IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 35, NO. 7, JULY 2017
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Rural Macrocell Path Loss Models for Millimeter
Wave Wireless Communications
George R. MacCartney, Jr., Student Member, IEEE, and Theodore S. Rappaport, Fellow, IEEE
Abstract— Little is known about millimeter wave (mmWave)
path loss in rural areas with tall base station antennas; yet, as
shown here, surprisingly long distances (greater than 10 km)
can be achieved in clear weather with less than 1 W of power.
This paper studies past rural macrocell (RMa) propagation
models and the current third generation partnership project
(3GPP) RMa path loss models for frequencies from 0.5 to 30
GHz adopted from the International Telecommunications UnionRadiocommunication Sector (ITU-R). We show that 3GPP and
ITU-R RMa path loss models were derived for frequencies below
6 GHz, yet are being asserted for use up to 30 GHz. Until this
paper, there has not been published data to support mmWave
RMa path loss models. In this paper, 73-GHz measurements
in rural Virginia are used to develop a new RMa path loss
model that is more accurate and easier to apply for varying
transmitter antenna heights than the existing 3GPP/ITU-R RMa
path loss models, and may be used for frequencies from 0.5 to
100 GHz. The measurement system used here has a measurement
range comparable to a wideband (800-MHz radio frequency
bandwidth) channel sounder with 21.7-dBW effective isotropic
radiated power. Measured data verify a new path loss model that
uses a close-in free space reference distance with a novel heightdependent path loss exponent (CIH model). This work shows
that the CIH model is accurate and stable, and is frequencyindependent beyond the first meter of propagation, and effectively
models the path loss dependence on base station height in rural
channels.
Index Terms— Millimeter wave, mmWave, rural macrocell
(RMa), 73 GHz, path loss, channel model, 3GPP, ITU-R,
standards.
I. I NTRODUCTION
I
N 1991, at the dawn of the cellphone revolution, it was
predicted that by 2020, wireless technology would be as
universal as electrical power [2]. Fifth-generation (5G) wireless technologies and the use of millimeter-wave (mmWave)
frequencies will make that prediction a reality and will offer
the promise of multi-gigabit per second data transfers and vast
new applications [1]–[5]. Many research groups have recently
developed channel models for mmWave frequencies, including
Manuscript received November 18, 2016; revised February 22, 2017 and
March 10, 2017; accepted March 27, 2017. Date of publication April 28,
2017; date of current version June 19, 2017. This work was supported in
part by the NYU WIRELESS Industrial Affiliates Program, in part by the
three National Science Foundation Research Grants under Grant 1320472,
Grant 1302336, and Grant 1555332, and in part by the GAANN Fellowship
Program. Portions of this paper were presented at the Workshop on All Things
Cellular held in conjunction with ACM MobiCom 2016 [1]. (Corresponding
author: George R. MacCartney, Jr.)
The authors are with the NYU WIRELESS Research Center, NYU Tandon
School of Engineering, New York University, Brooklyn, NY 11201 USA
(e-mail: gmac@nyu.edu; tsr@nyu.edu).
Color versions of one or more of the figures in this paper are available
online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JSAC.2017.2699359
Mobile and Wireless Communications Enablers for the
Twenty-twenty Information Society (METIS) [6], MillimetreWave Evolution for Backhaul and Access (MiWEBA) [7],
Millimetre-Wave Based Mobile Radio Access Network for
Fifth Generation Integrated Communications (mmMAGIC) [8],
European Telecommunications Standards Institute (ETSI) [9],
and IEEE 802.11ad [10]. The 3rd Generation Partnership
Project (3GPP), the global standards body of the wireless
industry, released its study on channel models for frequencies
above 6 GHz in 3GPP TR 38.900 V14.2.0 (Release 14) [11],
which has been aligned with channel models for below 6 GHz
such as 3GPP TR 36.873 (Release 12) or ITU-R M.2135
such that the models support comparisons from 0.5 GHz to
100 GHz [12].
The 3GPP channel model includes path loss models in [11],
using contributions from academic and industrial partners
from extensive mmWave measurement campaigns and raytracing simulations [13]–[21]. Scenarios specified in 3GPP TR
38.900 [11] include urban microcell (UMi), urban macrocell
(UMa), and indoor hotspot (InH) for office and shopping
mall [14], [15], [18]. Rural macrocell (RMa) is an additional
scenario that is included in 3GPP [11] and METIS path loss
models [6], although it has not been thoroughly investigated
for frequencies above 6 GHz. In fact, a search of the literature
and standards reveals only one very limited and unpublished
measurement campaign at 24 GHz that was used to attempt
to justify the 3GPP RMa path loss model [22]. The literature
shows that the RMa path loss models in [6] and [11] were
adopted from the International Telecommunications Union
- Radiocommunication Sector (ITU-R) M.2135 report [23]
for frequencies between 450 MHz and 6 GHz, and did not
include any empirical confirmation for use above 6 GHz or at
mmWave bands.
The FCC recently allocated 10.85 GHz of spectrum at frequencies above 24 GHz and proposes an additional 17.7 GHz
of spectrum [24], ensuring that vast amounts of wireless
bandwidth will be available for new systems and applications.
As shown in this paper, the coverage range for the RMa
scenario can be over 10 kilometers (km) in clear weather
and offers remarkable promise for fiber replacement and
backhaul networks, as well as for broadband services to homes
and mobile users. Given the huge spectrum allocation, this
motivates a more careful study for RMa path loss modeling
than what has occurred to date.
In Section II we investigate the development and origins of the existing RMa path loss models in 3GPP [1],
[11], [23], and reveal important inconsistencies with the
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line-of-sight (LOS) model equation when used at frequencies
above 9.1 GHz and at mmWave bands. This work also
illuminates numerous questionable empirical correction factors
used by ITU-R and 3GPP which make no physical sense for
rural environments. Section III describes 73 GHz propagation measurements conducted in rural Riner and Christiansburg, Virginia for LOS and non-LOS (NLOS) environments.
Section IV introduces a clear weather RMa multi-frequency
close-in reference distance (CI) path loss model and a new
RMa path loss model that consists of a close-in free space
reference distance and incorporates the base station transmitter
height (CIH). Section V discusses empirical model results and
uses the measured data and existing 3GPP RMa path loss
models to develop the CI and CIH RMa path loss models
that are accurate, simple to understand and implement, and
may be used for frequencies from 0.5 GHz to over 100 GHz.
Conclusions are drawn in Section VI, and derivations for
determining optimized CIH path loss model parameters are
provided in the Appendix.
II. 3GPP RMa PATH L OSS M ODELS
RMa path loss models are generally used for tall transmitter
heights above 35 meters [1], [11], and are important for
predicting the statistical behavior of received signal strength
and interference in rural settings. As shown in [16], [17], [21],
and [25]–[27], large-scale path loss models are independent
of frequency in outdoor macrocellular channels, except for the
first meter of propagation loss which is a function of the square
of the frequency. Besides the first meter of free space path
loss (FSPL), rain and oxygen absorption are also frequency
dependent across the mmWave bands [3], [28].
We note that directional antennas induce additional distance
dependent path loss compared to omnidirectional antennas,
since they act as spatial filters and miss multipath energy
from directions where antennas are not pointed, although they
offer greater link margin for multipath components captured
in the antenna beam pattern [16], [49], [52]–[54]. Researchers
must be cautious to not include directional antenna gains
to model path loss for directional antenna systems when
using omnidirectional path loss model formulations such as
found in 3GPP since this could dramatically overestimate
interference or coverage [16], [49], [51], [52]–[54].
A. 3GPP RMa LOS Path Loss Model Origin
The existing 3GPP/ITU-R [11], [23] RMa LOS path loss
model is used to provide statistical modeling of path loss over
distance for when there is a clear, unobstructed path between
the transmitter (TX) and receiver (RX). The 3GPP RMa LOS
path loss model consists of two sections separated by a breakpoint distance where the slope attenuation increases beyond
the breakpoint distance, as given in (1) below [11], [23]:
P L 1 [dB] = 20 log10 (40π · d3D · f c /3)
+ min(0.03h 1.72, 10) log10 (d3D )
− min(0.044h 1.72, 14.77)
+ 0.002 log10 (h)d3D ; σ S F = 4 dB
P L 2 [dB] = P L 1 (d B P ) + 40 log10 (d3D /d B P ); σ S F = 6 dB
(1)
TABLE I
3GPP TR 38.900 RMa PATH L OSS M ODEL D EFAULT PARAMETER VALUES
AND A PPLICABILITY R ANGES FOR LOS AND NLOS C ONDITIONS [11]
where f c is the center frequency in GHz, d3D is the threedimensional (3D) transmitter-receiver (T-R) separation distance in meters (m), h is the average building height in
meters (an odd parameter to have for rural environments and
for LOS), and d B P is the two-dimensional (2D) breakpoint
distance along the flat earth in meters ( [25] provides details
on large-scale path loss modeling). It is worth noting that
as the flat earth distance between the TX and RX becomes
large (say more than 1 km), the difference between d2D
and d3D becomes negligible for typical TX and RX heights.
