# Wideband Channel Modeling for mm-Wave inside Trains for 5G-Related Applications

Authors: Juan Moreno García-Loygorri; César Briso-Rodríguez; Israel Arnedo; César Calvo; Miguel A. G. Laso; Danping He; Florentino Jiménez; Vicente González Posadas
Journal: Wireless Communications and Mobile Computing
 (2018)

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## Abstract

Passenger trains and especially metro trains have been identified as one of the key scenarios for 5G deployments. The wireless channel inside a train car is reported in the frequency range between 26.5 GHz and 40 GHz. These bands have received a lot of interest for high-density scenarios with a high-traffic demand, two of the most relevant aspects of a 5G network. In this paper we provide a full description of the wideband channel estimating Power-Delay Profiles (PDP), Saleh-Valenzuela model parameters, time-of-arrival (TOA) ranging, and path-loss results. Moreover, the performance of an automatic clustering algorithm is evaluated. The results show a remarkable degree of coherence and general conclusions are obtained.


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## Body

## 1. Introduction

Metro lines are one of the most acknowledged high-density scenarios, as well as stadiums and other large venues. These places are a clear target for 5G mobile [1] deployments, which is intended to provide very large throughputs and ultra-low latencies in dense environments and sustain a high number of simultaneous connections, among others. It is noteworthy that it is possible to have more than 1200 people inside a 120-meter long train, which means around 5 persons/m2. There are many railway-related applications like Train-to-Ground, Train-to-Train, Train-to-Car, Train-to-Satellite, intratrain communications, and so on, which are usually grouped under the T2X notation, or perhaps in the more generic V2X notation, where “V” stands for vehicular. In this paper we focus on the intratrain channel, which has an enormous importance to provide connectivity to passengers. Also, this wireless channel could be used for the internal communications of the train, which is one of the objectives of the EU-H2020 Roll2Rail Project [2].There is still some vagueness in the frequency bands to be assigned, but some things are clear: there will be 5G deployments both above and below 6 GHz [3]. This fact has attracted much attention on millimeter waves (mm-wave) in order to have larger bandwidths than in lower frequencies, where the entire spectrum has been allocated. For example, in USA both the 28 GHz (27.5–28.35 GHz) and the 37 GHz band (37–40 GHz) have been licensed for mobile applications; in both China and the European Union, the 26 GHz band (24.25–27.5 GHz) is the chosen one. On the other side, there is no clear direction on which bands will be allocated for unlicensed use, but the 37 GHz band (37–37.6 GHz) is perhaps the most promising one. All these spectrum policies lead to the need of a proper channel model for 5G-related scenarios in the aforementioned bands.There are many papers related to channel measurements and modeling in railway scenarios but, as far as we know, only very few of them are focused on mm-wave for intratrain environments (i.e., the work carried out by ETRI in Korea [4]). Regarding the Train-to-Ground link for high-speed trains, a very complete reference is [5] but it is focused on frequencies below 6 GHz; for tunnels which are a very common scenario in railways, there are many papers, like [6, 7]; inside metro stations there are many research papers like [8]; and for mm-wave research in railways there are some ray-tracing simulations in mm-wave and THz [9]. For intratrain link, there are some recent papers but below 6 GHz [10, 11].The structure of the paper is the following: in Section2 we will describe the experiment setup, covering the environment details, the measurement setup, and the processing of the data; in Section 3 we will explain all the results obtained from the measurements, and, finally, in Section 4 a conclusion and some discussion are provided.


## 2. Experimental Setup

### 2.1. Environment

The environment for the measurement campaign is the train interior of a metro train. It is depicted in Figures1 and 2. This vehicle under test is a Madrid Metro train of the s3000 series. It has the capacity to carry 442 persons in the four-car consist, which amounts to 132 persons on each car.Figure 1
Rolling stock used in the measurements campaign. (a) The train interior and (b) the exterior are shown.
(a) (b)Figure 2
Top and lateral view of one car of the s3000 rolling stock.The maximum dimensions of the train are2.3×3.6×59.7 meters, but the interior of the train has a maximum section of 2.2 m × 2.2 m. As usual in this type of trains, there are many handholds, seats, and other furniture. The seats are resin-coated reinforced with glass fiber and both the handholds and the roof are made of stainless steel covered with a 500 micrometers thick yellow painting. The floor is made of stratified rubber, the windows are made of laminated glass and the doors are of aluminum and glass like the windows’ one. This layout and materials are very common in modern subway trains, with very small differences between them.


