1. Introduction
Millimeter wave (mm-wave) frequencies for 5G and beyond has gained considerable attention within the wireless industry. The main reason is the availability of large bandwidths from 30 GHz to 300 GHz that will be used to increase the wireless binary rates above 10 Gbps [
1]. The large blocks of spectrum in the mm-wave range allows the designers to tradeoff spectral efficiency for bandwidth in the early stages of deployment of this technology. Furthermore, the traditional sub-6 GHz bands cannot accommodate the enormous amount of data to be generated in 5G respect to previous generations.
The mobile data will reasonably grow up from 12 exabytes per month at the end of 2017 up to 77 exabytes per month in 2022 [
2]. The International Telecommunication Union (ITU) forecasted in its report of 2015 a global mobile data traffic of 5 zettabytes by the end of the 2020s [
3]. Thus, there is no doubt that a more comprehensive understanding of radio wave propagation is crucial to any further development of wireless networks. It is important to highlight the importance of advanced techniques as massive line-of-sight MIMO to achieve higher bit rates as seen in [
4] in vehicular communications, [
5,
6,
7] in wireless sensor networks and [
8] in ultra-dense networks; without a thorough analysis of the radio channel, massive MIMO will be of difficult application [
9].
The World Radio Conference established 5G frequency bands in WRC’15 [
10], and more recently in WRC’19 [
11]. Moreover, the first phase of EU’s Horizon 2020 5G Public Private Partnership initiative is investigating the 6–100 GHz frequencies, including mm-wave frequencies, for 5G’s ultra-high data rate mobile broadband, among other applications. While significant studies of the channel characteristics are available in the 28 GHz, 38 GHz, and 60 GHz bands for indoor and outdoor environments [
12,
13,
14,
15,
16,
17], only a few trials have been conducted in other mm-wave bands and for outdoor and outdoor–indoor environments, as well as scenarios with mobility. However, due to the higher frequencies and wider bandwidths, compared to existing standards below 6 GHz as 4G Long Term Evolution (LTE) and Wireless Local Area Network (WLAN), mm-wave applications need specific considerations.
Usually, the experimental analysis of the channel is completed using simulation tools. Ray-tracing and ray-launching techniques are among the most useful ones, due to their good tradeoff between accuracy and computational effort. Another advantage lies in the completeness of the analysis; path loss (PL), angular and delay parameters, frequency parameters as well as statistical parameters can be extracted from ray based simulations. Regarding the simulation of the mm-wave channel using the mentioned techniques, different analysis were done at 2 GHz and 18 GHz [
18], 28 GHz [
19], 28 GHz and 38 GHz [
20] and 60 GHz [
21].
To the best of the authors’ knowledge, little research dealing with MIMO propagation and channel modeling in the whole 1–40 GHz has been reported [
22]. As a preliminary work from the authors in [
23], the whole band was measured and several channel parameters were analyzed; particularly, the PL, the 1-slope model of the PL, the RMS DS, the 1-slope model of the RMS DS, and the K-factor were extracted. To compare the behavior of the channel throughout the whole band, the measured band was divided in sub-bands centered at 2 GHz, 10 GHz, 20 GHz, 30 GHz, 40 GHz with a 2 GHz bandwidth in all cases.
