Angular and Temporal Correlation of V2X
Channels Across Sub-6 GHz and mmWave Bands
Chethan Kumar Anjinappa and Ismail Guvenc

arXiv:1804.03505v1 [eess.SP] 6 Apr 2018

Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, NC
Email: {canjina,iguvenc}@ncsu.edu
Abstract—5G millimeter wave (mmWave) technology is envisioned to be an integral part of next-generation vehicle-toeverything (V2X) networks and autonomous vehicles due toits broad bandwidth, wide field of view sensing, and precise
localization capabilities. The reliability of mmWave links may
be compromised due to difficulties in beam alignment formobile channels and due to blocking effects between a mmWave
transmitter and a receiver. To address such challenges, out-ofband information from sub-6 GHz channels can be utilized forpredicting the temporal and angular channel characteristics inmmWave bands, which necessitates a good understanding of how
propagation characteristics are coupled across different bands.
In this paper, we use ray tracing simulations to characterize
the angular and temporal correlation across a wide range of
propagation frequencies for V2X channels ranging from 900 MHz
up to 73 GHz, for a vehicle maintaining line-of-sight (LOS) andnon-LOS (NLOS) beams with a transmitter in an urban environment. Our results shed light on increasing sparsity behavior of
propagation channels with increasing frequency, and highlightthe strong temporal/angular correlation among 5.9 GHz and
28 GHz bands especially for LOS channels.
Index Terms—5G, autonomous vehicles, mmWave, ray tracing,side information, sparsity, V2I, vehicular communication.

I. I NTRODUCTION
Next generation intelligent transportation systems (ITSs)
aim to enable safer, more efficient, and informed road experience for all road users, by applying wireless and IoTtechnologies to allow for vehicle-to-everything (V2X) communication across all elements of road transportation [1]. Existing
technologies for ITS such as 4G LTE and dedicated short range
communication (DSRC) fall short of meeting all requirementsof next generation ITS communications that require high data
rates, precise ranging/sensing capability, and ultra-reliable low
latency communications (URLLC). 5G technology involving
millimeter wave (mmWave) communications is expected toenable several new usecases for autonomous driving [2] andV2X communications, such as platooning capabilities, collusion/queue/curve warning, intersections without traffic lights,
and in-vehicle multimedia entertainment systems [3].
The mmWave systems will likely be initially deployed inconjunction with lower frequency (sub-6 GHz) anchor network
to provide wide area control signals [4]. The performance of avehicular (wireless) communication system critically depends
on the accuracy with which the channel is estimated, and thechannel estimation process can be a source of significant overhead in establishing mmWave links, especially for vehicularscenarios with high mobility. Since the mmWave networks will
co-exist along with the sub-6 GHz communication networks,
one can exploit the out-of-band (OOB) information obtained
from sub-6 GHz band as a side information to improve channel
estimation in mmWave bands [5]–[8]. It therefore carries

critical importance to better understand the behavior of V2X
propagation channel across different vehicular bands.
Use of side information from WiFi bands to improve
mmWave beam steering is studied for indoor scenarios in [5].
In [6], it is considered that side information such as position,
velocity, size, and heading can be communicated from neighboring vehicles using the DSRC technology to improve beamalignment at mmWave frequencies. In [7], authors estimate
the narrow-band multi-antenna channel at mmWave bands,
using the channel estimates at lower, sub-6 GHz bands.
In particular, the spatial correlation matrix from a uniform
linear array at lower bands is translated to correlation matrix
at mmWave bands through interpolation and extrapolation.
A better-performing parametric approach which theoreticallycharacterizes high-frequency correlation is also studied, requiring the knowledge of receiver array geometry and the
distribution of the direction of arrival. In [8], channel training
overhead reduction due to use of sub-6 GHz side information
for beam steering is explored.
To our best knowledge, the correlation among sub-6 GHz
and mmWave signals considering their temporal and angular domain features have not been studied in the literature
for vehicular scenarios. In particular, we consider a wideband single-input single-output channel, and study some key
multipath statistics of the time-of-arrival (TOA), angle-ofarrival (AOA), and angle-of-departure (AOD) of vehicularchannel realizations across a wide range of frequencies, andattempt to capture the channel correlation across different
bands. To analyze whether channel characteristics in lower
bands can be used to predict channel at mmWave frequencies,
we set-up a simple model in Remcom Wireless Insite ray
tracing simulator [9]. Subsequently, we study the correlation
characteristics across different sub-6 GHz and mmWave bands,
ranging from 900 MHz up to 73 GHz, for a vehicle travelingin an urban environment for line-of-sight (LOS) and non-LOS(NLOS) scenarios.
II. S YSTEM M ODEL
Consider the following physical propagation model between
the transmitter and receiver through the omni-directional channel impulse response (CIR):K̃(t)h(t, τ , ψ, θ) =Xρ e−jφk δ(τ − τ ) δ(ψ − ψ ) δ(θ − θ )| k {z } | {z k} | {z k} | {z k}k=1 AnP term

