Keywords

1 Introduction

Mobile communication is moving to fifth generation (5G) at millimeter wave (mmWave) frequencies in order to provide multi-Gigabit-per second (Gbps) data rates to a mobile device for video and the Internet-of-Things (IoT). In order to install communication station, the propagation path loss models are one of important things. There are three types of the path loss models namely, empirical model, semi-deterministic model and deterministic model. The empirical models for 5G [1, 2] are widely used since they need only frequency, PLE and distance to compute the path loss for macro and micro cell planning while the deterministic models need the details of digitize map and material of buildings. Additionally they use a lot of time for computing. Finally the semi-deterministic models [3,4,5,6,7,8,9] are also widely used since they are not only need the parameters of the empirical model but also require some information about buildings such as dimension and type of them together with wide and direction of road. This model provides more accuracy path losses and is used for planning and solving the communication system. For semi-deterministic models, there are previous studies as follows; Xia et al. [3, 4] proposed path loss formulas for micro-cells in low-rise and high-rise building environments. Additionally, COST 231 WI model [5,6,7] is also a popular prediction tool for micro cell environments. However, they need environment data base details. In case of the Xia model for non light of sight (NLOS), it requires a set of model parameters such as distance from the last roof top to receiver, average building height, and antenna heights as in our research [8, 9], while the WI model requires the road parameters such as height of buildings, width of the roads, building separation and road orientation with respect to the direct radio path. The aim of this research is a study the millimeter wave empirical path loss model also compares with semi deterministic models such as WI model and Xia model for present 4G network in order to develop the semi deterministic model for 5G networks in the next step.

2 Path Loss Models

2.1 A. Empirical Path Loss Model

This model does not utilize the parameter of specific area except the frequency and distance.

$$ PL_{LN} \left( {dB} \right)\, = \,PL\left( {d_{0} } \right)\, + \,10nlog_{10} \left( {\frac{d}{{d_{0} }}} \right)\, + \,x_{\sigma } $$
(1)

Where n is the path loss exponent, that indicates the attenuation rate at the distance (\( {\text{n}} = 2 \) for free space), \( PL\left( {d_{0} } \right) \) is the path loss at a reference distance 1 m. and \( X_{\sigma } \) is a zero mean random variable, that have Gaussian distribution with standard deviation \( \sigma \). The \( PL\left( {d_{0} } \right) \) is found from Eq. (2)

$$ PL_{FS} \left( {dB} \right)\, = \,32.44\, + \,20log_{10} \left( f \right)\, + \,20log_{10} \left( d \right) $$
(2)

It can find frequency f in unit of GHz and the distance d in meters. This case is valid for the free space and far-field region. If the ground reflection over an earth plain was included, the model becomes.

$$ PL_{GR} \left( {dB} \right)\, = \,PL_{FS} \left( {dB} \right)\, - \,20log_{10} \left[ {2\left| {\sin \left( {\frac{{\beta h_{T} h_{R} }}{d}} \right)} \right|} \right] $$
(3)

\( h_{T} \) and \( h_{R} \) are the transmitter and receiver antenna heights, respectively. \( \beta \, = \,2\pi /\lambda \) and \( \lambda \) is the wavelength. This case is valid for large distances from the transmitter, and \( \gg \beta h_{T} h_{R} \), that only depends on d, \( h_{T} \) and \( h_{R} \), and the attenuation which correspond to the free space.

2.2 Semi-deterministic Path Loss Model

There are two approach models which are used for a 2D map, are compared as follows:

  • Xia model

The original Xia model for low-rise environments with one five story building was applied to predict path loss because it needed 2D maps of buildings for calculation. There are three routes for prediction namely, staircase route, transverse route and lateral route as shown in Fig. 1. A transmitter (Tx) was located on the street in the middle of a building block. The original Xia path loss formulas for all non line of sight cases were written as,

Fig. 1.
figure 1

Geometry of Xia model

Full size image
$$ \begin{aligned} {\text{PL(d)}} & = \left[ {139.01 + 42.59\,\log \,{\text{fG}}} \right]\,{-}\,\left[ {14.97 + \, 4.99\,{ \log }\,{\text{fG}}} \right]{\text{sgn}}\left( {\Delta {\text{h}}} \right){ \log }\left( {1 + \left| {\Delta {\text{h}}} \right|} \right) \\ & \quad + \left[ {40.67\,{-}\,4.57{\text{sgn}}\left( {\Delta {\text{h}}} \right){ \log }\left( {1 + \left| {\Delta {\text{h}}} \right|} \right)} \right]{ \log }\,{\text{d}} \\ & \quad + 20\text{log}\left( {\Delta {\text{hm}}/7.8} \right) + 10{ \log }\left( {20/{\text{dh}}} \right) \\ \end{aligned} $$
(4)

Where d is the mobile distance from transmitter (km). [0.05 < d < 3], fG is the frequency (GHz). [0.9 < fG < 2], Δh is the relative height of transmitter to average building height (m). [–8 < Δh < 6], Δhm is the height of the last building relative to the mobile (m), dh is the distance of mobile from the last rooftop (m), hb is the transmitting antenna height from ground level (m), hm is the mobile antenna height from ground level (m) and λ is the wavelength (m).