P L 1 [dB] is path loss in dB before the breakpoint distance
with a Gaussian (in dB) shadow fading (SF) standard deviation
σ S F = 4 dB about the distant-dependent mean path loss in (1)
and P L 2 [dB] is path loss in dB after the breakpoint distance
with SF standard deviation σ S F = 6 dB. The P L 2 [dB]
equation in (1) indicates a path loss exponent (PLE) of 4
beyond the breakpoint distance, as derived by Bullington for
the asymptotic two-ray LOS ground bounce model [25], [29],
[30]. The breakpoint in (1) is defined as [31]:
d B P = 2π · h B S · h U T · f c /c
(2)
where f c is the center frequency in Hz, c is the speed of light
in free space in meters per second, h B S is the base station
height in meters, and h U T is the user terminal (UT) height
in meters. Table I provides the default parameter values and
applicability ranges for the 3GPP LOS and NLOS RMa path
loss models as given in [11].
After a thorough review of standards documents [1],
we found that ITU-R 5D/88-E [32] is the source of the
ITU-R M.2135 RMa LOS path loss model adopted in 3GPP
TR 38.900 (Release 14) for frequencies from 0.5 GHz to
30 GHz [11]. The LOS model in [32], however, was based
largely on a propagation measurement and modeling campaign
conducted at 2.6 GHz in 2000 in a downtown metropolitan
area of Tokyo (typical UMi) [33]. The measurements were
performed with a 30 Megabit per second pseudorandom
noise (PN) code at a center frequency of 2.6 GHz to obtain
both path loss and time delay statistics. The work in [33]
created elaborate correction factors for physical descriptors,
such as average building height in order to develop empirical
MACCARTNEY AND RAPPAPORT: RMa PATH LOSS MODELS FOR mmWAVE WIRELESS COMMUNICATIONS
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Fig. 1. Two-ray ground bounce simulation at 2.6 GHz with a TX and RX
height of 35 m and 1.5 m, respectively [29], [30].
LOS path loss models for use in urban cellular system design
in the low GHz range.
The RMa LOS path loss model equation (1) from ITU-R
M.2135 [23] and 3GPP TR 38.900 [11] is similar to the LOS
path loss model provided in [32], but is slightly different with
an additional height correction factor: min(0.044h 1.72, 14.77),
that adjusts path loss for low building heights. A different
formula is used for calculating path loss after the breakpoint
distance in (1) compared to what appears in [32]. Path
loss after the breakpoint distance, given by P L 2 [dB]
in (1), includes path loss up until the breakpoint distance
(P L 1 (d B P )), and an attenuation rate of 40 dB per decade
of distance beyond the breakpoint distance. In ITU-R 5D/
88-E, the LOS path loss equation after the breakpoint distance
includes the attenuation rate of 40 dB per decade of distance
but also includes correction factors for transmitter height,
mobile height, average building height, and street width, which
were not adopted by ITU-R or 3GPP for RMa LOS path
loss. There is also a noticeable discontinuity between path
loss before and after the breakpoint distance in [32].
The breakpoint distance was initially developed by Bullington [29] for far propagation distances (usually many kilometers), where the PLE transitions from free space (n = 2) to the
asymptotic two-ray ground bounce model of n = 4 [25], [30].
More recent work [31], [34] showed that the breakpoint
distance model by Bullington is a good fit to microcellular
channels, as well. A simulation of the two-ray ground bounce
model compared to FSPL is provided in Fig. 1 for a center
frequency of 2.6 GHz, a TX height of 35 m, an RX height of
1.5 m, and clearly shows that the log-distance path loss slope
changes from n = 2 to n = 4 at the breakpoint distance (d B P )
near 2.85 km. When used at mmWave frequencies, the breakpoint distance becomes very large, on the order of tens of km
[see Fig. 2(a)].
The precise RMa LOS path loss model in ITU-R M.2135
and 3GPP TR 38.900 was not given in [32] and [33], or
any other published material that we could find, leaving us
to conclude that the existing 3GPP RMa LOS path loss model
was never fully confirmed for a rural environment, nor was
it confirmed with propagation data above 6 GHz. For the rest
of this paper, when the 3GPP RMa model is mentioned, we
are referring to the 3GPP TR 38.900 (Release 14) standard
for frequencies above 6 GHz [11]. When the ITU-R model is
mentioned, we are referring to ITU-R M.2135 [23].
Fig. 2.
(a) LOS breakpoint distance vs. frequency in (2) for default
parameters: h B S = 35; h U T = 1.5 m [1]. This shows that the breakpoint distance in (2) exceeds 10 km at frequencies greater than 9.1 GHz.
(b) Frequency [GHz] and base station height (h B S ) combinations where the
RMa LOS path loss model in (1) reverts to a single-slope model, as identified
by the shaded area since the breakpoint distance in (1) and (2) is beyond
10 km (applicability range of model). The mobile height (h U T ) is 1.5 m.
B. 3GPP RMa LOS Path Loss Model Description
Upon inspection, (1) is a cumbersome equation without
an intuitive physical meaning [1]. This is clearly seen by
observing the correction factor “min” (minimum) functions
of average building height, that create an upper bound on path
loss for large average building heights. The “min” correction
factor terms are non-physical curve fitting adjustments. The
use of average building height h is quite odd, considering that
an RMa scenario does not have tall buildings. The breakpoint
distance used in (1) and (2), however, does have some physical
basis in representing the distance at which the PLE approaches
the asymptote of n = 4 [25]. While (1) has not been fully
explained in the literature, it is obvious that the first term –
20 log10 (40π · d3D · f c /3) – is the theoretical FSPL (in dB) at
distance d3D as shown here [16]:
4π · d3D · f c × 109
40π · d3D · f c
20 log10
= 20 log10
3 × 108
3
(3)
by Friis’ free space transmission formula for f c in GHz [25],
[28], [35].
The breakpoint distance for RMa LOS path loss in (2) has a
remarkable practical frequency limitation. This is easily seen
by using the 3GPP default height parameter settings from
Table I [11]. Using these default parameters, it is readily seen
that the breakpoint distance exceeds the defined maximum
usable distance of the 3GPP RMa LOS path loss model
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(10 km) for frequencies greater than or equal to 9.1 GHz,
as shown in Fig. 2(a). Thus, the 3GPP RMa LOS path loss
model must be assumed to be a single-slope model above
9.1 GHz (for distances within the applicable range) as given by
P L 1 in (1). Fig. 2(b) displays the region (shaded) for various
base station heights (h B S ) and frequency combinations where
the 3GPP RMa LOS path loss model breakpoint distance
exceeds the maximum 10 km propagation distance model
limit. Surprisingly, the breakpoint distance portion of (1) is not
usable above 32 GHz for any h B S base station height (mobile
height of 1.5 m) defined in the 3GPP and ITU-R RMa models,
leading us to conclude that the LOS breakpoint distance
(2) is not appropriate for mmWave bands in RMa scenarios.
