Verifying Ray Tracing Based CoMP–MIMO Predictions with Channel

Verifying Ray Tracing Based CoMP–MIMO
Predictions with Channel Sounding Measurements
1 Dresden
Richard Fritzsche1 , Jens Voigt2 , Carsten Jandura1 , and Gerhard P. Fettweis1
University of Technology, Vodafone Chair for Mobile Commnications Sytems, Dresden, Germany
2 Actix GmbH, Dresden, Germany, [email protected]
{richard.fritzsche, carsten.jandura, fettweis}@ifn.et.tu-dresden.de
Abstract— Multiple-Input Multiple–Output (MIMO) technology is ready for deployment in commercial cellular networks
in the very near future. Thus, the need of incorporating this
technology into radio network planning and optimization rises
dramatically for network operators. The main question to answer is how accurate MIMO channel models reflect the real
MIMO channel. In this contribution we verify a detailed ray
tracing channel simulator with channel sounding measurements
in the 2.53 GHz range by comparing simulated and measured
eigenvalue characteristics for various Single–User (SU) downlink
scenarios in a Coordinated Multi–Point (CoMP) environment.
From our comparison we can conclude that carefully performed
Geometrical Optics based ray tracing simulations are an adequate prediction model to reflect main characteristics of SU–
MIMO channels even in a CoMP scenario.
I. I NTRODUCTION
Due to spectral efficiency enhancements MIMO technology
is used in next generation communications systems. For a reliable planning and optimization of cellular radio networks accurate channel prediction models are required. An established
method to comprehend radio wave propagation is ray tracing.
Applying MIMO channels into ray tracing simulations was
little analyzed in the past, especially for cooperative network
structures (CoMP). A suitable method to verify the model
accuracy is comparing simulations with measured channel
data. In this contribution ray tracing simulation results are
compared with results from channel sounding, regarding SISO
(Single–Input Single–Output) channels, polarization MIMO
(POL–MIMO) as well as three different spatial SU–MIMO
scenarios. All cases are illustrated in Fig. 1. The measurement
campaign was performed in a European city cellular network
with three base stations having three sectors each.
Our general comparison methodology is illustrated in Fig. 2.
The comparison for the four MIMO cases is based on the
evaluation of the MIMO channel matrix H ∈ CM ×N , where
N and M denotes the number of transmit and the number
of receive antennas, respectively. The matrix elements are
obtained from the channel impulse response hm,n (k) ∈ C
applying a combining scheme (e.g. selection combining),
where k denotes the sample index in time domain. Considering
a cellular network with multiple antennas at each base station
sector, index n can denote an antenna element of an uniform
linear array (ULA), a single column sector antenna, where
the alternative sectors are placed at the same base station
(SEC – sector), or a single column sector antennas, where the
Fig. 1. Classification of SISO, polarization MIMO (POL) and spatial SU–
MIMO (ULA, SEC, and NET) channels. Green arrows represent spatial links,
blue arrows are polarization links.
alternative sectors are places at different base stations (NET –
network), also known as CoMP. At the receiver, m can denote
an antenna array element assigned to a single user or one of
multiple users (MU) equipped with single antenna terminals.
The SU–MIMO cases presented in this paper are illustrated in
Fig. 1. The MU–MIMO cases are analyzed in [1] using the
same measurements and evaluation methodology.
MIMO channel measurements in a similar frequency range
are documented in the literature, see e.g. the recent publications [2]–[5], without comparisons in CoMP–MIMO scenarios
however.
This paper is organized as follows: In Section II the channel sounding measurement campaign is introduced, where in
Section III the ray tracing channel simulator is presented.
In Section IV the comparison methodology is introduced.
We present our comparison results in Section V, before we
conclude this contribution in Section VI.
TABLE I
PARAMETERS FROM THE MEASUREMENT CAMPAIGN
Parameter
Center Frequency
Bandwidth
Transmit Power
Time Window
Samples K
Base Stations / Sectors
Tx Antennas
Rx Antennas
Inter Site Distance
Average Rx Velocity
Snapshots per Route
Fig. 2.
Approach to compare measured and simulated channel data.