TOA term

AOA term

AOD term(1)where t is the time at which the channel is excited, τk
is the considered time delay, ψk and θk are the AOA andAOD associated with the k th multi-path component (MPC),
respectively. ρk is the amplitude which is based on the path

TABLE I
Frequency bands used in ray tracing simulations.
Band
Frequency(GHz)

Fig. 1: Side view: Vehicular ray-tracing scenario in NorthMoore Street, Rosslyn, Virginia.
loss and shadowing associated with the k th MPC and φk is thephase component associated with the k th MPC which primarily
depends on the time delay and the Doppler shift. All the TOA,AOA, and AOD components are further clustered into thevectors τ = [τ1 , ..., τK̃(t) ], ψ = [ψ1 , ..., ψK̃(t) ], and θ =[θ1 , ..., θK̃(t) ], respectively. The amplitude and phase terms
are merged under the amplitude and phase (AnP) variable,
α = [ρ1 exp(−jφ1 ), ..., ρK̃(t) exp(−jφK̃(t) )]. Intuitively, (1)is the sum of the contributions of discrete MPCs, where, thenumber of MPCs K̃(t) may itself be time-varying due to themobility of the vehicle and the surrounding scatterers.
A main goal in this paper is to investigate the question“What can we say about the CIR h(t, τ , ψ, θ, fi ) at frequency
band fi , given that we know the CIR h(t, τ , ψ, θ, fj ) at frequency band fj ?”. We are primarily interested in the 5.9 GHz
DSRC band commonly considered for V2X communication,and the popular 28 GHz mmWave band. One simple way
to look into this problem is to see if we can have one-toone mapping for the AnP, TOA, AOA and AOD terms fromfi to fj . If there exists a way to translate information fromone frequency band to another then it is easy to answer thequestion. However, while the mechanism for RF propagationis the same, their subtle effects are different at different
frequencies. For instance, at mmWave frequency, diffraction
is not as important, scattering can be higher, MPCs observe
higher path loss, and blockage is more significant.
To quantify the relation between the TOA, AOA, and AOD
at fi and fj , we study their correlation using representative
ray tracing simulations for a V2X scenario. The importance ofstudying correlation across different frequency bands is twofold. First, correlation (or lack of correlation) between thevariables of interest helps us to rule out (or not rule out) the
existence of a one-to-one mapping. Second, correlation can beused to make the prediction at fi , provided estimates at fj .
If variables of interest are highly related then it can be used
to make a more accurate prediction when side informationfrom another band is provided. We revisit the question on sideinformation once we find out the level of correlation acrossdifferent bands. In the next section, we describe the simulation
scenario to study the correlation across different bands.
III. R AY- TRACING S IMULATIONSIn this work a full 3D ray-tracing (RT) simulator, Wireless
Insite [9], is used as a tool for the analysis of site-specific radio
wave propagation. In the past, RT has been reasonably suc-

