Path-Based Spatial Channel Modeling
The concept of RF signal fading is a familiar one to engineers who deal with wireless RF, but today’s focus on advanced radio techniques (e.g., MIMO, spatial channel modeling) begs for more than a superficial understanding of these complex subjects.
Spirent’s Doug Reed has authored a trio of thoughtful yet accessible white papers that will provide a better understanding of the RF challenges faced by every engineer working in the wireless industry. This white paper specifically addresses the most commonly encountered spatial models used by the wireless industry today.
Topics that are addressed include:
- Path Characteristics
- Introduction to the Spatial Channel Model (SCM) & Spatial Channel Model [Extended] (SCME)
- Model Overview
- Correlation between Modeled Components
- Why Are Wideband Parameters Correlated?
- Generating the SCM Model Components
- Path Characteristics
- SCME
- Tap Delay-line Model
- WINNER-II
- SCM & SCME in Standards
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Path-Based Spatial Channel Modeling
SCM/SCME
White Paper 102
2 | Path-based Spatial Channel Modeling
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White Paper 102 | 3
1.1. Introduction
The Spatial Channel Model (SCM) [i][ii] was designed for evaluating multiple-antenna
systems and algorithms. The model was developed within a combined 3GPP-3GPP2 ad-
hoc group to address the need for a precise channel model able to facilitate fair
comparisons of various MIMO proposals. The model uses a system-level approach to
simulate performance across the range of conditions expected in a cellular system. This
ensures that multiple-antenna algorithms are not only optimized for a few test conditions,
but across the system as a whole.
In the following sections, the concepts of spatial channel modeling are introduced and
explained.
1.1.1. Introduction to SCM & SCME
The SCM specifies a set of paths between the Base Station (BS) and the Mobile Station
(MS) based on a stochastic model of correlated random variables to establish the spatial,
temporal, and propagation characteristics for a particular channel realization. The model
is antenna-independent, and specifies path characteristics to establish the fading and
correlation behavior between antenna elements. The SCM standard is based on a sum-
of-sinusoids technique wherein the paths are assumed to be composed of a number of
sinusoids representing plane waves. Due to the effects of scattering these plane waves
are distributed across angle. The SCM may alternatively be implemented via a filtered
noise approach where the temporal characteristics are set by a Doppler filter, and the
spatial characteristics are set by a correlation matrix.
For large-scale channel characteristics such as delay Spread (DS), shadow fading (SF),
and angle spread (AS), the model incorporates pre-defined correlated distributions
extracted from measured data. The correlated spatial and temporal characteristics of the
model are generated from random variables to produce a double-directional channel
realization for evaluation. Each channel is unique and represents one possible channel
out of an ensemble of possible channels.
The SCM has been extended by a modification proposed by, The European Wireless
World Initiative New Radio (WINNER) project to increase the bandwidth from 5 MHz up to
100 MHz [iii]. The modified model is called the Spatial Channel Model Extended (SCME)
and is fully described in [iv].
4 | Path-based Spatial Channel Modeling
1.2. Model Overview
There are six different models included in the SCM. Each represents a unique
environment and a unique set of conditions for testing multiple-antenna scenarios at the
system level. The Urban model is the most popular and will be described further below.
The six models presented in the SCM are:
1. Urban
This is a full system-level model. It uses correlated parameters in spatial and
temporal domains to specifying the fading seen by a subscriber. It models medium-
to-dense urban environments.
The angle spread may be selected to be either 8º or 15º.
2. Suburban
This model has a reduced delay spread and is used for modeling lower density
environments.
3. Urban Micro-cell
The micro-cell model uses a uniform departure distribution, a unique delay spread
and propagation models, and includes the option for line-of-site paths.
4. Polarization Model
This model applies a cross-polarization discrimination function (XPD) to specify the
ratio of powers of orthogonal vertical and horizontal components.
The TX source polarization is mapped to vertical and horizontal components for
calculating path correlation and XPD, and is then mapped to the polarization of the
RX antennas.
5. Far Scattering Cluster
“Bad Urban” models typically have a component that arrives relatively late. Bad
Urban models are described by the far-scattering cluster model.
6. Urban Canyon Model
When on a street with tall buildings on either side, the signal is often received from
only one direction. This model aligns the AoAs to simulate this effect.
One additional model included in the SCM is a link-level model used for calibration. It is
not listed as an SCM model because it was only designed for calibrating simulators and
not as a way to compare multiple-antenna algorithms.
