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and wideband measurements are included for verification. I. INTRODUCTION. ESPITE cable and satellite communications, the number. D of terrestrial radio ...
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 44, NO. 3, MARCH 1996

393

Evaluation and Verification of the VHFKJHF Propagation Channel Based on a 3-D-Wave Propagation Model Thomas Kiirner, Member, IEEE, Dieter J. Cichon, Member, IEEE, and Werner Wiesbeck, Fellow, IEEE

Abstract-This paper is intended to increase and improve the knowledge concerning the characterization of digital VHFNHF communication channels. This characterization of the propagation channel is based on the fieldstrength-delay-spectrum(FDS) of the three-dimensional (3-D) multipath wave propagation. A statistical superposition of the predicted multipath signals yields the probability density function of the narrowband signal and the averaged channel impulse response of the wideband propagation channel. Thereof, the relevant parameters, e.g., standard deviations, mean values, delay spread, and correlation coefficients, are derived both in time and frequency domain. The angles-ofarrival of the multipath signals are used to calculate the Doppler spectra of moving receivers for the characterization the timevariant properties of the propagation channel. In total, a rather complete summary of derivations, algorithms and characteristics of the VHFKJHFpropagation channel is presented. Narrowband and wideband measurements are included for verification.

I. INTRODUCTION

D

ESPITE cable and satellite communications, the number of terrestrial radio communication services is increasing. Typical networks are personal communication systems (PCS), mobile radio, digital audio broadcast, and digital directional radio. Several papers [l], [2], stress the need for detailed information concerning multipath effects and their implications to reception quality, especially in high-bit rate digital systems. To avoid service failures due to multipath fading and to make use of the total channel capacity, digital radio systems apply equalizers, spread spectrum techniques, and Viterbi decoding of convolutional codes, respectively. Up until now the essential information, i.e., the parameters for these multipath countermeasures could only be obtained by measurements or hardware simulations [3]-[6]. Measurements require the installation of a complete system. They are not well suited for a quick analysis of the multipath situation in different terrain during the design of a network. Hardware or software simulations are generally based on typical standard situations Manuscript received May 6, 1994; revised October 9, 1995. This work was supported by the Department for Science and Research of the State Government of Baden-Wurttemberg within the project “Forschungsverbund Medientechnik Sudwest (FMS)”. T. Kurner is with E-Plus Mobilfunk GmbH, Ulmenstrasse 125, D-40476 Dusseldorf‘, Germany. D. J. Cichon is with the Institut fur Hochstfreqnenztechnik und Elektronik, University of Karlsruhe. W. Wiesbeck is with the Institut fur Hochstfrequenztechnik und Elektronik, University of Karlsruhe, Kaiserstrasse 12, D-76128 Karlsruhe,

Germany.

Publisher Item Identifier S 0018-926X(96)01825-X.

such as the impulse responses as defined by COST 207 [7], [SI. For an optimum transmitter assignment the propagation channel data have to include the fieldstrength-delay-spectrum (FDS), the frequency-correlation-function (FCF), the Doppler spectrum (DS), and thereof, derived deterministic and statistic channel characteristics. A better and adequate source for the required information are wave propagation models that consider multipath propagation in natural terrain. For the past several years the Institut fur Hochstfrequenztechnik und Elektronik (IHE), University of Karlsruhe has had wave propagation models available that supply the required information. These models are used for an evaluation of the propagation channel. The bases are the 3-D-wave propagation models [9]-[ 111, as described in Section 11. From the FDS, the characteristic parameters for the narrowband propagation channel are derived in Section 111. The evaluation of the magnitudes of the multipath signals yields the probability density function (PDF) of the field strength magnitude (Section 111-A). An efficient algorithm for the calculation of the averaged received power based on the series-wide expansion of characteristic functions is presented in Section 111-B. In Section 111-C, the multipath angles-of-arrivals are used to derive the spatial and temporal fading characteristics. A wideband analysis of the multipath signal which requires the consideration of the receiver filter characteristics is given in Section IV. Time variant properties due to Doppler shifts are subject to investigations in Section V, yielding the scatter function which is adapted to characterize wide sense stationary uncorrelated scatterer systems (WSSUS). In Section VI, the results are compared with both narrowband and channel sounder measurements in an existing GSMnetwork, which is affected by severe multipaths in a hilly terrain. 11. WAVE-PROPAGATION MODEL-SHORT DESCRIPTION

The wave-propagation models used for these investigations have been published recently by Lebherz et al. and Kiirner et al. [9]-[ 111. In the following, a short description is given. The ray-optical wave-propagation models take into account the propagation paths in a vertical TxRx-plane and the contributions by scattering from the 3-D terrain off this vertical TxRx-plane, based on a topographical and land usage database. The applied asymptotic methods (UTD, Kirchhoff method) are valid as long as one pixel (e.g., resolution cell) is

0018-926X/96$05.00 0 1996 IEEE

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IEEE TRA]VSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 44, NO. 3, MARCH 1996

-3Okm-----------------+

Fig. 1. Test area south of Stuttgart, Germany with the base stations (Txl, Tx2) and the receiver positions (Rxl, Rx2); the arrow shows the movement of Rxl and Rx2, where applicable. Fig. 2.

