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Volume 2, Issue 9, September 2014
Propagation Characteristics of a Mobile Radio
Channel for Rural, Suburban and Urban
Environments
Mr. ANIL KUMAR KODURI1, Mr. VSRK. SHARMA2, Mr. M. KHALEEL ULLAH KHAN3,
1
STUDENT, M.TECH
ASSOCIATE PROFESSOR
DEPARTMENT OF ECE, KRISHNA MURTHY INSTITUTE OF TECHNOLOGY & ENGINEERING
2,3
ABSTRACT
With the introduction of high speed data transmission over wireless networks, higher carrier frequencies and due to
increase in buildings and other obstacles in the environment, transmission losses have been a major parameter
while setting up a wireless network. Transmission channel analysis is done before setting up of a wireless network to
estimate the parameters like the coverage area, link budget, SNR, cell capacity etc. There are two types of variations
of radio signals. First, the long-term variations where the average value of signal depends on its distance, carrier
frequency, antenna height, atmospheric conditions and so on which results in loss of signal power at the receiver.
The second type of variation, short-term variations, is due to multipath reflections and Doppler and degrades the
quality of signal received at the receiver. In this project the Hata-Okumura model was employed for estimating the
pathloss experienced by the signal in the wireless channel. The pathloss variation in Rural, Urban and Suburban
environments is described with respect to the change in parameters like antenna heights, carrier frequency and
separation between transmitter and receiver. Also the sum of sinusoids method is used for evaluating the received
signal for various multipath environments and the effect of Doppler spread on the signal and generated Rayleigh
and Rician channel.
Keywords: Pathloss models, Propagation characteristics, Large scale variations of Wireless networks, Short term
variations of Wireless networks.
1. INTRODUCTION
Large-scale variations can be observed in a signal over large distances. Received power or its reciprocal, pathloss, is
generally the most important parameter predicted by large scale propagation models. Large-scale variations in a signal
are mainly due to Pathloss and shadowing. Pathloss is caused by dissipation of the power radiated by the transmitter as
well as by effects of the propagation channel. Path-loss models generally assume that pathloss is the same at a given
transmit–receive distance (assuming that the path-loss model does not include shadowing effects)[1]. Shadowing is
caused by obstacles between the transmitter and receiver that attenuate signal power through absorption, reflection,
scattering, and diffraction. When the attenuation is strong, the signal is blocked. Received power variation due to
pathloss occurs over long distances, whereas variation due to shadowing occurs over distances that are proportional to
the length of the obstructing object. 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. Because the signal received over each path
has a random amplitude and phase, the instantaneous value of the composite signal is found to vary randomly about a
local mean. Since these variations are rapid and occur over short distances these variations are termed as short term
variations[3]. The prediction of pathloss is a very important step in planning a mobile radio system, and accurate
prediction methods are needed to determine the parameters of a radio system which will provide efficient and reliable
coverage of a specific service area. Earlier the factors influencing the radio signal are explained and with that
knowledge we develop a mobile propagation model. The mobile radio channel is usually evaluated from 'statistical'
propagation models: Three types of channel models are proposed to model wireless channels: Empirical channel
models, Statistical channel models and Semi-empirical models. Out of these models, Empirical channel models are
derived based on a large amount of experimentally obtained data. These models have a higher efficiency but are
complex to design as the variable parameters increase. The area mean is directly related to the pathloss, which predicts
how the area mean varies with the distance between the BS and MS. Early studies by Okumura and Hata yielded
empirical pathloss models for urban, suburban, and rural areas that are accurate to within 1 dB for distances ranging
from 1 to 20 km and this analysis is best suitable for Large scale analysis of mobile radio signal. In this, Statistical
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channel models are derived by assuming various probability distributions to the signal parameters like the angle of
arrival, path delays etc. such models have lower accuracies but are easy to derive and may aid in estimation of channel
performance. In this paper, we used Rayleigh channel model for the analysis of Multipath environment, Rician channel
model has been used for Doppler spreads.
2. CHANNEL MODELS FOR LARGE SCALE ANALYSIS
Large scale variations are very slow and are calculated over a large area. These variations are generally assumed to
have lognormal distribution. Empirical channel models have been the best for analysis of large scale variations in this
section; we present some models which we will use in this paper for large scale variation analysis[3].
