ANALYSIS , SIMULATION AND MODELLING OF MOBILE AND …



ANALYSIS, SIMULATION AND MODELING OF MOBILE AND FIXED FADING CHANNELS

Feras A.K Al-Zuraiqi

Undergraduate Project Report

submitted in partial fulfillment of

the requirements for the

degree of Bachelor of Science (B.S.)

in

Electrical and Electronic Engineering Department

Eastern Mediterranean University

June 2004

Approval of the Electrical and Electronic Engineering Department

______________________________

Assoc. Prof. Dr. Derviş Z. Deniz

Chairman

This is to certify that we have read this thesis and that in our opinion it is fully adequate, in cope and quality, as an Undergraduate Project.

______________________________

Asst. Prof.Dr. Erhan INCE

Supervisor

Members of the examining committee

Name Signature

1. Asst.Prof.Dr. Aykut HOCANIN. …………………….

2. Asst.Prof.Dr. Hasan ABOU RAJAB. .……………………

3. Assoc.Prof.Dr. Huseyin OZKARAMANLI. .……………………

4. Asst.Prof.Dr.Rasime UYGUROGLU. .……………………

Date: 28-June-2004.

Abstract

ANALYSIS , SIMULATION AND MODELING OF MOBILE AND FIXED FADING CHANNELS

by

Feras A.K Al-Zuraiqi

Electrical and Electronic Engineering Department

Eastern Mediterranean University

Supervisor: Asst. Prof. Dr. Erhan INCE

Keywords: Wireless Communications, microwave propagation , mobile radio propagation , small-scale fading and multipath , statistical models for fading channels , delay spread and Doppler spread , radio channel modeling.

In small-scale propagation,fading is used to describe the rapid fluctuation of the amplitude of a radio signal over a short period of time or travel distance , so that large-scale path loss effects may be ignored. The presence of reflecting objects and scatterers in the channel creates a constantly changing environment that dissipates the signal energy in amplitude ,phase and time. Fading is caused by interference between two or more versions of the transmitted signal which arrive at the reciever at slightly different times.These waves called multipath waves, combine the reciever antenna to give a resultant signal which can vary widely in amplitude and phase , depending on the distribution of the intensity and relative propagation time of the waves and bandwidth of the transmitted signal. Multipath propagation is one of the most challenging problems encountered in a wireless data communication link. It causes signal fading, delay spread, and Doppler spread, and can greatly impair the performance of a data communication system. Multipath propagation, speed of the mobile ,speed of surrounding objects , and the transmission bandwidth of the signal are the most important physical factors in the radio propagation channel influence small scale fading. For mobile radio applications ,the channel is time-variant because motion between the transmitter and receiver results in propagation path changes. The rate of change of these propagation conditions accounts for the fading rapidity (rate of change of the fading impairments). Small-scale fading is called Rayleigh fading because if the multiple reflective paths are large in number and there is no line-to-sight signal component, the envelope of the received signal is statistically described by Rayleigh PDF.

This project will cover small-scale propagation effects such as fading, time dalay spread, and Doppler spread, and describes how to measure and model the impact that signal bandwidth and motion have on the instantaneous received signal through the multipath channel.

In mobile (outdoor) radio channels, the Rayleigh distribution is the commonly used to describe the statistical time varying nature of the received envelope of a flat fading signal, or the envelope of an individual multipath component. The first part of this project will provide a statistical models analysis for multipath fading channels, using Clarke’s model for flat fading in which a developed model where the statistical characteristics of the electromagnetic fields of the receiver signal at the mobile are deduced from scattering. In this project I will do a simulation of Clarke and Gans fading model by using the concept of in phase and quadrature modulation paths to produce a simulated signal with spectral and temporal characteristics very close to measured data, this simulation will be done using MATLAB.