large in its dimensions compared to the wavelength A. On the other hand, these dimensions have to be small enough to ensure a detailed modeling. A digital terrain model with 50 m x 50 m resolution is appropriate from 300 MHz to 3 GHz. For each multipath signal “i” the 3-D-model calculates the following parameters -magnitude Ei, -phase $2 due to reflection, scattering or diffraction, -time delay ri with respect to the direct signal, -incidence angles ai (azimuth) and ~2 (elevation), and -polarization state. These parameters completely characterize the signals in radio systems. The time delays ri and incidence angles ai>~i are deterministic values, whereas $2 and E, are statistically distributed [3]. The statistical nature of the 42 results from the local terrain roughness within the dimensions of one pixel, the influence of weather, and the limited resolution of the topographical and land usage database. It is assumed that the $2 are approximately rectangularly distributed. The width A$i and the mean value depend on the geometrical and surface properties of the reflecting or scattering objects, respectively, which can also be described statistically. The general formulation of rectangular distributions includes the special cases of a uniform distribution (A& = 27r) and of a deterministically known phase (A$; = 0, = 4 i , d e t ) . In many practical considerations, the assumption of a uniform distribution is reasonable especially at the higher frequencies. The fluctuations of the resulting signal due to changes of the $2 are large compared to those caused by variations of the magnitude. Therefore, the mean value of the bistatic scattering cross section is used as a deterministic value for the calculation of the Ei.

4

3-D-terrain around Rxl, fixed position, scattering pixels are red

isotropically radiated power (EIRP). Fig. 2 depicts the 3-D topography in the vicinity of the fixed Rxl. The locations of the scatterers, which are the sources of multipath signals, are red. The radiating transmitter Txl is 12 km northwest (see Fig. 1).

ANALYSIS 111. NARROW~AND Frequently failures of radio links are caused by interference or fading. Usually, the analysis of the interference situation is based on the standard deviation of the signals and the level which is exceeded with a certain probability [12], [13]. This requires the probability density functions, which are derived in Sections 111-A and 111-B. Burst errors in digital radio systems are caused by fading effects [14], which can be described by correlation coefficients. These are derived in Section 111-C. A. Statistical Superposition of Predicted Multipath Signals

The statistical superposition of all single propagation path signals E, results in the total fieldstrength ICtotal

4

A. Description of the Propagation Site Unless otherwise stated, all presented signatures and results refer to a hilly area southeast of Stuttgart, Germany, as shown in Fig. 1, with base stations (Tx) and receivers (Rx) marked. The base stations are operating GSM-transmitters at 935.6 MHz and 946.8 MHz, respectively, transmitting 50 W effective

where &tal

E Er E,,, Eyr $% n

f 7 2

complex total field strength magnitude of the total field strength magnitude of i-th paths fieldstrength ,Gt realhmaginary part of E, i-th paths phase due to reflection, scattering or diffraction number of considered ray paths frequency time delay of the component E,.

KURNER et al.: EVALUATION AND VERIFICATION OF THE VHFRTHF PROPAGATION CHANNEL

395

concentric circles (7). For this purpose E, and Ey have to be transformed into polar coordinates

Based on f~ ( E ) the relevant statistical parameters-mean value, standard deviation and exceeding probability-are extracted according to [27].

Fig. 3. Phasor representation of multipath signals.

B. Asymptotic Methods for the Determination of the Mean Value

Fig. 3 depicts (1) in the complex plane. Each E, is represented by a phasor with a deterministic magnitude and a statistically varying phase. Due to the variation of $I,, the resulting vector Etotal ends up within the shaded area with a certain probability. Quantitative statements for the probability result from the computation of the two-dimensional (2-D) probability density function (PDF) in the complcx planc. Thc superiority of this approach, based on a 3-D wave propagation model and digital terrain data, is evident if the result is compared with commonly used standard PDF’s in propagation theory like Rayleigh, Gauss, Lognormal, Nakagamim and Rice. These PDF’s are given analytically in [15] and [ 161. Their validity depends on several assumptions made with respect to the multipath signal. In general, these basic assumptions are satisfied only by special terrain types. This is confirmed by independent measurements in different types of terrain [17]-[ 191. With the assumption of statistically independent variables E,, the complex PDF of the total field strength is evaluated by the product of the characteristic functions -2cp ( u , ~of) the signals

In this section, the computation of expected fieldstrength values is shown. The notation E [ . ]is used to express the expected value of the terms in brackets. The expression E ( . ) is applied to mark the dependence of the field strength E from the terms in brackets. In many applications, the expected value of the received power P is of main interest

with

transmit antenna pattern characteristics receive antenna pattern characteristics maximum gain of transmit antenna maximum gain of receive antenna magnitude of E: real part of E: imaginary part of E: free space wave impedance.

a2

L,

+m

cp2(u,v)

=

+-0O

f E x 9 , E y , ( E x z ,E y z )

x e32~(uExa+wEyz)dEx,dEY,. (3)

fE,,,E,, (E,,, Eyz)is the complex PDF of E, derived from the PDF of the $Iz and the corresponding magnitudes E,. The resulting characteristic function [20] cp(u,U) of the total receiver fieldstrength is

In the following, the constants in (9) are summarized in c1

n

cp(u,U ) = JJYi(U, U).