2.1 HATA-OKUMARA MODEL
The Hata-okumura model is a version developed for use in computerized coverage prediction tools. Hata obtained
mathematical expressions by fitting the empirical curves provided by Okumura[4]. Expressions for calculating the
pathloss, L (dB) (between isotropic antennas) for urban, suburban and rural environments are provided.
For flaturban areas,
where
is in MHz,
and
are in meters and d in km. Parameter
(2.1)
is the BS effective antenna height and
is the MS height, and d is the radio path length. For an MS antenna height of 1.5 m,
. Model corrections
are given next. The values of A , n are determined by the operating frequency, antenna heights and other influencing
factors. For example, if the base station antenna height is 50 m and the mobile antenna height 1.5 m, the model gives
the following pathloss at 900 MHz for a typical urban area:
(2.2)
Notice that the pathloss at 1 km from the transmitter is 123.33dB. Similarly, the pathloss for the same antenna heights
at 1,900MHz is given by
(2.3)
The pathloss in suburban and open areas is less than in urban areas. For example, at 1,950 MHz, this improvement in
pathloss isabout 12 dB for suburban and 32 dB for open areas. Corrections for determining pathloss in suburban and
rural areas are also determined by Hata as for a medium-small city,
(2.4)
For a large city,
(2.5)
(2.6)
For a suburban area,
(2.7)
For rural areas,
(2.8)
The model is valid for the following range of input parameters:
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Some years ago, in view of the need to deploy higher frequency systems, such as the GSM at 1800 MHz or PCS at 1900
MHz, a new revision of the Hata model (COST 231-Hata) Coverage and Interference 65 was developed using similar
methods to those used by Hata. The COST 231-Hata model follows the expression:
(2.9)
where
has the same expression as in the original model for a medium-small city and Cm is equal to 0 dB for
medium-size cities and suburban cities, and equal to 3 dB for metropolitan cities. The validity of this modification is
the same as for the original model, except for the frequency range which
2.2 SIGNAL VARIATIONS COMPARISON IN RURAL, SUBURBAN AND URBAN AREAS
In propagation studies for mobile radio, a qualitative description of the environment is often employed using terms such
as rural, suburban, urban and dense urban. Dense urban areas are generally defined as being dominated by tall
buildings, office blocks and other commercial buildings, whereas suburban areas comprise residential houses, gardens
and parks. The term ‘rural’ defines open farmland with sparse buildings, woodland and forests. So far, we have only
discussed signal variations in urban areas. Because the effect of the environmental clutter in suburban or rural areas is
not as severe, the average signal level in these areas is comparatively better[2]. This improvement in the signal levels
increases with frequencies, but does not appear to depend on the distance between base stations and mobile terminals or
on the antenna heights. With the help of some examples evaluated, we can observe the variation of signal levels in
rural, sub-urban and urban areas.
Improvement in signal level with distance
According to Hata model, For an transmitting antenna height ht =30.48 m; Receiving antenna height hr = 3m;
Carrier frequency fc = 850Mhz Pathloss in urban areas
Pathloss in rural areas
(2.10)
Pathloss in sub-urban areas
(2.11)
Where, d is in Km
(2.12)
400
350
p a th lo s s (d b )
300
250
Urban
200
Rural
Sub-urban
150
100
50
0
1
2
3
4
5
6
7
distance(km)
Figure 2.1: Comparison between pathloss in urban, sub urban and rural areas with change in distance
Improvement in signal level with antenna height:
For a Receiving antenna height hr = 3m; Distance between transmitter and receiver d = 20km Carrier frequency
Pathloss in urban areas
(2.13)
Pathloss in rural areas
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Pathloss in sub-urban areas
Where
is transmitter height in meters
220
200
180
Urban
p a th lo s s (d b )
160
Rural
Sub-urban
140
120
100
80
60
0
20
40
60
80
100
120
140
160
180
200
antena height(m)
Figure 2.2: Comparison between pathloss in urban, sub urban and rural areas with change in antenna heights
Improvement in signal level with frequency:
For a transmitting antenna height ht = 30.48 m Receiving antenna height hr = 3m Distance between transmitter and
receiver d = 20km
Pathloss in urban areas
Pathloss in rural areas
Pathloss in sub-urban areas
300
280
260
p a th lo s s (d b )
240
Urban
Rural
220
Sub-urban
200
180
160
140
120
800
900
1000
1100
1200
1300
1400
1500
frequency(Mhz)
Figure 2.3: Comparison between pathloss in urban, sub urban and rural areas with change in carrier frequencies
Signal level improvement is high with change in frequency when compared with change in other parameters in rural
and urban areas[6].