II. C HANNEL S OUNDING M EASUREMENT C AMPAIGN
This work is based on channel sounding measurements
carried out in downtown Dresden, Germany, in August 2008 in
the 2.53 GHz range. The map in Fig. 3 shows the deployment
and measurement scenario. The campaign was arranged in
Value
2.53 GHz
21.25 MHz
44 dBm
12.8 µs
273
3/3
XX-POL (BS1), X-POL (BS2, BS3)
PUCA 8
≈ 750 m
4.2 m/s
≈ 450.000
and [2].
During the campaign, Nw = 29 routes were measured
using the RUSK HyEff channel sounder [6]. Every 5.2 ms
a snapshot was recorded, consisting of a channel impulse
response (sampled with K = 273 taps and the sampling
interval ∆τ = 46.9 ns) for each of the 192 (96) links
between a base station and the receiver array, where numbers
in brackets refer to one–column sector antennas. Thus 12
(6) transmitter elements (Ns = 3 sectors with Nt =2 (1)
antenna columns and Nq = 2 polarization directions per
column) sent to 16 receiver elements (Nm = 8 patch antennas
with Np = 2 polarization directions per patch). For other
measurement parameters refer to Table I.
Measurements with a similar equipment have been reported
in e.g. [6] and further references of this group of authors.
For every measurement snapshot µr ∈ Mr the channel
between a transmitter and a receiver element is represented
by the channel impulse response
hM (k, νp , νq , νm , νn , µr , νw , νb ),
(1)
where the arguments denote the following indices:
k
νp
νq
νm
νn
µr
νw
νb
Fig. 3. Map of the measurement area in downtown Dresden. The dashed
green lines show the measurement routes. Base Stations with sector orientations are given as red ellipses.
terms of a cellular network structure with three base stations
and three sectors per base station in a standard tree-fold
sectorization, see Fig. 4 (a). We use one– (BS 2 and BS 3)
and two–column (BS 1) cross–polarized (slanted ±45◦ ) sector
antennas with a gain of +18 dBi. The distance between the
antenna elements at BS 1 is 0.6 λ. At the mobile station side a
uniform circular array with eight dual polarized patch antennas
was mounted onto the measurement car’s roof, see Fig. 4 (b)
—
—
—
—
—
—
—
—
sample index in time domain
polarization component at receiver side
polarization component at transmitter side
receiver patch (at UE)
transmitter element (at BS)
snapshot
measurement route
base station
According to the channel sounding data structure we
constitute
νn = (νs − 1)Nt (νb ) + νt ,
(2)
where νs and νt indexes the sector and the antenna column,
respectively. The number of available columns depends on the
base station:
(
2 for νb = 1
Nt (νb ) =
(3)
1 for 2 ≤ νb ≤ 3
Regarding (2), νn represents the νt -th antenna column of the
νs -th sector at base station νb . The polarization are set to νp =
[1/2] , [horizontal/vertical] and νq = [1/2] , [−45◦ / + 45◦ ].
Furthermore, M symbolizes the measurements.
The measured channel impulse response (1) includes Additive White Gaussian Noise n ∼ CN (0, σn2 ). For noise
reduction, every sample k that does not fulfill the constraint
|hM (k, νp , νq , νm , νn , µr , νw , νb )|2 > σn2
(4)
is excluded from any further evaluation. To estimate the
noise power threshold σn2 , the algorithm presented in [7] was
applied.
(a) Transmitter
Fig. 4.
(b) Receiver
Antennas at the base station (a) and the mobile station (b).
III. R AY T RACING C HANNEL S IMULATION
several meters, see Fig. 5 at a height of 1.8 m above the DEM.
The electrical beam pattern of the transmission and receiver
antennas were included in the ray tracing algorithm.
B. The full 3D GO/UTD Ray Launching Approach
We simulate the single–input single–output (SISO) channel
impulse response using a ray launching algorithm operating in
the above introduced 3D environment model as a deterministic
channel model. This algorithm regards a bundle of rays,
emanating from a transmitter source using a transmit angle
interval of 1◦ that are all traced along until their field strength
falls below a defined noise threshold. For our simulations the
smallest noise level threshold estimated from measurements
is applied, compare (4). This algorithm accesses the 3D
topographical database of the buildings and the ground (see
Section III-A) to determine the nearest obstacle in the current
propagation direction of the ray. Once a ray hits an obstacle the
ray launching algorithm includes the radio wave propagation
effects specular reflection, diffraction, and diffuse scattering in
its ongoing calculation based on the algorithms of Geometrical
Optics, the Uniform Theory of Diffraction, and the Effective
Roughness approach, see Fig. 6. This algorithm calculates all
properties of the electromagnetic field (four complex polarimetric amplitudes, direction of departure (DOD), direction
of arrival (DOA), and time delay of arrival (TDOA)) for
every transmitter–receiver combination. Parameters of the ray
launching simulation are given in Table II.