### 2.2. Measurement Setup

The measurements were carried out using an Agilent 8722ES Vector Network Analyzer (VNA). The approach for this VNA-based measurement is the usual one: connecting the transmitter to port 1 and the receiver to port 2, measure the s21 parameter, which is a good approximation for the channel transfer functionH(f) [12]. The connection of both antennas to the VNA ports was done using phase stable RTK040 wires. The length of this wire was 18 m and we used 2.4 mm connectors.All the measurements but one were carried out using horn antennas (see Figure3), model 22240 by FLANN, which is an antenna designed to be used in the 26.5–40 GHz, which is the band where our experiment was focused on. The gain of this antenna is 20 dB, and the variations of this parameter are bounded to 2 dB in the band of interest, which gives us a great stability. In the last measurement an omnidirectional antenna (Vivaldi, see Figure 3) was used in the receiver as a replacement of the horn antennas mentioned before.Figure 3
(a) Measurement setup (from the receiver’s point of view). (b) Both horn antennas are shown.
(a) (b)The measured positions for the receiver (the transmitter was fixed) are depicted in Figure2. We measured at five different transmitter-receiver distances d = 2, 4, 6, 9.5, 17 m, moving only the receiver (in the last one the receiver is in the next train car). The height of both the transmitting and the receiving antennas was 1 m over the train floor. Both the transmitter and the receiver were placed inside the train at all time, as well as the VNA. In the measurement setup the number of dots in the 13.5 GHz wideband (26.5–40 GHz) was 1601. The processing of the data was done offline with MATLAB. As we explain in a more detailed form later in this paper, we decided to employ an automatic clustering algorithm instead of identifying them by visual inspection.


## 2.1. Environment

The environment for the measurement campaign is the train interior of a metro train. It is depicted in Figures1 and 2. This vehicle under test is a Madrid Metro train of the s3000 series. It has the capacity to carry 442 persons in the four-car consist, which amounts to 132 persons on each car.Figure 1
Rolling stock used in the measurements campaign. (a) The train interior and (b) the exterior are shown.
(a) (b)Figure 2
Top and lateral view of one car of the s3000 rolling stock.The maximum dimensions of the train are2.3×3.6×59.7 meters, but the interior of the train has a maximum section of 2.2 m × 2.2 m. As usual in this type of trains, there are many handholds, seats, and other furniture. The seats are resin-coated reinforced with glass fiber and both the handholds and the roof are made of stainless steel covered with a 500 micrometers thick yellow painting. The floor is made of stratified rubber, the windows are made of laminated glass and the doors are of aluminum and glass like the windows’ one. This layout and materials are very common in modern subway trains, with very small differences between them.


## 2.2. Measurement Setup

The measurements were carried out using an Agilent 8722ES Vector Network Analyzer (VNA). The approach for this VNA-based measurement is the usual one: connecting the transmitter to port 1 and the receiver to port 2, measure the s21 parameter, which is a good approximation for the channel transfer functionH(f) [12]. The connection of both antennas to the VNA ports was done using phase stable RTK040 wires. The length of this wire was 18 m and we used 2.4 mm connectors.All the measurements but one were carried out using horn antennas (see Figure3), model 22240 by FLANN, which is an antenna designed to be used in the 26.5–40 GHz, which is the band where our experiment was focused on. The gain of this antenna is 20 dB, and the variations of this parameter are bounded to 2 dB in the band of interest, which gives us a great stability. In the last measurement an omnidirectional antenna (Vivaldi, see Figure 3) was used in the receiver as a replacement of the horn antennas mentioned before.Figure 3
(a) Measurement setup (from the receiver’s point of view). (b) Both horn antennas are shown.
(a) (b)The measured positions for the receiver (the transmitter was fixed) are depicted in Figure2. We measured at five different transmitter-receiver distances d = 2, 4, 6, 9.5, 17 m, moving only the receiver (in the last one the receiver is in the next train car). The height of both the transmitting and the receiving antennas was 1 m over the train floor. Both the transmitter and the receiver were placed inside the train at all time, as well as the VNA. In the measurement setup the number of dots in the 13.5 GHz wideband (26.5–40 GHz) was 1601. The processing of the data was done offline with MATLAB. As we explain in a more detailed form later in this paper, we decided to employ an automatic clustering algorithm instead of identifying them by visual inspection.


