3.1. Path Loss Results
For each position of the URA, the path loss between the Tx and Rx antennas can be derived by averaging the CTF in frequency and taking into account the gain of both antennas in the direct path [
13]. Thus, the path loss in logarithmic units,
PL, can be derived as (see
Appendix A):
where
d refers to the separation distance between the Tx antenna and the center of the URA for each Tx location, indicated as Tx-Rx distance;
is the
nth frequency sample; and
and
are the gain of the Tx and Rx antennas, respectively, in the direction defined by the direct path contribution. The term
takes into account the mismatch of the antennas, and it is calculated by:
and
being the
scattering parameter of the Tx and Rx antennas, respectively.
The measured path loss (cross marker) for each Rx antenna position in the URA in terms of the Tx-Rx distance is shown in
Figure 6. Both LOS and OLOS propagation conditions were considered. It is worth noting that the spread values of the path loss along the URA due to the short-term fading was less than 2.5 dB, being less in LOS than in OLOS conditions. It can be observed that the spread values of the path loss did not exhibit any correlation with the Tx-Rx distance. The mean value of the path loss (square marker) for each Tx location is also depicted in
Figure 6.
The floating-intercept (FI) path loss model has been widely used to describe the behavior of the path loss in terms of the Tx-Rx distance in the microwave frequency band, particularly at the sub-6 GHz band and more recently in mmWave frequencies [
5,
14], being one of the propagation models adopted in channel standardizations, e.g., the WINNERII Project and 3GPP channel models [
15,
16]. From the FI model, the path loss is given by:
being the floating-intercept parameter (an offset term);
the path loss exponent, related to both the environment and propagation conditions; and
a zero mean Gaussian random variable, in logarithmic units, with standard deviation
, which describes the large-scale signal fluctuations about the mean path loss over distance, also known in the literature as the shadow factor (SF). The FI model has a mathematical curve fitting approach over the measured path loss set without any physical anchor.
On the other hand, the close-in (CI) free space reference distance path loss model is also adopted in many studies related to mmWave propagation [
5,
8]. In the CI model, the path loss is given by:
where
is the free space path loss for a Tx-Rx distance equal to 1 m, with
the speed of light;
n is the path loss exponent; and
is the SF term. Note that the CI model has certain physical support in the sense that there is an intrinsic frequency dependence of the path loss included in the 1 m FSPL term. Taking into account that
is equal to 60.74 dB at 26 GHz, (
4) can be rewritten as:
The path loss fitting results for the FI and CI models are also depicted in
Figure 6. Both models exhibit a good fit and predict similar path loss values for the Tx-Rx distance considered, particularly in OLOS conditions. It is worth noting that the maximum path loss difference between LOS and OLOS conditions was about 5 dB, increasing with the Tx-Rx distance.
Table 2 and
Table 3 summarize the mean value and their 95% confidence interval of the FI and CI model parameters. These parameters were derived from the measured path loss using the minimum-mean-squared-error (MMSE) approach.
For the FI model, had a mean value equal to 1.46, with 1.39–1.53 the 95% confidence interval, in LOS conditions. In OLOS conditions, had a mean value equal to 1.88, with 1.80–1.95 the 95% confidence interval. For the CI model, had a mean value equal to 1.27 and 1.79 for LOS and OLOS conditions, respectively. The 95% confidence intervals were narrower for the CI model. In both models, the SF had a similar value, being lower in OLOS conditions.
The values of the path loss exponent derived in this study were lower than the values reported in [
8], where path loss exponents in the order or 2.0 and 2.2 were measured at 28 GHz in LOS and non-LOS (NLOS) conditions, respectively, for the FI model. Nevertheless, higher values have been reported for the CI model, where the path loss exponents equal to 1.45 and 2.18 have been measured in LOS and NLOS conditions, respectively. These differences can be explained because the frequencies are slightly different and, of course, due to both the particular characteristics of the environments and propagation conditions. It is worth noting that in our OLOS measurements, only a few MPCs were blocked by the PC monitors, whereas in NLOS conditions, the Tx and Rx were usually separated by different obstructions, and in many cases, the Tx and Rx were not located in the same room. Despite this, our results were more in line with those published by Rappaport et al. in [
5,
17] for indoor environments at 28 GHz in LOS conditions, where exponents equal to 1.2 and 1.1 were derived for the FI and CI models, respectively, considering omnidirectional path loss modeling (Rappaport et al. used a sliding correlation channel sounder, synthesizing an omnidirectional path loss model from directional measurements). Furthermore, the SF derived was 1.8 dB in both the FI and CI model, a value very close to that obtained by us for the CI model (1.75 dB).