The SCM & SCME use a system-level approach to evaluate the range of possible
channels. The channel is drawn randomly from a set of correlated random variables and
is time-evolved for the duration of a call.
White Paper 102 | 5
Figure 1: SCM Path Angle Definitions
As illustrated in Figure 1, the channel model can be described as a geometric model with
one important caveat: due to the difficulty in concurrently generating angles at the BS
and MS, the assumption here is that of a virtual connection, where the AoD and AoA do
not need to align with a single reflector. Thus the model is somewhat more general that
the diagram indicates. A detailed description of Figure 1 is given in [v].
1.3. Correlation between Modeled Components
There are three separate large-scale parameters associated with the SCM. These are DS,
AS, and SF. These parameters have been shown to be log-normally distributed and are
highly correlated with each other.
The correlation coefficients are measured between the Gaussian random variables:
n
α
,
n
β
, and
n
γ
, which are used in the selection of the log-normal values:
DSn
σ
,
ASn
σ
, and
SFn
σ
, where the following equations represent the log-normally distributed variables:
nLNSFn
ASn
DSn
ASnAS
DSnDS
γσσ
σ
σ
μβε
μαε
=
=
=
+
+
)(
)(
10
10
The correlations selected by the model are:
Correlation between DS and AS: ραβ = 0.5
Correlation between SF and AS: ργβ = -0.6
Correlation between SF and DS: ργα = -0.6
6 | Path-based Spatial Channel Modeling
Highly correlated parameters indicate that a common effect is present and that the path
strength is the dominant cause of the high degree of correlation between the DS, AS, and
SF. In addition to these three large-scale parameters, a site-to-site correlation ζ = 0.5 is
applied to the SF component. This characteristic indicates the degree of independence
between paths to different base stations.
The correlated parameters are produced from the correlation matrices A and B, wherein
a difference matrix C = (A-B)½ is shown. C is then multiplied by a Gaussian white noise
vector to obtain the correlated random variables. A common term between sites is
added, being multiplied by a second noise term
ξ
, to produce the site-to-site correlation.
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
=
1
1
1
γβγα
γβαβ
γααβ
ρρ
ρρ
ρρ
A
, and
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
=
ζ00
000
000
Β
,
()
2/1
2/1
1
1
1
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
−
=−=
ζρρ
ρρ
ρρ
γβγα
γβαβ
γααβ
BAC
The resulting correlated Gaussian random variables:
n
α
,
n
β
, and
n
γ
, are obtained, and
used to further specify the Channel Model.
White Paper 102 | 7
1.4. Why are Wideband Parameters Correlated?
Consider a strong direct path, as illustrated in Figure 2. Only a few strong paths are
shown in this plot as the remaining weaker paths are below the dynamic range of the
receiver and can be ignored. In this case, the strong direct path dominates the rms DS
calculation, producing a low delay spread. The direct path dominates the rms AS
calculation, also producing a low angle spread. The direct path is responsible for a strong
received signal with an above average shadow faded signal, for example, the shadow
fade will be a large negative fade.
Low AS
Low DS
.
Low SF
Figure 2: Sample Correlation for Strong Signals
For the weak signal case in Figure 3, the lack of a single dominant signal implies a large
DS and AS. The SF will be a large positive value representing a deeper-than-average fade.
High AS
High DS
.
High SF
Figure 3: Sample Correlation for Weak Signals
It is clear that the magnitudes and the signs of the correlation coefficients for the DS, AS,
and SF parameters in this illustration match the expected behavior in each case.
8 | Path-based Spatial Channel Modeling
1.5. Generating the SCM Model Components
The model most commonly referenced in standards for multiple-antenna scenarios is the
SCM Urban model. As an option within the Urban model, the Base Station AS may be
selected as either 8º or 15º. The smaller value is consistent with data taken in European
cities and the larger value is more consistent with data from US cities, but either value
may be used. 3GPP typically uses 8º, and 802.16 typically uses 15º. Each model is
described in [v] and [vi].
The Urban Macro-cell model is implemented in several steps, as described in the
references. During a simulation, a random MS location is selected for evaluation. For this
location, an SCM channel realization is calculated. This includes the corresponding Path
Loss (PL) and SF to each simulated BS. The channel selected for this MS stays in effect
for a predefined duration, after which a new MS location is selected. Many mobile
locations and their corresponding randomly drawn channels will be evaluated during a
system simulation.
