0.29 \\  & 5 & 0.97 & 0.57 & 0.42 & 0.35 & 0.29 & 0.77 & 0.49 & 0.36 & 0.30 & 0.25 & 0.29 & 0.24 & 0.21 & 0.19 \\ \hline \multirow{2}{*}{\(\mathbf{\psi}\)} & 10 & 0.98 & 0.55 & 0.42 & 0.34 & 0.30 & 0.77 & 0.48 & 0.35 & 0.27 & 0.23 & 0.27 & 0.19 & 0.17 & 0.16 \\ \hline \multirow{2}{*}{\(\mathbf{\psi}\)} & 1 & 0.70 & 0.40 & 0.29 & 0.24 & 0.20 & 0.71 & 0.42 & 0.31 & 0.25 & 0.22 & 0.42 & 0.31 & 0.26 & 0.21 \\  & 2 & 0.83 & 0.40 & 0.27 & 0.21 & 0.17 & 0.66 & 0.38 & 0.27 & 0.22 & 0.19 & 0.31 & 0.24 & 0.19 & 0.17 \\ \hline \multirow{2}{*}{\(\mathbf{\psi}\)} & 5 & 0.92 & 0.42 & 0.28 & 0.22 & 0.18 & 0.65 & 0.36 & 0.27 & 0.20 & 0.16 & 0.20 & 0.15 & 0.13 & 0.11 \\  & 10 & 0.96 & 0.44 & 0.31 & 0.24 & 0.20 & 0.64 & 0.36 & 0.25 & 0.19 & 0.16 & 0.18 & 0.11 & 0.10 &obstructed by a building, the main propagation mechanisms that make the connection possible are over-the-rooftop diffraction and reflections from the walls of the surrounding buildings. As a result, the time-average pattern maximum is sometimes found _outside_ the cell boundary, as can be seen on the plots showing \(G_{MRT}^{36,5}\) (center-center) and \(G_{MRT}^{100,5}\) (bottom-center) in Figure 4.  
This effect is even more pronounced when ZF precoding was used, although the underlying reason is different. ZF minimizes interference between the target UEs by canceling the transmission via shared paths. In scenarios with a large number of spatially correlated UEs, a portion of the total transmit power dedicated to fighting interference may exceed that of the intended signal, i.e., an instantaneous ZF pattern can have higher gain in its side-lobes than in the beams intended to reach the UEs. Such effect is observed in the DOD distribution of \(G_{ZF}^{36,5}\) (center-right) in Figure 4. In the areas with the highest UE density, where both CB and MRT generally produced their time-average gain maxima most often, ZF showed very few time-average array pattern peaks. The ZF precoding efficiency generally increases with the \(N/K\) ratio [2]. For \(N=100\) the gain distribution (bottom-right) was similar in shape to what was obtained using MRT, although the spread of the gain locations noticeably exceeded both MRT and CB.