## 3. Channel Model

### 3.1. Path-Loss

The path-loss is obtained from the measured data in the VNA. This result is the average in the entire frequency range (26.5–40 GHz) [13]. N equals 1601 which is the number of dots(1)PL=10log10⁡1N∑i=1NHfi-2.The obtained values are detailed in Table1.Table 1
Path loss [dB].
Distance  [m] θ 0° 45° 90° 135° 180° P L - 2.0 29.37 61.71 63.19 60.70 57.72 54.54 4.0 36.77 61.24 61.69 60.78 62.75 56.65 6.0 40.62 60.86 61.23 62.58 62.26 57.51 9.5 45.52 53.98 65.84 64.67 65.23 59.05 17.0 54.94 54.97 66.48 66.71 66.93 62.01The path-loss increases together with the distance, both the average path-loss and the LOS (θ = 0°) scenario, as it was expected. Regarding the influence of the angle (θ), for θ = 0° the received power is the maximum one for every measured distance, and we can see a great increase in the path-loss when we misalign the antennas θ = 45°, 90°, 135°, 180°. This increase is more significant at lower distances. For example, the average path-loss increases 31.46 dB at d = 2 m and only 8.84 dB at d = 17 m. This is because at higher distances the multipath is less severe and the impact of reflections on handlers and other diffuse scatters is significantly lower (the so-called Waveguide Effect).The variation of the path-loss for the different angles (given a fixed distance) is more or less random. However, at the highest distancesd = 9.5, 17 m the angle that experiences a lower path-loss is clearly θ = 45°. The reason for this is the same as before: the Waveguide Effect. To properly assess the Waveguide Effect, we have calculated the path-loss exponent (n) for 0°. The obtained value is 1.6, which is below the free-space one (n=2) so, under this premises, we can conclude that we are experiencing this effect inside the train at this frequency band. The whole one-slope model is shown in (2)Lx=L0+10nlog10⁡dd0=29+16.0log10⁡d,where Lx is the total losses in dB, d0 is the reference distance, L0 is the losses at the reference distance, n is the path-loss exponent, and d is the distance.We also measured the path-loss at a given distance (d = 9.5 m) with six people moving around between the transmitter and the receiver. This impact is an average path-loss 2.28 dB higher and some fading 30 dB deep.


### 3.2. Ranging

If we measure the time of arrival (TOA) we can easily estimate the distance between the transmitter and the receiver(3)d~=c·τ,where τ is the time for the first peak in the PDP (i.e., the first path that arrives to the receiver) and c is the speed of light. In Table 2 we can see the estimated distances using this TOA-based technique to estimate the distance between transmitter and receiver. The estimation based on the LOS path is the most accurate (5.56% error in the worst case and 0.35% in the best one); for θ = 45° it is slightly worse and for the other angles we have large errors. This method seems to be more accurate when the distance increases (for d = 17 m, the error is lower than 3% for θ = 0°, 45°, and 90° and 13.20% for θ = 180°). The reason behind this good performance at higher distances is because the impact of reflections from handlers and other furniture is less significant than at lower distances.Table 2
Estimated distances for TOA-based method (m).
Distance [m] θ 0° 45° 90° 135° 180° 2.0 2.11 2.02 2.51 2.51 14.09 % error<10% 10–50% >50% 4.0 4.18 6.42 6.38 13.16 5.02 6.0 6.13 7.02 6.40 8.69 11.20 9.5 9.47 10.00 10.49 10.91 9.8 17.0 16.89 16.89 17.47  19.24