Once the DS and AS are generated, the individual path delays and angles are generated
based on random draws from scaled distributions as described here. Six paths are
assumed for the urban model and used in the following abbreviated description.
The exponentially distributed random delays for each path
''
1
,...,
N
ττ
are generated from
'
ln
nDSDSn
rzτ=− σ
, where n = 1,…,N and
n
z
(n = 1,…,N) are i.i.d. random variables with
uniform distribution U(0,1). The value rDS describes how the powers are concentrated in
time. It is given by the relationship comparing the sigma of the delays to the delay spread
by:
DSDSDelays
r σσ =
and is further discussed in [v].
The un-normalized exponentially distributed path powers are given by:
10/
)()1(
10
)1()(
nDSDS
nDS
r
r
n
eP
ξ−σ⋅
τ′−τ′⋅−
⋅=′
, n = 1,…,6 where
n
ξ
(n = 1,…,6) are independent and
individually distributed (i.i.d.) Gaussian random variables with standard deviation
RND
σ
=
3 dB, which is a shadowing randomization effect on the per-path powers.
Average powers are normalized so that the total average power for all six paths is equal
to one:
∑
=
=
6
1
'
'
j
j
n
n
P
P
P
The AoD for each path is generated from i.i.d. zero-mean Gaussian random variables:
'2
~(0, )
nAoD
δησ
, n = 1… 6, where
ASASAoD
r σ=σ
. The value rAS describes the
degree to which the power is concentrated in angle, and is based on measured data. The
AoD angles are ordered in increasing absolute value so that
'' '
(1)(2)()
...
N
δ <δ < <δ
.
The AoA for each path is generated from i.i.d. zero-mean Gaussian random variables:
White Paper 102 | 9
2
,,
~ (0, )
nAoA nAoA
δησ
, n = 1,…, 6, where
( )( )
,10
= 104.12 1-exp -0.2175 10 log ( )
nAoA n
Pσ
and
n
P
is the relative power of the nth path.
Additional steps are used in the SCM [v], which include adding propagation slope,
correlated shadow fading, antenna patterns, etc.
1.6. Path Characteristics
The per-path fading behavior is characterized by a narrow angle spread consistent with
numerous field measurements. A narrow angle spread produces a one-sided Doppler
spectrum for most AoAs. The combination of sub-paths still produces a Rayleigh
distributed envelope, but the narrow angle spread limits the individual sub-path Doppler
shifts to a limited range of values based on the geometry of the AoA and direction of
travel (DoT).
The per-path power azimuth spectrum (PAS) is a description of the power and angle
distribution, and is typically assumed to follow a Laplacian distribution. This is a two
sided exponential, which is an isosceles triangle when plotted in dB. The center of the
distribution is at zero degrees relative to the average AoA or AoD, as shown in Figure 4.
Si
gnal
Level
(
d
B)
Angle of Arrival 0º
Laplacian Power Azimuth Spectrum
Figure 4: Power Azimuth Spectrum
To emulate the Laplacian PAS, each path is comprised of 20 equal powered sub-path
components, spaced with increasing angle from the center so that the average power
falls at a rate that matches the envelope of the distribution. Equal powered sub-paths
were chosen so that no one or two sub-paths dominate, affecting the fading behavior of
the path. When a Path is defined, the angles of the sub-paths are shifted to match the
path angle, and the power sum is scaled to match the path power.
Figure 5 illustrates the sub-path spacing in degrees relative to the path AoD at the BS.
Since the BS antennas are somewhat isolated from the clutter, the angle spread (AS) is
quite small. The AS is 2 degrees as defined by the model, with 20 sub-paths of equal
power and a non-linear spacing as shown to approximate the Laplacian PAS.
10 | Path-based Spatial Channel Modeling
-10 -8 -6 -4 -2 0 2 4 6 8 10
0
0.05
Relative Angle of Departure (degrees)
Su
b
-
Pa
t
h
Po
w
e
r
Laplacian Angle Spread,
σ
= 2 degrees
Figure 5: Path Model at Base Station
Figure 6 describes the sub-path spacing in degrees relative to the path AoA at the MS.
The AS is 35 degrees, with 20 sub-paths of equal power and a non-linear spacing as
shown to approximate the Laplacian PAS. This value is significantly larger than the AS at
the BS, and is due to the significant clutter that is typically located near the MS.
