## 2 Measurement Methodology  
### Measurement Equipment  
#### 2.1.1 V-Band Channel Sounder  
The architecture of the channel sounder is presented in Figure 1. We use a signal generator type R&S SMB100A and spectrum analyzer type R&S FSVR40 to perform angular PL measurements. The signal generator generates a radio frequency (RF) source in the frequency range 8.3 GHz to 12.5 GHz, which is up-converted to the V-band via a frequency multiplier type R&S SMZ75 with multiplication factor 6. The signal is transmitted with 5 dBm output power using an omnidirectional antenna type Mi-Wave 267V/385 with a gain of 3 dBi and gain variations of 2 dB over the complete band. The transmit (TX) antenna has an elevation half-power beamwidth (HPBW) of 45\({}^{\circ}\) and is connected via a WR-15 rectangular waveguide. The signal is captured by a directional horn antenna type Steatite QSH-SL-50-75-V-20 with a gain of 20 dBi, and down-converted to an intermediate frequency (IF) in the range 5 MHz to 2 GHz, using a harmonic mixer type R&S FS-Z75. The receiving (RX) antenna has an HPBW of 18\({}^{\circ}\) at 60 GHz in both the elevation and azimuth plane. The harmonic mixer has a conversion loss of 18 dB and uses a local oscillator in the frequency range 8.0 GHz to 12.8 GHz which is provided by a spectrum analyzer that displays the received power. The analyzer's displayed average noise level (DANL) is \(-\)174 dBm/Hz and the noise figure at the IF port is 3 dB. The mixer's conversion loss is taken into account by the spectrum analyzer, and the cable losses and noise figure of the equipment are calibrated out. Therefore, the error margin is mainly defined by the gain variations of the antennas.  
A frequency sweep with a continuous wave signal is executed, with a frequency ranging from 50 to 75 GHz, in steps of 500 MHz. For each frequency, we perform a power measurement with the spectrum analyzer, using 501 frequency points, a span of 5 MHz, and an averaging factor of 4. We perform an angular scan, i.e., the receiving antenna is rotated in steps of 12\({}^{\circ}\), which corresponds to the antenna's HPBW at the upper frequency. For every angle, we convert the measured received power \(\mathrm{P_{RX}}\) in dBm to directional PL in dB via (1), with \(\mathrm{P_{TX}}\) the transmit power in dBm, \(\mathrm{G_{TX}}\) the antenna gain of the TX antenna in dBi, and \(\mathrm{G_{RX}}\) the antenna gain of the RX antenna in dBi.  
\[\mathrm{PL}=\mathrm{P_{TX}}+\mathrm{G_{TX}}+\mathrm{G_{RX}}-\mathrm{P_{RX}} \tag{1}\]  
Omnidirectional PL is calculated by interpolating the directional received power to an angle step-size equal to the antennas' HPBW, and summation of interpolated linear power values. With a TX power of 5 dBm, a total antenna gain of 23 dBi, a DANL of \(-\)151 dBm  
Figure 1: V-band channel sounding architecture.  
using a resolution bandwidth of 100 Hz, a noise figure of 3 dB, a minimum signal-to-noise ratio (SNR) of 8 dB, and a conversion loss of 18 dB, the maximum measurable PL is 150 dB.  
Based on the angular PL measurements, we calculate the mean angle of arrival \(\mathrm{AoA_{avg}}\) via (2) and root-mean-square (RMS) angular spread \(\mathrm{AoA_{RMS}}\) via (3), with \(P_{RX}(\theta)\) the received power at an angle \(\theta\) in degrees.  
\[\mathrm{AoA_{avg}}=\frac{\sum_{\theta}P_{RX}(\theta)\cdot\theta}{\sum_{\theta} P_{RX}(\theta)} \tag{2}\]  
\[\mathrm{AoA_{RMS}}=\sqrt{\frac{\sum_{\theta}P_{RX}(\theta)\cdot\theta^{2}}{ \sum_{\theta}P_{RX}(\theta)}-\left(\mathrm{AoA_{avg}}\right)^{2}} \tag{3}\]