### 3.3. Power-Delay-Profiles and Clustering

Regarding the Power-Delay Profiles (PDP) we have computed them for all the scenarios described in Section2. In Figures 5–9 we can see the PDPs for d = 2, 4, 6, 9.5, 17 m and an extra one for the omnidirectional antenna at a distance of d = 4 m.Multipath components are clustered according to Saleh-Valenzuela [14] model and the estimation of the clusters that these multipath components form has been done using the automatic algorithm proposed in [15]. This algorithm takes into account both the amplitude and time delay to form the clusters. The usual approach to identify multipath component clusters is the visual inspection [15] but we found preferable to use an automatic algorithm. The main advantage of this algorithm is that it allows us to do a fast estimation of the clusters, and that it takes into account both time and amplitude values. Therefore, the clustering process is very dependent on the thresholds we propose (as it is acknowledged in [15]), but after some iterations, it seems to have a good performance if we look to Figures 5–11. In these figures we have highlighted in red the clusters that this algorithm has identified (dots in red are the first ray from a cluster).Ford = 2 m (Figure 5) we can see that the number of clusters increases with θ. For θ = 90° the number of clusters increases significantly, and for θ = 180° it decreases. This is an expectable result, because as we go towards a pure NLOS scenario, with many scatters between transmitter and receiver, this leads to different times of arrival (i.e., clusters).Regarding thed = 4 m scenario (Figure 6) the number of clusters does not increase significantly from the previous scenario, but we have more or less the same dependence to θ. The difference between θ = 0° and θ = 45° is small if we visually inspect both PDPs, but for θ = 180° we have more clusters in the receiver. In our opinion, this is attributable to the layout of the train that makes this PDP possible for this angle. If we employ an omnidirectional antenna in the receiver (Figure 11) we can see that we are able to see a significantly higher number of clusters. This is an expected result because the wider radiation pattern allows more different directions of arrival to the receiver. We still have a strong first cluster, associated with the LOS direct link plus four more clusters for the reflection through the train car.In Figure7 we can see the PDPs for d = 6 m. The number of clusters remain stable and similar to d = 2, 4 m for θ = 0°. For θ = 45° we see more clusters for the same reason as before: losing the LOS link leads to more reflections due to the presence of obstacles inside the train. This is coherent with the fact that for θ = 90°, 180° the number of clusters does not increase.Ford = 9.5 m (Figure 8), the estimated number of clusters is stable (and lower than before) for both θ = 0°, 45° because we are experiencing a significant Waveguide Effect and there are many rays that are suppressed. For θ = 90°, 180° we have the same increase in the number of clusters experienced before. So the pattern does not change from the d = 6 m scenario. Nevertheless, for this distance we also measured the channel with people moving randomly inside the train (between transmitter and receiver). The result can be seen in Figure 10, and the number of clusters increases significantly from any other angle at the same distance. The reason is the expected one: people act as supplementary scatters, so the PDP changes (we have more clusters, obviously). This result is very important because intratrain-based applications will work on trains with people onboard.Finally, ford = 17 m (Figure 9), if we inspect visually the PDPs for the four angles considered, we can see that it does not change significantly, but the algorithm estimates 2, 6, 3, and 4, clusters for θ = 0°, 45°, 90°, 180°. This is perhaps the most debatable outcome of the algorithm. In this case, the distance is significantly higher than in the other scenarios, where the Waveguide Effect is dominant and the PDP is smoother (which means fewer clusters). It is also the scenario where we have less differences between angles (together with d = 2 m, where there were almost no scatters between transmitter and receiver). An expected result is that, at a distance like this, the power is mostly concentrated on the first cluster of rays that arrives to the receiver (this is easy to see in the θ = 0°, obviously). This is another consequence of the “Waveguide Effect.”