(4)

i=l

The inverse Fourier transform of (4) leads to the 2-D PDF f ~ , , (~E, z ,EY)of the total complex receiver field strength

J-m

Based on the 2-D PDF f ~ ;E;,(EL~, ~ , EL2)the 1-D PDF’s of ,), the real and imaginary part, ~E;~(EL.) and f ~ ; % ( E hare known as well. E [ E 2 ]is computed using the moments of the characteristic functions of these 1-D PDF’s

J--00

Starting with the 2-D PDF of &,tal in (5) the PDF ~ E ( E ) of the magnitude of E?total is derived by integration along

=

[

(?ELJ2] i=l

+E

[

i=l

(11)

E E E TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 44, NO. 3, MARCH 1996

396

Assuming statistical independence of all E:, the onedimensional (1-D) PDF's are computed as follows

E

[

z=1

J -cc

n

P-CW

The relation between the mean value E[zp]and the corresponding characteristic function p(u) is given in [20]

\

Application of (22) and (23) to (1 1) gives

yielding

With this algorithm, the time consuming calculation of the 2D PDF of (5) is not necessary to compute the mean value of the received power. In the special case of uniformly-distributed phases the well-known expression in (25), [21], can be derived from (24) n

El2.

E [ E 2 ]=

(25)

i=l

It is obvious that (15)-(19) do not require the knowledge of the whole characteristic function ( P k ( U ) . It is sufficient to know the value ( ~ (0) k ( 2 ) only. Therefore, the characteristic functions are developed into Taylor expansion series

Equation (24) is also valid if both phases and amplitudes are stochastic variables. C. Fading Mechanisms

Inserting (20)-(21) into (12), dropping higher order terms, and comparing the coefficients yields

Fading is the spatial or temporal fluctuation of field strength. In mobile communication two fading mechanisms are distinguished. The large-scale change of the location of the mobile causes variations of the propagation conditions, i.e., completely different signals amve at the receiver. Consequences are slowly varying field-strength levels. This effect is called long-term fading [2], [22]. It is described by the mean values of the received field strength along the mobile's run. Therefore, the algorithms presented in Section 111-B are applied. Phase shifts of the incident signals due to small-scale movements of the mobile cause a fast statistical variation of the envelope field strength. This effect is known as short term or fast fading. Long-term and short-term fading effects superimpose by multiplication

E ( t ) = Eo(t)r(t) (26) magnitude of the resulting field strength E(t) Eo(t) mean value of the field strength

~ ( t )fading factor.

KURNER et ai.: EVALUATION AND VERIFTCATION OF THE VHFRJHF PROPAGATION CHANNEL

In the following &(t) is assumed to be constant. Hence, the statistical properties of E ( t ) are given by the statistical process ~ ( t Generally ). fading processes like ~ ( tare ) characterized by the envelope correlation coefficient LEE(At), which describes the temporal fluctuations of the signal. However, the wavepropagation model used in this paper does not predict temporal processes but the spatial variations of field strength. Assuming the ergodicity of the stochastic process [23], it is possible to derive the temporal fluctuations from the spatial fluctuations if the direction and speed of the mobile is known. The assumption of ergodicity is reasonable, if the fluctuations are mainly caused by phase fluctuations. The spatial distance of maxima and minima of the fast fading process depends on the parameters Ei, &, r i , ai, and E ; . The phases are statistically distributed. Hence, the resulting interference pattern is a stochastic process, which can be described by correlation parameters. For the investigation of the spatial field-strength fluctuations (Fig. 4), one pixel of the terrain is considered. The following simplifying assumptions are justified: -the scatterers are constant if the mobile moves within one pixel; -the magnitudes Ei are constant with respect to the receiver location; -the time delays ri change with Ari due to the receiver movement; -the incidence angles a; change due to the receiver movement. If Ar; changes, $i shifts due to

A$; = 27r f Ari.

397

x-direction digital terrain data

\

/' / /

/

\

1' I'

scatterer \ \

I'

\

70

(27)

The resulting field strength is a function of the superposition of the complex multipath signals

0

n

i=l

In (28), the influence of the antenna pattern characteristics is neglected for localy small areas. According to the assumptions made, only the phases +i are functions of the location. For a single pixel, each multipath component is assigned a single phase angle, randomly derived, that is true for the entire pixel. This angle is then altered by the location-dependentdelta phase defined in (27). Fig. 4 shows the spatial interference pattern computed with (28) for one set of statistically distributed phases for the situation in Fig. 2. With the vectorial velocity of the mobile the spatial function E ( z ,y, Z ) is transformed to a temporal process &(t ) . The envelope correlation coefficient L E E of this process is given by

where E ( t ) is the magnitude o fE(t ). With the magnitude and phase of the field strength the complex correlation coefficient is computed

Fig. 4. Grid of the digital terrain data showing transmitter, scatterer, and receiver (top) and the derived spatial-field strength fluctuation within one pixel (bottom).

In most applications the envelope correlation coefficient is used. However, the complex correlation function allows the determination of the Doppler spectrum (see Section V-A). The knowledge of these correlation parameters is also useful for diversity investigations, such as space or antenna diversity ~31.

IV. WIDEBAND ANALYSIS With the information provided by the algorithms in Section 111, it is possible to characterize the field strength at any receiver location. The influence of multipath propagation on link performance and the signal characteristics of the propagation channel in time- and frequency-domain are the subjects of this section. Algorithms for the evaluation of significant propagation channel parameters as well as timeand frequency-domain signatures are presented. In this section, the time-invariant propagation channel is considered, i.e., a stationary receiver is assumed.