Section IV introduces a more reliable, accurate, and robust
single-slope CI path loss model [16]–[18], [21] that avoids the
breakpoint issue highlighted here, and is much simpler to use
than the 3GPP/ITU-R RMa path loss models [11], [23]. While
the ITU-R references the sub-6 GHz WINNER II channel
model for RMa, it includes traditional LOS path loss models
that were modified with COST231-Hata correction factors for
curve fitting and that do not match 3GPP [36].
a(h m ) = 3.2(log10 (11.75h m ))2 − 4.97
(5)
with h m as the mobile (UT) antenna height in meters. The
equation in (5) was used to curve fit path loss for frequencies
above 400 MHz and for UT heights above 1.5 m [37]. The
combination of expansions and extensions on the Sakagami
model explained above, is what appears in the final 3GPP and
ITU-R RMa NLOS path loss model as shown here [11], [23]:
P L = max(P L R Ma−L O S , P L R Ma−N L O S )
P L R Ma−N L O S = 161.04 − 7.1 log10 (W ) + 7.5 log10 (h)
− (24.37 − 3.7(h/ h B S )2 ) log10 (h B S )
C. 3GPP RMa NLOS Path Loss Model Origin
The RMa NLOS path loss model in 3GPP [11] is taken
directly from ITU-R [23] and originates from work by
Sakagami and Kuboi [37]. The empirical model in [37] was
developed from measurements in metropolitan Tokyo in 1991
at 813 MHz and 1433 MHz in a square shaped area with a total
length of 270 to 420 meters, and with measurement courses
along circles with radii of 0.5, 1, 2, and 3 km, for various
measurement distances. Parameters selected for the model [37]
include base station antenna height (h b0 ), base station antenna
height above the mobile station (h b ), building height near the
base station (H ), average building height (< H >), height of
buildings along the street (h s ), street width (W ), and street
angle (θ ), with all heights and distances in meters and θ in
degrees. The street angle was defined as the angle between the
line connecting the UT and the base station, and the street from
where the measurement was performed (a maximum angle of
90◦ induces 2.07 dB of additional path loss) [37]. Given that
this work was for a dense urban environment (Tokyo) and at
ultra high frequencies (UHF), many of these parameters do not
apply to RMa path loss modeling, since it makes no physical
sense to have correction factors for street width and building
height in rural environments that do not have large buildings
or urban canyons.
Using these physical parameters of the environment in
downtown Tokyo, a multiple regression analysis was conducted in [37] to simultaneously solve for nine model coefficients. The coefficients that minimized the residual variance
between the model and data were determined based on
1000 path loss data points and resulted in the following NLOS
path loss model [37]:
P L Sakagami = 100 − 7.1 log10 (W ) + 0.023θ + 1.4 log10 (h s )
+ 6.1 log10 (< H >) − (24.37 − 3.7(H / h b0)2 ) log10 (h b )
+ (43.42 − 3.1 log10 (h b )) log10 (d) + 20.4 log10 ( f )
where f is the frequency in MHz and d is the distance from
the base station in km. The model was extended from 450 MHz
to 2200 MHz with an additional frequency extension term not
shown here, but which is given in [37].
In the literature [38], [39], the extended version of the
Sakagami model (4) replaces all of the building height terms
with the median building height and substitutes the frequency
term with 20 log10 ( f ) [38], [39]. An expansion to account for
mobile heights above 1.5 m was adopted from the OkumuraHata model [40] and is formulated as: P L Sakagami − a(h m )
where [41]–[43]:
(4)
+ (43.42 − 3.1 log10 (h B S ))(log10 (d3D ) − 3) + 20 log10 ( f c )
(6)
− (3.2(log10 (11.75h U T ))2 − 4.97); σ S F = 8 dB
where W is the street width, h is the average building height
(by combining all building height coefficients [39]), h B S is the
base station height, h U T is the mobile UT height, and d3D is
the 3D T-R separation distance, where all distances and heights
are in meters. Additionally, f c is the center frequency in GHz
and the log-normal SF standard deviation is set to σ S F = 8 dB.
Applicability ranges for the model are provided in Table I as
extracted from [11]. The “max” (maximum) operator in (6)
acts as a strange mathematical patch and is used to solve a
model artifact, where the model predicts much stronger power
at close-in distances in NLOS (say within a few hundred
meters) than what physics dictates for LOS environments. The
patch is used to ensure that the estimated NLOS path loss
is always greater than or equal to the equivalent LOS path
loss at the same distance. This problem was shown to exist
in many other 3GPP-style path loss models [18], leading to
the optional CI path loss models in 3GPP [11], [16]–[18].
A footnote for (6) in [11] specifies the applicable frequency
range as 0.8 GHz < f c < 30 GHz in 3GPP, although evidence
suggests this is not valid, as is now explained.
D. 3GPP RMa NLOS Path Loss Model Description
Three differences between the extended Sakagami (4) and
the eventual 3GPP (6) and ITU-R RMa NLOS path loss
models are explained here. The first difference is the removal
of the street angle term: 0.023θ . The second change is the
modification of the first term from 100 in (4) to 161.04 in (6)
since the 3GPP model is in units of GHz rather than MHz
(FSPL difference at 1 m between 1 MHz and 1 GHz is 60 dB).
The additional 1.04 dB difference was not explained in the
standards, and while it appears in [44], it is not explained
MACCARTNEY AND RAPPAPORT: RMa PATH LOSS MODELS FOR mmWAVE WIRELESS COMMUNICATIONS
Fig. 3.
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73 GHz TX and RX measurement system diagrams [1].
there or in the literature. The last difference is the addition
of “−3” in (log10 (d3D ) − 3), to account for the fact that d3D
is in meters as compared to km in [37] (log10 (1000) = 3).
The use of (6) as a path loss model above 6 GHz for
rural environments is highly questionable based on the fact
that evidence shows measurements were made at frequencies
only up to 1433 MHz [37]. The measurement frequencies used
to generate (6) are much lower than the specified maximum
applicable frequency (30 GHz), since the original model is
based on measurements at 813 and 1433 MHz, with an
extension for up to 2200 MHz (although this extension is not
included in the 3GPP or ITU-R model [11], [23]). It is worth
noting that others in the literature have attempted to extend the
Sakagami model based on measurements up to 8.45 GHz in
urban environments, yet this introduced, even more, correction
factors and evolutions of the Sakagami model, leading to even
more complicated correction factors that can only be applied in
urban environments [39], [45]. While physical parameters such
as average building height and street width are sensible for
urban areas, they are not used in any of the other 3GPP outdoor
(e.g. UMi or UMa) path loss models [11], so they surely
do not make sense in a rural model. Even more concerning
is that the NLOS path loss model in 3GPP and ITU-R is
based on urban measurements, not the rural areas which are
to be modeled [1], [46], since the extended Sakagami path
loss prediction formula is unsuitable for areas with extremely
low average building height (i.e. rural and suburban areas).
Omote et al. [46] conclude that (6) is only applicable for
average building heights greater than 5 m, so they added a
new parameter to account for this based on occupancy ratio –
the ratio between the occupancy area of buildings in a sampled
area and the total sampled area [47].
The only effort we could find to validate (6) above 6 GHz
in [11] was from a small measurement campaign at 24 GHz
conducted over limited 2D T-R separation distances between
200 to 500 m [22], even though (6) is specified for 2D
distances up to 5 km (and the original Sakagami model
in [37] was valid up to 10 km). The work in [22] indicates
a reasonable match between the measurements and model
between 200-500 m, but LOS and NLOS path loss data were
combined together and best-fit indicators (e.g. RMSE) were
not provided, leading one to question the comparison validity.
The facts outlined here uncover the questionable origins
of (1) and (6) and the little empirical evidence to support the
3GPP RMa NLOS path loss model above 6 GHz. While the
WINNER II channel model [36] included sub-6 GHz RMa
path loss measurements, they were still limited according
to [48] and resulted in modifications of the COST231Hata path loss models that do not resemble or align with
those found in 3GPP or ITU-R [11], [23]. Given the fact
that other 3GPP models suffered from errors that required
mathematical corrections for relatively small T-R distances,
leading to much higher losses for large T-R separation distances [18], [21], we conducted a rural macrocell measurement
and modeling study in clear weather at the 73 GHz mmWave
band for LOS and NLOS conditions [1]. This empirical
data for RMa path loss above 6 GHz and in the mmWave
bands makes it possible to generate a generic but reliable
RMa path loss model for frequencies above 500 MHz and
beyond 100 GHz that could be used by 3GPP, ITU-R, and
others.
III. 73 GHz RMa M EASUREMENTS
A. 73 GHz Measurement Equipment
Path loss measurements were conducted in Riner and Christiansburg, Virginia, rural towns in southwest Virginia, USA, at
the 73 GHz frequency band. The TX was positioned on a porch
at Professor Rappaport’s mountain home at a height of 110 m
above the surrounding terrain [1]. A narrowband continuous
wave (CW) signal was transmitted with a maximum RF
power of 14.7 dBm (29 mW) using a rotatable 7◦ azimuth
and elevation half-power beamwidth (HPBW) horn antenna
with 27 dBi of gain for a total effective isotropic radiated
power (EIRP) of 11.7 dBW – relatively low EIRP compared to
currently deployed RMa cellular base stations. The transmitter
used a 5.625 GHz CW tone that was mixed with a 67.875 GHz
local oscillator (LO) signal (22.625 GHz frequency multiplied
x3 in an upconverter) as depicted in the TX schematic in
Fig. 3.