Indoor propagation channels are characterized by severe multipath propagation. As a signal is transmitted, a series of attenuated and delayed versions of the original signal is received leading to a typical multipath channel response. Furthermore, this channel response changes over time. The second part of this project will propose a stochastic model for the time-variance of channels for fixed wireless communications. In the classical Jake’s Doppler spectrum, the receiver (or transmitter) is assumed to move at certain speed. However ,in fixed wireless communication systems, both the transmitter and the receiver are stationary and time-variations are actually due to moving scatterers. This part will include also modeling the channel time-variance for fixed wireless communication, using a novel stochastic model for this sort of time-varying channels which was discussed in[1] .

Acknowledgments

First and foremost, I thank my advisor, Asst. Prof. Dr. Erhan INCE.

I am pleased to acknowledge the support of my instructors ,who have supported my educational activities in electrical and electronic engineering. I am grateful for the invaluable contributions from them. I consider myself fortunate to have been one of the many graduate students who have taken their education in the Eastern Mediterranean University, particularly the department of electrical and electronic engineering. During the past four years I have acquired from my instructors a great deal of technical knowledge, and a rigorous yet practical attitude towards research. Furthermore, I have learned from them that many problems cannot be solved without clearly specifying the assumptions and conditions.

Finally , I dedicate this project to my parents who supported me to reach this level .

Table of Contents

ABSTRACT ..…………………………………………………………………………...2

ACKNOWLEDGMENTS ..…………………………………………………………....4

TABLE OF CONTENTS ..………………………………………………………….....5

LIST OF FIGURES ……………………………………………………………………6

1. INTRODUCTION …………………………………………………………….…….7

2. MOBILE RADIO PROPAGATION ……………………….………………............9

2.1 LARGE-SCALE FADING AND SMALL-SCALE FADING ...........................9

2.2 MULTIPATH PROPAGATION.………………………………………….......11

2.3 SIGNAL FADING ………………………………………………………….....12

2.4 DELAY SPREAD.……………………………………………………………..16

2.5 DOPPLER SPREAD …………………………………………………………..20

3. SIMULATION OF MULTIPATH FADING CHANNELS ……………………....24

3.1 SIMULATION AND GENERATION OF RAYLEIGH FADING …….……...24

ENVELOPE

3.2 MODELING AND SIMULATION OF THE CHANNEL TIME-VARIANCE.

FOR FIXED WIRELESS COMMUNICATION. ……………………………..30

3.2.1 CLASSICAL JAKES’ MODEL FOR MOVING RECEIVER………..…31

3.2.2 PROPOSED MODEL FOR STATIONARY RECEIVER……………….32

4. CONCLUSION……………………………………………………………………... 36

5. REFERENCES……………………………………………………………………….37

List of Figures

Figure 2.1 Fading channels manifestations…………………………………………10

Figure 2.2 Multipath propagation In indoor environments……….………...……12

Figure 2.3 Rayleigh probability density function(pdf)………………………….......14

Figure 2.4 Power-delay profiles. (a)Normalized and (b)Gaussian…………….……18

Figure 2.5 Illustration of Doppler shift in the free-space propagation environment..19

Figure 2.6 The Doppler spectrum of uniformly distributed angles………………….21

Figure 3.1 Implementation of a rayleigh fading simulator at baseband …………….22

Figure 3.2 A typical Rayleigh Fading Envelope at 900 MHz…………………….…25

Figure 3.3 The Histogram of Rayleigh Fading Envelope..………………………….27

Figure 3.4 Rayleigh fading simulator for multipath channels ..…………………….28

Figure 3.5 The impact of multipath fading channels on a test signal...……………...29

Figure 3.6 Time correlation of the propagation channel…………………………..…30

Figure 3.7 Doppler spectrum of the propagation channels………………...…….…..35

1. INTRODUCTION

With recent advances in communications, signal processing, and computer technologies, the dream of wireless networking for data communication systems has become an achievable goal. One attractive application of wireless networking is the indoor wireless local area network (WLAN). First, since it allows for mobility of users, re-wiring is unnecessary when a user of a WLAN moves. This can be especially important for users of portable data terminals. Secondly, since the WLAN operates in indoor environments, high-speed data transmission is possible without requiring an unrealistic amount of transmitter power. This is an important aspect for many data applications.