398

A

E E E TEV.NSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 44, NO. 3, MARCH 1996

. Evaluation in Time Domain

By considering the propagation channel between the input to the transmit antenna and the output of the receive antenna, the FDS (Fig. 5) describes the impulse response g ( t ) o terrain in a narrow frequency band around f o , where f o is the carrier frequency for which the FDS was calculated n g(t)

aiej+aSo(t - Ti)

= i=l

where

a.-

~

Ea

' - Cy=,Ei

'

In Fig. 5, a sample of randomly distributed phase angles is used. The additional consideration of the receive and transmit antenna patterns is equivalent to a weighting of FDS components dependent on the transmit or receive aspect angles of the scatterers n

(33)

ER, QIT,

ET,

CT CR

10

20

30

50

40

time delay / ps Fig. 5. Field-strength delay spectrum for the situation displayed in Fig. 2.

-70 1

I

E

i=l OR,

"0

incidence angle at receiver (azimuth) with respect to the scatterer incidence angle at receiver (elevation) with respect to the scatterer exit angle at transmitter (azimuth) with respect to the scatterer exit angle at transmitter (elevation) with respect to the scatterer transmit antenna characteristic receive antenna characteristic.

The bandwidth of a receiver is limited; the signals arriving within a certain time period cannot be resolved. This is accounted for by the convolution of g,(t) with the receiver impulse response function ~ ( t )which , is matched to the transmit signal

a a

-80

23

-90

0

a

z-100

z

W 0

2.110 -120 -130 0

with / n

\

20

30

50

40

time delay / ps Fig. 6. Channel impulse response for the FDS in Fig. 5, and the filter according to (39). n

=

The instantaneous received power P ( t ) is

10

CAi. i=l

As the Ai are statistically independent variables the algorithm described in Section 111-B can be applied for the determination of P,(t). Fig. 6 shows an example for the impulse response P,(t) computed from the FDS in Fig. 5 applied to a GSMsignal, where ~ ( tis )

P ( t ) is a stochastic variable with the distribution fp(P), (39) which is dependent on the statistic properties of &. f p ( P ) is determined in the same way as ~ E ( E(7), ) separately for each corresponding to the GSM-wave form with At = 3 , 7 ps [24]. time delay r. The expected value of the received power-the Equation (39) is important, as the verification in Section VI-B power-delay-spectrum (PDS)-is of main interest is performed in a GSM network. Definition of Typical Time-Domain Parameters: Based on Pvx(t) = E[P(t)l= c ~ E [ ~ ( t ) ~ = * (c~EmaxE[h(t)h*(t)l t ) l2 P,(t), the delay spread S and t , can be derived for the (37) characterization of the propagation channel [4], [25], [26] with I

h ( t )= -

--

J,

g ( t ' ) w ( t - t') dt'

s=

+m

t2pm(tpt/S+-cc

P,(t)dt

-

tL

(40)

KURNER et al.: EVALUATION AND VERIFICATION OF THE VHFKJHF PROPAGATION CHANNEL

399

notch exists within the considered bandwidth. To better understand this effect, the attenuation difference p ( AS) at different frequencies is computed in a Monte Carlo simulation for 10 000 samples of transfer functions with randomly generated phase samples $i

0

a

9

g -10

2 22 -20 (d

.......................................................

-30

-40

935

935.25

935.5

...............................

.)

935.75

936

frequency / MHz Fig. 7

Two samples of transfer functions for the FDS in Fig. 5.

where +m

tm

Lcc

t P, (t) d t / /

=

+Ix

P, ( t )d t .

(41)

-cc

S is a rough criterion to assess the performance of a digital system. As long as S is small compared to the duration T of the digital symbol the channel can be assumed to be resistant to intersymbol interference. Another parameter commonly used to characterize GSM systems is the interference ratio QT which describes the ratio between power received within a time window of the width T to the power outside this window

Usually, p ( A f ) is called the linear amplitude distortion. The probability that the attenuation difference p remains under the level Ap for different frequency differences is shown in Fig. 8. By starting from this signature, the mean value and standard deviation are calculated as a function of the frequency difference A f . The mean value is zero for all distributions whereas the standard deviation changes according to Fig. 9. Based on the results of these investigations, a quantitative description of the fading statistics becomes possible. As the Monte Carlo simulation of transfer functions is a very time consuming procedure a more efficient method to investigate frequency selective effects is the application of correlation functions. A weak stationary process is described by its autocorrelation function [27]. One autocorrelation function that describes a random process in frequency domain is the frequency correlation function (FCF)

H(f)N*(f+Af)df (45)

H ( f )= G ( f ) w ( f )

W ( f O.)-

7

-cc

where

W ( f )is the Fourier transform of

t,,,

.I'

+cc

LHAAf) = H ( f ) H * ( f+ A f ) =

(46)

~ ( tin)(34) W(t)

(47)

Z H H ( A ~is) a measure for the probability that H ( f ) is equal + A f ) . l m ( A f )is computed based on a Monte Carlo

= maximum length of the impulse response

Hf(

= variable

simulation as shown above. A second, more efficient method uses the theorem of Wiener-Khintchine: L=(Af) is related to P,(t) (37) by a Fourier transform

S and QT(T = 16 p's) are used for comparisons between predictions and channel sounder measurements in Section VIB. B. Evaluation in Frequency Domain For many applications like frequency hopping or spread spectrum techniques, it is necessary to characterize the propagation channel in frequency domain. The relation between the complex impulse response g ( t ) and the complex transfer function G(f ) is given by the Fourier transform n

