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14 MIMO System Technology for Wireless Communications

where E

represents the reference ﬁeld, f

and f

the transmitting and receiv-

ing antenna ﬁeld radiation patterns in the direction of the ray, R

the reﬂection

coefﬁcient for the j

reﬂector, T

the wall transmission coefﬁcient for the k

transmission, D

the diffraction coefﬁcient for the l

diffracting wedge and

–jkd

the propagation phase factor due to the path length d (k = 2U/Q, with Q

the wavelength). The diffraction coefﬁcients are also multiplied by a factor

(se,s) which ﬁnds the correct spatial attenuation of the diffracted rays, given

the 1/d dependence in the last term. An advantage of ray-tracing models

over other propagation models is the ability to incorporate antenna radiation

patterns and particularly to consider the effect of the radiation pattern on

each ray individually.

In order to trace rays that are generated and launched from the transmit-

ting antenna, two methods have been developed: the imaging technique and

the ray launching technique. The imaging technique (e.g., [39, 40]) is based on

the electromagnetic theory of images and works by generating an image

table for each BS location, considering all the various wall reﬂection, trans-

mission and diffraction permutations that are possible in a given area. The

image information is then stored and used to compute the channel charac-

teristics at each mobile location. In the ray launching approach (e.g., [41, 42]),

rays are sent out at various angles and their paths are traced until a certain

power threshold is reached. The number of rays considered and the distance

from the transmitter to the receiver location determined the available spatial

resolution and the accuracy of the model.

In the image-based models presented in [40] (for microcells), [43] (for

indoor) and [44, 45] (for macrocells), the geometry of each ray is examined

in three-dimensional (3D) space, and hence, both the azimuth and the ele-

vation angles of arrival at the antennas are available. Moreover, the 3D

antenna radiation patterns can be used and steered in any direction in space

so that the channel can be examined for any antenna orientation. Note that

the model works with the electromagnetic ﬁeld of the rays and, hence, uses the

radiation patterns of the ﬁeld components. This feature, in conjunction with

the fact that all reﬂections, transmissions and diffractions are computed

using 3D vector mathematics, makes the models very useful in the study of

different antenna polarizations and the examination of depolarization effects.

Since the ﬁeld components can be calculated for each antenna element

separately, as explained above, the MIMO channel matrix can be generated,

as shown in Figure 1.10 and Figure 1.11. Figure 1.10 shows the geographical

database of the area and examples of 2D-3D multipath visualization. It can

be seen that ray tracing offers site-speciﬁc information for the radio channel

characteristics and, hence, provides more accurate predictions. Figure 1.11

shows an example of the 3D impulse responses (amplitude-delay-AoA) for

a MIMO scenario (between Tx element m and Rx element n). It shows polar

plots for the AoA (azimuth) vs. power at the BS (a) and MS (b), the AoA

(elevation) vs. power at the BS (c) and MS (d) and, ﬁnally, the ToA vs. power (e).

The application of ray-tracing models to study several aspects of propa-

gation modeling has proven to be a popular method.

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Spatio-Temporal Propagation Modeling 15

In [46, 47] the spatial characteristics of microcellular environments are stud-

ied. Results showed that the signal is not uniformly distributed in the spatial

domain, but instead is contained in a few narrow clusters. Although the number

of clusters increases under NLOS conditions, for both LOS and NLOS positions,

90% of the power is contained within two clusters. Also, although the angular

FIGURE 1.10

Map of the environment under investigation with 2D (a) and 3D (b) multipath examples.

5000

4500

4000

3500

3000

2500

500 1000 1500 2000

(a)

(

)

2500 3000

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16 MIMO System Technology for Wireless Communications

FIGURE 1.11

Example of ray-tracing 3D impulse responses for a MIMO scenario: AoA (azimuth) vs. power

at the BS (a) and MS (b). AoA (elevation) vs. power at the BS (c) and MS (d). (e) ToA vs. power.