One of the most important building blocks for an indoor WLAN is the wireless data communication link. For a WLAN to function properly, reliable wireless data communication links must first be established. Multipath propagation is one of the most challenging problems encountered in a wireless data communication link. In a multipath propagation environment, the transmitted electro-magnetic signal propagates to the receiver via many different paths. In general, these propagation paths have different amplitude gains, phase shifts, angles of arrival, and path delays that are functions of the reflection structure of the environment. The effects of multipath propagation include signal fading, delay spread, and, when there is relative motion between the transmitter and receiver, Doppler spread. Signal fading refers to the phenomenon that in a multipath propagation environment, the received signal strength is strongly dependent on the locations of the transmitter and receiver. This is caused by the interference between signals propagating through different paths. Delay spread refers to the spread of the duration of the received signal with respect to the transmitted signal. This is due to the different delays associated with the propagation paths. Delay spread introduces inter-symbol interference (ISI) in a digital wireless communication system, which limits the achievable transmission rate. It also causes difficulties for symbol-timing recovery in a digital demodulator. Doppler spread, on the other hand, refers to the spread of the frequency spectrum of the received signal with respect to that of the transmitted signal, when there is relative motion between the transmitter and the receiver. This is due to the different angles of arrival associated with the propagation paths. Since the spectrum of the received signal is wider in frequency than that of the transmitted signal, the multipath propagation channel is clearly a time-varying system. Adaptive signal processing techniques are therefore required to track channel variations for a mobile digital wireless communication system operating in a multipath propagation environment.

This project discusses the performance of a point-to-point single-user indoor and outdoor high-speed wireless data communication link. In this project I will discuss the small scale fading which is used to describe the rapid fluctuation of the amplitude of a radio signal over a short period of time or travel distance. This project will also provide a simulation of different cases related to multipath fading using Clarke and Gans fading model by implementing a frequency domain simulator for Rayleigh fading at base band.

Many simulations in this project will be done using MATLAB, they will show that Multipath in the radio channel creates small-fading effect. And the three important effects are:

• Rapid changes in signal strength over small travel distance or time interval

• Random frequency modulation due to varying Doppler shifts on different multipath signals.

• Time dispersion (echoes)caused by multipath propagation.

Chapter 1

2. MOBILE RADIO PROPAGATION

2.1 Large-Scale Fading and Small-Scale Fading

Figure. 2.1 represents an overview of fading channel manifestations [2]. It starts with two types of fading effects that characterize mobile communications: large-scale and small-scale fading. Large-scale fading represents the average signal power attenuation or path loss due to motion over large areas. In Fig.2.1, the large-scale fading manifestation is shown in blocks 1, 2, and 3. This phenomenon is affected by prominent terrain contours (hills, forests, billboards, clumps of buildings, etc.) between the transmitter and receiver. The receiver is often represented as being “shadowed” by such prominences. The statistics of large-scale fading provide a way of computing an estimate of path loss as a function of distance. This is described in terms of a mean-path loss (nth-power law) and a log-normally distributed variation about the mean. Small-scale fading refers to the dramatic changes in signal amplitude and phase that can be experienced as a result of small changes (as small as a half-wavelength) in the spatial separation between a receiver and transmitter. As indicated in Fig.2.1, blocks 4, 5, and 6, small-scale fading manifests itself in two mechanisms, namely, time-spreading of the signal (or signal dispersion) and time-variant behavior of the channel. For mobile radio applications, the channel is time-variant because motion between the transmitter and receiver results in propagation path changes. .Small-scale fading is also called Rayleigh fading because if the multiple reflective paths are large in number and there is no LOS signal component, the envelope of the received signal is statistically described by a Rayleigh probability density function (pdf). A mobile radio roaming over a large area must process signals that experience both types of fading: small-scale fading superimposed on large-scale fading. There are three basic mechanisms that impact signal propagation in a mobile communication system. They are reflection, diffraction, and scattering [3]:

• Reflection occurs when a propagating electromagnetic wave impinges on a smooth surface with very large dimensions compared to the RF signal wavelength ([pic]).

