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A Link-Level MIMO Radio Channel Simulator for
Evaluation of Combined Transmit/Receive Diversity
Concepts within the METRA project
Laurent Schumacher1, Klaus I. Pedersen2,
Jean Philippe Kermoal1 and Preben Mogensen1, 2
1 Center for PersonKommunikation, Aalborg University, Fredrik Bajersvej 7A-5,
DK-9220 Aalborg East, Denmark, email: {schum,jpk,pm}@cpk.auc.dk
2 Nokia Networks, Niels Jernesvej 10,
DK-9220 Aalborg East, Denmark, email: klaus.i.pedersen@nokia.com
Abstract: This document presents a simple framework for Monte-Carlo simulations of a multiple-
input-multiple-output (MIMO) radio channel. A stochastic model including the partial correlation
between the paths in the MIMO channel, as well as fast fading and time dispersion is proposed. Its
implementation in a COSSAP® primitive model is described. Simulations verify the features of this
primitive model. However, the stochastic model still needs to be validated by comparison with
results of measurement campaigns currently in progress [1,2]. This COSSAP® block will later help
to investigate combined transmit/receive diversity concepts as part of the European IST
(Information Society Technologies) METRA (Multi Element Transmit and Receive Antennas)
project [3].
1. Introduction
The remarkable Shannon capacity gains available from deploying multiple antennas at both the
transmitter and receiver of a wireless system, has generated great interest recently [4, 5]. Large
capacity is obtained via the potential decorrelation in the multiple-input-multiple-output (MIMO) radio
channel, which can be exploited to create many parallel subchannels. However, the potential gain is
highly dependent on the multipath richness in the radio channel, since a fully correlated MIMO
channel only offers one subchannel, while a completely decorrelated channel offers multiple
subchannels depending on the antenna configuration. Today, most simulation studies have been
conducted assuming either fully correlated/decorrelated channels, while a partially correlated channel
should be expected in practice. The objective of this document is therefore to derive and to implement
in COSSAP® a realistic MIMO channel model, which is applicable for link level simulations in order
to perform evaluation studies of combined transmit/receive diversity concepts under realistic
propagation conditions, including channel estimation errors and other algorithmic imperfections.
During the last decade, there has been many studies focusing on single-input-multiple-output (SIMO)
radio channel models for evaluation of adaptive antennas at the base station [6]. In this study, the goal
is to take advantage of the numerous results obtained from studying SIMO channels, and to try to
extrapolate these findings into a simple wideband stochastic MIMO channel model to be implemented
in a COSSAP® primitive model.
2. Stochastic model
Let us consider the set-up pictured in Fig. 1 with M antennas at the base station (BS) and N
antennas at the mobile station (MS). The signals at the BS antenna array are denoted
T
Mtytytyt )](),...,(),([)( 21
=y, where )(tym is the signal at the th
m antenna port and
[]
T
. denotes
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transposition. Similarly, the signals at the MS are the components of the vector
T
Ntststst )](),...,(),([)( 21
=s.
Mobile station (MS) Base station (BS)
N-antennas M-antennas
s(t) y(t)
Scattering
medium
y1(t)
s1(t)
y2(t)
s2(t)
sN(t)
.............
.............
yM(t)
Figure 1: Arrays in a scattering environment
The wideband MIMO radio channel which
describes the connection between the MS and the
BS can be expressed as
()
∑
=−= L
lll
1
)(
ττδτ
AH
where ∈)(
τ
H MxN,
[
]
NM
l
mnl ×
=)(
α
A is a
complex matrix which describes the linear
transformation between the two considered
antenna arrays at delay l
τ
and )(l
mn
α
is the
complex transmission coefficient from antenna n
at the MS to antenna m at the BS.
Notice that this is a simple tapped delay line model, where the channel coefficients at the L delays are
represented by matrices. The relation between the vectors )(t
y and )(t
s can thus be expressed as
∫−=
τττ
dtt )()()( sHy (1) or ∫−=
τττ
dtt T)()()( yHs (2)
depending on whether the transmission is from MS to BS, or vice versa. The potential gain from
applying diversity concepts is strongly dependent on the correlation coefficient between the
components of )(
τ
H and thus of l
A.