As the phases of scattered waves can be described by their statistical distributions only, in (43) is also a variable of a stochastic process. Any sample of randomly distributed phases leads to a different transfer function, as shown for two transfer functions in Fig. 7. Although the form of the function samples in Fig. 7 is quite different, the single function samples show a common statistical behavior. There is a certain probability that a deep

Ic(f)l

Normalizing L m ( A f )to its maximum yields to the normalized FCF II(Af) (49) An example of a FCF is shown in Fig. 10. A comparison of Fig. 9 and Fig. 10 shows that the principal behavior of the displayed signatures is very similar. The sharp increase of the standard deviation, especially, is in the same frequency range, where a sharp decrease of the FCF occurs. Also the asymptotic behavior of the two signatures is similar. If the variation AV of the transfer function is used instead of Ap, an analytical relation is given by [28]

A V ( A f )= IH(f)- rrif + A f ) l E[AV(Af)'] = 2(1 - Re{B(Af)}). This underlines the significance of the FCF.

(50) (51)

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a 3-D wave-propagation model, Section V-B deals with the characterization of a WSSUS channel by the propagation model.

820

c

5 9

A. Doppler Spectra

'0

a

The Doppler frequency of each multipath depends on the velocity of the vehicle, the wavelength, and the angle-ofarrival

-20

where -30

'U

.01

I

1

S 10 2030

50

7080 90 95

9!l

93.9 99.99

CO

probability / %

f d

ai

Fig. 8. Probability that the attenuation difference remains under the specified level for three different frequency separations, based on the FDS of Fig. 5.

fdma

vehicle velocity speed of light Doppler shift incidence angle in azimuth maximum Doppler shift.

The maximum Doppler shifts result for 01 = 0" and a = 180". As each multipath signal has a different angle-of-

1

arrival and amplitude a wide Doppler spectrum exists. This phenomena is well known in the literature [26], [29]. For planning purposes, usually the simplified case of the so-called Jakes-Spectrum is applied, which assumes that all incoming signals have the same magnitudes and equal distributed anglesof-arrivals. This assumption characterizes the worst case only. Based on 3-D wave-propagation models the Doppler spectrum is more accurately determined as follows: the calculation is based on a similar representation of the impulse response as used in (33)

m

P \

4 D

n

ij ( a )= CAi(ai)GO(a- ai) -a

Af/ MHz

(53)

i=l

Fig. 9. Standard deviation of the attenuation difference as a function of frequency difference, based on the FDS of Fig. 5.

where

Ai(%)= CR(QR,%,E R , i ) a i e j ~ " T ( w , i , E T $ ) .

(54)

The received power within a small range da! is given by

P(a!)da= c&a)E*(a)da!

(55)

where Jqa) =

G",(a).

(56)

Application of the transform

1 0

0.4

06

Idfd(a)\ = f d m . a x / f dmmax \ d @ \

(57)

0.8

6 /MHz Fig. 10. Frequency correlation function for the CIR in Fig. 6.

given in [26] yields the received power within the small frequency band of width df

Previously, in Section IV, the time-invariant propagation channel was considered. The incoming multipath signals at a moving receiver are Doppler shifted yielding time-variant effects. In Section V-A the Doppler spectrum is derived from

The expected value of (58) is the mean received power Em(f d ) and (59), shown at the bottom of the next page. Fig. 11 displays the Doppler spectrum corresponding to the scatter diagram depicted in Fig. 2. The vehicle moves with 30 d s e c

KURNER et al.: EVALUATION AND VERIFWATION OF THE VHFNHF PROPAGATION CHANNEL

40 1

-50

g l

3

-75

................

-94

I................. I................. 1..................

-47

0

47

94

Doppler frequency / Hz Fig. 11. Doppler spectrum for the situation in Fig. 2.

South. This spectrum, derived from a 3-D wave-propagation Fig. 12. Scatter function derived from the FDS in Fig. 5 and the Doppler model is quite different from the Jakes-Spectrum. spectrum in Fig. 11. In Section 111-C the complex correlation coefficient is derived, which depends on the angles-of-arrivals too. The relation between the Doppler spectrum and the complex comela- scatter function is also called Doppler-delay-spectrum.Based on the complex scatter function, it is possible to compute the tion coefficient in (30) is given by [29] time-variant impulse response [311

S_,

+m

h(t77) =

The knowledge of the Doppler spectrum and the FDS are used in the following section to characterize WSSUS systems.

In the characterization of linear time-variant systems the consideration of WSSUS systems is essential [29]. These systems assume that the time delays 7%and the Doppler shifts f d a are uncorrelated. Usually these conditions are fulfilled in mobile communication [30].Therefore, WSSUS systems are of practical significance. In the above algorithms for processing the predicted multipaths, uncorrelated signals are assumed, too. Consequently the propagation channel model as introduced in this paper is assumed to be a WSSUS channel. WSSUS systems are mainly characterized by the scatter function s(7, f d )

The scatter function describes the power of the multipath with a time delay 7%and a Doppler shift fdz. Hence, the scatter function (Fig. 12) is derived directly from the FDS and the Doppler spectrum (Figs. 5 and 11). Sometimes the

(62)

aaeJ'"go(7 - 7 a 7 fd - fdz).