### 3.4. Saleh-Valenzuela Parameters

The classical Saleh-Valenzuela (SV) model is intended for indoor scenarios and we have chosen it for its statistical nature and simplicity: it describes the channel with only four parameters (λ, Λ, γ, and Γ). Λ is the cluster arrival rate, which is assumed to follow a Poisson distribution [14], the same distribution as the ray arrival rate “λ”; “γ” is the exponential decay within a cluster; and “Γ” is the exponential decay for the whole PDP. In Table 3 we have included our estimation of these four SV parameters for all the scenarios that we have measured.Table 3
Saleh-Valenzuela parameters.
Distance [m] Parameter Angle [°] Average 0° 45° 90° 180° 2.0 γ 0.058 0.172 0.264 0.124 0.155 Γ 0.046 0.196 0.448 0.139 0.207 λ 3.944 3.728 3.728 4.065 3.866 Λ 0.152 0.151 0.302 0.201 0.202  4.0 γ 0.236 0.256 0.198 0.104 0.199 Γ 0.323 0.338 0.249 0.129 0.260 λ 3.600 3.563 3.742 3.965 3.718 Λ 0.100 0.151 0.152 0.201 0.151  6.0 γ 0.116 0.173 0.199 0.221 0.177 Γ 0.173 0.209 0.206 0.248 0.209 λ 3.929 4.000 3.476 3.800 3.801 Λ 0.101 0.250 0.101 0.100 0.138  9.5 γ 0.090 0.118 0.351 0.315 0.219 Γ 0.136 0.140 0.395 0.429 0.275 λ 3.700 3.576 4.115 3.650 3.760 Λ 0.200 0.201 0.251 0.250 0.226  17.0 γ 0.145 0.117 0.200 0.187 0.162 Γ 0.203 0.163 0.158 0.208 0.183 λ 3.700 3.513 3.539 3.800 3.638 Λ 0.150 0.301 0.152 0.100 0.176If we look at the average SV parameters in the column on the right of Table3, we can see that we have a “slow” decay. This is because the distance between the objects that reflect the signal is very low, and all of them are very similar (metallic surfaces). That is for the “overall decay” (parameter Γ). If we look inside the clusters, we can see that they decay rapidly (parameter γ), which means a higher attenuation (due to the high frequencies) and very few reflections (apart from the first one). Anyway, this is coherent because the clustering algorithm that we chose is adequate, because the calculation of SV model parameters is very dependent on the clustering algorithm.Explaining properly all the estimated SV parameters would take a lot of time, so here we will discuss some of the most significant parameters. First of all, it is noteworthy thatλ (ray arrival rate) has small variations no matter in which scenario we are. This parameter is very dependent on the limitations of the measurement devices, so perhaps with a different device able to increase the number of resolvable rays this parameter could experience higher variations. The main difficulty to improve this is that the VNA employed is a state-of-the-art device, so it will take some time to achieve a better resolution in this parameter.The cluster arrival rate (Λ) has a direct relation with the number of clusters and we have gone through this parameter in Section3.3. Regarding the overall decay rate (Γ), it is generally higher than the cluster decay rate (γ), which is an expected result. Moreover, the clustering algorithm does not allow negative slopes (if it resolves a cluster with a negative slope; that cluster is joined to the next one) which increases—in general terms—the values of γ. If we look at some particular results, we can see that the Γ for the shortest distance (d = 2 m) and LOS scenario has the smallest value calculated. For higher distances and angles, the Γ increases, but the general trend is to decrease (but for d = 2 m), which is an expected result. It is hard to find a clear pattern in the angle variation, but a possible reason behind this behavior is that the first ray of the cluster is not always the one with more power [15]. This could lead to an underestimation of the Γ parameter.We also took two more measurements: with people moving around inside the train (d = 9.5 m) and also using an omnidirectional antenna (d = 4 m). The Saleh-Valenzuela model parameters for the omnidirectional antenna are γ = 0.187; Γ = 0.208; λ = 3.800; Λ = 0.277. This is similar “γ” and “λ” for horn antenna in the receiver at the same distance. The apparent invariability of “λ” was discussed before and for “γ” it could be an impact of the clustering algorithm, which prevents higher variations inside a cluster, which leads to an approximately constant “γ.” The number of clusters is significantly different, as the parameter “Γ” highlights, so this is coherent with the “conservative” nature (regarding “γ”) of the clustering algorithm.If we consider the difference between having people in motion between transmitter and receiver (the SV parameters areγ = 0.134; Γ = 0.188; λ = 3.745; Λ = 0.277) and not, using horn antennas and the same distance, equal to 9.5 m, we can see that we have a lower “Λ” when we have people in motion, and also a lower “Γ.” It is also noteworthy that the average parameters using horn antennas (this is θ = 0, 45°, 90°, 180°) are a good approximation of the scenario with an omnidirectional antenna. This is a coherent result because using an antenna like this is the same as we average the contributions from all directions. However, as we can see in Figure 4, the radiation pattern of the Vivaldi antenna is not perfectly omnidirectional, so this “averaging” process is not as precise as it could be otherwise.Figure 4
Radiation patterns at 25 GHz for E-plane (a) and H-plane (b) for the Vivaldi antenna. (c) The antenna is shown being installed near the top of one of the handholds of the train.
(a) (b) (c)Figure 5
Power-Delay Profile and cluster identification ford = 2 m. (a) θ = 0°. (b) θ = 45°. (c) θ = 90°. (d) θ = 180°.
(a) (b) (c) (d)Figure 6
Power-Delay Profile and cluster identification ford = 4 m. (a) θ = 0°. (b) θ = 45°. (c) θ = 90°. (d) θ = 180°. For the θ = 0° setup there is almost no room for reflections to arrive to the receiver. As we increase θ, many more clusters surge.
(a) (b) (c) (d)Figure 7
Power-Delay Profile and cluster identification ford = 6 m. (a) θ = 0°. (b) θ = 45°. (c) θ = 90°. (d) θ = 180°. At this distance, the clustering algorithm behaves in a very similar manner as for d = 2 m, but for θ = 90°, 180° there are fewer clusters than in d = 2 m.
(a) (b) (c) (d)Figure 8
Power-Delay Profile and cluster identification ford = 9.5 m. (a) θ = 0°. (b) θ = 45°. (c) θ = 90°. (d) θ = 180°. We still have many clusters, especially in the angles different to 0°.
(a) (b) (c) (d)Figure 9
Power-Delay Profile and cluster identification ford = 17 m. (a) θ = 0°. (b) θ = 45°. (c) θ = 90°. (d) θ = 180°. The automatic algorithm identifies very few clusters for the θ = 0°, but many more rise if we misalign the antennas.
(a) (b) (c) (d)Figure 10
Power-Delay Profile ford = 9.5 m, θ = 0°; using horn antennas and people moving around between transmitter and receiver. The effect of people increases the number of clusters and impacts the overall PDP.Figure 11
Power-Delay Profile ford = 4 m, with the Vivaldi antenna in the receiver. The automatic algorithm identifies 5 clusters.


