Abstract—In this paper we present a simulation tool for macro

cell environment based on geometrical and statistical

representation of the scatterers and on the COST 259

Directional Channel Model (DCM).

This tool uses gaussianly distributed scatterers for each

cluster. This distribution is naturally more realistic than the

uniform distribution leading to time-of-arrival (TOA) and

angle of arrival (AOA) distributions closer to experimental

results.

This geometrically based model simulates the TOA

dispersion present in wide band channel models and the AOA

dispersion necessary for systems that explore spatial diversity.

This tool also incorporates the concept of line-of-sight (LOS) and non-line-of-sight (NLOS) and its birth and death as the

mobile station (MS) moves in a cell, as well as the appearance

and disappearance of additional clusters of scatterers.

The output provided by this simulation tool is comprised of

all the complex amplitudes, delays and angles of arrival of all

multipath components associated with each cluster of

scatterers. Mean attenuation and slow fading effects are also

incorporated to the model and fast fading appears as a

consequence of the multipath interference .

Index Terms—communication channel, propagation,

geometrically based model, mobile communication,COST 259

DCM

I. INTRODUCTION

ODELLING and simulation of mobile radio channels is

an essential tool for the optimization of mobile

communication systems.

The basic mechanisms that affects propagation are

reflection, diffraction and scattering. These mechanisms

change the characteristics of the channel and can generate

multipath components that arrive from different directions as

the mobile travel in a cell. These multipath components can

degrade the channel characteristics [1-3].

For a realistic design and system simulation, accurate

channel models are required. For the first and second

generation of mobile radio systems the prediction of the

mean attenuation based in semi deterministic and empirical

models [4] and Doppler spectrum [5] was enough.

Most recently, the third generation of mobile radio

channel and systems, using spatial diversity (adaptive

antennas), requires the use of directional channel models, for

the determination of the power azimuth spectrum (PAS) and

the power delay spectrum (PDS). Some of these channel

Manuscript received April 14, 2006.

L C. Trintinalia and S. D. Castilho are with the Department of

Telecommunications and Control Engineering, Escola Politécnica da

Univercidade de São Paulo, São Paulo SP 05508-900, Brazil (e-mail:

trinti@lcs.poli.usp.br and sergiocastilho@uol.com.br).

models are geometrically based, with the scatterers

distributed uniformly in circles or ellipses[6].

In this paper we present a simulation tool that can provide

the following characteristics of the mobile radio channel:

• Directional information. Essential for the analysis of

adaptive antennas and spatial diversity.

• Polarization. Important for polarization diversity

systems.

• Dynamic changes. Important for mobile receiver

design.

• Four different macro cell scenarios: Typical Urban

(TU), Bad Urban (BU), Rural Area (RA) and Hilly

Terrain (HT).

The paper is organized as follows: Section II discusses the

propagation models for macro-cells. Section III specifies the

distribution of the scatterers inn the cluster and its

probability density function (pdf). Section IV presents the

simulation tool and specifies the parameters used for

simulation, and Section V presents the conclusion.

II. PROPAGATION MODELS FOR MACRO-CELLS

The mean power prediction is based on the knowledge of

topography, land usage and building height information [1],

[7].

This simulator use the following prediction models in

LOS:

• COST 231 – Hata [4] is used for RA and HT

• COST 231 – Walfisch-Ikegami [4] is used for TU

and BU

For NLOS only COST 231 [4] – Walfisch-Ikegami is

used for all types of scenario.

These two models are widely used and accepted for mean

power loss prediction.

III. SCATTERERS DISTRIBUTION

The whole set of scattering centers used to model the

multipath propagation can be divided into clusters. The first

cluster is located around the MS and moves with it. This

cluster is denominated local cluster. Additional clusters, far

from the MS will be fixed, and are denominated far clusters.

These clusters represent higher buildings, mountains, etc.

These cluster structures have LOS to both BS and MS and

are allowed to appear and disappear as the

M

Communication Channel Simulation Tool Based

on Geometrical and Statistical Model for Macro

Cell Environments

Luiz Cezar Trintinalia and Sergio Duque Castilho

85-89748-04-9/06/$25.00 © 2006 IEEE ITS2006171

mobile moves.

For all clusters the scatterers will be geometrically

distributed with a Gaussian density, as shown in Fig. 1 for a

cluster located 1000 m far from the base station (BS).