(63)

where n

~ ( 7 f d ,)

B. WSSUS Systems

s(7,f d ) e " * f d t d f d

= a=1

This function can be used for more realistic fading simulations of time-variant propagation channels. VI. VERIFICATION The verification and demonstration of results of the model and the algorithms presented in this paper is performed with four typical situations in an operating GSM network. The first two situations are in a hilly terrain near Diisseldorf, Germany, for which the evaluation of narrowband field-strength measurements is presented in Section VI-A. The channel impulse response (CIR), measured with a channel sounder is compared with the results derived from the 3-D wave-progation model for a characteristic multipath situation near Stuttgart, in Section VI-B. A. Narrowband Measurements

The narrowband field-strength measurements at 947 MHz were recorded in 20 cm intervals. The results of a straight

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 44, NO. 3, MARCH 1996

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80

I



I

1

a;

20

26

1

20 32

38

44

50

field strength / dBpV/m Fig. 13. Measured and computed probability density functions for a multipath situation.

run within one 50 rn x 50 m pixel are compared to the PDF computed for that pixel applying the algorithms in Section IIIA. Fig. 13 shows bioth measured and computed PDF’s. The agreement in terms of mean value, standard deviation, and shape is very good For a comparison, a Rician distribution with the same moments (mean value and standard deviation) is added. The Rician distribution fits better than a Rayleigh, Nakagami, Lognormal, or Weibull distribution, which were examined, too. However, the Rician distribution does not fit as well as the PDF calculated from the 3-D-wave propagation model. The verification of the computed mean received power according to (25) is given by comparison with measurements in a hilly terrain east of Dusseldorf at the same frequency. Fig. 14 shows a S lun run, where frequent changes between line-of-sight conditions and nonline-of-sight conditions occur. At some points, local minima or maxima of the prediction seem to be shifted versus measurements. This shift is explained by the resolution of the database (SO m) and 50-100 m uncertainty of the receiver position, recorded with the global positioning system ICGPS).

50

70

i

i:

I 110

90

I

I

130

150

Pixel

km-----------.----,

-5

Fig. 14. Field-strength prediction for a 5 km long run in a hilly terrain, 1 pixel = 50 m.

Fig. 15. Measured and predicted channel impulse responses for receiver Rxl of Fig. 1.

B. Channel Sounder Measurements Wideband measurlsments are performed in the operating D2GSM-network with a channel sounder (Rohde and Schwarz, receiver ESVD and impulse response analyzer PCS [32]). For the determination of the channel impulse response the synchronization burst of the broadcast control channel (BCCH) of the GSM signal is, evaluated. Hence, the CIR is determined with a resolution of 3.7 ps and a maximum delay of 80 ps. Fig. 15 displays the CIR’s of the link Txl-Rxl from Fig. 1. The principle behavior of the measured and the predicted signal is very good. Usually, multipath situations are characterized by the delay spread or the interference ratio as defined in (40) to (42). These two parameters are displayed in Fig. 16 and Fig. 17 for the link Tx2-Rx2 in Fig. 1. The Rx2 is moving 2 km along a highway. Both delay spread and interference ratio coincide in the first part of the run. They show a relatively good agreement

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in the last part. However, in the center part, measurement and prediction disagree. In that part of the run the direct signal disappears in the measured CIR, which does not happen to the predicted CIR. A site inspection of the area reveals

KURNER et al.: EVALUATION AND VERIFICATION OF THE VHFKJHF PROPAGATION CHANNEL

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different digital transmission schemes like PCS, mobile radio, digital audio broadcast, and digital directional radio. Coverage predictions including multipath information are possible. The derived algorithms are the basis to estimate the influence of multipath propagation on the bit error rate of digital radio systems [ll], [34]-[36]. ACKNOWLEDGMENT

The authors would like to thank Mannesmann Mobilfunk GmbH Diisseldorf for supplying the measured data. I

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an absorbing rock wall-not included in the digital terrain data-along the highway, which obstructed line-of-sight to the transmitter. In practical network planning it is of main interest to identify critical areas by their statistical parameters of the delay spread. In the following, for three situations described in Table I, comparisons are made between predictions and measurements. Rxl and Rx2 each move over 2 km highway. The mean values and standard deviations of S and Q shown in Table I are determined for both measured and predicted CIP’s over the 2 km runs. The good agreement in the mean values of both shows that the methods presented in this paper are applicable to identify areas with critical multipath propagation. This is also stressed by another investigation of Kiirner et al. [33], where a comparison between predicted and measured scatterers locations using both Doppler spectra and time delay shows reasonable good agreement. VII. CONCLUSION The extraction of information from a ray optical 3-D wavepropagation model has been shown. Detailed statistical parameters regarding the field strength and the signal characteristics o f the VHFAJHF propagation channel can be derived. The multipath propagation influence on narrowband and wideband channel characteristics is very well predicted, but one has to keep in mind that the results will never be better than the quality of the digital topography data allow. The algorithms presented can be used to study the influence and the corresponding countermeasures of multipath signals on