## 3.1. Path-Loss

The path-loss is obtained from the measured data in the VNA. This result is the average in the entire frequency range (26.5–40 GHz) [13]. N equals 1601 which is the number of dots(1)PL=10log10⁡1N∑i=1NHfi-2.The obtained values are detailed in Table1.Table 1
Path loss [dB].
Distance  [m] θ 0° 45° 90° 135° 180° P L - 2.0 29.37 61.71 63.19 60.70 57.72 54.54 4.0 36.77 61.24 61.69 60.78 62.75 56.65 6.0 40.62 60.86 61.23 62.58 62.26 57.51 9.5 45.52 53.98 65.84 64.67 65.23 59.05 17.0 54.94 54.97 66.48 66.71 66.93 62.01The path-loss increases together with the distance, both the average path-loss and the LOS (θ = 0°) scenario, as it was expected. Regarding the influence of the angle (θ), for θ = 0° the received power is the maximum one for every measured distance, and we can see a great increase in the path-loss when we misalign the antennas θ = 45°, 90°, 135°, 180°. This increase is more significant at lower distances. For example, the average path-loss increases 31.46 dB at d = 2 m and only 8.84 dB at d = 17 m. This is because at higher distances the multipath is less severe and the impact of reflections on handlers and other diffuse scatters is significantly lower (the so-called Waveguide Effect).The variation of the path-loss for the different angles (given a fixed distance) is more or less random. However, at the highest distancesd = 9.5, 17 m the angle that experiences a lower path-loss is clearly θ = 45°. The reason for this is the same as before: the Waveguide Effect. To properly assess the Waveguide Effect, we have calculated the path-loss exponent (n) for 0°. The obtained value is 1.6, which is below the free-space one (n=2) so, under this premises, we can conclude that we are experiencing this effect inside the train at this frequency band. The whole one-slope model is shown in (2)Lx=L0+10nlog10⁡dd0=29+16.0log10⁡d,where Lx is the total losses in dB, d0 is the reference distance, L0 is the losses at the reference distance, n is the path-loss exponent, and d is the distance.We also measured the path-loss at a given distance (d = 9.5 m) with six people moving around between the transmitter and the receiver. This impact is an average path-loss 2.28 dB higher and some fading 30 dB deep.


## 3.2. Ranging

If we measure the time of arrival (TOA) we can easily estimate the distance between the transmitter and the receiver(3)d~=c·τ,where τ is the time for the first peak in the PDP (i.e., the first path that arrives to the receiver) and c is the speed of light. In Table 2 we can see the estimated distances using this TOA-based technique to estimate the distance between transmitter and receiver. The estimation based on the LOS path is the most accurate (5.56% error in the worst case and 0.35% in the best one); for θ = 45° it is slightly worse and for the other angles we have large errors. This method seems to be more accurate when the distance increases (for d = 17 m, the error is lower than 3% for θ = 0°, 45°, and 90° and 13.20% for θ = 180°). The reason behind this good performance at higher distances is because the impact of reflections from handlers and other furniture is less significant than at lower distances.Table 2
Estimated distances for TOA-based method (m).
Distance [m] θ 0° 45° 90° 135° 180° 2.0 2.11 2.02 2.51 2.51 14.09 % error<10% 10–50% >50% 4.0 4.18 6.42 6.38 13.16 5.02 6.0 6.13 7.02 6.40 8.69 11.20 9.5 9.47 10.00 10.49 10.91 9.8 17.0 16.89 16.89 17.47  19.24


## 3.3. Power-Delay-Profiles and Clustering

Regarding the Power-Delay Profiles (PDP) we have computed them for all the scenarios described in Section2. In Figures 5–9 we can see the PDPs for d = 2, 4, 6, 9.5, 17 m and an extra one for the omnidirectional antenna at a distance of d = 4 m.Multipath components are clustered according to Saleh-Valenzuela [14] model and the estimation of the clusters that these multipath components form has been done using the automatic algorithm proposed in [15]. This algorithm takes into account both the amplitude and time delay to form the clusters. The usual approach to identify multipath component clusters is the visual inspection [15] but we found preferable to use an automatic algorithm. The main advantage of this algorithm is that it allows us to do a fast estimation of the clusters, and that it takes into account both time and amplitude values. Therefore, the clustering process is very dependent on the thresholds we propose (as it is acknowledged in [15]), but after some iterations, it seems to have a good performance if we look to Figures 5–11. In these figures we have highlighted in red the clusters that this algorithm has identified (dots in red are the first ray from a cluster).Ford = 2 m (Figure 5) we can see that the number of clusters increases with θ. For θ = 90° the number of clusters increases significantly, and for θ = 180° it decreases. This is an expectable result, because as we go towards a pure NLOS scenario, with many scatters between transmitter and receiver, this leads to different times of arrival (i.e., clusters).Regarding thed = 4 m scenario (Figure 6) the number of clusters does not increase significantly from the previous scenario, but we have more or less the same dependence to θ. The difference between θ = 0° and θ = 45° is small if we visually inspect both PDPs, but for θ = 180° we have more clusters in the receiver. In our opinion, this is attributable to the layout of the train that makes this PDP possible for this angle. If we employ an omnidirectional antenna in the receiver (Figure 11) we can see that we are able to see a significantly higher number of clusters. This is an expected result because the wider radiation pattern allows more different directions of arrival to the receiver. We still have a strong first cluster, associated with the LOS direct link plus four more clusters for the reflection through the train car.In Figure7 we can see the PDPs for d = 6 m. The number of clusters remain stable and similar to d = 2, 4 m for θ = 0°. For θ = 45° we see more clusters for the same reason as before: losing the LOS link leads to more reflections due to the presence of obstacles inside the train. This is coherent with the fact that for θ = 90°, 180° the number of clusters does not increase.Ford = 9.5 m (Figure 8), the estimated number of clusters is stable (and lower than before) for both θ = 0°, 45° because we are experiencing a significant Waveguide Effect and there are many rays that are suppressed. For θ = 90°, 180° we have the same increase in the number of clusters experienced before. So the pattern does not change from the d = 6 m scenario. Nevertheless, for this distance we also measured the channel with people moving randomly inside the train (between transmitter and receiver). The result can be seen in Figure 10, and the number of clusters increases significantly from any other angle at the same distance. The reason is the expected one: people act as supplementary scatters, so the PDP changes (we have more clusters, obviously). This result is very important because intratrain-based applications will work on trains with people onboard.Finally, ford = 17 m (Figure 9), if we inspect visually the PDPs for the four angles considered, we can see that it does not change significantly, but the algorithm estimates 2, 6, 3, and 4, clusters for θ = 0°, 45°, 90°, 180°. This is perhaps the most debatable outcome of the algorithm. In this case, the distance is significantly higher than in the other scenarios, where the Waveguide Effect is dominant and the PDP is smoother (which means fewer clusters). It is also the scenario where we have less differences between angles (together with d = 2 m, where there were almost no scatters between transmitter and receiver). An expected result is that, at a distance like this, the power is mostly concentrated on the first cluster of rays that arrives to the receiver (this is easy to see in the θ = 0°, obviously). This is another consequence of the “Waveguide Effect.”


