Dlctcr J. Clchon. W a n e r Wle~~skck ... The PDF of the resultlng fieldstrength is computed .... PDF of j$l can be calculated using characteristic functions slmilar to ...
WIDEBAND CHARACTEFUSATiON OF PERSONAL COMMUNICATiON NEIWORKS BY PROPAGAmON MODELS Thomas KOmer. Dlctcr J. Clchon. Waner W l e ~ ~ s k c k JnsUtut Nr H6chstfrcquerxtechnUr und Elektmnlk (IHE), Unlverslty of Karbruhe. Germany
ABSTRACT An efflclent planning method for personal
communication networks [pCN requires versatile wave propagatlon modelllng In the considered environment. Narrowband wave propagation models allow an assessment on the tlcldstrmghth level only. Propagation models considering 3D paths can be used for a statistical analysis of the resulting fadlng processes. As multipath propagation can cause severe signal disturbances due to intersymbol interference. the knowledge of additional parameters describing the propagation channel are required. Parameters of interest are the delay spread, coherence bandwldth, doppler characteristics and the bit error rate @ER). Concemlng the digital radlo systems (e. g. DECTStandard). the BER of the unprotected propagation channel is an important parameter. In this paper I t is shown how 3 D wave propagation models with automatic ray-traing can be used to gain Information about the multlpath sltuatlon. Based on these results tlme and frequency domain characterlstlcs of the propagation channel are dertved. The BER of the unprotected channel Is estimated with respect to the modulation scheme and the received multipath signals.
INTRODUCTlON
The complete characterisation of a digital radio system has to be done In succesive steps. The first step includes the physical modelling of the propagation channel, which leads to a fieldstrength prediction If a 2D model is applied and to a Fieldstrength-Delay-Spectrum(FDS). see Fig. 1, if a 3D model is applied.
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Delay ols) Fig. 1 Fleldstrength-Delay-Spectrum
Based on the FDS.which can be interpreted as the Impulse reponse of the terrain, a characterisation uslng communication theory is possible. A narrowband processing of the statistical propertles of the FDS leads to the probabuity density function (PDD of the resulting fieldstrength. Further consideration of system aspects, especially the digital modulation scheme, and the filter characteristics of the rrcefver. can be used to determine the BER of the system, which Is the most relevant parameter for a complete coverage prediction.
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The characteristics for wave propagation in urban and rural areas are multlpath effects due to multiple reflection and diffraction. In this contribution ray optical models for the VHF/UHF range with an automatic ray tracing algorithm arc applied. based on topographical and morphographical data. The model for rural areas was presented durtng ]CAP ‘ 89 and ICAP ’ 91 by the authors 11.21. A &Wed description Is glven In [31. A description of the model for urban areas can be found in 14.51. The calculation of the scatterlng and dlffraction processes are based on Physical Optacs (PO) and the Unvnm ‘Iheary of DLtFactbn WID).
The multipath propagatlon of dlffracted, scattered and reflected signals results in numerous contrlbutions to the total fieldstrength. Each slngte fieldstrength contribution is calculated by the propagation model In terms of I t s amplltude El, phase vi, time delay r l (with respect to LOS). and polarisatlon state. In this approach the amplltudes El are assumed to be determinlstlc, whereas the phases yri are statistically dlstrlbuted. The PDF of the resultlng fieldstrength is computed according to I2.31. Instead of postulating one of the closed-form functions (e.g. Gauss or Raylelgh dlstrlbution). Fig. 2 shows a comparison of measured and computed PDFs corresponding to the FDS in Rg. 1 for a stationary receiver. I.e. the received fieldstrength variations arc temporal. aOth PDFs are refemd to the mean neldstrcngth value. The shapes and the standard devlations of both signatures are very similar and do not coincide with one of the above mentioned closed-form PDFs. By the propagation model not only the mean fleldstrength level can be determined.
El@* lntemallonal Confcmnx on Anteand hpagatlon Herlot-Watt Unhrrrslty. Edinburgh. UK. 30 march-2 aprlllS93
Further information can be extracted for the expected standard deviatlon and the exceeding proballlity for a certah fieldstrength level.
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FDS. where El Is dlsplayed versus r l . One property of the FDS. that offers further posslbllltles of analysis. Is that It can be Interpreted as the Impulse response h(t) of the propagation medium "terrain" In a small frequency range around the center frequency fo for whlch the propagatlon modellhg was performed.
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Flg. 2 Comparlson of measured and predicted PDF a t 925 MHz. (..... measured, predlcted).The measured data was gained by 15000 samples. For the computatlon a dlgltal terraln model with lOOm x lOOm resolutlon was used. Flg. 3 shows predlcted and measured mean path loss for an urban area at Aalborg/Denmark. The resolutlon of the database was 12.5m x 12.5m. Both stgnatures show a good agreement.
Flg.
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Varlatlon of Fleldstrength-Delay-Spectrum
Flg. 4 shows the varlatlon of the FDS for a simulated drive test along a 4 km route inside a valley, where the transmltter slte Is ldentlcal to a real operatlng CSM-transmltter. From thls I t Is possible to compute the multlpath or delay spread [6] as a functlon of locatlon. whlch glves a rough criterion for the performance of a dlgltal system, see Fig. 5.
