Channel Modeling for 60 GHz Fixed mmWave O2I and O2O Uplink with Angular Misalignment

Abstract

In this paper, we examine the effect of misalignment angle on cluster-based power delay profile modeling for a 60 GHz millimeter-wave (mmWave) uplink. The analysis uses real-world data, where fixed uplink scenarios are realized by placing the transmitter at ground level and the receiver at the building level. Both outdoor-to-indoor (O2I) and outdoor-to-outdoor (O2O) scenarios are studied. Using the misalignment angle and the scenario as inputs, we propose a statistical power delay profile (PDP) simulation algorithm based on the Saleh-Valenzuela (SV) model. Different goodness-of-fit metrics reveal that our proposed algorithm is robust to both O2I and O2O scenarios and can approximate the PDPs fairly well, even in case of misalignment.

Full text

IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. XX, NO. X, XXX 2024 1
Channel Modeling for 60 GHz Fixed mmWave O2I
and O2O Uplink with Angular Misalignment
Nitisha Singh ID , Sahaj K. Jha ID , Aniruddha Chandra ID , Radek Zavorka, Petr Horky, Tomas Mikulasek ID ,
Jiri Blumenstein ID , Ales Prokes ID , Jaroslaw Wojtun ID , Jan M. Kelner ID , Cezary Ziolkowski ID
Abstract—In this paper, we examine the effect of misalignment
angle on cluster-based power delay profile modeling for a 60 GHz
millimeter-wave (mmWave) uplink. The analysis uses real-world
data, where fixed uplink scenarios are realized by placing the
transmitter at ground level and the receiver at the building level.
Both outdoor-to-indoor (O2I) and outdoor-to-outdoor (O2O)
scenarios are studied. Using the misalignment angle and the
scenario as inputs, we propose a statistical power delay profile
(PDP) simulation algorithm based on the Saleh-Valenzuela (SV)
model. Different goodness-of-fit metrics reveal that our proposed
algorithm is robust to both O2I and O2O scenarios and can
approximate the PDPs fairly well, even in case of misalignment.
Index Terms—60 GHz mmWave band, misalignment angle,
Saleh-Valenzuela model, power delay profile.
I. INTRODUCTION
Realizing more than 20 Gbps data rates for sixth generation
(6G) dream use cases, such as holographic communication or
tactile internet, is not possible without climbing the spectrum
ladder till the millimeter wave (mmWave) frequencies [1]. The
3rd generation partnership project (3GPP) is currently creating
provisions in the fifth generation new radio (5G NR) frequency
range 2(FR2) up to 71 GHz with a special priority given to 60
GHz [2]. This unlicensed band alleviates hefty spectrum fees,
offers a contiguous band avoiding complex carrier aggregation,
and provides an order of higher bandwidth than sub-6GHz
FR1.
The 60 GHz band suffers from regular mmWave disadvan-
tages, i.e., high directionality and large attenuation, limiting
60 GHz propagation investigations concentrated primarily on
indoor and short-range communication, as evident from some
articles [3], [4] that appeared in the back issues of the
current journal. In most outdoor 60 GHz sounding studies
for link lengths of ∼100m [5]–[7], measurement results were
This work was developed within a framework of the research grants: project
no. 23-04304L sponsored by the Czech Science Foundation, MubaMilWave
no. 2021/43/I/ST7/03294 funded by National Science Centre, Poland under
