International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 3, Issue 3, March 2014
ISSN 2319 - 4847
Modelling of WCDMA Base Station Signal in
Multipath Environment
Ch Usha Kumari1 , G Sasi Bhushana Rao2
1
Department of Electronics and Communication Engineering,
G Narayanamma Institute of Technology and Sciences
2
Department of Electronics and Communication Engineering
Andhra University College of Engineering, Visakhapatnam
Abstract
The performance of wireless communication systems is mainly limited by mobile radio channel. In urban or dense urban areas,
there may not be any direct line-of-sight path between a mobile and a base station antenna. Instead, the signal may arrive at a
mobile station over a number of different paths after being reflected from tall buildings, towers, and so on. The signal received
over each path has a random amplitude and phase. These variations are very rapid and occur over short distances called as fast or
short-term variations. In this paper, the short-term variations, called multipath variations in the received signal at the base
station of a WCDMA network are modelled for a typical dense populated urban environment. The transmitted RF carrier wave
undergoes Doppler shift and fading in the multipath environment. If the MS is moving away from BS or towards the BS then
there occurs apparent shift in frequency of the received signal, which is called Doppler shift. These effects are modelled and
simulated. In the simulation, the relationship between Doppler shift and the arrival angle (  ) of the received signal with respect to
the mobile direction of travel is evaluated. It is observed that deeper fades occurred for arrival angle of  =1800 and =900 and
fades are reduced for arrival angles of  =450 and =300. So fade rate decreases as the angle spread ( ) decreases. It observed that
the wider the spectrum the faster the variations.
KEYWORDS: WIDEBAND CDMA, MULTIPATH, FADING, DOPPLER SHIFT, RAYLEIGH DISTRIBUTION.
1. INTRODUCTION
The transmission path of signal between the transmitter and receiver varies due to obstructions from buildings,
mountains, trees, etc. The three basic mechanisms that effect the signal propagation in mobile communication system are
Reflection, Diffraction and Scattering. These effects normally occur due to environmental features close to mobile station
(MS) and when the base station (BS) is surrounded by local features effecting propagation characteristics. The
electromagnetic wave travels along different paths of varying lengths due to multiple reflections from the various objects.
Interaction between these electromagnetic waves causes multipath fading and the strength of these waves decreases as
distance between the transmitter and the receiver increases. Propagation models are used for predicting the average
received signal strength for a given distance from transmitter and also the variation of signal strength.
Three levels of signal variations [1,2,4] can be seen on the received signal at base station of a WCDMA cellular network.
 Very slow variations are mainly due to range.
 Slow/long term variations are due to shadowing.
 Fast/short term variations are due to multipath.
The signal strength at any point may vary and it depends on distance, carrier frequency, type of antenna used, the antenna
height, atmospheric conditions. This type of signal variation that is observed over long distances i.e, a few tens or
hundreds of wavelengths follows lognormal distribution and is termed as large scale variation.
Propagation models that characterize rapid fluctuations of received signal strength over very short travels distances say
few wavelengths or for short time durations say order of seconds can be classified as small scale fading models. This type
of variation in the signal is due to multipath reflections. This is observed in urban and dense urban areas where there is
no direct line of sight between mobile station and base station antenna and the signal may arrive the MS over different
paths after reflecting from tall buildings or towers and so on.
The most two common scenarios seen in signal propagation are LOS (Line of Sight) and NLOS (Non Line of Sight) [1].
LOS is the case where a strong direct signal is available along with the number of weak multipath echoes. This generally
occurs in open areas and in city centres such as cross roads with good visibility of Base Station (BS). Rice Distribution
models these variations of the received RF signal envelope. NLOS is the case where there is no direct signal but very
week multipath echoes are present. This is generally seen in big urban environments and also seen in rural environments
where the signal is blocked by dense masses of tress. Under these conditions, the received signal amplitude variations are
modeled with Rayleigh Distribution.
The main objective of this paper is to determine short-term variations/multipath variation in the received signal at the
base station in a typical environment.
Volume 3, Issue 3, March 2014
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 3, Issue 3, March 2014
ISSN 2319 - 4847
2. BACKGROUND
A. Doppler Shift
Doppler shift is an important phenomenon in multipath conditions[1,3,4,7]. Due to relative motion between the mobile
and the base station, every multipath wave experiences an apparent shift in the frequency. This shift in frequency in the
received signal is called Doppler shift. The relation between Doppler shift and arrival angle/radio path length is
V
(1)
f D    f max cos( )  cos( )
c
Where - arrival angle/radio path
f D -is the Doppler shift
V -is the mobile speed
Multipath components from a continuous wave (CW) signal from different directions contribute to the Doppler spreading
of received signal and increase the signal bandwidth.
B. Rayleigh Distribution
The radio wave that is transmitted from the BS to MS radiates in all directions. These radio waves may be reflected or
scattered due the obstacles between BS and MS. In this case the path lengths of the reflected, diffracted, and scattering
waves are different, the time each takes to reach the mobile station will be different. The direct signal is assumed to be
completely blocked in multipath signal variations. These variations are usually modeled by Rayleigh distributions.
The Probability Distribution function (PDF)of Rayleigh distribution is derived from [1,4,7]
 r 2 
r
(2)
f R  r   2 exp  2  all r  0