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3. CHANNEL MODELS FOR SHORT TERM ANALYSIS
Short term variations are are rapid and occur over short distances. These variations are generally assumed due to
Multipath environment and Doppler spreads. Statistical channel models have been the best for analysis of Short term
variations in this section; we present some models which we will use in this paper for Short term variation analysis[8].
3.1 SIMULATION MODEL OF A MOBILE RADIO CHANNEL
Consider the transmission of the band-pass signal
where is the channel response at time t due to an impulse applied at time and is the dirac delta function. When the Line
of sight component is present, the signal is assumed to undergo fading which follows Rician distribution and when the
Line of sight component is absent, the signal undergoes fading corresponding to Rayleigh distribution. In the next
section we present these distribution functions and equations for Rayleigh and Rician channel transfer functions.
3.2. RAYLEIGH FADING CHANNEL
The path between the base station and mobile stations of terrestrial mobile communications is characterized by various
obstacles and reflections[2]. The general characteristics of radio wave propagation in terrestrial mobile communications
are shown in Figure 3.1. The radio wave transmitted from a base station radiates in all directions these radio waves,
including reflected waves that are reflected off of various obstacles, diffracted waves, scattering waves, and the direct
wave from the base station to the mobile station. In this case, since the path lengths of the direct, reflected, diffracted,
and scattering waves are different, the time each takes to reach the mobile station will be different.
Figure 3.1: Principle of multipath channel.
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In addition the phase of the incoming wave varies because of reflections. As a result, the receiver receives a
superposition consisting of several waves having different phase and times of arrival[7]. The generic name of a radio
wave in which the time of arrival is retarded in comparison with this direct wave is called a delayed wave. Then, the
reception environment characterized by a superposition of delayed waves is called a multipath propagation
environment. In a multipath propagation environment, the received signal is sometimes intensified or weakened. This
phenomenon is called multipath fading, and this section discusses the concept of multipath fading and explains a
programming method for simulations of multipath fading[8]. Let us begin with the mechanism by which fading occurs.
The delayed wave with incident angle  n is given by (3.7) corresponding to Figure 3.1, when a continuous wave of
single frequency fc (Hz) is transmitted from the base station.
where Re[ ] indicates the real part of a complex number that gives the complex envelope of the incoming wave from the
direction of the number n. Moreover, j is a complex number. en(t ) is given in (2.10) by using the propagation path
length from the base station of the incoming waves: Ln (m), the speed of mobile station, v (m/s), and the wavelength,
λ(m).
where Rn and fn are the envelope and phase of the nth incoming wave. xn(t ) and yn(t ) are the in-phase and quadrature
phase factors of en t  , respectively. The incoming nth wave shifts the carrier frequency by the Doppler effect. This is
called the Doppler shift in land mobile communication. This Doppler shift, which is described as fd, has a maximum
value of n/l, when the incoming wave comes from the running direction of mobile station in cosθn = 1. Then, this
maximum is the largest Doppler shift. The delayed wave that comes from the rear of the mobile station also has a
frequency shift of -fd (Hz). It is shown by (4.9), since received wave r(t) received in mobile station is the synthesis of
the above-mentioned incoming waves, when the incoming wave number is made to be N.
where x(t ) and y (t ) are given by
and x(t) and y(t) are normalized random processes, having an average value of 0 and dispersion of σ, when N is large
enough. We have (3.24) for the combination probability density p(x, y), where x = x(t), y = y (t)
In addition, it can be expressed as r (t) using the amplitude and phase of the received wave.
R(t) and  are given by
By using a transformation of variables, p(x,y) can be converted into p(R,  )
By integrating p(R,  ) over q from 0 to 2, we obtain the probability density function p(R)
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Moreover, we can obtain the probability density function p(  ) by integrating p(R,  ) over R from 0 to 
From these equations, the envelope fluctuation follows a Rayleigh distribution, and the phase fluctuation follows a
uniform distribution on the fading in the propagation path[6]. Next, let us try to find an expression for simulations of
this Rayleigh fading. Here, the mobile station receives the radio wave, the arrival angle of the receiving incoming wave
is uniformly distributed, and the wave number of the incoming waves is N. In this case, the complex fading fluctuation
in an equivalent lowpass system is,
Consider an unmodulated signal S(t)=cos(2πfct). Let αn be the angle of arrival of nth ray at the receiver. Φn be the
phase shift of nth ray due to multipath. v be the velocity of the receiver and wd be the Doppler shift. Assume there are N
scaterers in the environment. The received signal will be of the form
We consider the second product term as the low pass equivalent response of the channel and is evaluated as
It should be obvious at this point why simulators which produce signals of the form of equation, or equivalently
equation, are called sum-of-sinusoids simulators[2]. The distinguishing feature of this type of simulator is that it
contains a low-frequency oscillator for each Doppler shift, wn=wdcos(αn), i.e., is made up of N oscillators.