• Diffraction occurs when the radio path between the transmitter and receiver is obstructed by a dense body with large dimensions compared to [pic], causing secondary waves to be formed behind the obstructing body. Diffraction is a phenomenon that accounts for RF energy traveling from transmitter to receiver without a line-of-sight path between the two. It is often termed shadowing because the diffracted field can reach the receiver even when shadowed by an impenetrable obstruction.

• Scattering occurs when a radio wave impinges on either a large rough surface or any surface whose dimensions are on the order of [pic] or less, causing the reflected energy to spread out (scatter) in all directions. In an urban environment, typical signal obstructions that yield scattering are lampposts, street signs, and foliage.

[pic]

Figure 2.1.Fading channels manifestations.

Fig.2.1 examines the two manifestations of small-scale fading: signal time-spreading (signal dispersion) and the time-variant nature of the channel. These examinations will take place in two domains, time and frequency, as indicated in Fig. 2.1, blocks 7, 10, 13, and 16. For signal dispersion, Fig.2.1 also categorizes the fading degradation types as frequency-selective or frequency-nonselective (flat), as listed in blocks 8, 9, 11, and 12. For the time-variant manifestation, the figure categorizes the fading degradation types as fast- or slow-fading, as listed in blocks 14, 15, 17, and 18.

In this chapter I will discuss the small-scale fading due to small changes in position .

2.2 Multipath Propagation

In a wireless communication channel, the transmitted signal generally propagates to the receiver antenna through many different paths. This phenomenon, depicted in Figure 2.2 for indoor environments, is termed multipath propagation. Multipath propagation is due to the multiple reflections caused by reflectors and scatterers in the environment. Possible reflectors and scatterers may include mountains, hills and trees in rural environments, buildings and vehicles in built-up urban environments, or walls and floors in indoor environments. The receiver antenna will therefore receive multiple copies of the transmitted signal. Since different versions of the signal propagate through different paths, they will in general have different attenuation, phase shifts, time delays and angles of arrival. The receiver antenna output is the sum of the multiple signal copies weighted by the antenna gain pattern.

Multipath propagation is a complicated phenomenon that is very difficult to characterize. One common approach is to treat the received signal as a spatial-temporal random process. The statistics of this random process can be collected from extensive field measurements in selected operation environments. Since the properties of the received signal are clearly a strong function of the multipath environment, statistical characterization of the received signal is often done in a two-step process. In the first step, it is assumed that the multipath environment is fixed, and variations of the received signal are measured for the given multipath environment. The statistics thus collected are referred to as small-scale variations, because they are usually obtained from measurement data obtained at various locations in a small area.

[pic]

Figure 2.2: Multipath propagation In indoor environments. The signal transmitted by the

transmitter (T) is attenu ated and reflected by the walls and floors. As consequence the receiver

(R) receives multiple distorted copies of the transmitted signal.

In the second step, variations of the small-scale statistics are determined from measurements taken in different multipath environments. These variations are referred to as large-scale variations, because they are obtained from measurement data taken at various locations in a large area. In this project, I focus on mitigating the effects of the small-scale variations using digital signal processing techniques. These small-scale variations, including signal fading, delay-spread and Doppler-spread, are discussed in the remainder of this chapter. For a treatment of large-scale variations, reader can see [4].

2.3 Signal Fading

Signal fading refers to the rapid change in received signal strength over a small travel distance or time interval. This occurs because in a multipath propagation environment, the signal received by the mobile at any point in space may consist of a large number of plane waves having randomly distributed amplitudes, phases, delays and angles of arrival. These multipath components combine vectorily at the receiver antenna. They may combine constructively or destructively at different points in space, causing the signal strength to vary with location. If the objects in a radio channel are stationary, and channel variations are considered to be only due to the motion of the mobile, then signal fading is a purely spatial phenomenon. A receiver moving at high speed may traverse through several fades in a short period of time. If the mobile moves at low speed, or is stationary, then the receiver may experience a deep fade for an extended period of time. Reliable communication can then be very difficult because of the very low signal-to-noise ratio (SNR) at points of deep fades.