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An identical rotatable antenna with 27 dBi of gain and 7◦
azimuth and elevation HPBW was used at the RX to capture
the RF signal. The received 73.5 GHz signal was downconverted (with 29.9 dB of gain) with a 67.875 GHz LO (identical
to the TX) to a 5.625 GHz intermediate-frequency (IF) and
then amplified by a 35 dB low-noise amplifier (LNA) after
which the IF signal entered a manual step attenuator to ensure
linear operation when recording power levels with a Keysight
E4407B ESA spectrum analyzer (see Fig. 3 for RX schematic).
Received power levels were recorded in zero-span mode on the
spectrum analyzer, with a 15 kHz bandwidth setting, where
occasional frequency tuning was performed as required due to
oscillator drift. Local time and spatial averaging were used to
obtain received power at each RX location, with a maximum
measurable path loss of 190 dB.
The narrowband receiver used an intentionally insensitive
receiver threshold in order to emulate the equivalent range in
a much wider bandwidth channel than the CW signal used during the measurement campaign. The detector was configured
to ignore any power level below −58 dBm (such that weaker
signals were treated as noise and an outage). This noise vs.
bandwidth tradeoff applies for all radio transmissions, since
the average received power over time (for CW) and over
frequency (for wideband signals), results in identical average
local power levels, independent of bandwidth [25], [28]. As
noted below, the measured RMa channel offered no detectable
angular diversity, due to limited multipath scattering, so that
directional and omnidirectional antennas would be expected to
experience nearly identical distance-dependent path loss with
antenna gains removed. Thus, the 190 dB of measurement
range (including antenna gains) used in this measurement
system accurately predicts path loss for wideband signals, on
the order of hundreds of MHz. This is evidenced by the fact
that the total measurement range of the narrowband system is
190 dB, which is 10 dB greater than the measurement range of
the wide bandwidth channel sounder used in [49] and which
had an 800 MHz bandwidth and 180 dB of dynamic range
to measure downtown Manhattan. Since both measurement
systems employed 11.7 dBW of EIRP transmit power (still a
very small transmission power compared to today’s cellular),
it is reasonable to model an additional 10 dB of EIRP transmit
power for the sounder used in [49], yielding the observation
that the measurement system used here has comparable range
to a sliding correlator with 800 MHz of bandwidth and
190 dB of maximum measurable path loss (with a TX EIRP
of 21.7 dBW).
Our measurements considered a single direction of arrival
and departure using narrowbeam TX and RX antennas, since
only one spatial direction with signal strength was observed
in the RMa scenario, and multipath from other angles was
weak or non-existent. Therefore, unlike in InH, UMa, or UMi
scenarios (see for example, [16], [19], [49], [51], [52], [54]),
the distance-dependent directional path loss models developed
here are expected to have nearly identical PLEs (with antenna
gains included in the link budget as in [28, Eq. (3.9)]) as
compared to omnidirectional path loss models, due to the lack
of angular diversity (e.g. only one spatial lobe) in the RMa
channel.
Fig. 4. (a) Example of receiver measurement van and receiving antenna on a
tripod [1]. (b) Image of TX on the porch with the antenna pointing outwards
towards the undulating terrain [1].
B. Measurement Locations and Methodology
The RMa measurements were made over a two-day period
of clear weather using a receiver measurement van (see
Fig. 4a), with the receiving antenna fixed on a tripod outside
of the van at an average height between 1.6 m and 2 m above
the ground along country roads and streets near rural homes
and businesses. Measurements were made at 14 LOS and
17 NLOS locations where a measurable signal was detected,
while also inducing movement in space (a few mm to cm)
to ensure there was no noticeable constructive or destructive
interference. Five additional locations were tested but the
signal was not detectable and resulted in outages. The 2D
T-R separation distance for LOS locations ranged from 33 m
(free space calibration distance) to 10.8 km, and from 3.4 km
to 10.6 km for NLOS locations. The TX antenna on top of the
mountain ridge and on the porch of the home (see Fig. 4b)
was ∼110 meters above the surrounding countryside and was
located approximately 31 m from the edge of the mountain
drop off as depicted in Fig. 5, and pictured in the northerly
view from the TX in Fig. 6 [1]. During the measurements, the
TX antenna remained at a fixed downtilt of 2◦ . The TX antenna
MACCARTNEY AND RAPPAPORT: RMa PATH LOSS MODELS FOR mmWAVE WIRELESS COMMUNICATIONS
Fig. 5.
Sketch of the TX location on the porch of the mountain home, and surrounding areas [1].
Fig. 6.
Outward view from TX of surrounding area and terrain [1].
azimuth pointing angle and RX antenna azimuth and elevation
pointing angles were manually adjusted to simultaneously
point in the direction that maximized received power at each
RX location. To ensure measurement accuracy, the system was
periodically calibrated at a distance of 33 meters to validate
theoretical FSPL and was reproducible within 0.2 dB of theory
over the two-day measurement campaign.
The TX and RX locations are displayed in Fig. 7 via
Google Earth imagery with lines that show the TX azimuth
scanning window of ±10◦ relative to true North, used to avoid
diffraction from the mountain on the west side of the antenna
(not shown), and the rising slope in the front yard of the
mountain property on the east side of the TX antenna (see
Fig. 6). RX locations where a few small trees blocked the
LOS path were used as LOS locations. Two additional LOS
locations (RX 31 and RX 32) measured during the campaign
were just outside the TX azimuth angle window on the east
side of the TX antenna (see Fig. 7 and green diamonds in
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Fig. 7. Map of TX and RX locations. The yellow star represents the TX,
red pins indicate NLOS locations, and blue pins indicate LOS locations [1].
Figs 9a & 9b), and thus were not used to derive the LOS path
loss models due to diffraction loss from the sloping front yard
(see Fig. 6).
IV. N OVEL RMa PATH L OSS M ODELS AND S IMULATIONS
We now present two simple alternative path loss models
to the existing 3GPP/ITU-R RMa path loss models in (1)
and (6), which can be used from 500 MHz to over 100 GHz.
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These new models are based on the optional path loss models
in 3GPP [11] and the CI models as found in [16]–[19]
and [21]. Here, we propose a physically-based CI RMa largescale path loss model using a 1 m free space reference
distance [16], [18], [50] and develop a new model with
a base station height dependent path loss exponent (CIH).
Both models have a solid physical basis, are proven to be
accurate, reliable, to match measured data well, and are easy
to understand and apply. As noted in Section III, the lack
of spatial lobes [19] in the RMa channel allows the same
path loss model parameters to be used for both omnidirectional and directional antenna systems [25], [28], [52]–[54].∗
Furthermore, models of this form have been shown to work
well for all frequencies from 0.5 GHz to 100 GHz, specifically in the mmWave bands [13]–[18], and are already in
use in 3GPP [11]. CI models have also proven to have
excellent stability and accuracy when predicting path loss
values for scenarios and distances outside the scope of the
original measurements used to create the model [18], [21].
Although measurements were conducted at a single frequency
(73 GHz), evidence in the literature shows that measurement
from 500 MHz to 73 GHz generate accurate path loss models that work well up to 100 GHz [13], [14], [18], [21].
Therefore, we make the reasonable assumption that beyond
the first meter of propagation, the path loss exponent may be
frequency independent as this has been proven many times
from measurements and models across many mmWave bands
in UMa scenarios [11], [13], [14], [16], [18], [19], [21], [54].
Fig. 8. Relationship between TX base station height (h B S ) and decrease in
NLOS path loss for T-R separation distances of 150 m, 500 m, 1 km, 2.5 km,
and 5 km, for the 3GPP RMa NLOS path loss model (6). The UT height
(h U T ) is 1.5 m.
such as in the RMa scenario, the distance d may be represented
by the 2D or 3D distance, as the difference is minuscule.
The first term after the equality sign in (7) models
frequency-dependent path loss up to the close-in reference
distance d0 = 1 m [25], and is equivalent to Friis’
FSPL [25], [35]:
FSPL( f c , 1 m)[dB] = 20log10
4π f c ×109
c
= 32.4 + 20log10 ( f c )
(8)
where f c is the center frequency in GHz, c is the speed of
light in free space or air, 3 × 108 m/s, and 32.4 dB is the
FSPL at 1 m at 1 GHz. Thus, (7) is given by:
PLCI ( fc , d)[dB] = FSPL( f c , 1 m)[dB] + 10n log10 (d) + χσ
A. CI Path Loss Model
CI path loss models have been used for decades for estimating path loss in a variety of scenarios and environments [25]
and have recently been shown to represent outdoor channels
over a vast range of mmWave frequencies with surprisingly
good and robust accuracy [16], [18], [21]. The simplest form
of the model, with a 1 m free space reference distance (d0 ),
led to its adoption as an optional model for UMa, UMi, and
InH scenarios in 3GPP [11], based on numerous experiments
at mmWaves [13]–[17]. Thus, it would also seem reasonable
to consider a CI option for the RMa scenario. We show
subsequently from the measured data that indeed the CI model
offers a good fit for RMa, with a much simpler expression
than (1) and (6).