 2 
The Cumulative Distribution Function is derived from [1, 4, 7]
  r 2  for all r  0
(3)
FR  r   1  exp 
2 
 2 
The parameters of Rayleigh distribution are defined as follows

mean(R)  E  R   Rf (R)dR 


 1.2533
2
(4)

rms 2 ( R)  E  R 2  
R
2
f ( R )dR 2 2
(5)


 2 
2
2  4  
2
variance(R)=E  R 2   E  R    2 2 
  
  0.4292
2
 2 


 R2 
1  exp   2   0.5 , thus, median  R  
 2 
E[ ] is the expectation operator
(6)
2 2 ln  2   1.1774 (7)
3. ASSUMPTIONS
CASE A
The simulation is done by assuming the MS is moving towards the BS with a constant velocity V=36Km/hr (10m/s),
distance between the MS and BS is 1Km (1000m). It is assumed only direct signal is present. Figure 1 shows the
simulation geometry. The simulation is done for a short stretch of the mobile route, so the received signal has constant
amplitude, but rapid variations in phase. And at the same time the received carrier frequency is shifted i.e. Doppler shift.
3G WCDMA system is assumed so the frequency is taken as 2GHz (2000MHz). The mobile route is sampled
8
with a spacing ∆x=/16. The corresponding wavelength is   c / f  310  0.15m , where c is the speed of light,
c
c
2000 106
8
310 m/s. The sampling spacing ∆x=/16=0.0094= 9.375mm. The sampling interval ts depends on mobile speed V, thus
ts=∆x/V = 0.000937. Sampling frequency fs=1/ts=V/∆x=1067Hz.
Volume 3, Issue 3, March 2014
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Volume 3, Issue 3, March 2014
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If the MS is approaching the BS at a speed V, then the received complex envelope, r(t) is
 2