f1
0.9

f2
1.8

f3
2.1

f4
5.0

f5
5.9

f6
28

f7
38

f8
73

cessful at predicting site-specific mmWave propagation [10].
The mmWave frequencies can be well approximated by ray
optics approaches as the diffraction is low and scattering
are mostly limited to surface reflections [11]. Hence, withproper approximations RT simulators can accurately model themmWave and sub-6 GHz channels. We consider a vehicle-toinfrastructure (V2I) scenario where a moving vehicle communicates with an infrastructure (cellular base station (BS)) asin Fig. 1. We set up a vehicular user equipment (UE) (redpath) and a BS node (green point). All the nodes use halfwave dipole antennas that are excited with varying frequencies.
For simplicity, single input single output (SISO) model isconsidered in this work, that is, we assume both the transmitterand receiver are equipped with a single antenna. In our future
work, we will extend it to the multiple antenna case.
The BS antenna in the RT simulations is placed at a heightof 10 m from the ground and transmits at a power level of
0 dBm. The moving UE antenna is placed at a height of 2 mfrom the ground and takes the indicated route in Fig. 1; this canbe implemented in Wireless Insite using the “Route” feature.
There exists a total of 100 vehicle locations (points) in theroute: the first 30 points correspond to the NLOS trajectory
and the latter 70 points corresponds to the LOS trajectory.
The rationale behind choosing separate LOS and NLOS paths
is that the mmWave channel is often a LOS or quasi-LOS
channel with few dominant path clusters. Thus, it is expectedthat if there exists correlation, then it will be lower in the
NLOS case relative to the LOS case, which will be discussed
further in Section VI. With these settings, we carry out RT
simulations considering the popular sub-6 GHz and mmWave
bands shown in Table I.
From RT simulation, we collected a total of 250 MPCs foreach vehicle location on the route. We note that out of 250
paths only a few paths have non-negligible energy. In order tolimit the number of paths, we employ a thresholding approach.
That is, we consider the path to be present if and only if it isabove a threshold from the main tap (most dominant path). We
refer to this threshold as our “MPC Threshold (MPCT)”. The
choice of MPCT depends on the trade-off between an accurate
representation of the channel and implementation complexity.
Based on the statistics obtained from our experiment, we set
MPCT to 40 dB; See section IV for details. Thus, before we
perform any data processing on the collected data, we apply
an MPCT of 40 dB on the collected data and process it further.
We note that channel parameters extracted from the data canbe significantly different when using a different MPCT value.
The next section provides the statistics obtained from datacollected through RT simulation1 .
IV. M ULTIPATH C HANNEL S TATISTICS OVER SUB -6 GH Z
AND MM WAVE BANDS
Based on the RT simulation framework in Section III, in
this section we provide some key multipath channel statistics
across different frequency bands corresponding to the same
1 Matlab script and data are available online: https://research.ece.ncsu.edu/
mpact/data-management/

90

5.5
f
f

Number of MPCs

70

f

Number of MPCs normalized
wrt delay of the largest arriving MPCs

f1

80

2
3
4

f5

60

f6
f7

50

f8

40
30
20
10

f1

5

f
f

4.5

f

2
3
4

f5

4

f6
f7

3.5

f8

3
2.5
2
1.5

0

1
5

10

15

20

25

30

35

40

45

50

5

25

30

(a) LOS trajectory.

f

Number of MPCs normalized
wrt delay of the largest arriving MPCs

f4
f5
f6
f7
f8

100

50

0

35

40

45

50

35

40

45

50

×10 7

1

f3

150

20

(a) LOS trajectory.

f2

200

15

MPCT (dB)

12
f

10

MPCT (dB)250

Number of MPCs

×10 7

1

f2

10

f3
f4
f5

8

f6
f7
f8

6

4

2

0
5

10

15

20

25

30

35

40

45

50

5

10

15

20

25

30

MPCT (dB)

MPCT (dB)(b) NLOS trajectory.

(b) NLOS trajectory.

Fig. 2: Number of MPCs as a function of MPCT.