[l] T. S. Rappaport, “Wireless personal communications: Trends and challenges,” IEEE Antennas Propagat. Mag., vol. 33, no. 5, pp. 19-29, 1991. [2] J. Shapira, “Channel characteristics for land cellular radio, and their systems implications,” IEEE Antennas Propagat. Mag., vol. 34, no. 4, pp. 7-16, Aug. 1992. [3] W. R. Braun and U. Dersch, “A physical mobile radio channel model,” IEEE Trans. Veh. Technol., vol. 40, pp. 472-482, May 1991. [4]D. C. Cox and R. P. Leck, “Correlation bandwidth and delay spread multipath propagation statistics for 910-MHz urban mobile radio channels,” IEEE Trans. Commun., vol. COM-23, pp. 1271-1280, 1975. [5] P. Eggers, C. Jensen, A. Oprea, K. Davidsen, and M. Danielsen, “Assessment of GSM-link quality dependence on radio dispersion in rural environments,” in Proc. Veh. Technol. Soc. 42nd VTS Con5 1992, Denver, CO, May 1992, pp. 532-535. [6] J. Lavergnat and P. GolC, “Statistical behavior of a simulated microwave multipath channel,” IEEE Trans. Antennas Propagat., vol. 39, pp. 1697-1706, Dec. 1991. [7] COST 207, “Digital Land Mobile Radio Communications,” Final Rep., Office Official Publ. Eur. Comm., ISBN 92-825-9946-9, 1989. [8] GSM-Recommendation 05.05-DCS Version 3.1 .O, Eur. Dig. Cell. Telecommun. Syst. (Phase I): Radio Transmission Reception, ETSI/PT12, Feb. 1992. [9] M. Lebherz, W. Wiesbeck, and W. Krank, “A versatile wave propagation model for the VHFNHF range considering three dimensional terrain,” IEEE Trans. Antennas Propagat., vol. 40, pp. 1121-1131, Oct. 1992. [lo] T. Kurner, D. J. Cichon, and W. Wiesbeck, “Concepts and results for 3D digital terrain based wave propagation models-An overview,” IEEE J. Sel. Areas Communicat., vol. 11, pp. 1002-1012, Sept. 1993. [ l l ] T. Kurner, “Charakterisierung digitaler Funksysteme mit einem breitbandigen Wellenausbreitungsmodell,” Ph.D. Thesis, Univ. Karlsuhe, published in Forschungsberichte aus dem Institut fur Hochstfrequenztechnik und Elektronik, Band 3, ISSN 0942-2935, 1993. [ 121 “Planning Parameters and Methods for Terrestrial Television Broadcasting in the VHFAJHF Bands,” EBU-Tech. 3254-E, Tech. Ctr. Eur. Broadcasting Union, May 1988. [13] R. French, “The effect of fading and shadowing on channel reuse in mobile radio,” IEEE Trans. Veh. Technol., vol. VT-28, pp. 171-181, Aug. 1979. [14] T. Muller and H. Rohling, “Verteilung der Schwunddauem bei schmalbandigen Mobilfunkkanalen,” Nachrichtentech. Elektron., Berlin, no. 6, pp. 296-300, 1993. [15] H. Suzuki, “A statistical model for urban radio propagation,” IEEE Trans. Communicat., vol. COM-25, no. 7, pp. 673-680, July 1977. [16] M. Nakagami, “The m-distribution-A general formula of intensity distribution of rapid fading,” in W. C. Hoffmann, “Statistical methods of radio wave propagation,” in Proc. Symp. Univ. California, Los Angeles, USA, June 18-20, 1958, 1960. [17] T. Aulin, “A modified model for the fading signal at a mobile radio channel,” IEEE Trans. Veh. Technol., vol. VT-28, pp. 182-203, Aug. 1979. [18] J. D. Parsons and M. F. Ibrahim, “Signal strength prediction in built-up areas, part 2: Signal variability,” Proc. IEE, Pt. F , vol. 139, no. 5, pp. 385-391, 1983. [19] S. Mockford, A. M. D. Turkmani, and J. D. Parsons, “Characterisation of mobile radio signals in rural areas,” in IEE URSI Proc. 7th h t . Con$ Antennas Propagat., 1991, part 1, no. 333, pp. 151-154. [20] K. W. Cattermole, Statistische Analyse und Struktur von Information. Germanv: Verlag, VCN, FRG, 1988. [21] P. Beckmann, Probability in Communication Engineering. Orlando, FL:Harcourt, Brace, Library of Congress cat. # 67-12495, 1967.