(8)
r (t )  a0 exp   jK C d  t    a0 exp   j
d  t 
 C

Where d  t  is the BS-MS distance or radio path, which varies according to the mobile speed V. If the term
d  t  increases the phase decreases and vice versa
CASE B
In this section, the signal is considered to be completely blocked and two point scatters are assumed through which the
transmitted signal arrives at the receiver. The two main aspects to be observed here is fade rate and Doppler spread. The
scattering is caused due to reflection from small objects like lamp posts, traffic signals, cars, trees and rough surfaces. The
simulation geometry is shown in Figure 2.
Here it is assumed that scattered signals are located in front and behind the MS. Thus echoes from the two point scatters
arrive at angles of =00 and =1800 which are shown in Figure 2 and the Doppler shifts depend on the arrival angles.
The point scatter is observed by changing the angles between 300 <<1800.
Figure 2: Simulation Geometry
The complex envelope is calculated as
r  n  exp   jKC d1 n    exp   jKC d 2  n 
(9)
4. RESULTS AND DISCUSSION
Figure 3 shows Rayleigh PDF and CDF functions for mode value () of 1. CDF gives the probability that a given signal
level is not exceeded. i.e., if this signal level is set as the system’s operation threshold, then this gives the probability that
the signal level is equal to or below the threshold. The CDF is very useful in computing outage probabilities in link
budgets i.e, CDF gives the outage probability. Knowing the CDF fade margins can also be set up. Table3.1shows the
parameters values for mode value () of 1
TABLE 1: RAYLEIGH DISTRIBUTION PARAMETERS FOR MODE VALUE OF 1
S.NO
PARAMETERS
VALUES
1
1
MODE ()
2
MEDIAN
1.18
3
MEAN VALUE
1.2500
4
RMS VALUE
1.4100
5
STANDARD DEVIATION
0.665
The below Table 3.2 shows the cumulative distribution function values and probability density function values for the
mode value of 1.
TABLE 2 CDF AND PDF FOR RAYLEIGH DISTRIBUTION
S.NO
CDF
PDF
1
0
0
2
0.0049875
0.099501
3
0.076884
0.36925
4
0.1175
0.44125
5
0.27385
0.58092
6
0.45393
0.60068
7
0.62469
0.52544
8
0.76425
0.40077
Volume 3, Issue 3, March 2014
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
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Volume 3, Issue 3, March 2014
9
10
11
12
13
14
15
0.83553
0.88975
0.95606
0.98508
0.99402
0.99781
0.9995
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0.3125
0.23153
0.10984
0.04327
0.019123
0.0076562
0.001942
The phase changes with time and distance as the MS is moving. The absolute phase increases when the MS is moving
towards the BS. This is shown in Figure 4. It is observed from the plot that when distance is decreasing phase increases
thus gives rise to positive Doppler shift. Comparison between the plots is shown by varying  which is called the radio
path angle or arrival angle. When arrival angle =900 the Doppler shift is 0Hz. Here the radio path is perpendicular to
the MS route. But when =600, 300 and 00 the arrival angle increases as MS moves towards the BS. That means phase
increases with increases in distance.
Figure 5 shows the absolute phase when the MS station is moving away from BS. It is observed from the plot, when MS is
moving away from the BS, the phase decreases, thus gives negative Doppler shift. Comparisons are shown in the plot for
different arrival angles. The first one corresponds to when the MS is travelling away from BS with =900. The phase
decreases further more for =1200 , =1500 and =1800 with greater slope. It is concluded that for arrival angle <900
positive increments in phase occurred with positive Doppler shift, for >900 the phase decreases with negative Doppler
shift and for arrival angle of =900 the phase increment is zero and so Doppler shift is also zero.
Absolute phase when MS is moving towards the BS
Absolute phase when MS is moving away from BS
5
Absolute phase of complex envelope (rad)
Absolute phase of complex envelope (rad)
45
alpha=0
alpha=30
alpha=60
alpha=90
40
35
30
25
20
15
10
5
0
0
-10
-15
-20
-25
-30
-35
-40
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
alpha=90
alpha=120
alpha=150
alpha=180
-5
1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Traveled distance (m)
Traveled distance (m)
Figure 4 Absolute phase when MS is approaching
the BS
Figure 5 Absolute phase when MS is moving
away from BS
Figure 6 and 7 shows the Doppler spectrum when MS is moving towards the BS. This spectrum is simulated for arrival
angles of =00and =900. Figure 6 shows Doppler shift if 66.67Hz for arrival angle of =00 i.e. positive Doppler
frequency. Figure 7 shows zero Doppler shift i.e. 0Hz for =900 .
0
0
X: 0
Y: 0
-10
-10
Norm aliz ed frquenc y res pons e (dB )
Norm alized frque ncy response (dB)
X: 66.67
Y: 0
-20
-30
-40
-50
-60
-70
-600
-400
-200
0
200
400
Dopple r shift (Hz)
Figure 6: Doppler Spectrum when MS is
approaching the BS, =00
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600
-20
-30
-40
-50
-60
-70
-600
-400
-200
0
200
400
600
Doppler shift (Hz)
Figure 7: Doppler Spectrum when MS is
approaching the BS, =900
Page 327
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
2
2
1.8
1.8
Magnitude of complex envelope
Magnitude of complex envelope
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Volume 3, Issue 3, March 2014
1.6
1.4
1.2
1
0.8
0.6
0.4
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0.2
0
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0
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
Time (s)
Time (s)
Figure 12 Received Signal pattern for =450
Figure 13 Received Signal pattern for =300
Figures 8 and 9 shows the Doppler spectrum when MS is moving away from BS. In Figure 8 it is observed that the
Doppler shift is negative which is equal to -66.67 Hz for arrival angle of , =1800. Negative frequency or negative
Doppler shift implies that the mobile is moving away from BS. In Figure 9 the Doppler shift is -33.33 Hz for =1200.