Fig. 3: Average normalized number of MPCs with respect tolargest delay of the arriving MPCs as a function of MPCT.

vehicular trajectory in Fig. 1, to better understand how theV2X propagation behavior are coupled across sub-6 GHz andmmWave bands. First, Fig. 2 plots the average number of
MPCs as a function of MPCT at different frequency bands
for both the LOS and NLOS scenarios, respectively. As seen
the average number of MPCs monotonically increases with the
MPCT threshold. This is because with increase in threshold,more MPCs fall within the threshold range. Also, the average
number of MPCs decreases with increase in frequency becauseof higher path loss with traveled MPC distance for higher frequencies. With increase in MPCT, there will be a considerable
mismatch in the number of MPCs at different frequencies.
Fig. 3 plots the number of MPCs normalized with respect
to the excess delay of the latest arriving MPC as a function of
MPCT for both the LOS and NLOS scenarios. This normalized
metric is expected to be more representative of the sparsity of
the channel, since it directly captures the time support of the
propagation channel. Note that the metric decreases with theincrease in the maximum delay and increases with the numberof MPCs when the largest delay of MPC has already arrived.

At first glance, Fig. 3(a) may seem counter-intuitive, this isbecause the metric initially increases with the MPCT followed
by a downfall and then further increase monotonically beyond
a point. The trend is similar at all the frequency bands. The
possible explanation for this phenomenon is that at lower
MPCT the LOS paths arrive upfront followed by the MPCs
clustered around the LOS MPC. These MPCs clustered aroundthe LOS MPC increases the number of MPCs and are often
single bounce reflections which slightly increases the largest
delay resulting in the slight increase of the metric (increasein the number of MPCs is significant) as seen in Fig. 3(b).
As we further increase the threshold, later on, NLOS paths
are pulled into the picture which results in the increase in the
delay by large margin resulting in the reduction of the metric.
Beyond a point, the latest arriving MPC with significant poweris captured. After this point, the increase in threshold only
increases the MPCs which arrive earlier and at lower strength
relative to the latest arriving MPC.
With an MPCT of 40 dB in Fig. 3(a), the latest arriving MPC

7that in practice, there is some correlation between these RVs,
and independence assumption will not usually hold. The RVs
for correlation are defined for different parameters as follows.
Step 1: MPC thresholding:
αk , if |αk | ≥ max |α| − MPCT,
αMPCT (k) =0,otherwise×10 -8
f1
f

6

f
f

RMS-DS (s)

5

2
3
4

f5
f6
f7

4

f8

3

2

1

0
0

5

10

15

20

25

30

35

40

45

50

MPCT (dB)(a) LOS trajectory.
3

×10 -7
f1
f2
f3

2.5

f4
f5

RMS-DS (s)

2

f6
f7
f8

1.5

1

0.5

0
0

5

10

15

20

25

30

35

40

45

50

MPCT (dB)(b) NLOS trajectory.

Fig. 4: RMS-DS as a function of MPCT.

with strong power can be captured; for higher MPCT all the
incoming MPCs tend to have a lower delay but a higher pathloss because of multiple bounce specular reflections which
decreases the signal strength. However, the same phenomenon
is missing in the NLOS trajectory in Fig. 3(b).
In Fig. 4, we present the root-mean-square delay spread(RMS-DS) of the MPCs as a function of MPCT captured at
different frequency bands for the LOS and NLOS trajectories,
respectively. We see that the RMS-DS increases with theincrease in MPCT and saturates beyond a point for both the
LOS and NLOS trajectory. From the plots, it is evident thatsetting MPCT to 40 (25) dB would capture the RMS-DS for
the LOS (NLOS) scenario significantly in all the frequency
bands. For consistency, we set the MPCT to 40 dB in thesequel for both the LOS and NLOS scenarios.
V. C ORRELATION ACROSS D IFFERENT BANDSIn order to assess the temporal and angular correlation
across different bands, we assume TOA, AOA, and AOD terms
as random variables (RVs) and that they are independent. Note