The original idea of geometric models [8-10] for

propagation prediction was proposed by Jakes [11], where

the scatterers that generate multi path components were

assumed to be uniformly distributed in a circle around the

mobile with equal scattering coefficients and uniform

random phase.

The scatterers distribution directly influence the PDS and

PAS, and the computed value from these models must be in

reasonable agreement with the measured values [12].

The signal transmitted by the MS is received at BS from

different directions and with different delays, therefore the

instantaneous power azimuth-delay spectrum can be defined

as:

( )2

( , , ) ( ) ( ) ( )1

L tP l l l iL

lθ ϕ τ α δ θ θ δ ϕ ϕ δ τ τ∑= − − −

= (1)

where α denotes the absolute value of the complex

amplitude of each multipath component, ϕ is the elevation, θ is the azimuth, τ is the delay of each multi path and ( )L t

is the time variant number of multipath components.

Using a large number of scatterers gaussianly distributed

in a cluster around the MS, a relative angle versus delay

plot, as seen by the BS, is shown in Fig. 2, for a distance of

1000 m between MS and BS and with radius of the cluster

equal to 100 m.

The positions of these scatterers were generated with a

probability density function given by

2 21 ( ) ( )0 0( , ) exp( )2 22

x x y yf x yxy

ssσπσ

− + −= (2)

with (x0, y0) being the center of cluster relative to the BS

position and σS the standard deviation of this distribution.

The power azimuth-delay spectrum is proportional to the

conditional expected power of the multipath components

multiplied by the azimuth-delay pdf [13] and can be

expressed as

{ }2( , ) , ( , )P E fτ θ α τ θ τ θτθ τθ= (3)

where { }2,E α τ θ is the expected power of the multipath

components conditioned to their delay and azimuth and

( , ),f τ θτ θ is the joint pdf of time delay and angle of arrival.

Considering the mean power of each component inversely

proportional to the square of its delay, expression (3) can be

rewritten as

2( , ) ( , ), ,

cP fτ θ τ θτ θ τ θτ

∝

(4)

The expression for this joint pdf can be found in [14], and

will be omitted here, and it is a function of D, the distance

between MS and BS and sσ , the standard deviation of the

scatterers distribution.

Simulating the PAS using expression (4), for linear

distribution of scatterers in a circle around the mobile with

ray equal to 23 m and for gaussian distribution of scatterers

with sσ = 16 and D equal to 1000 m for bough, and

comparing them with a Laplacian distribution, which was

shown to agree quite well with experimental results [12], we

obtained the curves shown in Fig. 3.

We can see that the gaussian distributed model is closest

to the expected PAS profile and therefore should be chosen

for a better geometrically based model of scatterers

distribution.

Fig. 1. Gaussian scatter density model.

-6 -4 -2 0 2 4 6

-80

-70

-60

-50

-40

-30

-20

-10

0Histogram of PAS

Normalised power dB

Angle of arrival

Unifor scatters distribution

Laplacian function

Gaussian scatters distribution

Fig 3 The PAS simulation compared with

Laplacian function

3.3 3.35 3.4 3.45 3.5 3.55 3.6 3.65 3.7 3.75

x 10-6

-3

-2

-1

0

1

2

3

Teme of Arrival (sec)

Angle of Arrival (degrade)

Scatter plot with Gaussian diatribution

Fig 2 – Angle versus delay scatter plot as seen by the BS

172

IV. SIMULATION TOOL

As systems become more elaborate more requirements for

channel models are demanded. Components like spatial

domain (smart antennas) and delay domain (Rake receivers)

demand that the tools used to simulate the communication

channel model accurately the delay and angular spread

perceived at the receiver.

In the developed tool, here presented, the delay and

angular dispersion are simulated using clusters of scatterers.

We must have at least one cluster, the one around the MS,

and some additional far clusters, for which the concept of

visibility regions is introduced. Basically, each far cluster

will have LOS to BS and MS simultaneously only in some

regions (visibility regions) and might appear and disappear

along the trajectory followed by MS as it moves. The

transition between LOS/NLOS is implemented using a

smooth transition functions as shown in Fig. 4.

This tool was implemented in Matlab® and most of its

features are based on COST 259-DCM report [15]. The

novelty introduced in the present implementation is the use

of a geometrically based model for the scatterers with a

gaussian distribution, as explained in section III. The model

proposed for implementation in COST 259 is not

geometrically based.

The input parameters for simulation are:

• Type of scenario • Carrier frequency [Hz] • Vector positions of MS ([x, y]) • MS antenna height • BS antenna height The parameters necessary for simulation for each scenario

are presented in Table I, extracted from [15].