The general expression for the CI path loss model is:
d
CI
+ χσ ;
PL ( f c , d)[dB] = FSPL( f c , d0 )[dB]+10n log10
d0
where d ≥ d0 and d0 = 1 m
(7)
where d (usually 3D distance) is the T-R separation in m
between the TX and RX, d0 is the close-in free space reference
distance in m, n represents the PLE [16], [25], [51], and f c
is the frequency in GHz. Shadow fading is represented by
the zero-mean Gaussian random variable χσ with standard
deviation σ in dB [16]. For large T-R separations (several km)
∗ As mentioned in Section II, the subtraction of antenna gains while keeping
the omnidirectional PLE can be done in RMa channels because of the lack
of energy arriving from directions other than the dominant angle.
= 32.4 +10n log10 (d) + 20 log10 ( f c ) + χσ ;
where d ≥ 1 m
(9)
Setting the free space reference distance d0 = 1 m provides
a standardized and universal modeling approach for path
loss comparison with a single parameter, the PLE [13]–[16],
[25], [51], and was approved as an optional model for UMa,
UMi, and InH in 3GPP TR 38.900 [11]. The CI model for
RMa (9) requires only a single model parameter, n, also
called PLE, to describe the distant-dependent average path loss
over distance for a wide range of mmWave bands [11], [16],
[18], [21]. The use of 1 m makes sense, because there are
clearly no obstructions in the first meter of propagation from
a transmitting antenna, it models the frequency dependency
of propagation in outdoor channels over a vast span of frequencies, and has exhibited consistent accuracy and parameter
stability across numerous scenarios, distances, and frequency
ranges [16], [18], [21].
B. CIH Path Loss Model
When considering the existing RMa path loss models in
3GPP and ITU-R (see (1) and (6)), there are clearly terms such
as building height and street width that do not make physical
sense, yet there are others, such as TX and RX height above
ground, which would be expected to impact path loss in rural
environments. Since the current 3GPP/ITU-R RMa models
considered TX heights as low as 10 m and as tall as 150 m,
this parameter clearly has much greater range and physical
MACCARTNEY AND RAPPAPORT: RMa PATH LOSS MODELS FOR mmWAVE WIRELESS COMMUNICATIONS
significance than other model parameters (a simulation to
follow shows this). The RX height in the rural scenario, as
specified in 3GPP, ranges from only 1.5 m to 10 m, which is
negligible when considering T-R separation distances of many
kilometers, suggesting the TX height would be the single most
significant physical parameter to include in an RMa path loss
model, besides the close-in free space reference distance.
Fig. 8 shows the effect of base station height (h B S ) on
NLOS path loss for five 3D T-R separation distances (150 m,
500 m, 1 km, 2.5 km, and 5 km) using (6), and the average
decrease in path loss over all of the T-R distances, as a function
of base station height. The results in Fig. 8 are independent
of frequency from (6), and show that by increasing the base
station height from 10 m to 150 m, the path loss is effectively
reduced by approximately 26 dB and 32 dB for T-R separation
distances of 150 m and 5 km, respectively, with an average
decrease of 29 dB over all of the T-R distances.
Here we extend the CI model to include various base station
heights (CIH model), such that the model remains physically
grounded to FSPL at a close-in distance but also models
the PLE dependence on base station height. The CIH model
was inspired by the CIF model introduced in [17] and [18],
which was shown to accurately model the frequency dependence of path loss in indoor environments. This model highlights the importance of the PLE in being able to model
the physical effects in the environment, and encapsulates
a fundamental physical basis of the frequency dependence
due to Friis’ equation at close-in distances (while avoiding
the need for mathematical patches and ensuring remarkable
accuracy when applied for values outside of the measurement
set [16]–[18], [21]).
Work to date used an ad hoc, non-physical basis for modeling the impact of TX height [11], [33], [37]–[39], [43].
By incorporating the TX height as an adjustment to path loss,
we postulated that it would be possible to model secondary
path loss effects due to antenna height, just as the CIF model
accounts for secondary frequency-dependent effects while
retaining the physics of the primary frequency dependency
of FSPL at close-in distances.
The CIH model uses the same mathematical form as the
CIF model [17] and is given here for d0 = 1 m:
PLCIH ( f c , d, h B S )[dB] = FSPL( f c , 1 m)[dB]
h B S − h B0
+ 10n 1 + bt x
log10 (d) + χσ ;
h B0
where d ≥ 1 m
(10)
requires two optimization parameters, the PLE n, and bt x :
PLCIH ( fc , d,h B S )[dB]= 32.4 + 20
log10 ( f c )
h B S − h B0
+ 10n 1 + bt x
log10 (d) + χσ ;
h B0
(11)
where d ≥ 1 m, and h B0 = avg. BS height
As with the CIF model, the CIH model simplifies to the CI
model when bt x = 0 (no dependence on base station height),
or when h B S = h B0 . The closed-form solutions for deriving
the optimal CIH model parameters n and bt x are provided
in the Appendix.
C. 3GPP RMa Monte Carlo Simulations
To compare the modeling accuracy of the CI and CIH RMa
path loss models (9), (11) with the current RMa LOS (1) and
NLOS (6) path loss models in [11], we used the 3GPP default
parameters in Table I and performed Monte Carlo simulations
for two cases. Case one is for a fixed base station height and
case two is for a range of base station heights.
1) Case One—Simulation for 3GPP Default Parameters:
In case one, 50,000 random path loss samples (with 3GPP
default parameters from Table I) were generated from (1)
and (6), for the following frequencies: 1, 2, 6, 15, 28, 38,
60, 73, and 100 GHz, resulting in 450,000 samples each
(50,000 samples × 9 frequencies) for LOS and NLOS. Frequencies below and above 6 GHz were used for the multifrequency simulation and modeling since the overall frequency
applicability range covers 0.5 GHz to 100 GHz for a majority
of path loss models in [11]. The CI model (9) ensures a
seamless path loss model for frequencies from 0.5 GHz to
100 GHz, without discontinuities as demonstrated in [13],
[14], [16], and [18]. Each path loss sample was randomly
generated for a 2D T-R separation distance ranging between
10 m and 10 km for LOS and between 10 m and 5 km
in NLOS,1 along with the corresponding SF values (in dB)
from (1) and (6). When simulating (1), path loss samples for
frequencies above 9.1 GHz were generated from the singleslope portion of (1), based on the breakpoint distance (2) in
LOS. From the simulated 3GPP path loss samples for each
environment, CI models that best fit the data were derived
that resulted in the minimum root mean squared error (RMSE)
between the model and the data. The CI models derived from
) and NLOS (PLCI-3GPP
simulated LOS (PLCI-3GPP
LOS
NLOS ) path loss
samples, were found to be:
PLCI-3GPP
( f c , d)[dB] = 32.4 + 23.1 log10 (d) + 20 log10 ( f c ) + χσLOS ;
LOS
where d ≥ 1 m, and σLOS = 5.9 dB
where h B S is the RMa base station antenna height in meters,
and h B0 is the default base station height or is taken as
the average of all TX heights from a measurement set. The
distance dependence of path loss is denoted by n (identical to the PLE from the CI model), and bt x is a model
parameter that is optimized and which quantifies the linear base station height dependent PLE about the average
base station height h B0 . An effective PLE (PLEe f f ) results
from the scaling of n by bt x andthe TX heights such
B0
. The CIH model only
that: PLEe f f = n · 1 + bt x h B Sh−h
B0
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(12)
PLCI-3GPP
NLOS ( f c , d)[dB] = 32.4 + 30.4 log10 (d) + 20 log10 ( f c ) + χσNLOS ;
where d ≥ 1 m, and σNLOS = 8.2 dB
(13)
Both the LOS and NLOS CI models in (12) and (13) emphatically show that the complicated 3GPP/ITU-R RMa path loss
models in (1) and (6) can be reformulated into succinct and
easy to understand equations with nearly identical performance
1 2D distances were randomly generated per the limits defined in TR
38.900 [11] and Table I, from which 3D distances were calculated using
antenna heights and trigonometry, for simulations.