the OPUS call in the Weave programme, grant no. UGB/22-748/2024/WAT
sponsored by the Military University of Technology, and chips-to-startup
(C2S) program no. EE-9/2/2021-R&D-E sponsored by MeitY, Government
of India.
N. Singh, S. K. Jha and A. Chandra are with the Department of Electronics
and Communication Engineering, National Institute of Technology Durgapur,
West Bengal-713209, India (e-mail: aniruddha.chandra@ieee.org).
R. Zavorka, P. Horky, T. Mikulasek, J. Blumenstein and A. Prokes are with
the Department of Radio Electronics, Brno University of Technology, 61600
Brno, Czech Republic.
J. Wojtun, J. M. Kelner and C. Ziolkowski are with the Institute of
Communications Systems, Faculty of Electronics, Military University of
Technology, Warsaw, Poland.
compared against the standard 3GPP urban micro (UMi)
street canyon model, except [8], where a physics-based model
was developed. On the other hand, geometry-based stochastic
modeling was attempted in [9], while authors in [10], [11]
focused on validating ray tracing based simulation against 60
GHz outdoor measurements.
This motivated us to test the suitability of the band for
outdoor low-mobility links between an user equipment (UE)
and an access point (AP) at a customer premise; often placed
on a rooftop, a window, or mounted on a wall inside a building
[12]. The cellular uplink coverage footprint is smaller than
the downlink coverage footprint, irrespective of the center
frequency. This is because the AP antenna gain is higher than
the one in UE. The presence of antenna arrays at AP increases
the gain difference as well as the coverage gap for 60 GHz
mmWave. Thus, it is important to model 60 GHz uplink, which
defines the lower bound of a cell coverage radius. Further,
narrow beamwidth affects the angular property of the uplink,
and it is worth studying how misalignment can impact the
received signal [13].
In this paper, we investigate the misalignment of 60 GHz
outdoor uplinks in outdoor-to-indoor (O2I) and outdoor-to-
outdoor (O2O) scenarios. We present an algorithm based on
the Saleh Valenzuela (S-V) model, which takes the O2I or
O2O scenario and misalignment range as inputs and simulates
a power delay profile (PDP). Moreover, we employ statistical
metrics such as the root-mean-square (RMS) delay spread,
correlation, and the two sample Kolmogorov-Smirnov (K-S)
test to show that the generated PDPs closely follow the PDPs
in a given case. The major contributions of this paper include:
•We show, based on actual field test data, PDP for both the
outdoor scenarios (O2I/ O2O) can be modeled through an
unified approach. It may be noted that separate measure-
ment based channel models for O2I and O2O cases exist
in the current literature [14, Table 1]. Also, we focus on
rms delay spread, which is a dense multipath component
(MPC) dominated parameter. Although MPCs outnumber
specular components (SCs) in indoor mmWave propa-
gation, the contribution of MPCs is non-negligible for
outdoor propagation environments.
•We show that S-V model, with suitable modification,
can be applied to characterize outdoor long-distance 60
GHz mmWave link. As far as this specific band is
concerned, S-V model implementation was restricted to
short distances, e.g., a 60 GHz desktop channel [15].
•We were able to show that power angular spectrum (PAS)
can be broadly divided into two angular regions, namely