A. Environment Model
For simulation purposes, the environment of the measurement campaign as shown in Fig. 3 was modeled in a three–
dimensional vector building model that was placed on top of
a Digital Elevation Matrix (DEM) modeling the ground, see
Fig. 5 for a part of this environment model highlighting the
level of detail in it. This vector building uses polygons of any
shape and position to model the buildings in three dimensions.
The transmission antennas were placed in the exact position
Fig. 6. Building model of the whole measurement environment with receiver
planes, placed along the measurement routes.
C. Diffuse Scattering
Fig. 5.
Three–dimensional building model of the environment.
with real azimuth and mechanical tilt values. Receivers are
modeled by horizontal square planes with a lateral size arx of
As strongly suggested by e.g. [8] and [9], we also implemented a diffuse scattering model into our ray launching algorithm. In general we use the Effective Roughness approach of
[10]. Due to the characteristics of our dense urban environment
(having coarser irregularities like windows and ornaments),
we decided to use the Directive Model to determine the
amplitude and direction of scattered rays, hereby reducing the
power (density) of the specular reflected ray accordingly. This
model steers the scattering lobe more into the direction of the
specular reflection than the conventional Lambertain Model,
see especially [9] for a description and discussion. See again
Table II for the parametrization of the diffuse scattering.
D. SISO Channel Impulse Response
The direct result of the ray launching algorithm is the time–
invariant (one sample point) and flat fading (symbol duration
root mean square delay spread) complex polarimetric
(polarization–dependent) impulse response of a single link
radio channel, that can be described as:
X
−j2πdl
al (νp , νq )exp
δ(τ − τl ), (5)
h(τ, νp , νq ) =
λ
scattered rays. As alternative, we introduce two ways to obtain
a polarization direction of a scattered ray:
• random polarization
• mean polarization
The first option randomly distributes the sum power to the co–
and cross– component. Mean polarization, which is used for
the simulations discussed in this paper, assigns equal power
to the co– and cross– component. From (5) we can write
1
|h(τ, i, i)|2 + |h(τ, j, i)|2 ,
2
(6)
where h and h̃ represent the channel before and after diffuse
scattering, respectively.
|h̃(τ, i, i)|2 = |h̃(τ, j, i)|2 =
l
In (5) the following additional representations are used:
l
al (νp , νq )
dl
τl
λ
—
—
—
—
—
one propagation path
the complex attenuation of path l
the length of path l
the propagation delay of path l
the carrier wave length
In contrast to the measurements, in the simulation only
horizontal and vertical polarization directions were used, thus
νp/q = [1/2] , [horizontal/vertical].
E. Polarization Issues
Since all measurement antennas have two polarization directions, polarization MIMO properties were also accessed
during the channel sounding measurement campaign. Consequently, the ray tracing algorithm also needs to model
cross–polarization issues correctly in order to make its results
comparable with the measurements. Polarization issues need
strongly to be divided into two parts (e.g. [11]):
• The polarization de-coupling of the antennas. This is described by the cross–polarization discrimination (XPD),
which is an antenna property.
• The polarization behavior of the channel. This is described by the cross–polarization ratio (XPR), which is a
property of the channel.
Our modeling approach for both parts is described below.
1) Polarization Behavior of the Channel: In order to correctly model the polarization behavior of the channel, a polarimetric (polarization–dependent) calculation of the propagation
effects specular reflection, diffraction, and diffuse scattering is
necessary. The GO/UTD algorithms described in Section IIIB correctly handles the polarization decoupling during specular reflections and diffractions and gives the four complex
polarimetric amplitudes as results. The Effective Roughness
based approach of diffuse scattering instead only calculates
the amplitude of the scattered rays. Phases and polarization
characteristics are unknown due to the incoherent nature of
the Effective Roughness approach, see [9]. Consequently, [9]
suggests a complete incoherent handling of the power of
2) Polarization Properties of the Antenna: The polarization
properties of an antenna due to their XPD property need to be
differently handled at the transmission and receive antennas.