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in RMSE. The CI LOS model results in an RMSE of 5.9 dB,
within the 4 to 6 dB SF specified for the 3GPP LOS model
in (1). In NLOS the CI model was found to result in an RMSE
of 8.2 dB, very close to the 8 dB SF specified by the 3GPP
NLOS model in (6). The distinguishing observation here is
that the CI model offers a simple and seamless model for all
frequencies from 500 MHz to beyond 100 GHz and has nearly
identical performance in terms of shadowing, yet, does not use
complicated and unreasonable correction factors. Additionally,
the CI models in (12) and (13) exhibit the physics of free
space transmission in the first meter of propagation, and show
that RMa path loss can be modeled by a single parameter,
the PLE, which is independent of frequency for all distances
beyond the close-in distance of one meter. A notable aspect
of the CI model in (13) is the 30.4 coefficient, which corresponds to a PLE n value of 3.04, which is equivalent to
10n = 10 × 3.04 = 30.4, or 30.4 dB of loss per decade
increase in distance.
2) Case Two—Simulation for 3GPP Default Parameters
With Varying Base Station Heights: For case two, the LOS
and NLOS 3GPP models in (1) and (6) were simulated again,
but in this case with samples for varying base station heights
(h B S ) from 10 m to 150 m in 5 m increments, and across
the frequencies previously specified, resulting in 13,050,000
samples each (50,000 samples × 9 frequencies × 29 base
station heights) for LOS and NLOS. From these samples, the
best CIH path loss models (11) were derived to minimize the
RMSE between the model and simulated data. In order to
coincide with the 3GPP model simulations, h B0 was set to
35 m (3GPP default height from Table I). The best fit CIH
) and NLOS (PLCIH-3GPP
) path loss models
LOS (PLCIH-3GPP
LOS
NLOS
derived from the simulations are:
( f c , d, h B S )[dB]
PLCIH-3GPP
LOS
= 32.4 + 20 log10 ( f c )
h B S − 35
+ 23.1 1 − 0.006
log10 (d) + χσLOS ;
35
where d ≥ 1 m, and σLOS = 5.6 dB
(14)
PLCIH-3GPP
( f c , d, h B S )[dB] = 32.4 + 20 log10 ( f c )
NLOS
h B S − 35
+ 30.7 1 − 0.06
log10 (d) + χσNLOS ;
35
where d ≥ 1 m, and σNLOS = 8.7 dB
(15)
The LOS CIH path loss model in (14) was the best fit
model to the simulated LOS 3GPP data from (1), and shows
that estimated path loss in LOS is slightly dependent on the
base station height, as the value bt x = −0.006 shows a very
slight decrease in the effective PLE (the coefficient before the
log10 (d) term in (14)) as the base station height is increased.
This is also confirmed by the fact that (12) and (14) both have
a PLE of 2.31. This lack of sensitivity to TX height stems
from (1) not having an explicit correction factor for the TX
height, although the breakpoint distance (2) is a function of
the TX height (h B S ). The SF of 5.6 dB in the LOS CIH model
as compared to 5.9 dB from the CI model in (12), indicates
that the use of the CIH model (and the second parameter bt x )
reduces the model error by 0.3 dB. This shows that the CIH
model fits the simulated data well and is reasonable to use for
RMa path loss modeling since the SF in (1) is 4 to 6 dB.
Fig. 9. (a) Measured 73 GHz RMa path loss vs. T-R separation distance
along with LOS and NLOS CI path loss models with a 1 m close-in free
space reference distance. (b) Zoomed in view of Fig. 9(a).
For the NLOS CIH path loss model (15) best fit to the
simulated data from (6), the dependence of base station height
is more noticeable than LOS, with bt x = −0.06. From (15) it
is clear that as the base station height increases from 10 m to
150 m, the effective PLE reduces from 3.2 to 2.5, or a 7 dB per
decade of distance reduction in estimated path loss for base
stations with 150 m heights compared to 10 m heights, which
is a considerable contrast at long-range distances. The RMSE
of the CIH model fit to the simulated data is 8.7 dB, similar to
the 8.0 dB from 3GPP (6), thus indicating it is reasonable to
use the simple CIH model to estimate NLOS RMa path loss
for various base station heights.
The similar RMSE values for the CI and CIH models (12)-(15) when fit to simulated data versus the 3GPP
RMa path loss models in (1) and (6), show that the CI and
CIH models are useful for accurately predicting RMa path
loss in LOS and NLOS, and have much simpler forms and
fewer parameters than 3GPP [11]. The best-fit CI and CIH
model parameters and corresponding equation numbers from
the simulated data are provided in Table II. It must be stressed
that (12)-(15) are merely fit to simulated 3GPP data which
have not been validated by extensive measurements above
6 GHz. Section V proceeds to determine new CI and CIH
RMa path loss models based on empirical data.
MACCARTNEY AND RAPPAPORT: RMa PATH LOSS MODELS FOR mmWAVE WIRELESS COMMUNICATIONS
TABLE II
CI AND CIH PATH L OSS M ODEL PARAMETERS FOR LOS AND NLOS
F ROM S IMULATIONS AND M EASUREMENTS , AND C ORRESPONDING
E QUATIONS FOR E ACH PARAMETER S ET. R EFERENCE BASE
S TATION H EIGHT FOR THE CIH M ODEL I S h B0 = 35 m,
AND THE UT H EIGHT I S h U T = 1.5 m
V. E MPIRICALLY BASED RMa PATH L OSS M ODELS
Path loss values at 73 GHz for LOS and NLOS were calculated from measurements described in Section III and were
used as sample data to derive the best-fit model parameters
for the CI and CIH path loss models (See the Appendix
and [17], [18] for closed-form best-fit MMSE optimization
approach).
A. Empirical CI Model Results
Measured path loss data in clear weather and the corresponding CI models are compared with FSPL in Fig. 9(a)
and 9(b). The measured path loss data versus log-distance is
displayed in Fig. 9(a), whereas Fig. 9(b) is a “zoomed in”
view of the measured path loss data. Local time and smallscale spatial averaging were used to record the received power
levels at each location to mitigate small fluctuations in received
power observed in the field that ranged from fractions of a dB
about the mean power in LOS locations, and approximately 35 dB in NLOS locations (likely due to small-scale variations
and foliage movement caused by wind). This allowed us to
capture the mean path loss observed at each location. In
Figs. 9a and 9b, blue circles represent the measured LOS path
loss values, red crosses represent measured NLOS path loss
data, and two green diamonds denote measured LOS data with
partial diffraction from the right edge of the yard near the
mountain top TX (see Fig. 6 [1]).
The LOS CI PLE value calculated from the 73 GHz
measured data is 2.16 and very close to FSPL (PLE of 2 [16],
[25], [35]). The distances (up to and beyond 10 km in clear
weather) achieved are quite remarkable, especially given the
close agreement with FSPL and the very small EIRP of
41.7 dBm. The green diamond LOS path loss values include
diffraction loss and were not used for the CI LOS path loss
model derivation, but are shown to indicate the impact of
diffraction edges close to the transmitter (15-20 dB additional
path loss over long distances, see [1]).
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Measured data in RMa NLOS provided a CI PLE of 2.75,
which is lower than the NLOS UMi and UMa mmWave PLEs
reported in the literature (between 2.9 and 3.2 [16], [18]),
and those defined in the optional 3GPP path loss models
(3.0 for UMa and 3.19 for UMi). This indicates a slight
improvement in received signal level over distance due to taller
base station heights and the lack of building obstructions in
RMa or rural microcell (RMi) scenarios. Tall rural cell sites
are called “boomer cells”, as they can increase coverage in a
rural area beyond a typical 2-3 mile radius by using very tall
transmission points.
The RMSE values for SF of 1.7 dB and 6.7 dB observed in
LOS and NLOS, respectively, are both below the respective
RMSE and SF values provided by 3GPP in (1) and (6)
and from the CI models derived from simulated data
in (12) and (13), which are greater than 4 dB in LOS and
8 dB or higher in NLOS. Additionally, the CI models from
measurements have lower PLEs compared to the CI models
derived from 3GPP simulations, where the measured PLE
in LOS is 2.16 and the 3GPP simulation resulted in a PLE
of 2.31. Similarly, the NLOS PLE from measurements is
2.75, whereas the PLE from 3GPP simulations is 3.04. The
higher PLEs in the models derived from 3GPP simulations
could potentially lead to underestimating interference at large
distances [18].