The results obtained from the simulation, for each

position of the mobile, are:

• total number of clusters;

• complex amplitude of each multipath component;

• time delay of each multipath component;

• azimuth and elevation of each multipath component

(at the BS and at the MS);

• mean normalized power from each cluster (includes

slow fading);

• mean delay and standard deviation for each cluster;

• mean angles of arrival and standard deviation for

each cluster.

The following sequence is used to create the simulation

environment:

A. Number of far cluster and its location

At least one cluster is present, the one around the MS.

Additional cluster may be present and its number is taken

from a Poisson distribution with average 0N .

The location of each additional cluster is determined from

a Uniform distribution, with minimum distance (RM),

maximum distance ( maxD ) and radius of cluster is fixed

(RC). The angular position of the cluster, with respect to the

BS is a random variable, uniformly distributed between 0

and 2π .

B. The cluster power

The path loss for each cluster is given by:

1i adL L L= + (5)

0(0, 20) ( ) /ad iL U sτ τ µ= + − (6)

where U(a,b) means a uniform distribution between a and b,

0τ is the time delay of the direct signal from MS to BS and

iτ is the time delay of the signal traveling from MS to i-th

cluster and then to BS.

The parameter 1L is the mean loss obtained from the

propagation models discussed in section II.

For the cluster around the MS the term adL is not present

but the slow fading attenuation, modeled, in dB, by a

gaussian random variable of zero mean and deviation σd,

must be added as explained in section D.

C. Cluster appearance and disappearance

The concept of visibility regions is introduced in order to

determine where the far clusters can be seen by the MS and

BS as it moves. A visibility region is a circular area of radius

RD , and transition length LD . As shown in Fig 4, as the MS

enters each visibility region the corresponding cluster is

made active in a smooth way.

Each far cluster is associated with one visibility region.

D. The mean power received at BS as MS moves.

The mean power received at the BS as the MS moves in a

cell is composed of up to four parameters: mean power loss,

slow-fading, fast-fading and Rice K-factor as shown in Fig.

5. The mean power loss is determined using Section II and

depends on the scenario simulated.

TABLE I

PARAMETERS FOR SIMULATION

Parameters TU BU RA HT

Average of additional cluster, 0N 0.17 1.18 0.06 1.18

Max. cell distance, maxD [m] 3000 3000 20000 20000

Radius of visibility, RD [m] 100 100 300 300

Radius of cluster RC [m] 50 50 300 300

Std. Cluster distance deviation Rσ [m] 500 500 5000 5000

Minimum distance of cluster RM [m] 1000 1000 3000 3000

Transition length LD [m] 20 20 20 20

Cut off distance Dcor [m] 500 500 5000 5000

Median building height Hb [m] 15 30 5 5

Std deviation of slow fading dσ [dB] 9 9 6 6

Correlation distance of slow fading

L dσ [m] 11 11 500 500

XPD mean power ratio XPDµ 6 6 12 12

XPD std. Power ratio XPDσ 6 6 3 3

Correlation distance XPDD [m] 6 6 6 6

173

The slow-fading follows a log-normal distribution [1-3].

To simulate it, a zero-mean Gaussian distributed random

variable, with standard deviation dσ (in dB), is generated

for each position. Correlation with distance is enforced by

filtering these data with a filter with correlation distance

L dσ . This log-normal variable must be added to the mean

power loss. This phenomenon is referred to as log-normal

shadowing.

The fast-fading is the result of incoherent superposition of

multi-path components. As the MS moves, the superposition

of their complex amplitudes generates a variation in the

received amplitude (Rayleigh fading). Depending on the

speed of the mobile a Doppler spectrum will also arise.

Therefore these two effects appear automatically due to the

multipath components generated as explained in section III.

The variation of the Ricean K-factor is also modeled in

the implemented tool as:

( ) 20log (4 / )1 10EPL d L d cπ λ= − (10)

( ) (26 ( ) / 6,6)K EPL N EPL drice = − (11)

where d is the distance between MS and BS, ( )EPL d is the

excess path loss and ( , )N a b is a Gaussian random variable

with mean a and standard deviation b.

E. Cross polarization XPD

This tool simulates only cases where the primary

polarization is vertical. Co-polarization in this context means

Vertical-Vertical and cross-polarization Vertical- Horizontal

as follows:

( , )XPD N XPD XPDµ σ= (12)

/XPD Pvv Pvh= (13)

where XPDµ is the mean and XPDσ is the variance of

XPD. This parameter is modeled as log-normal correlated

variable with correlation distance XPDD .