where the index k refers to the k th MPC, α corresponds
to the AnP vector as defined in Section II, and the vector
αMPCT contains the MPCs that are within the threshold range.
In other words, it contains only the MPCs that have nonnegligible energy. We next proceed to place the MPCs in avector according to the bins in which they fall. That is, weform a vector h(x) of size N , where the value of N depends
on the domain and the resolution of choice. The process ofconstructing a sparse vector from αMPCT is as follows.
Step 2: Sparse representation of the CIR:
αMPCT (k) , if k th MPC is present in bin n,h(x) (n) =0,otherwise
where x ∈ {τ , ψ, θ}. Here, h(x) = [h(x) (1), ..., h(x) (N )]represents the CIR in the domain of x, and is a sparse vector
whose length depends on the domain of x and the resolution.
For instance, if x = τ , then h(τ ) corresponds to the CIR
in TOA domain whose length depends on the time resolution
and time range considered. In our simulations, we capture the
TOA terms in the range of 1 nanoseconds to 1000 ns with aresolution of 1 ns. Thus, h(τ ) is a vector of size 1000 capturing
the AnP term with respect to the TOA. Similarly, when x =ψ it corresponds to the AOD term and N depends on the
resolution of elevation and azimuth angle. In our simulations,
we choose the angular resolution of 1 degree. Based on the(x)
above notation, hi is the RV h(x) at frequency band fi .
In order to assess the amount of correlation for a given
RV across different bands, we use the Pearson correlation
coefficient formula which is given by (x)∗  (x)Nhj (n) − µh(x)1 X  hi (n) − µh(x)
j
i
 

Ψh(x) ,h(x) =N − 1 n=1
σh(x)
σh(x)
i
j
i

1
N

where µh(x)=PN i (x)1n=1 |hi (n) − µh(x) |
N −1
(x)

j

(x)
n=1 hi (n)
2

PN

and

σh(x)

=

i

are the mean and standardi

deviation of RV h
at frequency band fi , and (.)∗ denotes
conjugate operation. Similarly, µh(x) and σh(x) are the meanjjand standard deviation of RV h(x) at frequency band fj .
To make the notation and correlation experiment moreclear to the reader we provide the following example. For
instance, consider Ψh(τ ) ,h(τ ) with x being the TOA term. This1
8
corresponds to the TOA correlation2 across frequency band f1
and f8 evaluated at a particular vehicle location. The modulusof Ψh(τ ) ,h(τ ) provides us with the insight of how correlated the
1
8
TOA terms are at f1 and f8 evaluated at a location of interest.
Similar to this we calculate the correlation of TOA, AOA,
and AOD terms at each location for different frequencies and2 We used Matlab’s corrcoef function to calculate correlation. The µxi andσxi are taken care by the Matlab function.

f1
1.00
0.90
0.90
0.93
0.90
0.91
0.91
0.89

f2
0.83
1.00
0.93
0.93
0.95
0.93
0.93
0.88

f3
0.84
0.85
1.00
0.93
0.93
0.92
0.94
0.89

f4
0.81
0.84
0.82
1.00
0.94
0.94
0.95
0.80

f5
0.81
0.83
0.84
0.86
1.00
0.94
0.94
0.90

f6
0.65
0.65
0.67
0.68
0.69
1.00
0.95
0.98

f7
0.56
0.56
0.61
0.64
0.65
0.72
1.00
0.99

f8
0.45
0.45
0.45
0.48
0.60
0.60
0.62
1.00

f6
0.46
0.48
0.52
0.65
0.66
1.00
0.90
0.90

f7
0.46
0.58
0.52
0.65
0.65
0.79
1.00
0.99

f8
0.45
0.48
0.49
0.62
0.62
0.76
0.80
1.00

RP (W)

fi
f1
f2
f3
f4
f5
f6
f7
f8

10-10

f2
0.57
1.00
0.90
0.76
0.77
0.74
0.74
0.74

f3
0.56
0.57
1.00
0.74
0.78
0.77
0.74
0.74

f4
0.48
0.53
0.57
1.00
0.87
0.84
0.87
0.87

f5
0.47
0.53
0.55
0.72
1.00
0.84
0.86
0.86

fi
f1
f2
f3
f4
f5
f6
f7
f8

f1
1.00
0.91
0.91
0.93
0.91
0.90
0.90
0.90

f2
0.74
1.00
0.93
0.94
0.96
0.94
0.93
0.93

f3
0.74
0.78
1.00
0.95
0.95
0.93
0.93
0.93

f4
0.76
0.80
0.79
1.00
0.95
0.94
0.95
0.93

f5
0.75
0.81
0.77
0.79
1.00
0.94
0.94
0.95

f6
0.63
0.63
0.68
0.68
0.65
1.00
0.96
0.94

f7
0.55
0.59
0.59
0.61
0.61
0.72
1.00
0.96

f8
0.47
0.51
0.55
0.54
0.53
0.69
0.74
1.00

(c) AOA: Azimuth angle.