-100 -80 -60 -40 -20 0 20 40 60 80 100
0
0.05
Relative Angle of Arrival (degrees)
Su
b
-
P
a
th
Po
w
e
r
Laplacian Angle Spread,
σ
= 35 degrees
Figure 6: Path Model at Subscriber
To generate a model with the correct temporal characteristics, the proper Doppler
spectrum is required. When implementing the SCM with a sum-of-sine waves approach
using sub-paths, the Doppler is accounted for automatically within the sum-of-sinusoids
calculation based on the geometry shown in Figure 7. The fading rate is based on the AS,
AoA, and DoT of the subscriber.
DoT
AoA
AS
Figure 7: Signal and Antenna Positioning
The Power Delay Profile (PDP), the PAS at the base station, and the PAS at the subscriber
are shown in Figure 8 for a given channel realization.
The Laplacian PAS is also used at the base station, but it is observed as an average long-
term envelope; the values used in the average are taken over many channel realizations
of the composite multi-path signal. This is illustrated by example in
Figure 8: Power Delay and Angle Profiles
where the average of many channel realizations is shown with a dashed line. The PDP
plot also has a long term average exponential response shown with the dashed line.
White Paper 102 | 11
Power Delay Profile
P
o
w
e
r (d
B
)
Delay t (ns)
Power Azimuth Spectrum
P
o
w
e
r (d
B
)
AoD @ BS (degrees)
Power Azimuth Spectrum
P
o
w
e
r (d
B
)
AoA @ MS (degrees)
Figure 8: Power Delay and Angle Profiles
1.7. SCME
Due to the assumption that each path is flat-faded, there are some inherent bandwidth
concerns with the SCM when operating in bandwidths above 5 MHz. In order to address
this, the Wireless World Initiative New Radio (WINNER) group proposed an extension to
the SCM, called the SCM Extended (SCME).
This approach duplicates most of the original SCM, but changes the path characteristics
to induce additional de-correlation in the frequency domain. For particular paths, the
SCME distributes the path into 3 distinct “mid-paths” having slightly different powers and
delays as shown in Figure 9. This adds a delay spread per path for those paths that are
split in this way. If all of the original 6 paths of the SCM are modeled with mid-paths this
effectively increases the model to 18 “paths”, producing a slightly improved spaced-
frequency correlation function. By dividing the 20 sub-paths into groups of 10, 6, and 4,
the relative powers of each mid-path are now scaled by this ratio.
Relative Power
0.5 0.3 0.2
Delay spread per
path = 9.76 ns
6 original paths Æ
18 mid-paths Mid-path 1 2 3
Figure 9: SCME Path Modification
12 | Path-based Spatial Channel Modeling
Table 1 illustrates the specific modifications that were made to each path. The original
20 sub-paths of the SCM were reallocated into the three mid-paths as shown. By
specifying these specific allocations, the mid-paths maintain nearly the same AS as the
SCM, with each mid-path having a zero inter-path delay as before. Figure 10 illustrates
the sub-path AoA distribution for mid-path #1. Figure 11 shows the various mid-paths.
White Paper 102 | 13
Table 1: SCME Mid-path Details
Mid-
path
# of
Sub-
paths
Relative
Power
Excess
Delay
Sub-path Index ASmidpath/ASsubpath
1 10 0.5 0 ns 1,2,3,4,5,6,7,8,19,20 0.9865
2 6 0.3 12.5 ns 9,10,11,12,17,18 1.0056
3 4 0.2 25 ns 13,14,15,16 1.0247
Mid-path #1
Selected Sub-paths are assigned to each Mid-path to
Maintain original Angle Spread
Figure 10: SCME – Mid-path #1 Sub-path Distribution
-100 -50 0 50 100
0
0.05
Relative Angle of Arrival (degrees)
S
u
b
-
Pa
th
Po
w
e
r
Laplacian Angle Spread,
σ
= 35 degrees
Figure 11: Distribution of SCME Mid-paths
By adding the mid-paths, the channel now behaves as if there are 18 paths. This tends to
de-correlate the Spaced-Frequency Correlation function, as shown in Figure 12. For
convenience, the Vehicular-A channel model is used as an example. It is clear that the
path-splitting has produced some improvement.