Extensive field measurements have previously been done [5, 6, 7, 8] to characterize the small-scale spatial distribution of the received signal amplitude in multipath propagation environments. It has been found that for many environments, the Rayleigh distribution provides a good fit to the signal amplitude measurement in environments. where no line-of-sight or dominant path exists[5, 8, 9]. The probability density function of the Rayleigh distribution is given by [3]:

[pic] (2.1)

Where [pic] is the parameter of the distribution. A plot of the Rayleigh probability density function is shown in Figure 2.3. The Rayleigh distribution is related to the zero-mean Gaussian distribution in the following manner. Let[pic] and[pic]be two independent, identically distributed, zero-mean Gaussian random variables with variance[pic].The marginal probability density functions of [pic] and [pic]are given by :

[pic] (2.2)

Then the random variable [pic], defined as :

[pic] (2.3)

is distributed according to the Rayleigh probability density function given in Equation (2.1). The fact that the Rayleigh distribution provides a good fit to the measured signal amplitudes in a non-line-of-sight environment can be explained as follows. When a signal is transmitted through a multipath propagation channel, the in-phase and quadrature-phase components of the received signal are sums of many random variables. Because there is no line-of-sight or dominant path, these random variables are approximately zero-mean. Therefore, by the central limit theorem, the in-phase and quadrature-phases components can be modeled approximately as zero mean Gaussian random processes.

The amplitude, then, is approximately Rayleigh distributed.

[pic]

Figure 2.3:Rayleigh probability density function(pdf).

On the other hand, when line-of-sight paths exist in a multipath propagation environment, or when there is a dominant reflected path, the Ricean distribution is a good statistical characterization of the signal amplitude distribution [7, 8]. The Ricean distribution is related to the Gaussian distribution in a manner similar to the relationship between the Rayleigh and Gaussian distributions. In particular, let[pic] and [pic]be independent Gaussian random variables with variance [pic]. Furthermore, assume that [pic][[pic]] = [pic]and [pic] [[pic]] = 0. Then the random variable [pic], defined in Equation 2.3, is distributed according to the Ricean distribution. Thus, one can see that when a dominant path exist in a multipath propagation environment, by the central limit theorem, the signal amplitudes are approximately Ricean distributed when the number of paths is large. The probability density function of the Ricean distribution is given by [3]:

[pic] (2.4)

Where

[pic] (2.5)

is the zeroth-order modified Bessel function of the first kind. There are two parameters in Equation (2.4). [pic] is the variance of the underlying Gaussian random variable and [pic] is the amplitude of the line-of-sight or dominant component. When [pic]= 0 corresponds to the Rayleigh distribution. As [pic] tends to infinity, the Ricean distribution converges to a Gaussian distribution.

2.4 Delay Spread

As mentioned previously, in a multipath propagation environment, the received signal consists of a large number of components having different delays. Consequently, when a “narrow” pulse is transmitted over a multipath propagation channel, distorted replicas of the transmitted pulse arrive at the receiver at various different times, making the received signal “wider” in time than the transmitted signal. This phenomenon is referred to as delay spread. The significance of delay spread depends on the time-width of the signal relative to that of the channel , hence a quantitative characterization of the severeness of channel delay-spread is necessary.