finally average over across all the locations in the LOS andNLOS trajectory separately. The averaged correlation for TOA,AOA, and AOD terms for both LOS and NLOS trajectory at
different frequency bands are tabulated in Table II.
A. Correlation Results
The correlation matrix is normally symmetric since the cor(x)(x)
relation between hi and hj is the same as the correlation(x)(x)
between hj and hi . In order to save on the space, we merge
the correlation results of the LOS and the NLOS trajectoryin the same table: the upper triangular matrix corresponds
to the correlation of the NLOS trajectory while the lower
triangular matrix (in red) corresponds to the correlation of the
LOS trajectory. Table II(a) captures the correlation results of
the TOA, while Table II(b) and Table II(c) correspond to theresults of the azimuth angle of AOD and AOA, respectively.
Results of elevation angle are omitted due to space constraint,
but we note that the trend is similar to the azimuth angle.
From Table II, it is evident that there exists a positive
correlation for TOA, AOA, and AOD terms across all thefrequency bands for both the LOS and the NLOS trajectory.
In fact, the correlation is nearing 1 for LOS trajectory which
implies that the terms of interest have a strong correlation.
Thus, the information from fj can be used to make a moreaccurate prediction at fi . On the other hand, for the NLOS
trajectory, the correlation is moderate. This is because signals
propagate poorly in NLOS conditions both in the sub-6 GHz
and mmWave regime.
VI. C HANNEL P REDICTION WITH OOB MEASUREMENTS
In this section, we discuss whether/how we can predict
the “coarse CIR” at fi provided the estimates at fj . From

300

400

500

600

700

800

900

10-10

1000

f5
f6

10-15
100

(b) AOD: Azimuth angle.

200

Time of arrival (nano seconds)

200

300

400

500

600

700

800

900

1000

900

1000

Time of arrival (nano seconds)
10-10

RP (W)

f1
1.00
0.86
0.85
0.76
0.77
0.73
0.75
0.75

f6

10-15

(a) TOA.
fi
f1
f2
f3
f4
f5
f6
f7
f8

f5

100

RP (W)TABLE II
Correlation across different central frequencies for TOA,AOA, and AOD (MPCT= 40 dB).

f5
f6

10-15
100

200

300

400

500

600

700

800

Time of arrival (nano seconds)

Fig. 5: Received power versus TOA at 5.9 GHz and 28 GHz.
Top/middle/bottom: vehicle location 10/35/60.
the previous section, we know that the temporal and angularcharacteristics of the LOS trajectory are highly correlated at
different frequencies. Hence, we can make a more accurate
prediction of TOA, AOA and AOD terms at fi provided
measure at fj for the LOS trajectory. Thus, from here on, we
restrict our discussion to the LOS trajectory. Without loss ofgenerality, we consider predicting coarse CIR at f6 = 28 GHz
provided estimates at f5 = 5.9 GHz. We split the problem of
CIR prediction into 4 sub-problems: Finding the TOA term,
the AOA term, the AOD term, and the AnP term at 28 GHz
provided the estimates at 5.9 GHz.
1) TOA Term: Fig. 5 shows the received power (RP) in the
TOA domain with MPCT of 40 dB. The subplots correspondto CIR at 3 randomly picked vehicle locations (vehicle location
10, 35, and 60) in the LOS trajectory. It is evident fromthe plots that the TOA of the dominant paths at 5.9 GHz
overlaps with the dominant paths at 28 GHz with a very
high probability. In other words, there is a significant overlap,
albeit not perfect. Due to the mismatch in the MPCs, we
can only obtain a coarse CIR estimate and not perfect CIR.
Based on Fig. 5, we can say that the support set of the TOA
terms are identical at 5.9 GHz and 28 GHz with a very
high probability. Also, note the difference in the RP of the
MPCs. This is obvious because the AnP behaves differently
at different frequencies. That is at mmWave frequency, the RP
is much lower due to diffuse scattering, and single/ multiplebounce specular reflections relative to sub-6 GHz band.
2) AOA and AOD Terms: Fig. 6 and Fig. 7 plot both theelevation and azimuth angles of the AOA and the AOD in thepolar domain, respectively. The radius in the circle corresponds
to the RP of the MPCs in dBm. Note that the RP of all the
MPCs is greater at 5.9 GHz relative to 28 GHz. Similar to
the TOA result, the angles at which the MPCs arrive at thereceiver and depart from the transmitter are almost the sameat 5.9 GHz and 28 GHz. That is, the spatial characteristics are
similar but not exact. Thus, the support set for the AOA andthe AOD terms are identical at f5 and f6 with a very highprobability.

