Wave Propagation Based Calculation of Bit Error Rates for a 2FSK-System in Indoor Environments Thomas Zwick, Frank Demmerle and Werner Wiesbeck Institut fur Hochstfrequenztechnik und Elektronik (IHE) University of Karlsruhe Kaiserstr. 12, D-76128 Karlsruhe, Germany Phone: +49-721-608 6256, Fax: +49-721-691865 E-mail:
[email protected] http://www-ihe.etec.uni-karlsruhe.de/
Abstract- For network planning purposes of wireless communication systems the transmission loss is a nonsufficient criterion. For digital systems the bit error rate is the most relevant criterion. In this paper a new method is presented t o predict the bit error rate for a 2FSK-modulation from the results of a ray optical wave propagation model. For verification a measurement system with 2FSK-modulation has been built up to measure the bit error rate and the transmission loss simultaneously. Measurement results are shown and compared with simulations.
I. INTRODUCTION Emerging radio systems like Digital Mobile Radio, PCN, DECT, Radio LANs, etc., are established in the UHF up to the EHF range. Especially the demand for short range systems with high data rates like Radio LAN's in a single building or a scenario of a few buildings increased rapidly during the last years. For these systems planning tools which only predict fieldstrength are no longer sufficient because they neglect effects which are caused by multipath propagation [l]. Therefore a ray optical wave propagation model for indoor environments has been developed at the Institut fur Hochstfrequenztechnik und Elektronik (IHE) of the University of Karlsruhe [2]. The complete knowledge of the radio channel impulse response for variable receiver locations enables the prediction of the bit error rate (BER) for any digital modulation [3]. In this paper a new model for the prediction of bit error rates in 2FSK-systems based on the channel impulse response is presented. For verification of the results a 2FSK-system at a frequency of 2.45GHz has been build up. The calculated results are compared with measurements which were performed in a typical indoor environments.
agation model INDOOR-3D is based on a ray tracing approach [2]. A ray optical approach is justified since the wavelength is small with respect to the objects to be regarded. A large number of rays, distributed over the whole solid angle, are sent out from the transmitter and traced through the building. Thereby multiple reflections and wall penetrations but no diffraction and scattering processes are regarded. Every time a ray is received the full polarimetric propagation matrix I?%, the transmitting ( ~ T , % , $ , T and , ~ ) receiving directions ( ~ R , % , $ R ,as % )well as the delay time (travel time) 7% of the path are saved. By including the complex antenna characteristics for transmitter CT and receiver C R the complex frequency response H ( f ) for the radio transmission can be calculated from the sum of all rays: N
H ( f ) = C A %. e--32afTt 2=
(1)
1
Ai = K T R . C TR ( ~ R , ~ , $ .' ri R , .~C) T ( ~ T$ ,~~, i,) (2) The antenna gains (GT,GR)and their impedances
(ZAR,ZAT) are summarized in KTR:
For a small bandwidth with respect to the center frequency the channel impulse response (CIR) h ( t ) yields [4]: N
Ai . &(7 - ~
h(7) =
i )
(4)
i= 1
11. THETHREE
DIMENSIONAL WAVE PROPAGATION MODEL
By assuming statistically independent propagation paths the mean total loss L = A& can be calculated by integrating the absolute square of the :hannel impulse response h(7) over the delay time 7
An indoor environment is an almost three-dimensionally closed area, e.g. a room, a building floor, a multifloored building, or a partially open building hall. Multiple reflections a t interior and exterior walls and a large number of transmissions through walls have to be taken into account. Therefore the new wave prop0-7803-5106-1/98/$10.00 0 1998 E E E
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observation
The mean received power PR of the signal can be calculated dependent on the transmitted power PT as follows:
time
The mean delay time r, together with the root mean square (rms) delay spread rT,, are the most important parameters to characterise the effects caused by multipath propagation:
amVal section
Fig. 1. Received propagation paths
probability 50% 100%
Comparisons with path loss measurements provided by VTT Finland showed a good agreement [ 2 ] . The multipath effects have been verified by channel impulse response measurements [5]. 111. BIT ERROR
t
RATE CALCULATION FOR THE 2FSK-MODULATION
The amplitudes lAtl and delay times rz of all propagation paths are calculated by the wave propagation model including the antenna characteristics. For the phases pz of each propagation path a uniform distribution is justified because of the statistical independence of the different signal paths. The calculated bit error rate is then a mean value averaged over a small area. The CIR as given in (9) is the basic of the BER calculation. N
1 ~ . ejv*ao(r ~ 1 -T
h ( r )=
~ )
(9)