A general relation between the Cn’s and the pdf of the angles of arriva1 is supplied by Jakes as
where f(αn) is the pdf of the nth angle of arrival and the cn's may be interpreted as the power ratio received within the
small arc dαn, about the angle of arriva1αn.The first step taken by Jakes is to restrict the angles of arriva1 from being
uniform i.e, fα1(α1)= fα2(α2)= ……….=fαN(αN)=1/2π to be uniformly spaced. And according to the formula
This, in turn, leads to the attenuation along the N paths being equal, i.e,
This amounts to observing that since the pdf of the angles of arrival f(αn) is uniform, the power received in each arc
dαn, is the same, as long as the αn,are uniformly spaced.
So equation (3.20) becomes
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When expanded the equation becomes
Where
 n and  n are uniformly distributed over 0 to 2π. Wd=Doppler frequency shift and N=number of scaterers.
The Doppler frequency shift is calculated by
Where v=mobile velocity, λ=wavelength of the carrier signal. The level crossing rate and average fade duration are
given by the formula
Where ρ=fade level
2.5
N o rm a lis e d a m p litu d e
2
1.5
1
0.5
0
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
time(seconds)
Figure 3.2: Rayleigh channel response for a relative velocity of 50m/s generated by sum of sinusoids method
We can calculate response of channel for different velocities of receiver by changing the value of wd in the MATLAB
code according to the equation 3.26.
3
N o rm a lise d a m p litu d e
2.5
2
1.5
1
0.5
0
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
time(seconds)
Figure 3.3: Rayleigh channel response for a relative velocity of 100m/s generated by sum of sinusoids method
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Observations- The level crossing rate (LCR) for a velocity of 100m/s is more than the level crossing rate for a velocity
of 50m/s for a fade level of 1. The average fade duration (AFD) for a velocity of 100m/s is more than the level average
fade duration for a velocity of 50m/s for a fade level of 1
3.2 SPECIAL CASE OF RAYLEIGH FADING SIMULATOR
For the simulation equation mentioned in 3.27, there is an exceptional case when the mobile receiver is stationary
(wd=0). For simplicity of implementation, we have assumed both the angles of arrival and the phase shift due to
Multipath are assumed to be uniformly distributed over 0 to 2π[2]. But in case when wd=0, 3.36 reduces to
We can observe that the equation is independent of time. This shows that when the receiver is stationary, the received
signal experiences a constant attenuation and a constant phase shift due to multipath components. If uniform
distribution of n is assumed in this case, the multipath components cancel each other for even number of scaterers and
resulting in 0 received signal. So we simulate this case by assuming to have N random values between 0 to 2π. Figure
3.4 shows the comparison between transmitted and received signals when only multipath effect is present.For such a
system, the received output is an attenuated and phase shifted version of the original wave. For an input signal, Tx(t)=
cos(2πfct) ; The received signal through the channel simulated is ; Rx(t)= 0.66 cos(2πfct-0.334)
1
0.8
transmitted signal
0.6
recieved signal
n o rm a lis e d a m p litu d e
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0
0.1
0.2
0.3
0.4
0.5
time(seconds)
0.6
0.7
0.8
0.9
1
-3
x 10
Figure 3.4: Received and transmitted signals when receiver is stationary
3.3. RICIAN CHANNEL
Rician distribution is used to model the channel when a direct line of site component exists between the transmitter and
receiver in addition with the multipath components[3]. It can be expressed as a phasor sum of a constant and a number
of scattering point sources.
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Where K is the ratio of multipath to direct component and
and
are angle of incidence and initial phase of direct
component respectively.