The depolarization handling due to transmission antenna XPD
is calculated from (5) by
2
|h̃(τ, i, i)|2 = (1 − β) |h(τ, i, i)| ,
(7)
2
|h̃(τ, j, i)|2 = β |h(τ, i, i)| ,
(8)
the depolarization handling due to receive antenna XPD is
considered by
2
2
2
|h̃(τ, i, i)|2 = |h(τ, i, i)| −β(|h(τ, j, j)| +|h(τ, j, i)| ), (9)
2
2
2
|h̃(τ, i, j)|2 = |h(τ, i, j)| + β(|h(τ, j, j)| + |h(τ, j, i)| ),
(10)
XPD
where 1 ≤ i, j ≤ 2, i 6= j and β = 10− 20 . Furthermore, h
and h̃ denote the channel impulse responses at the input and
the output of the antennas, respectively.
F. Uniform Antenna Arrays
In order to extend the ray tracing result towards a MIMO
channel impulse response matrix, the MIMO antenna type is
to be taken into account, see e.g. [12]. Because of the approximated building structures in our 3D environment, a separate
placement of transmitter and receiver antenna elements at a
ULA with a distance of several centimeters is not reasonable in
a ray launching model. Thus, for ULA antennas, links between
antenna array elements are constructed from the direct SISO
channel impulse response (5) (from tx array center to rx array
center) using the path wise phase shift ∆γi,l between the array
center and the antenna elements i (plane wave assumption).
The phase shift ∆γi,l can be obtained from the path wise angle
of departure (AOD) and angle of arrival (AOA) and the array
composition
∆γi,l =
−2πdi
cos(ϕi − ϕl ),
λ
(11)
where di , ϕi , and ϕl denote the distance between the array
center and element i, the direction of element i, and the
direction of path l, respectively (see Fig. 7).
A. Position Mapping
As mentioned in Section III a receiver plane in the ray
tracing simulation has a lateral size of arx = 10 m. During
the channel sounding measurements, the car’s speed was about
4.2 m/s (see Table I), while a snapshot was taken every 5.2 ms.
This leads to about 450 measurement snapshots per simulated
receiver plane. Based on geographical snapshot information
(xµr , yµr , zµr ) a set M(νr ) including the indices of all
snapshots lying inside the receiver plane νr is introduced
Fig. 7.
Calculation of the path wise phase shift at the array element i.
M(νr ) = {µr |xζ(νr −1)+1 ≤ xµr ≤ dx (νr − 1)arx ,
yζ(νr −1)+1 ≤ yµr ≤ dy (νr − 1)arx },
From (12) a generic channel impulse response considering
a uniform array at transmitter and receiver can be written as:
X
h(τ, νp , νq , νm , νn ) =
al (νp , νq )δ (τ − τl ) · ...
l
(12)
2πd
(−j λ l +∆γνrx
+∆γνtx
)
,l
,l
m
t
ψνm ,l · e
,
where the transmitter elements are indexed by
νn = (νs − 1)Nt (νb ) + νt ,
(13)
(16)
where the instantaneous route direction is formulated as
dx (νr ) = sgn(xζ(νr ) − xζ(νr −1)+1 ),
(17)
dy (νr ) = sgn(yζ(νr ) − yζ(νr −1)+1 ).
(18)
The function ζ maps the last element of M(νr ) to νr

0
for νr = 0
ζ(νr ) =
max
µ
for
1 ≤ νr ≤ Nr
r

(19)
µr ∈M(νr )
according to the notation from Section II.
Note that we model magnitude variations between array
elements at the receiver, e.g. due to fading effects, with
the random variable ψνm ,l ∼ N (1, σa2 ), where σa2 denotes
the variance of the magnitude of a in order to lower the
correlations between the ULA antenna elements further than
the phase shift of the plane wave model. Notice that ψνm ,l is
only considered in the ULA scenario. Otherwise we constitute
ψνm ,l = 1.
