## 2 Materials and Methods
### Data Processing  
An inverse Fourier transform is applied to the measured complex frequency responses of the radio channel in order to obtain the channel impulse responses \(h(t,\tau)\). Due to the limited frequency range of the measurements the frequency response is windowed and the impulse response may contain certain peaks originating from the side lobes of the window response in the time domain. To remove these peaks which do not correspond to actual propagation paths, as well as part of the noise, we set a threshold according to [6] and remove any sample below that threshold. Then we use those impulse responses to compute the power delay profile (PDP) as is shown in Equation (1) and represent the power received at a certain location as a function of the delay, \(\tau\)[7,8].  
\[PDP(\tau)=\frac{1}{N}\sum_{n=1}^{N}\left|h(\tau,n\cdot\Delta l)\right|^{2} \tag{1}\]  
where \(\Delta l\) is the step distance the receiver antennas are moved between successive measurements.  
As seen in Equation (1), there is an averaging process of N impulse responses to obtain the PDP. We used a sliding average with N = 11 to obtain the results of this paper [7]. Based on the PDP vectors some relevant time dispersion parameters were computed: The mean delay and the RMS delay spread. The mean delay is the first moment of the power delay profile, and it is defined as in Equation (2).  
\[\tau_{mant}=\frac{\sum_{k=0}^{\infty}PDP(\tau_{k})\tau_{k}}{\sum_{k=0}^{\infty }PDP(\tau_{k})} \tag{2}\]  
The RMS delay spread is even more interesting than the mean delay, as it is related to the inter-symbol interference (ISI) phenomenon giving cause to the irreducible bit error rate (BER) of the radio communication system. The RMS delay spread is the standard deviation of the delay of multipath components, weighted proportional to the energy transported by each of them. This RMS delay spread is also the square root of the second central moment of the PDP. The formula for the RMS  
Figure 5: Picture of the corridor during the measurement campaign.  
delay spread is shown in Equation (3) [8; 9]. The symbol interval used in the system has to be much larger than the RMS delay spread of the radio channel to avoid ISI [10].  
\[\tau_{rms}=\sqrt{\frac{\sum_{k=0}^{\infty}(\tau_{k}-\tau_{mean})^{2}PDP(\tau_{k })}{\sum_{k=0}^{\infty}PDP(\tau_{k})}} \tag{3}\]  
Both time dispersion and frequency selectivity are important factors when dealing with multipath channels. The most commonly used parameter to express frequency selectivity is the coherence bandwidth (Bc). This bandwidth is a statistical parameter, and can be defined as that part of the bandwidth where the channel response is considered flat. In other words, it represents the range of frequencies that experience correlated fading [11; 12].  
Computing the frequency correlation function (FCF or \(R\tau\)) is the first step to calculate the coherence bandwidth, Bc. The frequency correlation function is the Fourier transform of the PDP, as indicated in Equation (4). Typical values of the correlation level (\(\alpha\)) used to estimate Bc are 0.5, 0.7 and 0.9. The Bc is then that part of the frequency range where the FCF is above one of these levels [8; 11; 12].  
\[R_{\tau}(\Delta f)=\int_{-\infty}^{\infty}PDP(\tau)e^{-2\pi\Delta f\tau}d\tau \tag{4}\]  
Figure 6 depicts the estimation of coherence bandwidth at those correlation levels on the computed frequency correlation function for the auditorium at 40 GHz and received by antenna \"3\". The coherence bandwidths at which the frequency correlation function is above 0.9, 0.7 and 0.5, are, respectively 24 MHz, 138 MHz and 222 MHz.