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ANALYTICAL BIT ERROR RATE DETERMINATION FOR DIGITAL AUDIO BROADCASTING

F. Kuchen, T. C. Becker, W. Wiesbeck

Institut fur Hochstfiequenztechnik und Elektronik (IHE) University of Karlsruhe Germany

ABSTRACT

State-of-the-art design methods for Digital Audio Broadcasting (DAB) networks use the computer-aided prediction of received fieldstrength levels. However in certain terrain the performance of the DAB system may be insufficient whilst still meeting the required fieldstrength level. This is due to multipath propagation and extremely delayed transmitter signals causing intersymbol interference. Therefore it is necessary to consider multipath effects even in the planning phase in order to optimize the transmitter location and the antenna patterns. In this paper, the total fieldstrength delay spectra (FDS) of all transmitters of the single frequency network (SFN) is used to calculate the symbol error rate (SER) of the unprotected radio channel. This SER is of high interest for the planning of this digital data distribution system. For the 4-DPSK modulation scheme, the influence of the modelled time variation of the signal reception phase on the SER calculation is investigated.

INTRODUCTION

Digital Audio Broadcasting (DAB), see Draft (l), requires new planning methods which consider the typical features of Single Frequency Networks (SFN). It has to be taken into account, that a receiver location will be covered by several different transmitters. Hence numerous signal components contribute to the total fieldstrength at the receiver location, even though they have different spatial origins.

In this paper 2D and 3D ray optical models area applied, which determine the relevant propagation paths by an unsupervised automatic ray tracing algorithm, based on topographical and morphographical digitized data. The calculation of the scattering and diffraction processes are based on Physical Optics (PO) and the Uniform Theory of Diffraction (UTD), McNamara et a1 (2). The multipath propagation of diffracted, scattered and reflected signals results in numerous contributions to the total fieldstrength. At the receiver each single fieldstrength contribution is defined by its amplitude Ei, phase 'pi and time delay T, (with respect to line of sight (LOS)). In this approach the amplitudes Ei are assumed to be deterministic, whereas the phases cp, are statistically distributed. A fieldstrength delay spectrum

(FDS) can be defined by the parameters Ei and Ti, which are used to derive information about intersymbol interference due to multipath propagation.

In a narrowband analysis all predicted fieldstrength components, which arrive within the guard interval are superimposed using the power-sum method. In the same way a superposition of all signals from interferers is done. Interferers are those transmitters, whose signals arrive outside the guard interval due to long transit times. The resulting C/I ratio allows first approximations about the quality of the DAB signal to be made.

A more detailed and precise method is the wideband analysis where the fieldstrength delay spectra resulting from the application of the 3D-model are considered. The obtained total FDS can either be used to compute the fieldstrength at any receiver location or to determine the symbol error rate (SER) of the COFDM signal of the unprotected propagation channel.

THE WAVE PROPAGATION MODELS

The core of the IHE-RURAL propagation m'odels, Lebherz et a1 (3), Kiirner et a1 (4), is a 2D-model, which

International Broadcasting Convention, 12-16 September 1996 Conference Publication No. 428, 0 IEE, 1996

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considers propagation in a vertical plane, see Figure 1. Obstacles are modelled by wedges and convex surfaces. Diffraction processes are then computed with a UTD- method.

In the 3D-extension, obstacles off this vertical plane, which have a line-of-sight to both transmitter and receiver are considered. The scattering loss is computed using the bistatic theory of diffraction. The 3D-extension yields a fieldstrength-delay-spectrum (FDS), which contains information about both fieldstrength and delay of the different multipath signals.

Fig. 1 : Terrain modelling and considered propagation paths.

if the distance di between transmitter i and receiver fulfills the following equation:

d o < d i < c . t , + d o

do: distance between receiver and nearest

tg: duration of guard interval. transmitter,

Figure 2 shows the situation for an example assuming 5 transmitters Ti. All transmitters with exception of transmitter T3 contribute constructively to the signal at the receiver.

1 area of constructive / area of destructive transmitter signals 1 transmitter signals

Fig. 2: Constructive and destructive signal interference

2D-Model based on narrow band analysis 3D-Model based on wide band analysis

A main characteristic of a Single Frequency Network (SFN), Rau et a1 (3, is that one receiver uses several signals from several different but synchronous transmitters, which work on the same carrier frequency. Therefore a guard interval is implemented. All signals, which arrive within this guard interval, i. e. not later than the guard interval duration after the first signal, are superimposed constructively. In this model it is done by using the power-sum method. Signals, which arrive later, are superimposed in the same way assuming to contribute to the destructive noise level.

The different signals, which have to be heterodyned are obtained by determining one representative ray for each transmitter. The fieldstrength of this ray is computed by considering all propagation paths in the vertical plane between transmitter and receiver (Figure 1). The transit time of this ray is assumed to be that of the direct ray, because the differences in time delay of the rays within the vertical plane can be neglected.