One common measure for characterizing channel delay spread is the power-delay profile [9]. The power-delay profile of an environment is obtained through field measurements by transmitting a short pulse and measuring the received power as a function of delay at various locations in a small area. These measurements are then averaged over spatial locations to generate a profile of average received signal power as a function of delay. The second central moment of the power-delay profile is referred to as the root-mean-square (rms) delay-spread [9], and can be used as one quantitative measure of the severeness of multipath propagation. For outdoor wireless channels, the rms delay-spreads typically range from 1.5 to 5 ns ; while for indoor environments, the rms delay-spreads typically range from 10 to 100 ns. It should be kept in mind that the value of the rms delay-spread, just as any other parameter used to characterize wireless channels, is highly environment dependent. It is also dependent on the carrier frequency used for transmission. There is no universal value that can be applied to every multipath propagation channel. It is, therefore, extremely important for a wireless communication system to be robust against variations in channel parameters.

In general, for a wireless digital communication system, the significance of channel delay spread depends on the relationship between the rms delay-spread of the channel and the symbol period of the digital modulation[11]. If the rms delay-spread is much less than the symbol period, then delay spread has little impact on the performance of the communication system. In this case the shape of the power-delay profile is immaterial to the error performance of the communication system. This condition is often called “flat-fading.” On the other hand, if the rms delay-spread is a significant fraction of, or greater than, the symbol period, then channel delay spread significantly impairs the performance of the communication system. Furthermore, the error performance of the communication system depends on the shape of the power-delay profile. This condition is often referred to as “time-dispersive fading” or “frequency-selective fading”. Since the power-delay profile is an empirical quantity that depends on the operating environment, for computer simulation purposes we can only postulate functional forms of the profile, and vary the parameters of these functional forms in order to obtain results that are applicable to a broad spectrum of wireless environments.

The first is the exponential power-delay profile, given by:

[pic] ( 2.6)

The second is the Gaussian power-delay profile, defined as:

[pic] (2.7)

These power-delay profiles are plotted in Figure 2.4 (a) and (b). In Equations (2.6) and (2.7), S is the rms delay-spread. [pic] in Equation (2.7) refers to the average delay introduced by the channel. [pic] should be referred to as the truncated Gaussian power-delay profile, because it is the causal part of a Gaussian function. Furthermore, the rms delay-spread of a multipath propagation channel with power-delay profile described by Equation (2.7) is not equal to S.

[pic]

(a)

[pic]

(b)

Figure 2.4: (a) Normalized exponential power-delay profile. (b) Normalized Gaussian

power-delay profile. [pic] = 4S in this plot.

However, whenever Equation (2.7) is this project, [pic] is set to a value that is significantly larger than [pic]. In this case [pic] is essentially the same as the Gaussian function before truncation, and the rms delay spread is essentially equal to S. For the sake of brevity, [pic] simply refer to as the “Gaussian power-delay profile.”

2.5 Doppler Spread

When a single-frequency sinusoid is transmitted in a free-space propagation environment where there is no multipath propagation, the relative motion between the transmitter and receiver results in an apparent change in the frequency of the received signal. This apparent frequency change is called Doppler shift. To analyze this effect, consider the simple scenario shown in Figure 2.5. Assuming that the transmitter is far away so that plane wave approximations hold at the receiver location, and that the receiver is moving at a constant velocity v along a direction that forms an angle _ with the incident electro-magnetic wave, then it can be seen that the difference in path lengths traveled by the wave from the transmitter to the mobile receiver at points X and Y is given by

[pic] (2.8)

[pic] (2.9)

where [pic] is the time required for the mobile to travel from X to Y. The phase change in the received signal due to the difference in path lengths is therefore

[pic] (2.10)

[pic] (2.11)

where [pic]is the wavelength. Hence, the apparent change in received frequency, or Doppler shift, is given by:

[pic] (2.12)

[pic] (2.13)

[pic] (2.14)

[pic][pic]

Figure 2.5: Illustration of Doppler shift in the free-space propagation environment.

The receiver moves at a constant velocity v along a direction that forms an angle [pic]

with the incident wave.

In Equation (2.14), [pic] is the speed of light and [pic]is the frequency of the transmitted

sinusoid. In going from Equation (2.13) to (2.14), the relationship

[pic] (2.15)

is used.