V. CONCLUSION

We have presented a communication channel

simulation tool for macro-cell environments based on

geometrical and statistical models that allows a realistic

treatment for mobile system simulation.

This tool uses a gaussian geometrical distribution for

the scatterers in each cluster, allowing the existence of

additional (far from the mobile) clusters of scatterers. This

distribution provides a good agreement, in terms of power

angular spectrum, with measurements.

The Rayleigh and Doppler effects appear naturally as

function of variation of incoming multi-path components

when the MS moves.

The parameters generated by this tool characterize a

realistic mobile radio channel for third and fourth

generation of wireless systems that may use spatial

diversity.

REFERENCES

[1] Parsons, J. D. “The Mobile Radio Propagation Channel ”. 2nd. ed.

John Wiley & Sons LTD, 2000, pp. 18-42 and 115-121.

[2] Rappaport, T. S. “Wireless Communications Principles and Practice”

Prentice Hall, 1996, pp. 78-102.

[3] Lee, W. C. Y, “Mobile Communication Engineering” McGraw-Hill,

1982, pp.25-33.

[4] COST 231 “Digital Mobile Radio Towards Future Generation

Systems Final Report” dez. 1998, cap 4.

[5] Gans, M. J., “A power-Spectral Theory of Propagation in the Mobile-

Radio Environment” .IEEE Transaction on Vehicular Technology,

vol. 21, Feb. 1972, pp. 27-38,

[6] Ertel, R. B., Reed, J. H., “Angle and time of arrival statistics for

circular and elliptical scattering models” IEEE journal of selected

areas in communications, vol. 17, no. 11, 1999.

[7] Allsebrook, K., Parsons, J. D., “Mobile Radio Propagation in British

Cities at Frequencies in the VHF and UHF Bands” IEEE Transactions

on Vehicular Technology, vol. 26, no. 4 nov. 1977, pp. 313-312.

[8] Petrus, P., Reed, J.H., Rappaport, T. S. “Geometrically-Based

Statistical Channel Model for Macrocellular Mobile Environments”

IEEE Tr. on Communications vol. 50, no. 3 march 2002, pp. 1197-

1210

[9] Mahmoud, S. S., Hussain Z.M., Shea, P. “Space-Time Model for

Mobile Radio Channel with Hyperbolicaly Distributed Scatterers”

IEEE Antennas and Wireless PropagatioLetters, vol. 1, 2002, pp.

211-214

[10] Libert, J. C., Rappaport, T. S. "A Geometrically Based Model for

Line-of-Sight Multipath Radio Channels," IEEE Vehicular

Technology Conference, Atlanta, GA, May 1, 1996, pp 10-22

[11] Jakes, W. C. “Microwave Mobile Communication”

.Wiley, 1973, cap 2. [12] Laurila, J., Molisch, S. F. e Bonek, E. “Influence of the scattered

distribution on power delay profiles and azimuthal power spectra of

mobile radio channels” Proc. ISSSTA-98, 1998, pp. 267-271.

[13] Janaswamy, R. “Angle and Time of Arrival Statistics for the Gaussian

Scatter Density Model” .IEEE Transactions on Wireless

Communication july 2002, vol. 1, no. 3, pp. 488-497.

[14] Pedersen, K. I., Mogensen, P. E. e Fleury, B. H., “Stochastic Model

of Temporal and Azimuthal Dispersi Seen at the Base Station in

Outdoor Propagation Environments”. IEEE Transactions on

Vehicular Technology, mar 2000, vol 49,pp. 437-447.

[15] Correia, L. M., “Wireless Flexible Personalised Communications

COST 259: European Co-operation in Mobile Radio Research” John

Wiley & Sons March 2001, cap 3.

50 100 150 200 250 300 350 400

-260

-250

-240

-230

-220

-210

-200

-190

-180

-170

-160

Distance (m)

Power (dB)

Far-clusters visibility regions and power of arrival at BS

Fig 4 Far-cluster visibility regions and power

of arrival at BS

50 100 150 200 250 300 350 400 450-120

-110

-100

-90

-80

-70

-60

-50

-40

Distance (m)

Power (dB)

Mean power simulation

This simulation include

Mean power, fast-fading, slow-fading and Rice K-factor variation

Fig 5 Mean power received at the BS

174