2 IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. XX, NO. X, XXX 2024
Rx
Tx
Rx
Tx
Azimuth
misalignment
Elevation
misalignment𝜽
𝝓
𝝍Total
misalignment
Rx Tx
O2O uplink
𝒅 = 𝟏𝟏𝟎𝐦
O2I uplink
𝒅 = 𝟏𝟎𝟖𝐦
Fig. 1. Details of field measurement: [top] Aerial view of the test site showing
the position of Rx in FEKT building (rooftop for O2O/ wall-mounted for O2I)
and position of Tx at cell edge (≈100m) at ground level, [bottom] Total
Rx misalignment angle calculation from azimuth and elevation misalignment.
Aerial view image courtesy: mapy.cz.
(0◦, 10◦] and (10◦, 25◦], over which the PDP parameters
remain fairly constant, which greatly simplifies angle-
dependent channel model over the sophisticated angular
clustering algorithms [16].
II. FI EL D MEASUREMENT AND POS T-PROCESSING
Fig. 1 describes the O2I and O2O environments for field
measurements conducted at the campus of Brno Univer-
sity of Technology, Brno, Czech Republic (49◦13′37′′N,
16◦34′28′′E). For emulating an uplink scenario, the transmitter
(Tx) was placed at ground level at the edge of a fictitious
cell of radius ≈100m, typical for mmWave urban micro
implementations. The receiver (Rx) was placed at the building
level, inside a window for the O2I case, and on the rooftop
for the O2O case. On the Tx side, we used an analog signal
generator (model: Agilent E8257D) and on the Rx side, a
scalar signal analyzer (model: Rohde & Schwarz FSUP50) was
used like our earlier measurement campaigns [17]–[20], thus,
only the magnitude data is recorded [21]. The power received
was recorded for angular combinations over a frequency range
of 56 GHz to 64 GHz with a frequency resolution of 0.1 GHz
and a minimum angular resolution of 5◦. While the Tx was
realized with a custom-built one-sided SIW slot antenna [22],
the Rx was a standard gain directional horn antenna (model:
Quinstar QWH-VPRR00 50–75 GHz). The Rx antenna was
fitted on an astrotracker motorized mount for angular sweep
control. The half-power beamwidth of the antenna used is 10◦,
which is larger than the angular step variation and ensures
sufficient angular space to receive distinguished MPCs.
For the O2I scenario, the Tx was positioned at a tennis
court (1.6 m above ground) and the Rx was stationed inside
Technicka 12 building (13.5 m above ground level). The
receiver is rotated horizontally (-25◦to 35◦) and vertically
from (-5◦to 5◦)
For the O2O scenario, both the Tx and Rx are placed
outside. The height of the Tx is 1.6 m. The Rx is positioned
at the top of Technicka 12 building (18 m above the ground).
The Rx is rotated horizontally (-22.5◦to 22.5◦) for a vertical
misalignment of 4.33◦and -4.33◦, and from (-25◦to 25◦) for
vertical misalignment of 8.66◦and -8.66◦.
III. CHA NN EL MO DE L DEV EL OPMENT
In Fig. 2, we present the variation of received power with
angular misalignment in the elevation plane (θ)and in the
azimuthal plane (ϕ), measured with respect to the line-of-
sight (LOS), i.e. the line of perfect alignment. The total
misalignment angle ψof the receiver from the transmitter is
given by, ψ= cos−1[cos(θ) cos(ϕ)]. The effect of this total
misalignment on received power can vary across scenarios
(O2I/ O2O), as seen from the different trends in Fig. 1. For
a similar overall misalignment angle, O2I and O2O show
different features; specifically, there are dominant clusters in
the O2O case.
On the other hand, as seen from Fig. 2, for a given scenario,
there exists a strong correlation of power angle profiles (PAPs)
for similar absolute elevation angles. Overall, the PAPs reveal
that misalignment can severely affect the received power. This
motivated us to examine whether it is possible to develop a
model for a directional power delay profile (PDP), |h(τ, ψ)|2,
as a function of misalignment angle (ψ) and temporal index in
the delay domain (τ), which remains fairly stationary within
a given range of ψ.
Fig. 2. PAP(ϕ)and PAS heatmap for [top] O2I [bottom] O2O.
The S-V model is a non-geometry-based statistical model
to describe stochastic properties of delays and amplitudes of
MPCs, where individual MPCs or rays can be grouped into
clusters [23]. Along the clusters and within a cluster, the
amplitudes follow an exponential decay, whereas the delays
of rays and clusters follow Poisson processes. Mathematically,
the channel impulse response (CIR) is represented as [24]
h(t) =
Nc
X
n=1
Nr,n
X
m=1
βm,n exp(jϱm,n )δ(t−Tn−τm,n)(1)
where Ncis the number of clusters, Nr,n is the number of rays
in the nth cluster, and Tnis the arrival time of the nth cluster.
The magnitude, phase, and additional delay of the mth ray
within the nth cluster are given by βm,n,ϱm,n, and τm,n ,
respectively. The inter- and intra-cluster exponential decay