14 | Path-based Spatial Channel Modeling
0 2 4 6 8 10 12 14 16 18 20
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Spaced-Frequency Correlation Function, Vehicular A
Δf (MHz)
|
φ
(
Δ
f)
|
vehicular A w/midpaths
vehic ular A
Figure 12: Effect of Mid-paths on Frequency De-correlation
1.8. Tap Delay-line Model
The WINNER group presented a simplified SCME Tap Delay-Line Model, also called
Cluster Delay-Line Model, in [iv]. This model was created for calibration and comparison
purposes and portions of this model have been adopted by the 3GPP. In this model, the
specific AoDs and AoAs are specified and fixed for each path. Also, fixed delays are
defined, resulting in a fixed PDP. Each path is modeled with a set of equal-powered
sinusoids combined vectorially to produce a fading characteristic. The delays were
selected to optimize the frequency decorrelation characteristic. The fading is determined
from the Doppler characteristic and is a function of the AoA for the sub-paths, the MS
speed, DoT, and antenna patterns.
Cluster Delay-Line models with parameter tables are described for the following
scenarios:
• Indoor Small Office
• NLOS Indoor Environment
• Indoor to Outdoor / Outdoor to Indoor
• Urban Microcell
• Bad Urban Microcell
• Indoor Hotspot
• LOS model
• NLOS model
• Urban Macro-cell
• LOS model
• NLOS model
White Paper 102 | 15
• Bad Urban Macro-cell
• Outdoor to Indoor (Urban) Macro-cell
• Rural Macro-cell
• Fixed Links
• Rooftop to Rooftop
• Street to Street
Tables of these fixed values are recorded in the WINNER document [vii].
1.9. WINNER-II
A second model proposed by WINNER is called WINNER-II [iv].
This model includes the following environment types:
• Indoor office
• Large indoor hall
• Indoor-to-outdoor
• Urban micro-cell
• Bad urban micro-cell
• Outdoor-to-indoor
• Stationary feeder
• Suburban macro-cell
• Urban macro-cell
• Rural macro-cell
• Rural moving networks
The WINNER-II models use a stochastic ray-based approach to generate geometry based
random double directional channels. The model is antenna independent and generated
from distributions extracted from measured data. Several different distributions are used
to generate a channel, including: delay spread, delay values, angle spread, shadow
fading, and XPD ratio. The parameters, which are stored in tables, are adjusted to obtain
different scenarios. Some specific clustered delay line (CDL) models have been created
for calibration purposes for making comparisons. An example is shown in Figure 13,
showing the Urban Macro-cell NLOS CDL model.
16 | Path-based Spatial Channel Modeling
Figure 13: WINNER-2 Scenario C2 – NLOS Clustered Delay Line Model
The corresponding PDP is shown in Figure 14. Based on this PDP, the Spaced-Frequency
correlation function is shown in Figure 15. The performance of the SFCF is reasonable
due to the 20 path model combined with an optimization of powers and delays to
achieve a good roll-off in frequency.
Figure 14: WINNER-2 PDP for Urban Macro NLOS CDL
White Paper 102 | 17
Figure 15: WINNER-2 Spaced-Frequency Correlation for Urban Macro NLOS CDL
The WINNER II model is designed to operate in the 2-6 GHz band with up to 100 MHz of
bandwidth. The model includes polarization, and supports multi-user, multi-cell, and
multi-hop networks.
1.10. SCM & SCME in Standards
The SCM & SCME is adopted in part or in whole in 3GPP, 3GPP2, and 802.16e. In
addition, the WINNER models have been further included in the recent ITU-Advanced
models.
References
i Calcev, etal., “A Wideband Spatial Channel Model for System-Wide Simulations,” IEEE Transactions on
Vehicular Technology, Vol. 56, No. 2, March 2007.
ii 3GPP, TR25.996, Spatial Channel Model for Multiple Input Multiple Output (MIMO)
iii D.S. Baum, etal., “An Interim Channel Model for Beyond-3G Systems,” IEEE Vechicular Technology
Conference, Spring, 2005.
iv IST-4-027756 Winner II Channel Models, Deliverable D1.1.2V1.2
v 3GPP, TR25.996, Spatial Channel Model for Multiple Input Multiple Output (MIMO)
vi 3GPP2, C30-20030915-006, Spatial Channel Model for Multiple Input Multiple Output (MIMO)
vii IST-2003-507581 WINNER D5.4 v. 1.0 Final Report on Link Level and System Level Channel Models