Some works have analyzed the channel behavior in specific bands between 1 GHz and 40 GHz; for example, the path loss was studied at 26 GHz and 39 GHz in [
24] and at 28 GHz in [
25,
26,
27,
28], but a comparison between the path loss model values of different sub-bands is still missing in the literature; we can find the same absence in the RMS DS studies; analysis of delay dispersion at specific frequencies or sub-bands can be found as, for instance, the work carried out in [
25] and [
28] at 28 GHz and in [
29] at 26 GHz. Therefore, the objectives of the paper are the following. First, this paper presents a 1–40 GHz analysis in a series of sub-bands covering the complete band. Secondly, a specific analysis in the main WRC’15/19 bands is presented. The core microwave bands were selected in WRC’15 to fulfill the increase in traffic requirements for usual dense urban networks. The 24.25–27.5 GHz and 37–43.5 GHz bands were identified by the WRC’19. These two low-mmW bands provide an additional 3.25 GHz and 6.5 GHz of contiguous blocks of spectrum to enable the 5G enhanced mobile broadband (eMBB) experience. Thus, the selected bands are the microwave band between 3.3–4.99 GHz, which includes the C-band and the 4.8–4.99 GHz band, and the low-mmW 24.25–27.5 GHz and 37–43.5 GHz bands. Moreover, following our previous work [
23], we show models of the RMS DS versus the transmitter-receiver distance in logarithmic units which can be useful to predict the time dispersion in indoor environments. To fulfill the first two objectives a frequency based wideband measurement system was used; a calibration step was performed to guarantee the precision in all measured positions and the antenna patterns were carefully measured to extract their effect from the channel parameters. Finally, the third principal aim of the work is to show, thanks to an accurate ray-tracing tool, what are the main propagation mechanisms contributing to the radio channel. A tunning phase was applied to find the best diffuse scattering model values and appropriate permittivity values were assigned to the materials present in the scenario to achieve the desired accuracy.
The paper is organized as follows.
Section 2 describes the experimental setting.
Section 3 presents PL and K-factor.
Section 4 shows the RMS DS analysis.
Section 5 shows the comparison with ray tracing simulations; the simulation results for WRC bands are included in
Appendix A. Finally, in
Section 6 the conclusions are explained.
Notations: all magnitudes are written in italics. The symbol denotes average, the symbol represents the expectation operator and the symbol denotes absolute value. The base-10 logarithm is represented as log10. The PL and relative received power are expressed in dB, the frequency in GHz, the K factor in dB and the delay spread parameters in nanoseconds.
3. Path Loss and K-Factor
The power delay profile (PDP), represented as
is computed by averaging, spatially or temporally, the channel impulse response,
over a local area:
where
t is the time variable and
τ is the delay.
The channel impulse response
is obtained by applying the inverse Fourier transform to the frequency response
. In this work, the PDP used to compute the delay parameters is obtained by applying the Hanning window in the frequency domain. This method improves the identification of the multipath components. The path loss is computed without applying the Hanning window so the energy is not altered.
Figure 4 depicts the PDP for a given position (number 10 in
Figure 2) using all measured bandwidth (see
Table 2). In the horizontal axis, the distance in meters is shown by multiplying the delay τ by the speed c. Due to the large bandwidth used, all main multipath components are clearly differentiated.
From the power delay profile in time domain, or from the transfer function in frequency domain, the wideband PL can be computed either by integrating in delay domain or averaging in frequency, respectively. The measurements include the antenna effect; therefore, the antenna influence should be extracted from the measurements. The antenna gain depends on the frequency and the direction whereas the PL includes the effect in all frequencies of the bandwidth of all multipath components coming from different directions. Therefore, an estimation of the antenna effect has to be used; we computed this effect as the mean of the antenna gain in all frequencies and the mean in the azimuthal plane, the plane where the main multipath components and the direct ray are present. Thus, two values
Gtx and
Grx, are found for the transmitter and receiver. The path loss equation is:
where
the expectation (average) operator,
f is the frequency, and
τ is the delay.
The PL of one specific component in the time domain can be extracted by applying the time gating technique. It is interesting to compare the total wideband PL with the LoS component PL as seen in
Figure 5. For the sake of comparison, we have included in
Figure 5 the PL evaluated using the Friis model which is observed to be in rather good agreement with the estimated LoS PL. Furthermore, due to the large bandwidth more energy is received from specular components, leading to a low K-factor as it will be shown later.