The CI path loss models for the RMa LOS and NLOS
scenarios, as found from the measured data, are provided here
for 73.5 GHz, and are suitable replacements for the existing
3GPP/ITU-R RMa path loss models given in (1) and (6):
PLCI-RMa
( f c , d)[dB] = 32.4 + 21.6 log10 (d) + 20 log10 ( f c ) + χσLOS ;
LOS
where d ≥ 1 m, and σLOS = 1.7 dB
PLCI-RMa
NLOS ( f c , d)[dB]
(16)
= 32.4 + 27.5 log10 (d) + 20 log10 ( f c ) + χσNLOS ;
where d ≥ 1 m, and σNLOS = 6.7 dB
(17)
Equations (16) and (17) are based on the 73 GHz measurement
campaign reported here but may be assumed to be independent
of frequency beyond the first meter of propagation, similar to
previous UMa studies that showed the PLE is not a function
of frequency beyond the first meter of propagation, in the CI
model [14], [15], [18], [21]. The identical CI path loss model
form is used in 3GPP for the optional path loss models of UMi,
UMa, and InH [11]. The LOS and NLOS RMa CI path loss
models given here are also valid up to and beyond 10 km in
clear weather, based on the measurement study settings. Rain
attenuation has been shown to have a significantly negative
impact on mmWave propagation – 73 GHz experiences 10 dB
of attenuation loss per 1 km of distance for heavy rainfall [3].
Note that (16) and (17) have smaller standard deviations than
the existing 3GPP RMa LOS path loss models for frequencies
from 0.5 GHz to 30 GHz.
B. Empirical CIH Model Results
Path loss data from multiple TX (base station) heights can
be used to derive the optimal CIH path loss model parameters by using the closed-form solution equations provided in
the Appendix. Since path loss data from the measurements
described in Section III were obtained for only a single
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transmitter height (110 m), we must rely on the TX height
dependence in Fig. 8 from the 3GPP NLOS CIH model
derived from simulations, and relate that to bt x in the CIH
empirical model. We used the LOS and NLOS CI model
n parameters in (16)-(17) to solve for bt x . Thus, bt x is used
to model the PLE (n) dependency of base station height as
a mixture between the simulated 3GPP model data and our
measurements at 73 GHz. For example, to solve for bt x in
this case with limited empirical data, we set n CI (derived
from measurements)
from
the CI model in (9) equal to:
B0
from the CIH model (simulations)
n CIH 1 + bt x h B Sh−h
B0
in (11), such that:
h B S − h B0
(18)
n CI = n CIH 1 + bt x
h B0
Solving for bt x results in:
n CI
h B0
·
−1
bt x =
h B S − h B0
n CIH
Fig. 10. Effective PLEs (P L E e f f ) versus base station height in LOS and
NLOS for the RMa CIH path loss models in (21) and (22).
(19)
where in this case, h B S = 110 meters and h B0 = 35 meters.
Thus, to solve for the NLOS CIH model parameter bt x , n CI =
2.75 from (17) and n CIH = 3.07 from (15) are used:
35
2.75
(20)
− 1 = −0.049
bt x =
·
110 − 35
3.07
resulting in bt x = −0.049 for NLOS. Similarly, the bt x value
for LOS was found to be −0.03.
The empirically-based CIH RMa path loss models for LOS
) and NLOS (PLCIH-RMa
(PLCIH-RMa
LOS
NLOS ) are written as:
PLCIH-RMa
( f c , d, h B S )[dB] = 32.4 + 20 log10 ( f c )
LOS
h B S − 35
+ 23.1 1 − 0.03
log10 (d) + χσLOS ;
35
where d ≥ 1 m, and σLOS = 1.7 dB,
and: 10 m ≤ h B S ≤ 150 m
(21)
(
f
,
d,
h
)[dB]
=
32.4
+
20
log
(
f
)
PLCIH-RMa
BS
10 c
NLOS
c
h B S − 35
log10 (d) + χσNLOS ;
+ 30.7 1 − 0.049
35
where d ≥ 1 m, and σNLOS = 6.7 dB,
(22)
and: 10 m ≤ h B S ≤ 150 m
By setting h B S = 110 m, the path loss models in (21) and (22)
revert to the RMa LOS and NLOS CI path loss models
in (16) and (17) with PLEs of 2.16 and 2.75, respectively.
The bt x values of −0.03 and −0.049 in LOS and NLOS,
respectively demonstrate the same trend as the CIH models
from simulated data in (14) and (15) such that the base station
height influences the PLE. Negative bt x values reveal that the
effective PLE decreases as the TX height increases and this
intuitively makes sense since higher base stations would result
in fewer obstructions compared to transmitters closer to the
ground. Table II provides the empirical CI and CIH RMa path
loss model parameters in LOS and NLOS, for comparison with
the simulated RMa path loss model parameters.
The effect of base station height on RMa path loss with
the CIH model is evident in Fig. 10 where the effective RMa
LOS PLE reduces from 2.4 to about 2.1 when the base station
height ranges from 10 m to 150 m. Fig. 10 also shows that
Fig. 11. Relationship between TX base station height (h B S ) and decrease in
NLOS path loss for T-R separation distances of 150 m, 500 m, 1 km, 2.5 km,
and 5 km, for the CIH RMa NLOS path loss model in (22), and the average
decrease in path loss as a function of base station height over all of the T-R
distances. The UT height (h U T ) is 1.5 m.
the effective RMa NLOS PLE reduces from 3.2 with a base
station height of 10 m, to just under 2.6 with a TX height of
150 m. This implies a reduction of 3 dB and 6 dB path loss per
decade of distance in LOS and NLOS, respectively. For RMa
mmWave propagation, this difference can have an appreciable
significance in weather events, where 25 mm/hr rainfall can
result in 10 dB loss per km at 73 GHz [3]. Fig. 11 shows
the decrease in path loss for various T-R separation distances
and the average decrease over all of the T-R distances, as a
function of TX height (similar to Fig. 8 for (6)) for the CIH
NLOS path loss model in (22). This shows that for large T-R
separation distances (5 km), path loss can be reduced by up to
22 dB for a TX height of 150 m compared to 10 m. Note that
3GPP path loss models have been shown to overestimate path
loss at large distances [16], [18]. In Fig. 8 the CIH model from
3GPP simulations predicts, on average, 29 dB less path loss
for a TX height of 150 m compared to 10 m. On the other
hand, the CIH model that includes empirical 73 GHz data,
on average predicts 17 dB less path loss for a TX height of
150 m compared to 10 m. This difference in decrease of path
loss could result in overestimating interference and coverage
when using the 3GPP NLOS RMa path loss model compared
to the CIH NLOS path loss model. It is evident that the CIH
models in (21) and (22) preserve the PLE dependency of base
station heights in the RMa scenario, are accurate and reliable,
and are much simpler and easier to use than the complicated
models in 3GPP [11].
MACCARTNEY AND RAPPAPORT: RMa PATH LOSS MODELS FOR mmWAVE WIRELESS COMMUNICATIONS
VI. C ONCLUSIONS
This paper provided an in-depth study on the existing
3GPP [11] RMa LOS and NLOS path loss models for frequencies from 0.5 GHz to 100 GHz and found that no substantial
empirical evidence exists to date to support adoption of this
model by ITU-R [23]. Given that no work existed in the
literature, and the questionable parameters used in 3GPP
and ITU standards, this paper describes field measurements
conducted in rural Virginia and develops new RMa path loss
models that have been verified by field data and are shown to
be more accurate as well as much easier to use and understand,
based on the fundamental physics of radio propagation, and
include a height dependent PLE since the TX height can have
a considerable effect on RMa path loss.
The LOS CI path loss model in (12) derived from simulated
path loss samples resulted in an RMSE of 5.9 dB, a good
match with the 3GPP LOS model in (1) which specified a
SF of 4 to 6 dB. Similarly, the NLOS CI model in (13) that
was derived from simulating the 3GPP NLOS RMa path loss
model in (6), resulted in an RMSE of 8.2 dB compared to the
SF of 8 dB specified in 3GPP/ITU-R [11], [23]. The similar
performance in LOS and NLOS CI models optimized from
simulated data suggests that a model grounded in the true
physics of free space propagation within the first meter could
be used as an optional model in 3GPP for RMa path loss [17],
[18], [21].
It was also shown that the CIH model could effectively
model RMa path loss in LOS and NLOS environments for
a large range of base station heights. When optimized to fit
simulated 3GPP data from (1) and (6) across an array of
transmitter heights, the optimized CIH models in (14) and (15)
had comparable performance with RMSE values of 5.6 dB and
8.7 dB for LOS and NLOS, respectively, compared to 4 to 6 dB
and 8 dB SF values for the cumbersome 3GPP models in [11].