For a SFN containing n transmitters, there are n representative rays, which contribute either to the constructive signal fieldstrength or to the destructive noise level. The signal of a transmitter i is constructive,

In this method the complete FDS is considered rather than just the one representative ray. Figure 3 shows how the total FDS at the receiver location is determined from the individual multipath effect of the different transmitters.

FDS 1

t Fig. 3: Determination of the total FDS

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All delay times from the different transmitters are displayed with respect to the transit time of the direct signal from the nearest receiver.

Based on the total FDS two possibilities of evaluation exist:

The power-sum method can be used to compute the fieldstrength at the receiver location or the C/I ratio, respectively. Thus the guard interval (Figure 3) is considered. This possibility corresponds to the narrowband analysis used in the 2D-model as described before, see Becker at a1 (6).

By applying the wideband analysis as described in Kurner et a1 (7) the SER for digital communication systems - especially DAB - can be computed. This method also uses the duration of the guard interval.

The COFDM-signal consists of 4-DPSK-modulated carriers. The computation of the total SER can be performed using the probability density functions (PDF) of the single fieldstrength contributions of the total FDS. This method is the most detailed planning tool since it evaluates each possible ray path. It therefore shows most accurately the influence on coverage of both fieldstrength levels and transit times.

Computing the SER from the FDS

Characteristic functions. The PDF of the resulting signal vector is the basis for the SER calculation. Each partial wave that reaches the receiver is described by its phase and amplitude. The amplitudes of the fieldstrength contributions are assumed to be determined, but the exact phase information for the paths is unknown. The reason is the width of the topographical grid. It is too wide with respect to the wavelength. Therefore the phase is assumed to be equally distributed in the range [ 0 , 2 ~ ) :

For every partial wave the PDF of the signal vector is determined by

To calculate the PDF of the resulting total fieldstrength all PDFs have to be convoluted:

(4)

The two-dimensional convolution of N probability density functions can be replaced by the multiplication of the characteristic functions and an inverse Fourier Transformation. With Gui ,vi as the characteristic function of partial wave i, equation (4) is equivalent to

(5)

The multiplication described by equation (5) can be simplified due to the rotation symmetry of equation (2). Before convoluting the PDFs of the partial waves, three classes of signals have to be distinguished. For the following discussion it is assumed that the symbol A q = 0 is transmitted, this has no influence on the validity of the results. The receiver is assumed to trigger to the first incoming signal.

Direct signals. These signals arrive on a path with line of sight (LOS) between transmitter and receiver. Their phase is determined because there is no interaction with the terrain. However the absolute phase is unknown due to the limited resolution of the topographical grid compared to the wavelength. For the 4-DPSK modulation scheme, only the difference of the phase information is of interest for the symbol detection. If 'ps

is the phase of the transmitted signal and qr = 'ps + 'pu

the phase of the calculated received signal with the unknown part vu, the phase difference AV of two signals is computed to:

The PDF for this class of signals is the dirac impulse. Equation (6) is only valid for a stationary receiver, when the unknown part of the phase qU is assumed to be constant. For the time varying propagation channel, the signals have to be computed as described below.

For Cartesian coordinates equation (2) is transformed to

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Delay smaller than guard interval. All signals that reach the receiver within the guard interval carry the same information. Due to the statistical scattering processes, the fluctuating phase difference of the time varying vector cji (see Figure 4) is modelled as zero mean Gaussian distributed.

Y

X I Fig. 4: Two successive signals and the difference vector

Considering Figure 5 the total fieldstrength calculated to

is

N

1=1 %,tot =%,tot + Cdi

(7)

X I Fig. 5: Total fieldstrength of two successive symbols

If the standard deviation of the Gaussian distributed phase difference Aqi of signal i is small compared to .n , the absolute value of cli approximately is

The phase of cli is equally distributed like the phase cp1,i of E1,i. If Acpi in equation 8 is assumed to be Gaussian distributed, the absolute value of cIi will also be Gaussian distributed. The resulting distribution for cli is a two dimensional Gaussian distribution with zero mean:

and a standard deviation of

with 'sQ as the standard deviation of the phase of El,,

The convolution of PDFs as described in (9) again results in a Gaussian distributed PDF with the new standard deviation

with N as the number of signals reaching the receiver within the guard interval.

Signals later than the guard interval. The characteristic of this third class of signals is, that the information they carry is unknown. Four different phases 'ps2 might be transmitted related to the phase cpsl of the signal before (see Figure 6). Because an uncorrelated bit stream is assumed, all four cases are supposed to occur with the same probability of 0.25.

Fig. 6: The four possible vector positions of E2,i

The PDF for this class is calculated as the sum of the four cases:

with the index (j) describing case j .

Gaussian noise. The PDF to describe additional white gaussian noise

xi2+yi2 1 -~

fxi,yi(xi,yi)=-. 2 e 202 (13) 2no

with the noise power o2 completes the set of required PDF functions to calculate the SER.

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Integration of the PDF. The SER is computed by the integration of the total PDF, see Figure 7, resulting from the convolution of the probability density functions of all participating rays.

Fig. 7 : Total PDF from the FDS of all partial waves

This integration has to be performed in the signal vector diagram over the decision region. For symmetrical reasons and without loss of validity the integration can be performed with the center of the PDF on the x-axis as depicted in Figure 8.