The spatial correlation function observed at the BS has been studied extensively in the literature for
scenarios where the MS is surrounded by scatterers, while there are no local scatterers in the vicinity
of the BS antenna array, i.e. typical urban environment [7-10]. This basically means that the power
azimuth spectrum (PAS) observed at the BS is confined to a relatively narrow beamwidth.
Consequently, the correlation coefficient between antennas 1
m and 2
m at the BS,
2
)(
2
)(
2121 ,lnm
lnm
BS
mm
ααρ
= (3)
is easily obtained from the literature assuming that the BS antenna array is elevated above the local
scatterers. Notice from (3) that it is assumed that the spatial correlation function at the BS is
independent of n. This is a reasonable assumption provided that all antennas at the MS are closely co-
located and have the same radiation pattern, so they illuminate the same surrounding scatterers and
therefore also generate the same PAS at the BS, i.e. the same spatial correlation function.
The spatial power correlation function observed at the MS has also been extensively studied in the
literature [11,12], among others. Assuming an MS surrounded by local scatterers, antennas separated
by more than half a wavelength can be regarded as practically uncorrelated [13], so
2
)(
2
)(
2121 ,l
mn
l
mn
MS
nn
ααρ
= (4)
nearly equals zero for 21 nn ≠. However, experimental results reported in [14] show that in some
situations antennas separated with half a wavelength might be highly correlated, even in indoor
environments. Under such conditions, an approximate expression of the spatial correlation function
averaged over all possible azimuth orientations of the MS array is derived in [15]. The latter
expression is a function of the azimuth dispersion
[]
1;0∈Λ , where 0=Λ corresponds to a scenario
where the power is coming from one distinct direction only, while 1=Λ when the PAS is uniformly
distributed over the azimuthal range [0°; 360°[ [16]. As the MS is typically non-stationary, the results
presented in [15] are very useful since they are averaged over all orientations of the MS array.
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Given (3) and (4), let us define the symmetrical correlation matrices
[
]
MxM
BS
pqBS
ρ
=R and
[
]
NxN
MS
pqMS
ρ
=R for later use. The spatial correlation function at the BS and at the MS does not
provide sufficient information to generate the matrices l
A. The correlation of two transmission
coefficients connecting two different sets of antennas also needs to be determined, i.e.
)6(
)5(,
2121
2211
11
2
2
)(
2
)(
2
BS
mm
MS
nn
lnm
lnm
mn mn
ρρ
ααρ
≅
=
Neither a theoretical expression for (5) nor experimental results have been published according to the
authors’ knowledge. An approximation of (5) is therefore proposed in (6). This approximation is
motivated by [17], where it was found that the correlation between two spatially separated antennas
with different polarisations is given by the product of the spatial and polarisation correlation
coefficients. Relation (6) can be shown to be exact using definitions (3) and (4) and assuming that the
average power of the transmission coefficients is identical for a given delay, so
{
}
2
)(l
mnl EP
α
= for all
[]
Nn ,,2,1 K∈ and
[]
Mm ,,2,1 K∈.
3. Simulation of the MIMO channel
3.1. General description
The proposed stochastic model is implemented in a COSSAP® primitive model called
MIMO_CHANNEL whose functional sketch is shown in Fig. 2. It is a complex single-input single-
output (SISO) Finite Impulse Response (FIR) filter whose taps are computed so as to simulate time
dispersion, fading and spatial correlation. To simulate MIMO radio channels, it has to be preceded by
a parallel-to-serial (P/S) converter with turns the N signals transmitted from the MS into a single
complex signal. Similarly, at the output side, the complex signal is serial-to-parallel (S/P) converted
into M signals impinging the BS. On the other hand, its FIR structure enables the user willing to
shape the envelope of the impulse response either to define a synthetic power delay profile, or to use
profiles recorded during measurement campaigns. In the former case, the attenuation and the delay
with respect to the first tap are given for each tap in external files read at the initialisation step of the
block. In the latter case, sampled profiles would be fed directly to the FIR filter. However, this
functionality has not been implemented yet. A steering matrix is also applied to take into account
Direction of Arrival (DoA).