The CIH model’s effective scaling of PLE by the transmitter
height – a reasonable physically motivated correction factor –
is, therefore, an accurate option for RMa path loss modeling
from 0.5 GHz to 100 GHz.
The CI and CIH model parameters were optimized
from real-world measurement data with directional antennas
using [28, Eq. (3.9)] at mmWave frequencies, in clear weather
and in a rural setting with a TX height of ∼110 m and RX
heights from 1.6 m to 2 m. The derived CI models from measurements resulted in a LOS PLE = 2.16 (σ = 1.7 dB) and a
NLOS PLE = 2.75 (σ = 6.7 dB), indicating how models with
one parameter can faithfully estimate path loss in a much simpler form than 3GPP-style models. The solid physical basis of
the CI path loss model is an important feature as it models true
free space propagation in the first meter, compared to the 3GPP
models that contain numerous and odd correction factors. The
two models for RMa path loss in (16)–(17) and (21)–(22)
may be used for frequencies from 500 MHz and up to at least
100 GHz. It is noteworthy that the narrowband CW measurement system used here is equivalent to a wideband channel
sounder with 21.7 dBW EIRP of RF transmit power over
800 MHz of bandwidth and with 190 dB of dynamic range
(10 dB greater than in [49]), which is still a relatively small
transmit power compared to today’s cellular base stations.
1675
The RMa measurements were also used to derive the
optimal parameters for the CIH model since TX height has
historically been proven to have a large impact on path loss.
Since the measurements consisted of a single base station
height (110 m), we used the simulated CIH models in (14)
and (15) along with measured data to derive the optimal CIH
model parameters. Doing this ensured that for the conditions
of our measurement campaign (h B S = 110 m, and f c =
73 GHz), the CIH models in (21) and (22) revert to the
CI models in (16) and (17). It is obvious from the derived
CIH path loss models in (21) and (22) that the effective PLE
decreases as the base station height increases (bt x = −0.03 in
LOS; bt x = −0.049 in NLOS), where the average decrease
in path loss across all T-R distances, when considering a base
station height of 150 m compared to 10 m, is 17 dB. The
closed-form solution equations to derive optimal CIH model
parameters are provided in the Appendix so that others may
create similar models for RMa path loss.
This paper investigated the questionable use of the current
3GPP/ITU-R RMa path loss models for frequencies above
6 GHz. Empirically-based CI and CIH path loss models
were proposed in (16), (17), (21), and (22), that can be
considered for adoption in 3GPP and ITU-R for frequencies
above 500 MHz to beyond 100 GHz for the RMa scenario.
The models herein are validated with real-world mmWave
measurements at the 73 GHz mmWave band, and have the
same mathematical form as the optional UMa, UMi, and InH
path loss models already in 3GPP [11], and are proven to offer
superior prediction accuracy when applied to new frequencies,
distances, or use cases [18]. It is suitable to extrapolate the
CI and CIH models for 0.5 GHz to 100 GHz from 73 GHz
measurements since many measurements and models across
various macrocell scenarios and mmWave bands have shown
that the propagation path loss exponent (PLE) is independent
of frequency beyond the first meter of propagation. However,
more measurements for other heights and different frequencies
above 6 GHz and in the mmWave bands are needed to further
confirm the accuracy of the CI and CIH RMa path loss models
presented herein.
A PPENDIX
CIH PATH L OSS M ODEL PARAMETER D ERIVATION
The closed-form solutions for obtaining the CIH path
loss model parameters are found by solving for the optimal
parameters that minimize the SF standard deviation, i.e., the
minimum mean squared error (MMSE) between the model
and simulated or measured data. The CIH path loss model
parameter derivation is identical to the CIF model derivation
in [17] and [18], except that here, the frequency parameter is
replaced by a base station height parameter h B S and default
(or average) base station height h B0 .
The CIH path loss model in (10) is rearranged in the form:
PLCIH ( f c , d, h B S )[dB] = FSPL( f c , 1 m)[dB]
nbt x
h B S + χσCIH ;
+ 10 log10 (d) n(1 − bt x ) +
h B0
where d ≥ 1 m
(23)
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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 35, NO. 7, JULY 2017
where n is the PLE that is adjusted by bt x , and where bt x
balances the dependence of path loss in relation to the base
station height h B S . Let A = PLCIH −FSPL( f c , 1 m)[dB], D =
tx
10 log10 (d), H = h B S , and set a = n(1 − bt x ) and g = nb
h B0 ,
then we have:
χσCIH = A − D(a + g H )
(24)
where we wish to minimize the SF standard deviation σ CIH
of the form:
CIH2
χ
[ A − D(a + g H )]2
σ
σ CIH =
=
(25)
N
N
where N is the number of path loss data points. To minimize
the
simply take the partial derivative of
mean square error,
[ A − D(a + g H )]2 with respect to a and then with respect
to g and set both equal to zero as follows:
∂ [ A − D(a + g H )]2
=
D(a D + g D H − A)
∂a
=a
D2 + g
D2 H −
DA
∂
=0
(26)
[ A − D(a + g H )]2
=
D(a D H + g D H − AH )
∂g
=a
D2 H + g
D2 H 2
−
D AH
=0
(27)
which can then be simplified into the following two equations:
D2 H −
DA = 0
(28)
a
D2 + g
2
2 2
a
D H +g
D H −
D AH = 0
(29)
In matrix form, (28) and (29) can be re-written as:
2
2 a
DA
D2 H2
D2
= g
D AH
D H
D H
where a and g can be solved in closed-form by:
2
2 −1 a
D
DA
D2 H2
= 2
D AH
g
D H
D H
(30)
(31)
After solving the system of equations for a and g, the
optimized (minimum RMSE values) n and b parameters can
be calculated as follows:
n = a + g · h B0
g · h B0
bt x =
a + g · h B0
(32)
(33)
ACKNOWLEDGMENT
Special thanks are given to W. Johnston and B. Ghaffari at
the FCC for their assistance in obtaining experimental license
number: 1177-EX-ST-2016. The authors also thank S. Sun,
Y. Xing, H. Yan, J. Koka, R. Wang, and D. Yu, who helped
conduct the propagation measurements.
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George R. MacCartney, Jr. (S’08) received the
B.S. and M.S. degrees in electrical engineering from
Villanova University, Villanova, PA, USA, in 2010
and 2011, respectively. He is currently pursuing the
Ph.D. degree in electrical engineering with the NYU
WIRELESS Research Center, New York University
(NYU) Tandon School of Engineering, Brooklyn,
NY, USA, under the supervision of Prof. Rappaport.
He is a recipient of the 2016 Paul Baran Young
Scholar Award from the Marconi Society. He is also
the recipient of the 2017 Dante Youla Award for
Graduate Research Excellence in Electrical and Computer Engineering from
the NYU Tandon School of Engineering ECE Department. He has authored
or co-authored over 30 technical papers in the field of millimeter-wave
(mmWave) propagation. His research interests include mmWave propagation
test and measurement system design, and channel modeling and analysis for
fifth-generation communications.
Theodore S. Rappaport (S’83–M’84–SM’91–
F’98) received the B.S., M.S., and Ph.D. degrees
in electrical engineering from Purdue University,
West Lafayette, IN, USA, in 1982, 1984, and 1987,
respectively. He founded major wireless research
centers with the Virginia Polytechnic Institute and
State University (MPRG), The University of Texas
at Austin (WNCG), and NYU (NYU WIRELESS)
and founded two wireless technology companies
that were sold to publicly traded firms. He is an
Outstanding Electrical and Computer Engineering
Alumnus and a Distinguished Engineering Alumnus from Purdue University.
He is currently the David Lee/Ernst Weber Professor of Electrical and
Computer Engineering with the New York University Tandon School of
Engineering, New York University (NYU), Brooklyn, NY, USA, and the
Founding Director of the NYU WIRELESS Research Center. He also holds
professorship positions with the Courant Institute of Mathematical Sciences
and the School of Medicine, NYU. He is a highly sought-after technical
consultant having testified before the U.S. Congress and having served the
ITU. He has advised more than 100 students, has more than 100 patents
issued and pending, and has authored or co-authored several books, including
the best seller Wireless Communications: Principles and Practice–Second
Edition (Prentice Hall, 2002). His latest book Millimeter Wave Wireless
Communications (Pearson/Prentice Hall, 2015) was the first comprehensive
text on the subject.