## 3.4. Saleh-Valenzuela Parameters

The classical Saleh-Valenzuela (SV) model is intended for indoor scenarios and we have chosen it for its statistical nature and simplicity: it describes the channel with only four parameters (λ, Λ, γ, and Γ). Λ is the cluster arrival rate, which is assumed to follow a Poisson distribution [14], the same distribution as the ray arrival rate “λ”; “γ” is the exponential decay within a cluster; and “Γ” is the exponential decay for the whole PDP. In Table 3 we have included our estimation of these four SV parameters for all the scenarios that we have measured.Table 3
Saleh-Valenzuela parameters.
Distance [m] Parameter Angle [°] Average 0° 45° 90° 180° 2.0 γ 0.058 0.172 0.264 0.124 0.155 Γ 0.046 0.196 0.448 0.139 0.207 λ 3.944 3.728 3.728 4.065 3.866 Λ 0.152 0.151 0.302 0.201 0.202  4.0 γ 0.236 0.256 0.198 0.104 0.199 Γ 0.323 0.338 0.249 0.129 0.260 λ 3.600 3.563 3.742 3.965 3.718 Λ 0.100 0.151 0.152 0.201 0.151  6.0 γ 0.116 0.173 0.199 0.221 0.177 Γ 0.173 0.209 0.206 0.248 0.209 λ 3.929 4.000 3.476 3.800 3.801 Λ 0.101 0.250 0.101 0.100 0.138  9.5 γ 0.090 0.118 0.351 0.315 0.219 Γ 0.136 0.140 0.395 0.429 0.275 λ 3.700 3.576 4.115 3.650 3.760 Λ 0.200 0.201 0.251 0.250 0.226  17.0 γ 0.145 0.117 0.200 0.187 0.162 Γ 0.203 0.163 0.158 0.208 0.183 λ 3.700 3.513 3.539 3.800 3.638 Λ 0.150 0.301 0.152 0.100 0.176If we look at the average SV parameters in the column on the right of Table3, we can see that we have a “slow” decay. This is because the distance between the objects that reflect the signal is very low, and all of them are very similar (metallic surfaces). That is for the “overall decay” (parameter Γ). If we look inside the clusters, we can see that they decay rapidly (parameter γ), which means a higher attenuation (due to the high frequencies) and very few reflections (apart from the first one). Anyway, this is coherent because the clustering algorithm that we chose is adequate, because the calculation of SV model parameters is very dependent on the clustering algorithm.Explaining properly all the estimated SV parameters would take a lot of time, so here we will discuss some of the most significant parameters. First of all, it is noteworthy thatλ (ray arrival rate) has small variations no matter in which scenario we are. This parameter is very dependent on the limitations of the measurement devices, so perhaps with a different device able to increase the number of resolvable rays this parameter could experience higher variations. The main difficulty to improve this is that the VNA employed is a state-of-the-art device, so it will take some time to achieve a better resolution in this parameter.The cluster arrival rate (Λ) has a direct relation with the number of clusters and we have gone through this parameter in Section3.3. Regarding the overall decay rate (Γ), it is generally higher than the cluster decay rate (γ), which is an expected result. Moreover, the clustering algorithm does not allow negative slopes (if it resolves a cluster with a negative slope; that cluster is joined to the next one) which increases—in general terms—the values of γ. If we look at some particular results, we can see that the Γ for the shortest distance (d = 2 m) and LOS scenario has the smallest value calculated. For higher distances and angles, the Γ increases, but the general trend is to decrease (but for d = 2 m), which is an expected result. It is hard to find a clear pattern in the angle variation, but a possible reason behind this behavior is that the first ray of the cluster is not always the one with more power [15]. This could lead to an underestimation of the Γ parameter.We also took two more measurements: with people moving around inside the train (d = 9.5 m) and also using an omnidirectional antenna (d = 4 m). The Saleh-Valenzuela model parameters for the omnidirectional antenna are γ = 0.187; Γ = 0.208; λ = 3.800; Λ = 0.277. This is similar “γ” and “λ” for horn antenna in the receiver at the same distance. The apparent invariability of “λ” was discussed before and for “γ” it could be an impact of the clustering