−100

−150

120

150

180

210

240

270

(a) (b)

(c)

300

330

−100

−150

120

150

180

210

240

270

300

330

−100

−150

120

150

180

210

240

270

300

330

Power(dBm)

−100

−150

120

150

180

210

240

270

(d)

300

330

Power(dBm)

(e)

−100

−110

−120

−130

−140

−150

−160

Received power (dBm)

5000 6000 7000 8000

Time (nsec)

9000 10000 11000

4190_book.fm Page 16 Tuesday, February 21, 2006 9:14 AM

Spatio-Temporal Propagation Modeling 17

spread and the number of multipath rays almost doubles under NLOS condi-

tions, there are still only two important clusters that contain most of the power

with angular spread less than the beamwidth of an eight element array.

In [48] the spatial and temporal characteristics of 60GHz indoor channels

were analyzed. Multipath components were resolved in time by using a

sliding correlator with 10 ns resolution and in space by sweeping a direc-

tional antenna with 7° half power beamwidth in the azimuthal direction.

Power delay proﬁles (PDPs) and power angle proﬁles (PAPs) were measured

in various indoor and short-range outdoor environments. The measurement

results conﬁrm that the majority of the multipath components can be deter-

mined from image-based, ray-tracing techniques for LOS applications. For

non-LOS propagation through walls, the metallic structure of composite

walls must be considered. Also, statistical parameters of received power,

AoA and ToA, were calculated from the measurements, which agreed well

with the theoretical expectations.

Furthermore, ray-tracing models have also been used to produce the data

sets required for the statistical evaluation of the parameters of stochastic mod-

els, as in [49]. The advantage of using deterministic predictions instead of ﬁeld

trial measurements is mainly that large data sets can be easily produced for

many different test environments. Also, when using ﬁeld trial results in order

to produce a statistical model, the inﬂuence of the measurement antennas is

included in the results and cannot be eliminated afterward. In [49], a stochastic

model for the indoor mobile propagation channel is presented. The channel

is described by multipath components, including 3D angles of arrival at the

antennas. By relating the angle of arrival to the direct line between transmitter

and receiver, a universal modeling approach, which is independent of the

actual geometry, becomes possible. In each modeling step, path properties

change according to the movement of the radio stations. The appearance and

disappearance of multipath components are modeled by a genetic process.

1.3.2 Stochastic Propagation Modeling

There have been several such models proposed, analyzed and discussed the

last few years; some of the most representative are brieﬂy mentioned here:

• Wideband Directional Channel Model (WDCM), [50]. Geometrically

based, parameterized for macro, microcells, circular-elliptical scat-

tering area, single bounce.

• Geometrical MIMO channel model based on SISO parameters [51, 52].

Macrocellular broadband ﬁxed wireless, multiple delay ellipses, circle

of local scatterers around the MS, double bounces. To better repre-

sent such environments, two local rings are introduced in this model:

a disc of exclusion, representing a scatterer-free area around the BS,

and a smaller circular ring surrounding the CPE including a subset

of the scatterers in the ﬁrst ellipse (see Figure 1.12). The channel

matrix is then calculated using a ray-based approach.

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18 MIMO System Technology for Wireless Communications

• Generic MIMO model [53]. Double scattering, far clusters, wave-

guiding, guidelines to select the proper distribution of scatterers.

• Double Directional Channel Model (DDCM) [54, 55]. Parametric

stochastic model, parameters through spatial scatterer distribution

[1]. Tapped delay line with each multipath having complex charac-

teristics (amplitude, delay, AoA).

• Indoor MIMO models:

– EU IST METRA (Multi-Element Transmit Receive Antennas)

project: A stochastic MIMO radio channel model for non-line-of-

sight (NLOS) scenarios was proposed on the basis of the power

correlation matrix of the MIMO radio channel [56].

– EU IST SATURN (Smart Antenna Technology in Universal Broad-

band Wireless Networks) project: Based on the statistical charac-

teristics of the measured data, both narrowband [57] and wideband

[58] statistical models for NLOS MIMO propagation channels

were developed.

• One (two) ring(s) MIMO channel models [59, 60]. Extension of [6]

for MIMO channel modeling.

• One ring MIMO model with Von Mises angular distribution [61].