Fig. 2. Modeling plan. for a 2FSK-system
2=1
One of the parameters the radio system is characterised by is the bit time TB. Because of the synchronisation of the receiver the delay times of all propagation paths have to be related to the synchronisation time: = 7%- 7 ,
expected and the non-expected contributions respectively] all probability densitiy functions (PDF) have to be convoluted:
(10)
pzy(%iY)
After a guard interval TG the receiver integrates the received power over an observation time TO (Fig. 1). In some cases there is a rest time TR = TB - TG- TO. For each propagation path i the two-dimensional probability densitiy function p : , , ( z , y), P & ~ ( Zy) , can be calculated for both symbols, the expected ( e ) and the non-expected ( E ) symbol (Fig. 2 ) . The symbols are represented by the two frequencies of the 2FSKmodulation. The additive noise is considered by a Gaussian distribution pgy(xly) For both parts, the
= p z ~ , , ( ~ , y ) * . . . * P ~ y , N ( ~ , Y ) * p ~ y ( " , (11) Y)
Y) = p : ~ , l ( ~!/I*. i .*P;y,N(zi Y)*p:y(zi Y) (12) The BER then is the probability for which the power of the expected signal (e) is bigger than the power of the non-expected ( E ) signal. All PDFs of the propagation paths p:y,z(zly) and pEy,z(x,y) as well as the noise P D F pn (z,y) are rotationally symmet".y ric because of the uniformly distributed phases of the propagation paths. For this reason also the resulting PDFs of the expected pzy(z,y) and the non-expected '
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&(x, y) symbol show the rotational symmetry. For
d) The signal arrives during the observation time (TG< T,!5 TG+ T O ) : . The part of the signal which arrives during the ob-
a rotationally symmetric two-dimensional PDF the correspondin one-dimensional PDF is given by using r=d G $ a s pr(.) = 27rrp,,(r,O).
servation time carries the expected information and contributes exclusively to the expected symbol but the part of the before sent symbol which ends during the observation time contributes t o both, the expected and the non-expected symbol: .
(13)
The rotational symmetry enables the use of the Hankel transformation instead of the two-dimensional Fourier transformation to perform the convolution, which is the most computation time expensive part of the algorithm. Combined with a suited normalisation this simplification enables rather fast computing. For each propagation path i the one-dimensional PDF can be obtained by distinguishing between five arrival sections (Fig. 1):
(20)
e) The signal arrives after the end of the observation time (TG TO < T:):
+
a) The signal ends before the beginning of the observation time (T: 5 -TB + TG):
During the observation time only parts belonging to the last symbol can be seen, so the whole path energy has 50% probability for the expected as well as for the non-expected symbol:
During the observation time only parts belonging t o the next symbol can be seen, so the whole path energy has 50% probability for the expected as well as for the non-expected symbol: 1 ~ ; , i ( r ) -60 2 P;,,(T)
1
(TI + -60 2
IAil)
(14)
1 1 = -60 ( r ) + -60 (r - /Ail) 2 2
(15)
(T
-
b) The signal ends during the observation time (-TB
TG < T,!5 -TB
+ TG+To):
1 1 -60 ( r )+ -60 (T - IAil) (22) 2 2 1 1 P ; , ~ ( T ) = -60 ( T ) + -60 ( T - ]Ail) (23) 2 2 The additive noise is considered by a Gaussian distribution with expectation un: P;,~(T)=
+
(24)
The part of the signal which ends during the observation time carries the expected information and contributes exclusively to the expected symbol but the part of the symbol sent after it which arrives during the observation time contributes t o both, the expected and the non-expected symbol:
The signal-to-noise-ratio (SNR) can be given by:
PR SNR= on
(25)
For the BER-cal&lations it is reasonable t o assume a constant noise power instead of a constant SNR. After the convolution of the PDFs of all propagation paths for both symbols the BER can be obtained directly from the one-dimensional PDFs p : ( ~ )and p : ( ~ )
PI : 0
BER=
[p;-'((r)dr -CU
C) The signal is present during the whole observation time (-TB +TG +To < T,! 5 TG):
=
i
p ; ( ~ ) * p ; ( - - r ) d r (26)
-ca
Iv. MEASUREMENT SETUP At the Institut fur Hochstfrequenztechnik und Elektronik (IHE) of the University of Karlsruhe a measurement system has been developed t o observe the received power as well as the BER simultaneously. The setup is given in Fig. 3. A pseudo random bit sequence of 10Mbit/s is generated and transfered by an optic fiber to the transmitter. There the signal is transmitted at a frequency of fo = 2.45GHz 2FSK-modulated with a frequency difference of 10MHz. The observation time of the system
It arrives before the end of the guard interval and does not end before the end of the observation time so it is present during the whole observation time and therefore completely contributes to the expected symbol:
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transmtter
receiver radio channel
.
9
,
;. ..... ....;.............