algorithm, which prevents higher variations inside a cluster, which leads to an approximately constant “γ.” The number of clusters is significantly different, as the parameter “Γ” highlights, so this is coherent with the “conservative” nature (regarding “γ”) of the clustering algorithm.If we consider the difference between having people in motion between transmitter and receiver (the SV parameters areγ = 0.134; Γ = 0.188; λ = 3.745; Λ = 0.277) and not, using horn antennas and the same distance, equal to 9.5 m, we can see that we have a lower “Λ” when we have people in motion, and also a lower “Γ.” It is also noteworthy that the average parameters using horn antennas (this is θ = 0, 45°, 90°, 180°) are a good approximation of the scenario with an omnidirectional antenna. This is a coherent result because using an antenna like this is the same as we average the contributions from all directions. However, as we can see in Figure 4, the radiation pattern of the Vivaldi antenna is not perfectly omnidirectional, so this “averaging” process is not as precise as it could be otherwise.Figure 4
Radiation patterns at 25 GHz for E-plane (a) and H-plane (b) for the Vivaldi antenna. (c) The antenna is shown being installed near the top of one of the handholds of the train.
(a) (b) (c)Figure 5
Power-Delay Profile and cluster identification ford = 2 m. (a) θ = 0°. (b) θ = 45°. (c) θ = 90°. (d) θ = 180°.
(a) (b) (c) (d)Figure 6
Power-Delay Profile and cluster identification ford = 4 m. (a) θ = 0°. (b) θ = 45°. (c) θ = 90°. (d) θ = 180°. For the θ = 0° setup there is almost no room for reflections to arrive to the receiver. As we increase θ, many more clusters surge.
(a) (b) (c) (d)Figure 7
Power-Delay Profile and cluster identification ford = 6 m. (a) θ = 0°. (b) θ = 45°. (c) θ = 90°. (d) θ = 180°. At this distance, the clustering algorithm behaves in a very similar manner as for d = 2 m, but for θ = 90°, 180° there are fewer clusters than in d = 2 m.
(a) (b) (c) (d)Figure 8
Power-Delay Profile and cluster identification ford = 9.5 m. (a) θ = 0°. (b) θ = 45°. (c) θ = 90°. (d) θ = 180°. We still have many clusters, especially in the angles different to 0°.
(a) (b) (c) (d)Figure 9
Power-Delay Profile and cluster identification ford = 17 m. (a) θ = 0°. (b) θ = 45°. (c) θ = 90°. (d) θ = 180°. The automatic algorithm identifies very few clusters for the θ = 0°, but many more rise if we misalign the antennas.
(a) (b) (c) (d)Figure 10
Power-Delay Profile ford = 9.5 m, θ = 0°; using horn antennas and people moving around between transmitter and receiver. The effect of people increases the number of clusters and impacts the overall PDP.Figure 11
Power-Delay Profile ford = 4 m, with the Vivaldi antenna in the receiver. The automatic algorithm identifies 5 clusters.


## 4. Conclusion

The SV model can be applicable directly to an intratrain scenario, as it is an indoor scenario (the scope of the SV model). It is only necessary to estimate the parameters of the model to each environment. In particular, intratrain communications at high frequency are a high multipath environment, where SV model is intended to work.The intratrain link is one of the most likely scenarios to require high throughputs, ultra-dense networks, and very low latencies. These three requirements are the core of 5G technologies. In this paper we have assessed this link in a region of the spectrum related to future 5G developments (26.5–40 GHz), providing estimations for the path-loss, Power-Delay Profile and Saleh-Valenzuela model parameters. We have seen the dependence of all these results on distance and angle; moreover, we have seen the impact of people moving around and also the differences coming from the radiation pattern of the receiving antenna (using an omnidirectional antenna instead of the horn antennas used in all measurements but one). The performance of the clustering algorithm is remarkable (with some limitations, as we have discussed) and the obtained SV parameters are coherent as well.



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*Source: 6916954-2018-04-15.xml*