Von Mises angular pdf at the MS.

• Distributed scattering MIMO model [62]. Outdoor, narrowband, one

group of scatterers near the BS and one near the MS.

1.3.2.1 The 3GPP MIMO Channel Model [63]*

A serious attempt to unify the propagation modeling approach for space–

time models started a few years ago with the European Scientiﬁc Action

COST259 [1]. This work received even more attention when adopted as the

basis for spatial channel modeling in the context of the international stan-

dardization body of 3GPP. Naturally, it was inﬂuenced by many different

FIGURE 1.12

Physical combined model for macrocellular scenarios.

* 3GPP TSs and TRs are the property of ARIB, ATIS, ETSI, CCSA, TTA, and TTC who jointly own

the copyright in them. They are subject to further modiﬁcations and are therefore provided to

you "as is" for information purposes only. Further use is strictly prohibited.

BTS

CPE

Scatterer

free area

4190_book.fm Page 18 Tuesday, February 21, 2006 9:14 AM

Spatio-Temporal Propagation Modeling 19

proposals discussed in 3GPP (see technical documents for spatial channel

model). This section describes in greater detail the parametric stochastic

model that has been adopted recently by the 3GPP.

The combined 3GPP-3GPP2 spatial channel model ad-hoc group has spec-

iﬁed parameters and methods for spatial channel modeling. The scope is the

development of speciﬁcations for system-level evaluation with emphasis on

the physical parameters, and link-level evaluation, deﬁned only for calibra-

tion purposes (not for evaluation or comparisons).

As such, the following section presents the key characteristics of the spatial

channel model that has been adopted for system-level simulation studies.

(A detailed description is available in [63].)

1.3.2.1.1 Spatial Channel Model for Simulations

For an S element BS array and a U element MS array, the channel coefﬁcients

for one of N multipath components (note that these components are not

necessarily resolvable in the time domain, since the time difference between

successive paths may be less than a chip period) are given by an S-by-U

matrix of complex amplitudes. The channel matrix for the nth multipath

component (n = 1, …, N), H

(t), is a function of time, because the complex

amplitude undergoes fast fading due to the movement of the MS.

The overall procedure for generating the channel matrices consists of three

basic steps:

1. Specify an environment (either macro urban or macro suburban, or

micro).

2. Obtain the simulation parameters associated with each environment.

3. Generate the channel coefﬁcients based on these parameters.

Figure 1.13 shows the angular parameters used in the model. The following

deﬁnitions are used:

BS antenna array orientation, deﬁned as the difference between the broadside of the

BS array and the absolute North (N) reference direction

LOS AoD direction between the BS and MS, with respect to the broadside of the BS

array

n,AoD

AoD for the n

path (n = 1 … N) with respect to the LOS AoD V

)

n,m,AoD

Offset for the m

sub-path (m = 1 … M) of the n

path with respect to I

n,AoD

n,m,AoD

Absolute AoD for the m

sub-path of the n

path at the BS with respect to the BS

broadside

MS antenna array orientation, deﬁned as the difference between the broadside of

the MS array and the absolute North reference direction

Angle between the BS-MS LOS and the MS broadside

n,AoA

AoA for the n

path with respect to the LOS AoA V

)

n,m,AoA

Offset for the m

sub-path of the n

path with respect to I

n,AoA

n,m,AoA

Absolute AoA for the m

sub-path of the n

path at the MS with respect to the MS

broadside

v MS velocity vector

Angle of velocity vector with respect to the MS broadside: V

= arg(v)

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20 MIMO System Technology for Wireless Communications

For the simulations some general assumptions are made (Table 1.1):

a. Uplink-downlink reciprocity, i.e., the AoD/AoA values are identical

between the uplink and downlink.

b. For FDD systems, random sub-path phases between uplink and

downlink are uncorrelated. For TDD systems, the phases are fully

correlated.

c. Shadowing among different mobiles is uncorrelated.

d. The spatial channel model allows any type of antenna conﬁguration

(e.g., with size smaller than the shadowing coherence distance). In

order to compare algorithms, reference antenna conﬁgurations

based on uniform linear array with 0.5, 4 and 10 wavelength inter-

element spacing are used.