In order to study different bands, we have focused on central frequencies 5 GHz, 15 GHz, 25 GHz and 35 GHz with a 10 GHz bandwidth. The following expression has been used for computing the 1-slope model (Floating-Intercept (FI) path loss).
where:
L0 (in dB) and n are adjustment parameters;
d (in meters) is the distance between Tx and Rx, and
Xσ (in dB), a Gaussian random variable with zero means and standard deviation σ (in dB).
Figure 6 shows the relative received power mentioned bands and their corresponding 1-slope models.
The slope parameters of the model can be seen in
Table 3. The coefficient of determination R
2 indicates how linear the relation between variables is. We observe a nearly constant decay factor (
n), lower than 2 in almost all cases. This low value corresponds to typical indoor values in small distances, similar to those measured in [
22,
24,
25,
26,
27,
28,
33], as seen in
Table 4. Indoor scenarios are rich multipath environments and reverberation effects usually make the decay factor to fall below 2. All values correspond to FI model values in LoS conditions of the indicated references.
The 1-slope PL model has been also evaluated for the bands 3.3–4.99 GHz, 24.25–27.5 GHz and 37–40 GHz.
Figure 7 presents the PL as a function of these three bands and the respective 1-slope models (PL index shown in
Table 5). It is noteworthy that only 3 GHz of bandwidth was available for the 37–43.5 GHz band due to the maximum 40 GHz frequency measured in this contribution. The results indicate that even if both slope values are close, the PL index for the 37–40 GHz band is larger than that of the first band. Also, the PL for the second band is larger as expected with a 3.8 dB difference on average agreeing rather well with the 3.6 dB Free Space path loss.
The K-factor has been computed as the quotient between the LoS component and the remaining energy; the K factor is shown in
Figure 8.Negative values are measured, even in LoS situation due to the large number of contributions received (see PDP in
Figure 4). This has also been observed in [
19].
4. RMS Delay Spread
A wideband multipath channel can be described by its dispersion in the delay domain, which is usually expressed in terms of the RMS DS,
. The RMS DS is defined as:
In Equation (4),
τk are the delay values and
Pk the PDP values in linear units.
Figure 9 shows the RMS DS for a threshold of 30 dB, using the full bandwidth.
The RMS is observed to be increasing with distance, and as before, a simple 1-slope model can be derived:
where:
DS0 (in ns) and nDS are adjustment parameters;
d (in meters) is the distance between Tx and Rx, and
Xσ (in ns), a Gaussian random variable with zero means and standard deviation σ (in dB).
Figure 10 and
Table 6 summarize the results for RMS DS at bands 1–10 GHz, 10–20 GHz, 20–30 GHz, and 30–40 GHz using a 30 dB threshold.
From
Table 6 it is observed that the slope decreases with frequency. This effect is coherent with
Figure 5 and the increase of attenuation of multipath components. The R
2 parameter shows a significative linear relation between the distance in logarithm units and RMS DS.
In addition, the RMS DS slope values for the selected WRC bands is shown in
Figure 11, and tuned parameters in
Table 7.
Usually, when the RMS DS is measured in several positions, its mean and standard deviation are obtained because they are two of the main parameters of the RMS DS’ statistical characterization. In
Table 8, the mentioned parameters are shown for the WRC bands and they are compared with values found in the literature. To fairly compare the values of
Table 8 the type of environment is also shown. As seen in
Table 8, the mean and standard deviation of the RMS DS corresponding to large indoor environments, as large offices, industrial scenarios and auditoriums, are larger than the values found in a small open indoor environment, as the one measured in this work. This fact is due to the high number of large delay multipath components found in large rooms, whereas a fewer number of large delay components are present in smaller scenarios.
The multipath effect produces significant values of RMS DS which is one of the main factors that limit the system bit rate. Traditionally, the performance of the wireless system can be improved thanks to equalization algorithms; furthermore, the use of directional antennas along with circular polarizations can reduce the delay spread as indicated in [
34].