MxM
NxN
Lx[MNx1]
MNxMN
Lx[MNx1]
L
Lx[MNx1]
N
M
SP
PS
MS
(N antennas)
Delay Profile
FIR filter
(L taps)
Steering matrix
Spatial correlation
mapping matrix
Fading characteristics
RMS
RBS
Power Profile
Radiation
Pattern
BS
(M antennas)
COSSAP PRIMITIVE MODEL
Parameters: M, N, L, Max_L, Sampling_Frequency_Hz, Velocity_kmh,
Carrier_Frequency_Hz, IFFT_Length, Doppler_Oversampling,
Doppler_Spectrum_Type, Mean_DoA_BS_deg, Element_Spacing_BS_m,
Step_gai_deg, Random_Seed
Figure 2: Functional sketch of COSSAP® primitive model MIMO_CHANNEL
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3.2. Fast fading
Following the approach in [18], the correlated transmission coefficients can be obtained according to
lll PCaA =
~ where
[]
T
MNx
l
MN
lll
M
ll
l1
)()(
22
)(
12
)( 1
)(
21
)(
11
~
αααααα
KK=A, ∈CMNxMN is a symmetrical
mapping matrix defining the spatial correlation and
[]
T
MNx
l
MN
ll
laaa 1
)()(
2
)(
1K=awith )(l
x
a defined as
random processes. The fading characteristics of the taps )(l
mn
α
are defined by shaping an oversampled
Doppler spectrum in the spatial frequency domain. The inverse Fourier transform of this Doppler
spectrum defines the complex random fading coefficients )(l
x
a in the spatial domain. Then, it is a
simple operation to convert them into the time domain, by taking into account the speed of the mobile.
3.3. Spatial correlation
The symmetrical mapping matrix C results in a correlation matrix T
CCΓ= where the th
yx ),(
element of Γ is the root power correlation coefficient 11
22
mn mn
ρ
between the th
x and th
y element of
l
A
~. These coefficients are computed according to (6) from the symmetrical correlation matrices BS
R
and MS
R fed through external files. The symmetrical mapping matrix C is easily obtained by
applying square root matrix decomposition [19], provided that Γ is non-singular.
3.4. Steering matrix
Broad side
Mean DoA
towards the MS
BS antenna
array
-elementsM
MS antenna
array
-elementsN
Local
scatterers
Figure 3: Sketch of a scenario where all scatterers
are located near the MS so the impinging field at
the BS is confined to a narrow azimuth region with
a well defined mean DoA
()
∫−=
τττϕ
dtt BS )()()( sHWy (7)
The proposed stochastic model only reproduces
the correlation metrics and fast fading
characteristics of the radio channel, while the
phase derivative across the antenna arrays is not
necessarily reflected correctly in the model. The
current model gives rise to a mean phase variation
of 0° across the antenna array. This basically
means that the mean direction-of-arrival (DoA) of
the impinging field correspond to broadside.
However, the stochastic model is easily modified
to comply with scenarios like the one pictured in
Fig. 3, where the mean DoA at the BS °≠ 0
BS
ϕ
.
(1) is then modified to (7) where the steering
diagonal matrix is expressed as (8) with
()
ϕ
m
w
describing the average phase shift relative to
antenna number one assuming that the mean
azimuth DoA of the impinging field equals
ϕ
.
Thus, for an uniform linear antenna array with
()
() ()
()
MxM
M
w
w
w
=
ϕ
ϕ
ϕ
ϕ
L
LOMM
L
L
00
00
00
2
1
W (8)
element spacingd,
() ()
[
]
)sin(2)1(exp 1
ϕπλϕϕ
−
−−= dmjfw mm where )(
ϕ
m
f is the complex
radiation pattern of antenna m,
λ
is the wavelength, and j is the imaginary unit. In situations where
the antenna signals at the array are assumed statistically independent (uncorrelated), it does not make
sense to define a mean DoA, so (1) is applicable without the modification proposed in (7).