e. The composite AS (angle spread), DS (delay spread) and SF(shadow

fading) may be correlated parameters depending on the channel

scenario, and are applied to all the sectors or antennas of a given

base. The AS is composed of 6 × 20 sub-paths, and each has a precise

angle of departure, which corresponds to an antenna gain from each

BS antenna. The SF is a bulk parameter and is common among all

the BS antennas or sectors.

f. The elevation spread is not modeled.

g. To allow comparisons of different antenna scenarios, the transmit

power of a single antenna case is the same as the total transmit power

of a multiple antenna case.

h. The generation of the channel coefﬁcients assumes linear arrays

(although the procedure can be generalized for other array conﬁg-

urations).

FIGURE 1.13

BS and MS angle parameters for the 3GPP model [63].

n,AoD

n,AoA

Ω

Cluster n

Ω

BS array broadside

MS array broadside

BS array

MS direction of travel

MS array

Subpath m

∆

n,m,AoD

∆

n,m,AoA

n,m,AoD

4190_book.fm Page 20 Tuesday, February 21, 2006 9:14 AM

Spatio-Temporal Propagation Modeling 21

The following are assumptions for the macrocell suburban and urban

environments:

a. The macrocell pathloss is based on the modiﬁed COST231 Hata

urban propagation model:

TABLE 1.1

Environment Parameters [63]

Channel Scenario

Suburban

Macro Urban Macro Urban Micro

Number of paths (N)666

Number of sub-paths (M) per

path

20 20 20

Mean AS at BS E(X

) = 5° E(X

) = 8°, 15° NLOS: E(X

) = 19°

AS at BS as a lognormal random

variable

= 10°(J

x + µ

), x ~ M(0, 1)

= 0.69

= 0.13

8°

= 0.810

15°

= 1.18

N/A

= 0.34

= 0.210

= X

AoD

1.2 1.3 N/A

Per path AS at BS (ﬁxed) 2° 2° 5° (LOS and NLOS)

BS per path AoD Distribution

standard distribution

M(0,

AoD

)

where

AoD

= r

M(0, X

AoD

)

where

AoD

= r

U(–40°, 40°)

Mean AS at MS E(X

AS, MS

) = 68° E(X

AS, MS

) = 68° E(X

AS, MS

) = 68°

Per path AS at MS (ﬁxed) 35° 35° 35°

MS Per path AoA Distribution M(0, X

AoA

)) M(0, X

AoA

)) M(0, X

AoA

))

Delay spread as a lognormal

random variable

= 10°(J

x + µ

), x ~ M(0, 1)

= –6.80

= 0.288

= –6.18

= 0.18

N/A

Mean total RMS delay spread E(X

) = 0.17 µsE(X

) = 0.65 µsE(X

) = 0.251 µs

(output)

= X

delays

1.4 1.7 N/A

Distribution for path delays U(0, 1.2 µs)

Lognormal shadowing

standard deviation, X

8dB 8dB NLOS: 10 dB

LOS: 4 dB

Pathloss model (dB), d is in

meters

31.5 + 35log

(d) 34.5 + 35log

(d) NLOS:

34.53 + 38log

(d)

LOS:

30.18 + 6log

(d)

PL dB h

[] . .log log= 

()

44 9 6 55

1000

10 10

ºº

++ 

()()



45 5 35 46 1 1

13 82

...log

.log

MS c

07hhC

BS MS

()

++.

4190_book.fm Page 21 Tuesday, February 21, 2006 9:14 AM

22 MIMO System Technology for Wireless Communications

where h

and h

are the BS and MS antenna height (in meters), f

is carrier frequency (in MHz), d is the distance between MS and BS

(in meters) and C is a constant factor (C = 0 dB for suburban macro

and C = 3 dB for urban micro).

b. Site-to-site SF corelation is 0.5.