Furthermore, we sample the channel impulse response obtained from (12) to
Z k∆τ
h(k, νp , νq , νm , νn ) =
h(τ, νp , νq , νm , νn )dτ. (14)
The mapping procedure is illustrated in Fig. 8. By calculating
M(1) the first snapshots of a route are mapped to the first
receiver. The final receiver position is got from the average
of the related snapshot positions. The procedure is applied
until all snapshots of a route are mapped to receivers. At the
(k−1)∆τ
For the discussions in Section IV the channel impulse response
is written depending on the receiver plane νr , the measurement
route νw and the base station νb , compare to (1)
hS (k, νp , νq , νm , νn , νr , νw , νb ),
(15)
where S represents the simulation.
Fig. 8.
TABLE II
PARAMETERS FOR THE R AY L AUNCHING A LGORITHM
Parameter
Center Frequency
Relative Permittivity, real part
Effective Roughness [8], [9]
Scattering Directivity [8], [9]
Transmit Angle Interval
Max. Number of Reflections per Ray
Max. Number of Diffractions per Ray
Value
2.53 GHz
4.0
0.3
4.0
1◦
∞
2
IV. C OMPARISON M ETHODOLOGY
In this section we describe the mathematical approach
to map the ray tracing simulation results and the channel
sounding measurements to each other in order to be able to
compare them.
Illustration of the mapping function ζ.
simulation a receiver νr collects each wave front hitting its
plane. From M(νr ) we want to find the snapshot that received
the most dominant of these wave fronts. Hence, we select the
snapshot with the highest power. Based on (1) and (15) a
selection function can be written as follows:
XX
µ̂r (νr ) = argmax
pM (νm , νn , µr )
(20)
µr ∈M(νr ) νm νn
with
pM/S (νm , νn , µr ) =
XXX
k
νp
|hM/S (k, νp , νq , νm , νn , µr )|2 ,
νq
(21)
where we disclaim to explicitly note the arguments νw and νb .
B. SISO Channel Property Analysis
We compare the pathloss between the ray tracing simulation
and the channel sounding measurements as the main SISO
channel property. For this comparison the antenna element ν̂m
of the receiver array νr with the highest receive power during
the measurements is chosen:
X
ν̂m (νr ) = argmax
pM (νm , νn , µ̂r (νr )).
(22)
1≤νm ≤Nm ν
n
The pathloss is calculated out of the measurement results by
selecting the patch ν̂m at the receiver and the antenna element
ν̂n (νs , νb ) at the transmitter, where we appoint νt = 1 (selects
always the first column of a two column sector antenna) from
(21):
LM (νr ) = 10 log10 pM (ν̂m , ν̂n , µ̂r (νr )) .
(23)
The pathloss from simulation results is obtained again from
(21) by
LS (νr ) = 10 log10 pS (ν̂m , ν̂n , νr ) .
(24)
for later comparison. Thereby the channel impulse response
of a link has to be reduced to a single channel coefficient. We
considered selection combining (selection of the sample with
the highest power).
1) POL–MIMO: The elements of the polarization MIMO
channel impulse response matrix HPOL ∈ C2×2 for the
measurements are obtained from (1) by
POL,M
(k, νr , νw , νb ) = hM (k, i, j, ν̂m , ν̂n , µ̂r (νr ), νw , νb ).