3.5. Validation
Tests have been performed in order to check the consistency of the COSSAP® primitive model with
respect to the phenomena it simulates. Spatial correlation results are presented in Fig. 4, which shows
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the correlation between the 16 possible pairs of received signals in a 42×scenario, using white
gaussian noise sources at the transmitting end. Correlations are compared in a completely uncorrelated
case ( IRR == MSBS ), in a fully correlated case (
() ()
qpqpqp MSBS ,1,, ∀== RR ) and in a
partially correlated situation where BS
R and MS
R are worth respectively:
=
17,04,01,0
7,017,04,0
4,07,017,0
1,04,07,01
BS
R (21);
=13,0
3,01
MS
R (22)
As expected, the cross-correlation functions exhibit non-zero values in the correlated cases, whereas
they are close to zero in the uncorrelated case. It is also interesting to notice that in the partly
correlated case, the value of the cross-correlation peak does reflect the correlation degree of the BS
antennas as set through BS
R. Notice in that respect the decrease of the peak of the cross-correlation
for BS1, corresponding to the decrease of
()
m
BS ,1R for increasing m. Similar remarks can be made
for the three other BS antennas.
0
0.5
1
0
0.5
1
0
0.5
1
0
0.5
1
0
0.5
1
0
0.5
1
-5 0 5
0
0.5
1
-5 0 5
0
0.5
1
0
0.5
1
0
0.5
1
-5 0 5
0
0.5
1
-5 0 5
0
0.5
1
abs[E(y
2
,y
1
*
)/(
2
1
)] abs[E(y
2
,y
2
*
)/(
2
2
)]
abs[E(y
2
,y
3
*
)/(
2
3
)] abs[E(y
2
,y
4
*
)/(
2
4
)]
abs[E(y
3
,y
1
*
)/(
3
1
)] abs[E(y
3
,y
2
*
)/(
3
2
)]
*
abs[E(y
4
,y
1
)/(
4
1
)]
*
abs[E(y
4
,y
2
)/(
4
2
)]
*
abs[E(y
3
,y
3
)/(
3
3
)]
*
abs[E(y
3
,y
4
)/(
3
4
)]
*
abs[E(y
4
,y
3
)/(
4
3
)]
*
abs[E(y
4
,y
4
)/(
4
4
)]
0
0.5
1
0
0.5
1
0
0.5
1
13 13
0
0.5
1
abs[E(y
1
,y
1
*
)/(
1
1
)] abs[E(y
1
,y
2
*
)/(
1
2
)]
abs[E(y ,y
*
)/( )] abs[E(y
1
,y
4
*
)/(
1
4
)]
BS1
BS3
BS2
BS4
Figure 4: Magnitude of the correlation function of the signals received at the BS, 2x4 scenario. Square
markers: uncorrelated; circular markers: partly correlated; triangular markers: fully correlated.
4. Concluding Remarks
It is believed that the proposed MIMO channel model and its corresponding COSSAP®
implementation provide a simple framework for simulation of such channels. The model is designed
so that the required parameters are accessible in the open literature for various types of environments.
Thus, existing wideband tapped delay line SISO channel models are easily extended to include
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MIMO. However, the assumption stated in (6) still need to be verified in order to determine whether
the knowledge of BS
R and MS
R are sufficient to simulate the channel, or whether Γ is required.
5. Future work
Future versions of MIMO_CHANNEL will lift up its current limitations. The first one is related to the
hypotheses leading to relations (3) and (6), namely that all antennas at the MS are closely co-located
and have the same radiation pattern on the one hand, and that the average power of the transmission
coefficients is identical for a given delay on the other hand. Another limitation is to be circumvented.
As is, the model does not address some cases of polarisation diversity, where cross-polarisation is
experienced. Improved support of polarisation diversity is thus an item for future work. Besides these
issues, the following improvements will be included in later versions of the primitive model:
• Upload of user-defined sampled impulse responses instead of using only simulated ones
• Application of a steering matrix also at the transmitting end in order to apply beamforming
• Definition of spatial correlation on basis of Doppler spectra in a similar way to the fading
• Interface with network-level simulators
6. References
[1] J.P. Kermoal, P. Mogensen, S.H. Jensen, J. Bach Andersen, F. Frederiksen, T.B.Sørensen, K.I. Pedersen,
"Experimental Investigation of Multipath Richness for Multi-Element Transmit and Receive Antenna Arrays", IEEE
Proc. 51th Vehicular Technology Conference, pp.2004-2008, Tokyo, Japan, May 2000.