The following are assumptions for the microcell environment:

a. The microcell NLOS pathloss is based on the COST 231 Walﬁsh-

Ikegami NLOS model with the following parameters: BS antenna

height 12.5 m, building height 12 m, building to building distance

50 m, street width 25 m, MS antenna height 1.5 m, orientation 30 deg

for all paths, and selection of metropolitan center. With these param-

eters, the equation simpliﬁes to:

PL(dB) = –55.9 + 38*log

(d) + (24.5 + 1.5*f

/925)*log

)

The resulting pathloss at 1900 MHz is: PL(dB) = 34.53 + 38*log

(d),

where d is in meters. The distance d is at least 20 m. A bulk log

normal shadowing applying to all sub-paths has a standard devia-

tion of 10 dB.

The microcell LOS pathloss is based on the COST 231 Walﬁsh-Ikeg-

ami street canyon model with the same parameters as in the NLOS

case. The pathloss is

PL(dB) = –35.4 + 26*log

(d) + 20*log

)

The resulting pathloss at 1900 MHz is PL(dB) = 30.18 + 26*log

(d),

where d is in meters. The distance d is at least 20 m. A bulk log

normal shadowing applying to all sub-paths has a standard devia-

tion of 4 dB.

b. Site-to-site correlation is _ = 0.5.

In [63], the algorithm that generates the model parameters is

explained step by step for the different operational environments.

These parameters are then used to generate the channel coefﬁcients.

For an S element linear BS array and a U element linear MS array,

the channel coefﬁcients for one of N multipath components are given

by a U-by-S matrix of complex amplitudes. The channel matrix for

the nth multipath component (n = 1,…,N) is denoted as H

(t). The

(u,s)th component (s = 1,…,S; u = 1,…,U) of H

(t) is given by

Gjkd

usn

nSF

BS nmAoD s nm

,, ,

()

exp sin

()

,, ,

exp sin

AoD n m

MS n m AoA u

G jkd

()

nnmAoA

nmAoA v

jk t

exp cos

()



()

v VV

ªª

4190_book.fm Page 22 Tuesday, February 21, 2006 9:14 AM

Spatio-Temporal Propagation Modeling 23

where

is the power of the n

path.

is the lognormal shadow fading, applied as a bulk

parameter to the n paths for a given drop.

M is the number of sub-paths per path.

n,m,AoD

is the AoD for the m

sub-path of the nth path.

n,m,AoA

is the AoA for the m

sub-path of the nth path.

n,m,AoD

) is the BS antenna gain of each array element.

n,m,AoA

) is the MS antenna gain of each array element.

k is the wave number 2U/Q where Q is the carrier wave-

length in meters.

is the distance in meters from BS antenna element s

from the reference (s = 1) antenna. For the reference

antenna s = 1, d

=0.

is the distance in meters from MS antenna element u

from the reference (u = 1) antenna. For the reference

antenna u = 1, d

=0.

n,m

is the phase of the m

sub-path of the nth path.

㥋v㥋 is the magnitude of the MS velocity vector.

is the angle of the MS velocity vector.

The pathloss and the log normal shadowing is applied as bulk parameters

to each of the sub-path components of the n path components of the channel.

Also in [63], a method of using polarized antennas in the above model is

presented and the resulting channel characterization is given. Finally, the

model includes options for far scatterer clusters, line of sight and urban

canyon.

References

1. L.M. Correia, Ed. 2001. Wireless Flexible Personalized Communications, COST 259:

European Cooperation in Mobile Radio Research, Chichester: John Wiley &

Sons.

2. R.B. Ertel, P. Cardieri, K.W. Sowerby, T.S. Rappaport, and J.H. Reed. 1998.

“Overview of spatial channel models for antenna array communication

systems,” IEEE Personal Communications Magazine, Vol. 5, No. 1, Feb., pp. 10–22.

3. K. Yu and B. Ottersten. 2002. “Models for MIMO propagation channels: a

review,” Wireless Communications and Mobile Computing, Vol. 2: pp. 653–666.

4. J.C. Liberti and T.S. Rappaport. 1999. Smart Antennas for Wireless Communica-

tions, Upper Saddle River, NJ: Prentice Hall.

4190_book.fm Page 23 Tuesday, February 21, 2006 9:14 AM