-35.0...............
10-7
10-6
1.
~
105
1.'-
i
regression
0.01
0.1
..... ......i~ .............1...........
0.00oi BER
~
0.001
............
1
Fig. 5. BER versus received power for constellation 1
Fig. 3. Measurement setup
In constellation 2 both transmitter and receiver have been. located in a long corridor (Fig. 6) which leads to a wider delay spread and therewith to a CIR with relevant propagation paths delayed beyond the guard interval. Although there is line of sight the long delayed multiple reflections in this constellation cause a worse behaviour as depicted in Fig. 7. In this case there exists no definite relationship between received power and BER because of the interference of the multipaths. This fact could be proved by all other measurements which have been made too.
is To = 10ns. The guard interval TG can be variated between 10ns and 80ns. At the receiver the incoming signal is fed to a spectrum analyzer to measure the received power and to the 2FSK-receiver. The signal is demodulated and compared with the delayed original signal. The bit errors are counted during 1s and recorded by the computer. This leads to a minimum error rate solution of In order to perform plane covering measurements with a small solution automatically the transmitting antenna is mounted on a two dimensional scanner which is also controled by the computer. For the transmitter as well as for the receiver conical antennas have been used. They are omnidirectional in azimuth and have a wide bandwidth.
V. RESULTS Fig. 6. Constellation 2, line of sight (LOS)
The measurements have been performed in the building of the IHE. The guard interval was TG = 40ns. At several different locations the bit error rate has been obtained always covering a small plane of 5X x 5X with a resolution of A/24. Two extreme cases of these measurements are shown here to demonstrate the dependency of the BER on the received power. In constellation 1 the receiver was in the same small room (Fig. 4) as the transmitter so only small delay times result. Fig. 5 shows the received power versus the BER for all measured points. As expected in this simple case where always line of sight exists and the reflected paths are less delayed than the guard interval a linear decreasing of the received power versus the BER exists.
10.'
10-6
10-5
o.0001
0.001
0.01
0.1
I
BER
Fig. 7. BER versus received power for constellation 2
receiver
To compare the measured results with the calculations which are mean values for a small area the BERs have been averaged over all measured areas. The comparison of these mean values for the measured BER with the calculations showed a good agreement (Fig. 8).
transmitter area Fig. 4. Constellation 1, line of sight (LOS)
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For network planning purposes coverage predictions are needed which can not be performed by measurements. With the new wave propagation based method the transmission loss and the BER have been calculated for one floor of an office building in Karlsruhe (Fig. 9 and Fig. 10). It can be seen again that there is bad proportionality between the BER and the loss.
[6]
lOdB
60 dH
M
w ) dU
ICQ dB
-
120 dB
58m
b
Fig. 9. Coverage prediction of transmission loss
Fig. 10. Coverage prediction of BER
VI. CONCLUSIONS In this paper a new method for the BER prediction for 2FSK-systems from the results of a three dimensional ray optical wave propagation model has been presented. Measurements have been performed with a radio system which has been built up at the IHE to verify the simulations. These measurements showed clearly that the transmission loss is a non-sufficient criterion for the estimation of the real receiving quality. There is no definite relationship between received power and BER in a multipath environment at high data rates. It can be expected that this behaviour holds also true for other modulation schemes. For digital systems the BER has to be used as criterion for network planing. The comparison between measured
and calculated results shows a good agreement.
REFERENCES [l] G. Janssen, “Wideband indoor channel measurements and BER analysis of frequency selective multipath channels at
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2.4, 4.75, and 11.5GHz,” IEEE Trans. on Comm., vol. 44, no. 10, October, 1996, pp. 1272-1288. T. Zwick, D. J . Cichon, W. Wiesbeck, “Microwave propagation modeling in indoor environments,” Microwaves and Optoelectronics Conf., MIOP’ 95, Sindelfingen, Germany, Mai 30 - June 1, 1995, pp. 629-633. T. Kuerner, D. J. Cichon, T. C. Becker, “Degradation of digital communication systems in a multipath environment,” Proc. IEEE Intern. Vehicular Technology Conf. VTC’94, . Stockholm, Sweden, June 7-11, 1994, pp. 170-174. H. Hashemi, “Impulse response modeling of indoor radio propagation channels,” IEEE Journal on sel. areas i n Comm., vol. 11, no. 7, September, 1993, pp. 967-978. T. Zwick, F. Demmerle, W. Wiesbeck, “Comparison of channeI impulse response measurements and calculations in indoor environments,” Proc. IEEE AP-S Intern. Symp. AP’96, Baltimore, USA, July, 1996, pp. 1498-1501. J . G. Proakis, Digital Communications, McGraw-Hill Book Company, 2nd edition, 1995.