0
0
X: -33.33
Y: 0
-10
Normalized frquency response (dB)
Normalized frquency response (dB)
X: -66.67
Y: 0
-20
-30
-40
-50
-60
-70
-600
-400
-200
0
200
400
600
-10
-20
-30
-40
-50
-60
-70
-600
Dopple r shift (Hz)
-400
-200
0
200
400
600
Dopple r shift (Hz)
Figure 8: Doppler Spectrum when MS is travelling
away from the BS, =1800
Figure 9: Doppler Spectrum when MS is travelling
away from the BS, =1200
2
2
1.8
1.8
Magnitude of complex envelope
Magnitude of complex envelope
Figures 10, 11, 12 and 13 shows the received complex signal amplitude. It is seen how the received signal fluctuates
between 2(+6dB) and 0(-). Deep fades occurred for arrival angle of 1800 and 900. Fading is decreased for arrival angle
of =450 and =300. So the received signals fade rate decreases i.e. rate of change are slower, as the angle spread
decreases from 1800 to 300. When Doppler spread is, taken 00 then there is no fading.
1.6
1.4
1.2
1
0.8
0.6
0.4
1.4
1.2
1
0.8
0.6
0.4
0.2
0.2
0
1.6
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
Figure 10 Received Signal pattern for =180
0.1
0
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
Time (s)
Time (s)
0
Figure 11 Received Signal pattern for =90
0
Table 3 and 4 shows the normalized magnitude of the received complex signal at various time instances, when mobile is
moving with speed of 10m/s and for arrival angle =450 and =300.
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Volume 3, Issue 3, March 2014
Table 3 Normalized Magnitude of the
received signal for =450
=450
S.No Time Axis Magnitude
1
0
1.9352
2
0.0103
1.8589
3
0.0206
1.06
4
0.03
0.037973
5
0.0403
1.219
6
0.0506
1.9233
7
0.06
1.9091
8
0.0703
1.1757
9
0.0806
0.024826
10
0.0937
1.4754
Table 4 Normalized Magnitude of the
received signal for =300
=300
S.No
Time Axis
Magnitude
1
0
0.026407
2
0.010312
0.54586
3
0.020625
1.0736
4
0.03
1.4771
5
0.040313
1.8021
6
0.05625
2
7
0.069375
1.8608
8
0.079687
1.5692
9
0.089063
1.1861
10
0.09375
0.96063
0
0
Normalized frequency response (dB)
-5
Normalized frequency response (dB)
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-10
-15
-20
-25
-30
-35
-40
-10
-20
-30
-40
-50
-60
-45
-50
-600
-400
-200
0
200
400
-70
-600
600
-400
-200
0
200
400
600
Doppler shift (Hz)
Doppler shift (Hz)
Figure 14 Doppler Spectrum=1800
Figure 15 Doppler Spectrum =900
Figures 14, 15, 16 and 17 shows the Doppler spectrum for =1800, 900 , 450 and 300. It is observed here that the
maximum and minimum Doppler components are reduced for reduction in . It is observed that Doppler spread
parameter controls the bandwidth i.e. bandwidth decreases as the fade rate becomes slower. So Doppler spectrum
represents the fading process and the shape of the Doppler spectrum limits the bandwidth of fading process. A wider
spectrum means faster variations.
0
0
Normalized frequency response (dB)
N orm alized frequency response (dB)
-5
-10
-20
-30
-40
-50
-10
-15
-20
-25
-30
-35
-40
-45
-60
-600
-400
-200
0
200
400
Doppler shift (Hz)
Figure 16 Doppler Spectrum =450
600
-50
-600
-400
-200
0
200
400
600
Doppler shift (Hz)
Figure 17 Doppler Spectrum =300
5. CONCLUSIONS
This papers deals with short term fluctuations/multipath variations experienced by the WCDMA base station signal when
the mobile is moving with a speed of 36Km/hr. This paper gives a relationship between the Doppler shift after effecting
each echo, and their angle of arrival with respect to mobile direction of travel. It observed that phase increases when MS
is approaching the BS for arrival angle <900 and phase decreases when MS is moving away from BS for >900. In
addition, for arrival angle of =900 the phase increment is zero and so Doppler shift is also zero. Doppler spectrum is
Volume 3, Issue 3, March 2014
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
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Volume 3, Issue 3, March 2014
ISSN 2319 - 4847
simulated, it is observed for =00 Doppler shift is 66.67Hz which implies the MS is moving towards the BS. For =1800
the Doppler shift is -66.67Hz, for =1200 the Doppler shift is -33.33 Hz negative Doppler shift implies that MS is moving
away from BS. When two point scatter is considered deep fades occurred for arrival angle of =1800 and =900 and
fading is gradually reduced for arrival angles of =450 and =300. So fading decreases as Doppler spread decreases. The
maximum and minimum Doppler components are reduced with reduction in . It is observed that Doppler spread
parameter controls the bandwidth. A wider spectrum means faster variations. So Doppler spectrum represents the fading
process and the shape of the Doppler spectrum limits the bandwidth of fading process.
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AUTHORS
Prof. G Sasi Bhushana Rao is working as Professor in the Department of Electronics & Communication
Engineering, Andhra University Engineering College, Visakhapatnam. He has over 27 years of experience in
R&D, industrial and Teaching. He was involved in the development of GAGAN system which is jointly
developed by the ISRO and AAI. He has published more than 260 research papers in various reputed
International/National Journal/Conferences. He is a Senior Member of IEEE, FIETE, IEEE Com Society, IGU and
Member of International Global Navigation Satellite System (IGNSS), Australia. His area of research includes GPS/INS
Signal Processing, RADAR, SONAR and Acoustic signal modeling. He received "Best Researcher Award" from Andhra
University, Visakhapatnam.
Ms. Ch.Usha Kumari, is a Research Scholar at Jawaharlal Nehru Technological University, Hyderabad. She
has completed M.Tech in Radar and Microwave from Andhra University College of Engineering,
Visakhapatnam. She has 7 years of teaching experience in Engineering Colleges. She published 15 research
papers in various national, international conferences and journals.
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