Table 3.1: Normalised amplitude of the signal at various time instances received at a receiver moving with velocity of
50m/s and k=3
Time(msec) Normalised amplitude of received signal
1.845
0.1
2.103
0.2
2.066
0.3
1.601
0.4
0.608
0.5
1.984
0.6
2.708
0.7
2.305
0.8
0.8358
0.9
0.9792
1
3.5
3
Normalised amplitude
2.5
2
1.5
1
0.5
0
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
time(seconds)
Figure 3.5: Rician channel response for a relative velocity of 50m/s and K=3 generated by sum of sinusoids method
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Table 3.2: Normalised amplitude of the signal at various time instances received at a receiver moving with velocity of
50m/s and k=6
Time(msec)
Normalised amplitude of received signal
1.566
0.1
1.63
0.2
1.63
0.3
1.439
0.4
0.5227
0.5
1.591
0.6
2.315
0.7
1.911
0.8
0.5535
0.9
1.001
1
3
Noramlised amplitude
2.5
2
1.5
1
0.5
0
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
time(seconds)
Figure 3.6: Rician channel response for a relative velocity of 50m/s and K=6 generated by sum of sinusoids method
Table 3.3: Normalised amplitude of the signal at various time instances received at a receiver moving with velocity of
100m/s and k=3
Time(msec) Normalised amplitude of received signal
1.022
0.1
1.498
0.2
1.177
0.3
1.307
0.4
2.03
0.5
1.103
0.6
0.839
0.7
3.175
0.8
1.744
0.9
2.264
1
3
Noramlised amplitude
2.5
2
1.5
1
0.5
0
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
time(seconds)
Figure 3.7: Rician channel response for a relative velocity of 100m/s and K=3 generated by sum of sinusoids method
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Table 3.3 Normalised amplitude of the signal at various time instances received at a receiver moving with velocity of
100m/s and k=6
Time(msec)
Normalised amplitude of received signal
0.8199
0.1
1.174
0.2
0.8675
0.3
1.291
0.4
1.598
0.5
1.236
0.6
0.978
0.7
2.612
0.8
1.551
0.9
1.681
1
3
No ra m lise d am p litu de
2.5
2
1.5
1
0.5
0
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
time(seconds)
Figure 3.8: Rician channel response for a relative velocity of 100m/s and K=6 generated by sum of sinusoids method
4. CONCLUSION
In this paper, we have proposed certain empirical models for studying the pathloss and its dependence on various
factors like distances between the transmitter and the receiver, antenna heights and frequency. We have simulated the
results in MATLAB. We have compared these variations in Urban Rural, and Suburban areas. Also, discussed the short
term fluctuations experienced by the signal. In this paper, we have designed a transfer function to analyse the
performance of different modulation techniques in a channel and calculate the LCR and AFD. With the knowledge of
these parameters, the bit error rate can be calculated and thereby suitable coding scheme can be evaluated. We have
also simulated the effect of relative velocity of receiver and transmitter on the performance of the communication
system. This pathloss modelling and analysis can be extended easily to satellite wireless communication channel.
REFERENCES
[1] T.S Rappaport, “Wireless Communications”, Chs. 3 and 4, Upper Sadle River, NJ: Prentice Hall, 1996.
[2] Rayleigh Fading Channels in Mobile Digital Communication Systems, Bernard Sklar, Communication Engineering
Services.
[3] D. Greenwood and L. Hanzo, “Characterisation of Mobile Radio Channels”.
[4] M. Hata, “Empirical Formulae for Propagation Loss in Land Mobile Radio Services”, IEEE Trans. Vehic. Tech,
Vol. VT-29, No.3, 1980.
[5] Ali Abdi, Wing C. Lau and Mostafa Kaveh, “ A New Simple Model for Land Mobile Satellite Channel: First- and
Second-Order Statistics”, IEEE Transactions on Wireless Communications, Vol. 2, No. 3, May, 2003.
[6] Simulation and Software Radio for Mobile Communications, Hiroshi Harada, Ranjee Prasad.
[7] Gordan L. Stuber, “Principles of Mobile Communication”, Second Edition.
[8] Branka Veucetic and Jun Du, IEEE Journal on Selected areas in Communications, Vol. 10, No. 8, October, 1992.
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[9] Modelling the Wireless Propagation Channel, F. Pe’rez Fonta’ and P. Martin Espin ~ eira, University of Virgo,
Spain.
[10] Hess, G.C, “Hand Book of Land-Mobile Radio Sy
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