90

90
120

150

120

60

f5

-100

f6

-50

-100
150

30

30

f5

-50

f6

0

180

60

0

210

330

240

0

180

0

210

330

240

300

300
270

270

Fig. 6: AOA at 5.9 GHz and 28 GHz for the vehicle location
60 (LOS path); Left: azimuth angle, right: elevation angle.
90

90

120

60

120

150

30

150

30

-50
180

-50
0

0

f5

210

60
-100

-100

330

0

180

f5

210

f6
240

330

f6
300

270

0

240

300
270

Fig. 7: AOD at 5.9 GHz and 28 GHz for the vehicle location
60 (LOS path); Left: azimuth angle, right: elevation angle.
3) AnP Term: From the previous subsection we know thatthe support set of the TOA, AOA, AOD terms are the samewith a very high probability. However, as obvious, the pathloss (PL) terms are different. In other words, ρk (f5 ) 6= ρk (f6 )for all the considered MPCs k. Often the PL terms can betaken care by the PL models which calculate the RP basedon the distance dependency. For the sake of discussion, we
assume close-in (CI) free space reference distance PL model[12] as: d+ XσCI (2)P L(fi , d) = F SP L(fi , d0 ) + 10γfi log10d0where F SP L(fi , d0 ) = 20 log10 4πfci d0 is the frequency
dependent free space PL with c being the speed of light,
d0 and d being the reference distance for the antenna farfield and distance of UE from BS, respectively, γfi is thefrequency dependent PL exponent term. We assume that the
shadowing effect, XσCI , is independent of frequency. Findingρk (f6 ) provided ρk (f5 ), along with γf5 and γf6 is a simple
substitution problem. That is, we can find the difference in
RP by a simple substitution
given by F SP L(f6 − f5 , d0 ) + 
d10(γf6 − γf5 ) log10 d0 . This the difference in RP between
the two bands of interest. Note that the accuracy of theprediction depends on γfi , and that the PL model should becapable of capturing losses such as atmospheric, penetration,and reflection losses which can be predominant in mmWave
bands.
The term e−jφk (fi ) in (1), on the other hand, characterizes
the phase, where φk (fi ) can be written as:
φk (fi ) = 2πfi τk (t) − φDk − φ0 ,(3)Rv
where φDk = 2π λi t cos(θk (t)) is the Doppler phase shift
due to Doppler frequency. Here, v is the velocity term andλi is the wavelength of fi . If the Doppler frequency iszero or it is negligible, obtaining φk (fi ) provided φk (fj ) is
straightforward with some substitution effort.
In summary, it is possible to accurately predict coarse
CIR at fi provided estimates at fj for the LOS trajectory
because of significant similarity in the temporal and spatial
characteristics. Thus, using temporal and spatial characteristics
from the sub-6 GHz is highly beneficial in improving theresiliency and reliability of mmWave communication in thevehicular scenario.
VII. C ONCLUSION
We used ray tracing simulations to evaluate the joint multipath channel statistics and the correlation among sub-6 GHz
and mmWave bands for a vehicular trajectory in an urban
environment. Our results show that for MPCT of 40 dB, thetemporal/angular correlation among 5.9 GHz and 28 GHz
bands for LOS (NLOS) path range between 0.84 to 0.94 (0.64
