the additional gain of vertical beamforming is limited. If there are high-rise buildings or high mountains, the gain from 64TRX can be higher. Figure 10.35 illustrates the case with vertical beamforming for high-rise buildings. 10.7 Massive MIMO and Beamforming Algorithms 192 antenna elements 12x8x2 XXXXXXXX Logical antenna configurations XXXXXXXX XXXXXXXX 64 TRXs XXXXXXXX 4x8x2 XXXXXXXX XXXXXXXX XXXXXXXX 16 TRXs XXXXXXXX XXXXXXXX XXXXXXXX 1x8x2 XXXXXXXX XXXXXXXX XXXXXXXX XXXXXXXX XXXXXXXX 8 horizontal beams 8 horizontal beams XXXXXXXX 4 vertical beams 1 vertical beam XXXXXXXX Dual polarization Dual polarization Figure 10.34 Physical and logical antenna configurations. Figure 10.35 Vertical beamforming. Figure 10.36 summarizes spectral efficiency simulations in the urban macrocell envi- ronment using the 3.5 GHz spectrum. The number of studied TRXs is 8, 16, 32, and 64. The number of antenna elements is 64, 128, and 192. We can note the following: For both 128 and 192 antenna elements, the spectral efficiency improves with increas- ing TRXs. For 128 antenna elements, 32 and 64 TRXs give around 20% and 25% spectral effi- ciency gains, respectively, over 16TRX operation. For 192 antenna elements, 32 and 64 TRXs give around 26% and 33% spectral effi- ciency gains, respectively, over 16TRX operation. 192 antenna elements with 16 TRXs give similar spectral efficiency when compared with 128 antenna elements. However, 64 TRXs give around 10% better performance with 192 antenna elements compared to 128. 10.7.2 Beamforming Algorithms 10.7.2.1 Grid of Beams and User-Specific Beams The 3GPP specifications do not define algorithms for beamforming in the base sta- tion. Some simulations assume ideal beamforming algorithms in the downlink and in the uplink. The computational complexity of such algorithms may be too heavy for practical implementation. Therefore, we need to study simplified algorithms that can 10 5G Performance Massive MIMO spectral efficiency bps/Hz/cell 16TRX 32TRX 64TRX 16TRX 32TRX 64TRX 128 antenna elements 