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Flg. 3 Fleldstrength prediction and measurements for an urban terraln at Aalborg / Denmark at 955 MHz predlcted) measured, ._._._._
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WIDEBAND CHARACTERlSATION Regardlng the wldeband characterlstlcs of the propagatlon channel the calculated multlpath slgnals have to be analysed In the frequency or tlme domaln. Furthermore, tlme-varlant properties of the channel have to be conslderered for the case of a moving receiver. n m e domaln analvsls In tlme domaln one posslblllty of visuallslng the structure of the multlpath signal Is glven by the
Flg. 5 Multlpath spread as a functlon of locatlon Freauencv domain analvsls From h(t) the complex transfer functlon K(0 results by Fourier transform. By the dennltlon of a randomly dlstrlbuted phase yt. one can create complex transfer functlons that are themselves variables of a stochasttc process. Generating a large number of such transfer functlons, I t Is possible to evaluate the frequency sensltlvlty of the transmlttlng channel by computlng the correspondlng frequency correlatlon functlon I6.71. Uslng thls lnformatlon. typlcal frequency
domain parameters such as the coherence or correlation bandwidth can be derived, which can be used to check the suitablity of frequency hopping, for example.
The incoming multipath signals at a moving receiver have dopplershifts. The doppler frequency depends on the velocity of the vehicle, the wvekngth and the angle-of-arrival. As each multipath signal has different angles-of-arrival and amplitudes a complete doppler spectrum exists. This phenomenon is well-known in the literature [S. 91. Sophisticated measurement techniques exist to determine the doppler spectrum 1101. However. for planning purposes usually the simplifled case of the so-called Jakes-spectrum is applied. which assumes that all incoming signals have the same amplitudes and equal distributed angles-of-arrivals. Based on the presented 3D model both angks-of-arrival and amplitudes can be determined. Fig. 6 shows the prediction of the time-varying Dopplerspectrum corresponding to the FDS in Ftg. 5 for a vehicle movlng wlth a velocity of 70 km/h.
- n(t)additive white gaussian noise. with the knowledge of the stamtical properties of the impulse response of the channel and additional ~ ~ u m p t on i othe ~ a-priori-statistics of the transmitted signals. the probability density functions of all signals are known. The subdivision of the multipath signals into the and &(tI is due to the different aclasses aft) priori-statistice of the arrMng signals. Au slgnals N(t) originate from the same transmitted symbol which results in the nuisance signal a(t). The difference between a(t) and a(t)is only influenced by the statistical properties of the propagation channel, due to amplitude- and phase-shiftlng according to the different ) propagation paths. Regarding the FDS.all ~ ( tare caused by impulses with delay ‘ ~ < 1 T. On the other hand signals a ( t ) come from symbols transmitted at a tlme t > T before the transnbsion of the nuisance signal. i.e. all arc caused by Impulses wlth delay > T. Consequently. the aprlorl-statistics have to be considered. n(t) is modelled using a two-dimensional gaussian distribution. Assuming statistical independence of all contributions in (1) the two-dimensional PDF of j$l can be calculated using characteristic functions slmilar to the procedure applied for the PDF of the compkx fkldsircngth in 12.3). Starting from this. the bit error rate corresponds to the l off the correct decision probability that ~ ( t is area. In CSM-basedFCN-systuw usually CMSK. a special case of Minimum-Shift-Keylng (MSK)modulation, is applied. According to Ill]. I121 MSK. a nonlinear modulation scheme, can be transformed into a linear modulation scheme. Ftg. 7 shows the bit error rate (BENof an unprotected MSK-modulated system as a function of the signal-to-noise-ratio (SNR)
Fig.6 Vatlation of Doppkr-Spectrum
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The FDS includes information about the expected intersymbol interference of digital radio systems. In the case of a linear digital modulation scheme. the received compkx signal r(t) at sample-time t can be depicted as the sum of complex signal vectors in the complex signal space. This is equivalent to the formulation of the complex fieldstrength in I2,3]:
10) = s(t) +
C m(t) + 1
wlth
sk(t) k
+ n(t) (1)
- ~ ( nuisance 0 slgnal, - T duration of the nuisance signal, - ~ ( t si@ ) due to multipath propagation
with delay smaller than T. - e(t)signal due to multipath propagation with delay greater than T.
Signal-to-Noise-Ratb (dFi) Fig.7 Bit error rate for the two cases of gaussian noise only (case 1) and additional intersymbol interference caused by multipath propagation (case 2). corresponding to the FDS depicted in Fig. 1. In the above, unprotected means that no further interleavhg. coding or equalisation is performed. The duration of the single signal element was 4 ps. Note especially that the irreducible error floor (0.158 in the presented case 2) can be determined. Case 3 shows a n irreducible error floor of 0.025. if all signals with a delay 4 ps < T < 8 pa would not exist. The performance of widely
.,
used digital modulation schemes , e.g. 2-MSK.nPSK, n-PSK/ASK and n-QAM up to 64-QAM have been analysed up to now using thls method.
The suggested method to characterize FCN by a 3D wave propagtion model enables a detailed computer-slmulation for the synthesis and analysls of terrestrial radlo systems. All the relevant parameters for a complete coverage prediction can be extracted. Furthermore it is possible to study the relationship between the various parameters in different terrain; for example, the dependence of BER on fleldstnngth level and delay spread In order to derive semlemplrlcal or heuristic formulas for these parameters. investigations of how error coding and equalisation influence the irreducible error floor wlll be subject of further research.
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