to 0.69). The high correlation in the LOS channel characteristics can be utilized for predicting temporal and angularcharacteristics in mmWave bands for LOS path and improving
the resiliency and reliability of mmWave communications
for vehicular scenarios. Our future work includes explicitly
implementing beamforming and beam steering to evaluate correlation behavior and considering more complicated environments with multiple vehicles and mmWave access points. We
will also explore conducting channel propagation experiments
at multiple bands to verify that our observations from RT
simulations are accurate in practice.
ACKNOWLEDGEMENT
This research was supported in part by the U.S. National
Science Foundation under the grant number ACI-1541108.
R EFERENCES[1] S. H. An, B. H. Lee, and D. R. Shin, “A survey of intelligent
transportation systems,” in Proc. Int. Conf. Computational Intelligence,
Communication Systems and Networks, July 2011, pp. 332–337.
[2] C. Mc Goldrick, V. Rabsatt, and M. Gerla, “Independent active ageingthe role of 5G and autonomous vehicles,” IEEE COMSOC MMTC ELetter, 2015.
[3] V. Va, T. Shimizu, G. Bansal, and R. W. Heath Jr., “Millimeter wave
vehicular communications: A survey,” Found. Trends Netw., vol. 10,
no. 1, pp. 1–118, Jun. 2016.
[4] Y. Kishiyama, A. Benjebbour, T. Nakamura, and H. Ishii, “Future stepsof LTE-A: evolution toward integration of local area and wide areasystems,” IEEE Wireless Commun., vol. 20, no. 1, pp. 12–18, Feb. 2013.
[5] T. Nitsche, A. B. Flores, E. W. Knightly, and J. Widmer, “Steering witheyes closed: Mm-wave beam steering without in-band measurement,”in Proc. IEEE Conf. Computer Commun. (INFOCOM), Apr. 2015, pp.
2416–2424.
[6] J. Choi, V. Va, N. Gonzalez-Prelcic, R. Daniels, C. R. Bhat, and R. W.
Heath, “Millimeter-wave vehicular communication to support massive
automotive sensing,” IEEE Commun. Mag., vol. 54, no. 12, pp. 160–
167, 2016.
[7] A. Ali, N. Gonzlez-Prelcic, and R. W. Heath, “Estimating millimeterwave channels using out-of-band measurements,” in Proc. Information
Theory and Applications Workshop (ITA), Jan. 2016, pp. 1–6.
[8] N. Gonzalez-Prelcic, A. Ali, V. Va, and R. W. Heath, “Millimeter-wave
communication with out-of-band information,” IEEE Commun. Mag.,
vol. 55, no. 12, pp. 140–146, Dec. 2017.
[9] “Remcom Wireless Insite Ray Tracing Software,” Website. [Online].
Available: https://www.remcom.com/wireless-insite[10] B. Neekzad, K. Sayrafian-Pour, J. Perez, and J. S. Baras, “Comparisonof ray tracing simulations and millimeter wave channel sounding measurements,” in Proc. IEEE Int. Symp. Personal, Indoor, Mobile Radio
Commun., Sep. 2007, pp. 1–5.
[11] S. G. Larew, T. A. Thomas, M. Cudak, and A. Ghosh, “Air interface
design and ray tracing study for 5G millimeter wave communications,”in Proc. IEEE Globecom Workshops, Dec. 2013, pp. 117–122.
[12] T. A. Thomas, M. Rybakowski, S. Sun, T. S. Rappaport, H. Nguyen,
I. Z. Kovacs, and I. Rodriguez, “A prediction study of path loss models
from 2-73.5 GHz in an urban-macro environment,” in Proc. IEEE Vehic.
Technol. Conf. (VTC), May 2016, pp. 1–5.