Fig. 8: Integration of the PDF over the decision region

The gray area represents the field for correct 4-DPSK symbol detection. It is obvious that the minimum SER has the value of 0. The maximum occurring SER is 0.75 in case the PDF is positioned in the center of the signal vector diagram, i.e. an arbitrary decision is made.

The calculation of the symbol error rate is performed by computing the probability for a correct detection and subtracting:

The computation of equation (14) can be simplified when considering the Symmetrical structure of the PDF.

RESULTS

Area covering SER prediction As a test area for the fieldstrength prediction with the IHE-2D-RURAL model the Rhine Valley in the South-West of Germany was chosen. Figure 9 depicts the topography with the major cities in dark colors and the transmitter locations in a light shading. The SFN network consists of three transmitters in the Northern Black Forest on the right hand side of the Rhine Valley and three transmitters in the Palatinian Forest on the left hand side. The coverage area is a varying landscape of flat planes and mountains of up to lOOOm height. The grid of the digitized data is 100m.

rl 150km altitude - in meters

Fig. 9: Topography of the test area with 6 transmitters

For the exemplary calculation at a frequency of 230MHz all transmitters are assumed to radiate 1kW using an omnidirectional antenna. The receiving antenna is assumed to be located 1.5m above the ground. The result of the SER calculation for the marked square of 80km x 80km is presented in Figure 10.

percent 3

80km

Fig. 10: Result of the SER calculation

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The standard deviation oT of the phase difference was set to zero, i. e. a stationary receiver was assumed. To point out the effects of delayed signals, the guard interval was set to 5 0 p . In the South-West and North- East of the test area strong delayed signals exist exceeding the supposed guard interval of Sops. This corresponds to a multipath difference of 15km. Even close to the transmitters distorted reception could occur due to intersymbol interference. This result would not be expected by a conventional fieldstrength prediction.

The time variance. The influence of different standard deviations oq for the Gaussian distribution of the phase difference was investigated in the area between Karlsruhe (KA) and Pforzheim (PF). The difference between the stationary receiver with oT = 0 and the three other cases is presented in Figure 11. As expected, the SER gets worse as more the channel is assumed to be time variant. With a stationary receiver the influence of the additional time variance is negligible for a SER from off about ten percent.

1 , I I Is,,,=x/lO

+ 25km w Fig. 11: Simulation of the time variance

If a SER of six percent still provides an acceptable signal quality, see Becker at a1 (8), a standard deviation of the phase in the range of oT = n / 20 is acceptable.

CONCLUSIONS

A planning method was presented that enables complete SER predictions for DAB networks. It was shown how both fieldstrength levels and delay times of the different transmitters of the SFN have influence on the symbol error rate. Due to the extreme calculation times of the SER tool, especially when computing with a high resolution grid, it should only be used to investigate critical coverage areas. SER measurements in a real DAB-network to verify the models are subject to further research.

REFERENCES

1. Digital Audio Broadcasting (DAB) to Mobile, Portable and Fixed Receivers, 1994. Draft European Telecommunication Standard pr ETS 300 401. Radio Broadcasting System; ETSI

2. D. A. McNamara, C. W. I. Pistorius, J. A. G. Malherbe, 1990. Introduction to the Uniform Geometrical Theory of Diffraction. Artech House, ISBN 0-89006-301-X

3. M. Lebherz, W. Wiesbeck and W. Krank, 1992. A versatile wave propagation model for the VHF/UHF range considering three dimensional terrain. IEEE Trans. on Antennas and Propagation, Vol. 40, no. 10, pp. 1121- 1131, October 1992.

4. Th. Kurner, D. J. Cichon and W. Wiesbeck, 1993. Concepts and results for 3D digital terrain based wave propagation models - an overview. IEEE Journal on Selected Areas in Communications. Vol. 11, no. 7, pp. 1002- 10 12, September 1993.

5 . M. C. Rau, L. D. Lynn, S. Salek, 1990. Terrestrial Coverage considerations for digital audio broadcast systems. IEEE Transactions on Broadcast, Vol. 36, No 4, pp. 275-283, December 1990

6. T. C. Becker, D. J. Cichon, W. Wiesbeck, 1996. New Planning Methods for Single Frequency Networks. Proc. International Conference on Communications, Dallas, Texas, June 23-27 1996.

7. Th. Kurner, D. J. Cichon, W. Wiesbeck, 1993. Wideband characterization of personal communication networks by propagation models. IEE Proc. International Conference on Antennas and Propagation ICAP'93, Edinburgh / Schottland, pp. 865-868, 1993

8. T. C. Becker, F. Kuchen, W. Wiesbeck, 1996. Influence of the BER on the Intelligibility of the Received DAB Signal. Proc. International Conference on Communications, Dallas, Texas, June 23-27 1996.

ACKNOWLEDGEMENT

The authors would like to thank the Forschungsverbund Medientechnik Sudwest. The research program of the countries Baden-Wiirttemberg and Rheinland Pfalz supported this work.