SINGH et al.: 60 GHZ MMWAVE CHANNEL MODEL WITH MISALIGNMENT IN O2I AND O2O SCENARIOS 3
rates, namely Γand γ, define the magnitude of individual
rays according to
β2
m,n =β2
1,1exp[−(Tn−T1)/Γ] exp(−τm,n/γ)(2)
The duration of a cluster and the duration between rays within
a cluster follow exponential distributions
Pr(Tn|Tn−1) = Λ exp[−Λ(Tn−Tn−1)] (3a)
Pr(τm,n|τm−1,n ) = λexp[−λ(τm,n −τm−1,n)] (3b)
with parameters 1/Λand 1/λ representing the average dura-
tion of a cluster and the gap between two consecutive rays
within a cluster, respectively.
Algorithm 1: Simulating directional CIR, h(Sc, ψ)
Input : Sc,ψ
Output: h,t
1if Sc== 1 then
2Choose {γ, Γ, λ, Λ}from Table I for given ψ
3else
4Choose {γ, Γ, λ, Λ}from Table II for given ψ
5end
6Tn←0,ix ←0
7Initialize htand ttwith zero vectors
8for i←1to Ncdo
9Tn:= 0
10 while τm,n < k ∗γ(i)do
11 tval := Tn+τm,n
12 Compute hval according to (1)
13 ix := ix + 1
14 ht(ix) := hval ,tt(ix) := tval
15 τm,n is updated according to (3b)
16 end
17 Tnis updated according to (3a)
18 end
19 Sort and reshape htand ttto obtain ˘
hand t
20 hs∼ N (0, σ2
x)
21 h:= hs∗˘
h
In this paper, we modify the basic S-V model to account for
the misalignment angle as follows. First, the measured PDPs
are normalized and major MPCs are identified by considering
the peaks above the average of the PDP. Following this,
we visually identify the clusters in the measured PDPs. We
observe an average of 2 clusters for the PDPs from the O2I
scenario and an average of 3 clusters in PDPs from the O2O
scenario. Next, the four major S-V parameters, namely, ray
arrival rate (λ), cluster arrival rate (Λ), ray decay rate (γ), and
cluster decay rate (Γ)) are computed. The ray decay rate is
calculated by fitting regression lines through the major MPCs
and the cluster decay rate is calculated by fitting regression
lines through the first peaks in each cluster. The fitting is done
using the linear least squares criterion. The ray arrival rate
is obtained as the mean of time separation between MPCs
and the cluster arrival rate is obtained as the mean of the
time separation between clusters [25]. Further, based on the
results of [21], we divide misalignment into ranges of (0◦,
10◦] and (10◦, 25◦]. The S-V parameters for a particular range
are calculated as the mean of the previously obtained S-V
parameters for each angular position in that range.
We summarize the modified S-V algorithm to generate
directional CIR in Algorithm 1. We take two inputs, one
considering the scenario and the second the misalignment. The
S-V parameters based on the scenario and misalignment range
are used as inputs to generate the PDPs. The parameters used
are detailed in Table I for the O2I scenario and in Table II for
the O2O scenario.
TABLE I
PDP SIMULATION PARAMETERS FOR O2I SCE NAR IO
Misalignment Ncλ1λ2Λγ1γ2Γ
angle (ψ)[1/ns] [1/ns] [1/ns] [ns] [ns] (ns)
0°- 10° 2 6.97 7.29 0.31 0.21 0.79 0.93
10°- 25° 2 7.01 7.14 0.28 0.24 0.86 0.94
LOS 2 5.88 5.88 0.26 0.21 0.58 0.45
TABLE II
PDP SI MUL ATIO N PARA MET ER S FOR O2O S CE NAR IO
Misalignment Ncλ1λ2λ3Λγ1γ2γ3Γ
angle (ψ)[1/ns] [1/ns] [1/ns] [1/ns] [ns] [ns] [ns] [ns]
0°- 10° 3 7.42 4.53 6.86 0.57 0.74 0.69 0.78 4.5
10°- 25° 3 7.12 6.51 7.78 0.56 0.79 0.74 0.81 9.5
LOS 3 6.00 7.00 6.00 0.61 0.72 0.69 0.68 5.0
In our algorithm, we take the first cluster arrival (T1) to
occur at zero. We then run a loop for Nciterations. Thus, for
each cluster, we take the first ray arrival (Tn) to occur at the
beginning of their respective clusters. Within the ray loop, the
time of arrival of each ray (tval) is calculated and the index
of that ray is incremented. We compute the value of hval ,
CIR value according to (1) and update τm,n following the
(3b), while Tnis updated as given by (3a) for each cluster. To
account for the long-term fading and shadowing, we introduce
a log-normal random variable hs. A MATLAB-based code
implementation of the algorithm along with the measured
dataset is made available in a GitHub repository [26].
We obtain the CIR as the output of our algorithm, which is
utilized to generate the PDPs. We compare the performance
of simulated PDP, as obtained from the Algorithm-1, and the
observed PDPs in the following section.
IV. CHA NN EL MO DE L VALI DATIO N
Validation of the algorithm proposed in the previous section
is achieved through a comparison of the simulated PDPs
with the measured PDPs. The goodness of fit (GoF) metrics
quantifying the comparison are twofold. The first metric is the
correlation (ρ)[27],
ρ=