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W. C. Y. Lee, Mobile Cellular Telecommunications Systems. New York: McGraw-Hill, 1989. N.Geng, T. Kumer, and W. Wiesheck, “Envelope correlation coefficient between diversity channels based on a 3-D wave propagation model,” in 3rd IEEE Int. $amp. Personal, Indoor, Mobile Radio Communicat., Boston, USA, 1992, pp. 407-410. P. Fey, “GMSK-mcldulation fur digitale funktelefone,” Nachrichtentech. Elektron., vol. 41, no. 4, pp. 156-157, 1991. J. B.Andersen, “A note on definition of terms for impulse responses,” COST 231 TD (89) 60, Brussel, Oct. 1989. W. C. Jakes, Micrcswave Mobile Communications. New York: Wiley, 1974. A. Papoulis, Probability, Random Variables and Stochastic Processes. New York: McGrav-Hill, 1965. B. Fleury, “Charakterisierung von Mobil- und Richtfunkkanalen mit schwach stationiiren Fluktuationen und unkorrelierter Streuung (WSSUS),” Ph.D. thesis, Eidgenossische Technische Hochschule Ziirich/Switzerland, Diss. ETH Nr. 9030, 1990. P. A. Bello, “Charac:terizationof randomly time-variant linear channels,” IEEE Trans. Comm,unicat., vol. COM-11, pp. 360-393, 1963. R. Kennedy, Fadins: Dispersive Communication Channels. New York: Wiley, 1969. J. D. Parsons and A. S. Bajwa, “Wideband characterization of fading mobile radio channels,” Proc. IEE, Pt. F , vol. 129, pp. 95-101, 1982. P. Riedel, “Messung der Kanal-Impuls-Antwort im GSM-Funknetz mit TS 9955,” Neues w n Rohde Schwarz, vol. 137, pp. 12-14, 1992. T. Kurner, T. Becker, and W. Wiesbeck, “Comparison of measured and predicted locations of interfering scatterers,” in Proc. IEE Int. Con$ Antennas Propagat., Eindhoven, The Netherlands, Apr. 1995, pp. 363-366. T. Kurner, T. Becker, D. 5. Cichon, and W. Wiesbeck, “BER prediction for GSM-systems using digital terrain data,” in Proc. Int. Con5 Telecommunicat., Dubai, U.A.E., Jan. 10-12, 1994, pp. 55-58. T. Kurner, D. J. Cichon, and T. Becker, “Degradation of digital communication systems in a multipath environment,” in Proc. IEEE Veh. Technol. Soc. 44th Con$, Stockholm, Sweden, June 1994, pp. 170-174. T. Kurner and W. Vl‘iesbeck, “EinfluB der Mehrwegeausbreitung auf die Bitfehlerrate,” FREQUENZ., vol. 48, no. 11-12, pp. 270-278, 1994.

‘ThomasKiirner (S’91- M’94) was horn in Tailfin,gen, Germany in 1964. He received the DipLIng. ‘(M.S.E.E.) and the Dr.-Ing. (Ph.D.E.E.) degrees from the University of Karlsruhe, Germany, in 1990 ,and 1993, respectively. From 1990-1994, he was with the Institut f i r Hochstfrequenztechnik und Elektronik (IKE) at the :University of Karlsruhe, working as a Research .4ssistant. His research topics included digital radio :systems with emphasis on GSM/DCS1800 systems, digital audio broadcast, and wave propagation in natural and urban terrain. He is an actively Participating Expert ofCOST 231, Working Group 2 “UHF Propagation” and a Member of the German delegation in ITU-R SG 3 “Radiowave Propagation.” Until 1994 he was a Lecturer for the Carl Cranz Series for scientific education teaching wave propagation modeling and channel characterisation. He i s now with the DCS 1800 network operator E-Plus Mobilfunk GmbH in Dusseldorf, Germany as a Project Manager. Dr. Kiimer received the “ITG-Forderpreis” Award from the German VDE for his Ph.D. thesis in 1994, and in 1995 he was awarded the IEEIICAP’93 Best Propagation Paper Award.

Dieter J. Cichon (S’91-M’96) was born in Ehingen Donau, Germany in 1965. He received the Dip1.Ing. (M.S.E.E.) degree, in 1991, and the Dr.-Ing. (Ph.D.E.E.) degree (summa cum laude), in 1994, from the University of Karlsruhe, Germany. In 1990, he spent a four-month internship in the Radar Science Laboratory at the Environmental Research Institute of Michigan, Ann Arbor, where he worked on SAR antenna analysis. Since 1991, he has been with the Institut fur Hochstfrequenztechnik und Elektronik (IHE) at the University of Karlsruhe, Germany. His research interests are polarimetry and ray optical propagation modeling in urban outdoor and indoor environments. He is participating as an expert in the “European Cooperation in the Field of Scientific and Technical Research COST-23 l”, where he is a coeditor for the chapter on “Propagation Prediction Models” of the final report. Since 1995, he has organized and chaired conference sessions on polarimetry and wave propagarion. For the Carl Cranz Series for ScientiJic Education he is a Lecturer for radio wave propagation modeling and radio network planning, since 1993. Dr. Cichon was awarded the City of Karlsruhe Science Award for his diploma thesis in 1992, the IEEE/AP-S’93 Student Paper Award in 1993, and the EEDCAP’93 Best Propagation Paper Award in 1995.

Werner Wiesheck (SM’87-F’94) was born near Munich, Germany in 1942. He received the Dip1.Ing. (M.S.E.E.) and the Dr.-Ing. (Ph.D.E.E.) degrees from the Technical University Munich, Germany, in 1969 and 1972, respectively. From 1972-1983, he was with AEG-Telefunken in various positions including head of R&D of the Microwave Division in Flensburg and Marketing Director of Receiver and Direction Finder Division, Ulm, Germany. Since 1983, he has been director of the Institut fur Hochstfrequenztechnik und Elektronik (IHE)at the University of Karlsruhe, Germany. Present research topics include radar, remote sensing, wave propagation, and antennas. In 1989 and 1994, respectively, he spent six months sabbaticals at the Jet Propulsion Laboratory, Pasadena, CA. ET. Wiesbeck was a member of the IEEE GRSS AdCom (’92-’94), Chairman of the GRSS Awards Committee, and Treasurer of the IEEE German Section. He has been General Chairman of the 1993 Conference on Microwaves and Optics (MIOP ’93) and of the 1988 Heinrich Hertz Centenial Symposium in Karlsruhe, Germany. For the Carl Cranz Series for Scientific Education he has been a Lecturer for radar system engineering and for wave propagation since 1990. He is a member of an Advisory Committee of the European Union-Joint Research Centre (Ispralltaly) and he is advisor to the German Research Council (DFG).