(27)
Since the measurement transmit antennas use different polarization directions than the respective antennas in the simulation
case, the ±45◦ polarization at measurement transmit antennas
is shifted back to horizontal/vertical polarization (like the
transmit antennas at the simulation) using the rotation matrix
1
1 1
(28)
T= √
2 −1 1
h̄i,j
and calculating
POL,M
HPOL,M = H̄
C. MIMO Channel Property Analysis
The quality of the MIMO channel can be described by the
MIMO channel capacity. For an equal power distribution for
all antenna elements at the transmitter side the capacity in the
White Gaussian Noise channel can be calculated by
rH
X
σS2
(25)
log2 1 + 2 λi ,
C=
σN
i=1
where rH is the rank of H and λi are the eigenvalues of
2
is
H HH . The ratio of signal power σS2 to noise power σN
called Signal–to–Noise–Ratio (SNR). To obtain independence
from SNR only the distribution of the normalized eigenvalues
are considered for the following analysis, compare e.g. [13]. In
this contribution MIMO systems with a maximum rank rH ≤
3 are used. Because in this case the smallest eigenvalue is
usually negligible in reality, we assume that the consideration
of the two strongest eigenvalues is sufficient. As a reasonable
statistic to describe the MIMO channel structure we introduce
the eigenvalue ratio:


max
(λj )
j=1,...,rH |j6=i
,
reig = 10 log10 
(26)
max (λi )
i=1,...,rH
where the second best eigenvalue is divided by the best
eigenvalue. We now give the formulas to calculate the elements
of the channel impulse response matrices for the simulation
and measurement case for all four MIMO setups (compare
Fig. 1) that we used for our comparison:
• polarization MIMO (POL–MIMO),
• spatial MIMO with a ULA at transmitter (ULA–MIMO),
• cooperation of different sectors at the same site (SEC–
MIMO),
• cooperation of sectors at different sites (NET–MIMO).
Then, a respective channel matrix is constructed for every
setup and used to calculate the eigenvalues and their ratio
T.
(29)
The elements of the polarization MIMO channel impulse
response matrix for the simulation are obtained from (15) by
(k, νr , νw , νb ) = hS (k, i, j, ν̂m , ν̂n , νr , νw , νb ). (30)
hPOL,S
i,j
2) Spatial MIMO: For the three spatial MIMO cases a
reduced channel impulse response is used, where one polarization component is selected at the transmitter (νq = 1) and
the both resulting polarization components at the receiver are
added. From the matrix elements of (29) and from (30) we
get
M/S
h̃
X
(k, νm , νn , νr , νw , νb ) =
POL,M/S
hi,1
(k, νm , νn , νr , νw , νb ),
(31)
i
taking νm and νn into account.
a) ULA–MIMO: Based on (31) the coefficients of the
channel impulse response matrix for the ULA case HULA ∈
C8×2 are selected by
M
hULA,M
(k, νr , νw , νs ) = h̃ (k, i, νn (j, νs ), µ̂r (νr ), νw , 1)
i,j
(32)
from measurement results and by
S
hULA,S
(k, νr , νw , νs ) = h̃ (k, i, νn (j, νs ), νr , νw , 1)
i,j
(33)
from simulation results. Because BS 1 is the only base station
using two–column sector antennas, it is the only one used for
ULA analysis.
b) SEC–MIMO: The elements of the channel impulse
response matrix for SEC–MIMO HSEC ∈ C8×3 are obtained
by
M
hSEC,M
(k, νr , νw , νb ) = h̃ (k, i, νn (νb , j), µ̂r (νr ), νw , νb )
i,j
(34)
from measurement results and by
S
hSEC,S
(k, νr , νw , νb ) = h̃ (k, i, νn (νb , j), νr , νw , νb ) (35)
i,j
from simulation results, both from (31). We obtain the selected
transmitter elements by
νn (νb , j) = (j − 1)Nt (νb ) + 1.
(36)
Remember, as mentioned in Section II, Nt = 2 for BS 1 and
Nt = 1 for BS 2 and BS 3. In the case of SEC–MIMO only
one column of the two–column antennas at BS 1 is used for
analysis.
c) NET–MIMO: The elements of the channel impulse
response matrix for NET–MIMO HNET ∈ C8×3 are obtained
by
(k, νr , νw , νs , νb ) =
hNET,M
i,j
M
h̃ (k, i, νn (νs , νb , j), µ̂r (νr ), νw , νb )
Fig. 9. Comparison of the pathloss and its deviations between measurements
and simulation.
(37)
for the measured channel and by
S
hNET,S
(k, νr , νw , νs , νb ) = h̃ (k, i, νn (νs , νb , j), νr , νw , νb )
i,j
(38)
for the simulated channel, both again from (31). The transmitter elements are taken from
νn (νs , νb , j) = (νs − 1)Nt (νb ) + 1.
(39)
Obviously not every combination of sectors and base stations
is reasonable. Hence, preselections of sectors that cover the
same area were done.
V. R ESULTS
Fig. 10. Comparison of the eigenvalue ratio for measurements and simulation
for POL–MIMO.