(1/N)PN
n=1 |P(n)||Ps(n)|
q(1/N)PN
n=1 |P(n)|2(1/N)PN
n=1 |Ps(n)|2






(4)
where P(n)and Ps(n)denote discretized measured and
simulated PDPs of length N, while the second metric is two-
sample Kolmogorov–Smirnov (K-S) test statistic (SKS)[28],
SKS = max[F(|P(n)|)− F (|Ps(n)|)] (5)

4 IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. XX, NO. X, XXX 2024
Rx
Tx
Rx
Tx
𝝍
𝟎° < 𝝍 < 𝟏𝟎°
𝝍
𝟎° < 𝝍 < 𝟏𝟎°
Rx
Tx
Rx
Tx
𝝍
𝟏𝟎° < 𝝍 < 𝟐𝟓°
𝝍
𝟏𝟎° < 𝝍 < 𝟐𝟓°
Fig. 3. Comparison of normalized PDPs for O2O/ O2I uplink scenarios for two ranges of misalignment angle (ψ). [left-top] O2I (0°< ψ < 10°), [right-top]
O2I (10°< ψ < 25°), [left-bottom] O2O (0°< ψ < 10°)and [right-bottom] O2O (10°< ψ < 25°).
calculated with a 5% significance level, where F(·)denote
corresponding cumulative distribution functions. In addition
to these two metrics, we also compare the RMS delay spread
values.
In Fig. 3, we depict a comparison of three sets of measured
PDPs for a given range of misalignment angle with the PDP
simulated for that angular range. The simulated PDP (dotted
line) is able to follow the average trend slope for all three
instances and can capture most of the major peaks, i.e., the
multi-path components (MPCs). The claim is further demon-
strated in Fig. 4, where we depict the LoS (no misalignment)
cases and compare the measured and simulated PDPs.
𝝍 = 𝟎°
Rx
Tx
𝝍 = 𝟎°
Rx
Tx
Fig. 4. LOS (ψ= 0°) uplink PDP comparison: [top] O2I [bottom] O2O.
Table III compares the RMS delay spread of the simulated
PDPs with the actual PDPs for the O2I scenario and also
presents the GoF metrics. The RMS delay spread of the
generated PDP lies within 6% of the actual RMS delay spread
values.
The comparison of the RMS delay spread values and the
GoF metrics for the O2O scenario are given in Table IV. In
this case, the RMS delay spread of the generated PDP lies
within 4% of the RMS delay spread values of the actual PDPs.
TABLE III
GOFAND RMS DE LAY SPR EA D COM PARI SO N FOR O2I S CE NAR IO
Misalignment angle GoF RMS delay spread [ns]
ψ θ ϕ Correlation K-S test Measurement Simulation
7.06° 5° 5° 0.93 0.14 0.70
5.00° 0° 5° 0.94 0.21 0.66 0.86
5.00° -5° 0° 0.93 0.15 0.65
11.16° 5° -10° 0.93 0.28 0.94
30.37° -5° 30° 0.93 0.32 0.88 0.99
20.00° 0° -20° 0.93 0.24 0.86
0°(LOS) 0.93 0.22 0.53 0.65
TABLE IV
GOFAN D RMS DEL AY SPR EAD C OM PARI SON F OR O2O S CEN ARI O
Misalignment angle GoF RMS delay spread [ns]
ψ θ ϕ Correlation K-S test Measurement Simulation
5.00° -4.33° -2.5° 0.83 0.24 1.56
10.00° 8.66° -5.0° 0.78 0.35 1.70 1.63
5.00° -4.33° 2.5° 0.81 0.29 1.57
25.00° 0° 25.0° 0.86 0.38 1.74
18.01° -4.33° 17.5° 0.82 0.41 1.68 1.64
13.21° -4.33° -12.5° 0.86 0.38 1.57
0°(LOS) 0.81 0.42 1.72 1.72
V. CONCLUSION
In this paper, we examine 60 GHz fixed uplink channel
PDPs at the edge of a 100m cell in O2I and O2O scenarios
when Tx and Rx are not necessarily aligned with each other.
Based on real measurements, we propose a modified SV
model, and various statistical metrics show that the presented
model can approximate PDPs in both O2I and O2O scenarios.
Our model is a simple alternative to computationally extensive
ray tracing models that often require precise knowledge of the
environment geometry. Our work further shows that with small
modifications, the traditional S-V model developed originally
for characterizing ultra-wide-band channels in the 3-11 GHz
band, can be used to model outdoor mmWave channels at 60
GHz with sufficient accuracy.

SINGH et al.: 60 GHZ MMWAVE CHANNEL MODEL WITH MISALIGNMENT IN O2I AND O2O SCENARIOS 5
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