  • WI model

WI model is written in case of non line of sight as follows:

$$ {\text{L}}({\text{NLOS}}) = 32.4 + 20{\text{log(f)}} + 20{\text{log(d)}} + {\text{L(diff)}} + {\text{L(mult)}} + 3 $$
(5)

Where

$$ {\text{L}}\left( {\text{diff}} \right) = - 6.9 + 10\log \left( {\text{w}} \right) + 10\log \left( {\text{f}} \right) + 20\log \left( {\text{dhm}} \right) + {\text{Lori}} $$
(6)

When f is frequency (MHz), d is distance (km.), W is width of road (m.), hb is base station antenna height (m.), hm is mobile height (1.8 m.) hroof is average height of roof top, Δhm is distance between hm and hroof.

$$ \begin{aligned} {\text{Lori}} & = - 10 + 0.354\upphi\,{\text{for}}\,0 \le\upphi < 35 \\ & = 2.5 + 0.075\left( {\upphi - 35} \right)\,{\text{for}}\,35 \le\upphi < 55 \\ & = 4 - 0.114\left( {\upphi - 55} \right)\,{\text{for}}\,55 \le\upphi < 90 \\ \end{aligned} $$
(7)

where ϕ is the angle between incidences coming from base station and road

$$ {\text{L}}\left( {\text{mult}} \right) = {\text{k}}0 + {\text{ka}} + {\text{kd}}\log \left( {\text{d}} \right) + {\text{kf}}\log \left( {\text{f}} \right) - 9\log \left( {\text{W}} \right) $$
(8)

Where k0 = 0, kd = 18–15(Δhb/hroof), ka = 54–0.8 (Δhb), and kf = –4 + 0.7[(f/925)–1] in case of sub-urban.

3 Measurement and Location

This paper used measured data in the dense urban environment around New York University’s (NYU) Manhattan campus at both 28 GHz and 73 GHz [1, 2],and around the campus of The University of Texas at Austin (UTA) at 38 GHz. These measurements will be Omni directional large-scale line-of-sight (LOS) and non-line-of-sight (NLOS) directional measurements. In the NYU, the building density is about 65% while the building height is about 5–50 m. In the UTA, the building density is about 55% while the building height is about 5–30 m. The measurement procedure and description of the equipment can be found for details in [1]. The transmitting antenna heights of 28 GHz and 73 GHz are 7 and 17 m while the transmitting antenna heights of 38 GHz are 8 m, 23 m, and 36 m. The receiving antenna heights of 28 GHz and 38 GHz are 1.5 m while the receiving antenna heights of 73 GHz are 2.0 m and 4.06 m.

4 Results and Analysis

The empirical path loss model at frequencies of 28 GHz, 38 GHz and 73 GHz are respectively as following.

4.1 Empirical LOS

$$ \begin{aligned} & PL_{28 GHz} \left( {dB} \right)\, = \,61.3\, + \,21log_{10} \left( d \right) \\ & PL_{38 GHz} \left( {dB} \right)\, = \,60.0\, + \,19log_{10} \left( d \right) \\ & PL_{73 GHz} \left( {dB} \right)\, = \,69.7\, + \,20log_{10} \left( d \right) \\ \end{aligned} $$

4.2 Empirical NLOS

$$ \begin{aligned} & PL_{28 GHz} \left( {dB} \right)\, = \,61.3\, + \,34log_{10} \left( d \right) \\ & PL_{38 GHz} \left( {dB} \right)\, = \,60.0\, + \,25log_{10} \left( d \right) \\ & PL_{73 GHz} \left( {dB} \right)\, = \,69.7\, + \,34log_{10} \left( d \right) \\ \end{aligned} $$

4.3 Semi Deterministic Models

$$ \begin{aligned} PL_{28 GHz,NLOS,Xia} \left( {dB} \right) & \, = \,53.5 + 51.8log_{10} \left( d \right) \\ PL_{38 GHz, LOS,WI} \left( {dB} \right) & \, = \,56.2 + 26log_{10} \left( d \right) \\ PL_{73 GHz,NLOS,Xia} \left( {dB} \right) & \, = \,61.9 + 58.2log_{10} \left( d \right) \\ \end{aligned} $$

Note that the models are still applied for frequency range of 0.8 to 3 GHz. This needs correction factors to adjust these models. The Xia model provides over estimate path loss about 15% comparing with the measurement while the comparisons in this paper are only LOS situation for WI model. We also found an agreement for LOS while the NLOS of semi deterministic models have to adjust in order to meet good agreement for the fifth generation (5G) at millimeter wave (mmWave) frequencies.

In case of Xia model for NLOS, it requires a set of model parameters such as distance from the last roof top to receiver, average building height, and antenna heights. While the WI model require height of buildings, width of the roads, building separation and road orientation. These intonations are available in 3D map.

5 Conclusion

We present path loss models of fifth generation (5G) wireless communication systems. Propagation parameters such as path loss at reference distance (PL(d0)), path loss exponent (PLE) are calculated both line-of-sight (LOS) and non line-of-sight (NLOS) at the frequencies of 28, 38 and 73 GHz. We used measured data in the dense urban environment around New York University’s (NYU) Manhattan campus at both 28 GHz and 73 GHz and around the campus of The University of Texas at Austin (UTA) at 38 GHz. This paper also compares with semi deterministic Xia and WI model. The results shown that the NLOS of semi deterministic models provide over estimate path loss from the measured data. So they have to adjust in order to meet good agreement for the fifth generation (5G) at millimeter wave (mmWave) frequencies.