[2] J.P. Kermoal, K.I. Pedersen, P. Mogensen, "Experimental Investigation of Correlation Properties of MIMO Radio
Channels for Indoor Picocell Scenarios", accepted for IEEE 52th Vehicular Technology Conference, Boston, United
States, September 2000.
[3] http://www.ist-metra.org
[4] G.J. Foschini, "Layered Space-Time Architecture for Wireless Communication in Fading Environment When Using
Multi-Element Antennas", Bell Labs Technical Journal, pp. 41-59, Autumn 1996
[5] G.G. Raleigh, J.M. Cioffi, "Spatio-Temporal Coding for Wireless Communication", IEEE Trans. on
Communications, Vol. 46, No. 3, pp. 357-366, March 1998.
[6] R.B. Ertel, P. Cardieri, K.W. Sowerby, T.S. Rappaport, J.H. Reed, "Overview of Spatial Channel Models for
Antenna Array Communication Systems", IEEE Personal Communications, pp. 10-21, February 1998.
[7] W.Lee, "Effects on Correlation Between Two Mobile Radio Base-Station Antennas", IEEE Trans. on
Communications, Vol. 21, No. 11, pp. 1214-1224, November 1973.
[8] F. Adachi, M. Feeny, A. Williamson, J. Parsons, "Crosscorrelation between the envelopes of 900MHz signals
received at a mobile radio base station site", IEE Proc. Pt. F., Vol. 133, No. 6, pp. 506-512, October 1986.
[9] J. Salz, J. Winters, "Effect of Fading Correlation on Adaptive Arrays in Digital Mobile Radio", IEEE Trans. on
Vehicular Technology, Vol. 43, No. 4, pp. 1049-1057, November 1994.
[10] K.I. Pedersen, P.E. Mogensen, B.H. Fleury, "Spatial Channel Characteristics in Outdoor Environments and Their
Impact on BS Antenna System Performance", IEEE Proc. Vehicular Technology Conference (VTC'98), Ottawa,
Canada, pp. 719-724, May 1998.
[11] W.C. Jakes, "Microwave Mobile Communications", IEEE Press, 1974.
[12] T. Aulin, "A Modified Model for the Fading Signal at a Mobile Radio Channel", IEEE Trans. on Vehicular
Technology, Vol. 28, No. 3, pp. 182-203, August 1979.
[13] R.H. Clark, "A Statistical Theory of Mobile Radio Reception", Bell Labs System Technical Journal, Vol. 47, pp.
957-1000, July-August 1968.
[14] P.C.F. Eggers, "Angular Dispersive Mobile Radio Environments Sensed by Highly Directive Base Station
Antennas", IEEE Proc. Personal, Indoor and Mobile Radio Communications (PIMRC'95), pp. 522-526, September
1995.
[15] G. Durgin, T.S. Rappaport, "Effects of Multipath Angular Spread on the Spatial Cross-Correlation of Received
Voltage Envelopes", IEEE Proc. Vehicular Technology Conference, pp. 996-1000, Houston, Texas, May 1999.
[16] G. Durgin, T.S. Rappaport, "Basic relationship between multipath angular spread and narrowband fading in wireless
channels", IEE Electronics Letters, Vol. 34, No. 25, pp. 2431-2432, December 1998.
[17] P.C.F. Eggers, J. Toftgaard, A.M. Oprea, "Antenna Systems for Base Station Diversity in Urban Small and Micro
Cells", IEEE Journal on Selected Areas in Communications, Vol. 11, No. 7, pp. 1046-1057, September 1993.
[18] T. Klingenbrunn, P.E. Mogensen, "Modelling Frequency Correlation of Fast Fading in Frequency Hopping GSM
Link Simulations", IEEE Proc. Vehicular Technology Conference, pp. 2398-2402, Amsterdam, Netherlands,
September 1999.
[19] G.H. Golub, C.F. Van Loan, "Matrix Computations", Third Edition, Johns Hopkins University Press, 1996.