A. SISO Analysis
The cumulative distribution function (CDF) of the simulated
pathloss (24) is compared to the CDF of the measured pathloss
(23) on the left side of Fig. 9. The point-by-point deviation between simulation and measurement results (∆L = LS − LM )
is shown on the right side of Fig. 9. The results indicate that
for 75% of the analyzed receiver positions in our environment
the pathloss deviation between simulation and measurement is
less than 10 dB. The average value of the difference is 0.11 dB.
B. MIMO Analysis
1) Polarization MIMO: For POL–MIMO the channel impulse response matrices are given in (30) for simulation
data and in (27) for measurement data. The result of the
eigenvalue difference is shown in Fig. 10. The separation
of the results into line–of–sight (LoS) and non–line–of–sight
(NLoS) situations illustrates a better fitting for NLoS scenarios. The difference for LoS is considerably smaller when the
XPD properties of the transmission and receive antennas are
correctly handled in the ray tracing simulation, see Section IIIE.2. Enabling the diffuse scattering option in the ray tracing
simulation results in negligible differences in the eigenvalue
ratio deviation for POL–MIMO only, compare Fig. 11.
Fig. 11. Eigenvalue ratio deviation for POL–MIMO with and without Diffuse
Scattering option in the simulation.
2) Spatial MIMO: For the three different spatial MIMO setups ULA–MIMO, SEC–MIMO, and NET–MIMO the channel
impulse matrices for simulation and measurements are given
in (32) to (38). As can clearly be seen from Fig. 12, for
ULA–MIMO more than 98% of all receiver positions have
an eigenvalue ratio deviation of less than 10 dB in the case
of ψνm ,l ∼ N (1, σa2 ), see (12). For the case of ψνm ,l = 1 in
(12), the ULA scenario has an average deviation of -17.63 dB
between measurements of simulation, compare Fig. 12. The
In contrast to the influence of diffuse scattering to the receive
power reported in [8] and [9], we could not observe noticeable differences in POL–MIMO comparisons by enabling our
diffuse scattering option in the ray tracing simulator, however.
ACKNOWLEDGMENT
We would like to thank Mr. C. Schneider and Mr. G.
Sommerkorn of Ilmenau University, Germany, and Mr. S.
Warzügel of MEDAV GmbH, Germany, for the assistance
during the measurement campaign as well as Mr. Karthik
Kuntikana Shrikrishna of IIT Madras, Chennai, India, for his
help and fruitful discussions in the correction of the ULA–
MIMO simulation results. The work presented in this paper
was partly sponsored by the German federal government
within the EASY-C project under contracts 01BU0630 and
01BU0638.
R EFERENCES
Fig. 12. Comparison of the eigenvalue deviations between measurements
and simulation for ULA–, SEC–, and NET–MIMO.
difference in the eigenvalue ratio is less than 10 dB in the
SEC–MIMO scenario for about 65% and in the NET–MIMO
scenario for about 85% of all considered receiver positions,
in both cases for ψνm ,l = 1 in (12). Mean value and standard
deviation are summarized in Table III.
TABLE III
R ESULT OVERVIEW
Channel Type
SISO
POL-MIMO
ULA-MIMO
SEC-MIMO
NET-MIMO
Statistic
∆P L
∆reig
∆reig
∆reig
∆reig
Mean [dB]
0.11
0.04
2.04
-4.31
1.08
Std. Deviation
9.27 dB
7.57 dB
3.94 dB
10.47 dB
7.27 dB
VI. C ONCLUSIONS
We compared channel sounding measurements with detailed ray tracing based channel simulations in a European
test CoMP–MIMO network at 2.53 GHz for several MIMO
scenarios. We can conclude that ray tracing simulations are
an adequate prediction technique for main characteristics of
polarization MIMO and various spatial SU–MIMO channels
even in a CoMP scenario, in case:
• Geometrical Optics based polarimetric reflections and
• a limited number of Uniform Theory of Diffractions
based diffractions are considered,
• the diffuse scattering power is correctly modeled,
• for LoS conditions in POL–MIMO, the antenna property
XPD is correctly handled, and
• for ULA–MIMO a statistical term is applied to de–
correlate the ULA elements more than the pure plane
wave reconstruction.
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