It can be seen from Equation (2.14) that Doppler shift is a function of, among other

parameters, the angle of arrival of the transmitted signal. In a multipath propagation environment in which multiple signal copies propagate to the receiver with different angles of arrival, the Doppler shift will be different for different propagation paths. The resulting signal is the sum of the multipath components. Consequently, the frequency spectrum of the received signal will in general be “wider” than that of the transmitted signal, i.e. it contains more frequency components than were transmitted. This phenomenon is referred to as Doppler spread. Since the received signal occupies a wider band than the transmitted signal, the multipath propagation channel is a time-varying linear system when there is relative motion. The amount of Doppler spread, then, characterizes the rate of channel variations. Doppler spread can be quantitatively characterized by the Doppler spectrum [3].

[pic]

Figure 2.6: The Doppler spectrum corresponding to uniformly distributed angles of arrival (see

Equation 2.16).

The Doppler spectrum is the power spectral density of the received signal when a single-frequency sinusoid is transmitted over a multipath propagation channel. In a static environment in which the reflectors stay immobile, the Doppler spectrum is simply an impulse located at the frequency of the transmitted sinusoid when there is no relative motion. When there is relative motion, the Doppler spectrum occupies a finite bandwidth. The exact shape of the Doppler spectrum depends on the configuration of the reflectors. It can be shown[3] that when the mobile receiver moves at a constant speed [pic] and the signal power received by the receiver antenna arrives uniformly from all incident angles in [pic], the Doppler spectrum takes a form of :

[pic] (2.16)

where [pic] is a proportionality constant and [pic]is the maximum Doppler shift. This Doppler spectrum is plotted in Figure 2.6. In reality, however, the exact shape of the Doppler spectrum can only be obtained by extensive field measurements, and Equation (2.16) is approximately true only in certain environments. The bandwidth of the Doppler spectrum, or equivalently the maximum Doppler shift [pic], is a measure of the rate of channel variations. When the Doppler bandwidth is small compared to the bandwidth of the signal, the channel variations are slow relative to the signal variations. This is often referred to as “slow fading.” On the other hand, when the Doppler bandwidth is comparable to or greater than the bandwidth of the signal, the channel variations are as fast or faster than the signal variations. This is often called “fast fading.”.

Chapter II

3. Simulation of Mulipath Fading Channels

3.1 Simulation and Generation of Rayleigh Fading Envelope

Is often useful to simulate multipath fading in hardware or software .A popular simulation method uses the concept of in-phase and quadrature modulation paths to produce a simulated signal with spectral and temporal characteristic very close to measured data.

As shown in figure 3.1,two independent Gaussian low pass noise sources are used to produce in-phase and quadrature fading branches [3]. Each Gaussian source may be formed by summing two independent Gaussian random variables which are orthogonal .By using the spectral filter defined by equation (3.1.1) For Doppler spectrum to shape the random signals in the frequency domain ,accurate time domain waveforms of Doppler fading can be produced by using an inverse fast fourier transform (IFFT) at the last stage of the simulator.

[pic] (3.1.1)

The method in Figure 3.1 uses a complex Gaussian random number generator (noise source) to produce a baseband line spectrum with complex weight in the positive frequency band. The maximum frequency component of the line spectrum is [pic] . Using the property of real signals, the negative frequency component are constructed by simply conjugating the complex Gaussian values obtained for the positive frequencies .IFFT of the signal is purely real Gaussian random process in the time domain which is used in one of the quadrature arms shown in Figure 3.1.The random valued line spectrum is then multiplied with a discrete frequency representation of [pic] having the same number of points as the noise source.

[pic]

Figure 3.1:Frequency domain implementation of a rayleigh fading simulator at baseband .

To handle the case where equation (3.1.1) approaches infinity at the passband edge, the value of [pic]is truncated by computing the slope of the function at the sample frequency just prior to the passband edge and extended the slope to the passband edge. Simulation using the architecture in Figure 3.1 is usually implemented in the frequency domain using complex Gaussian line spectra to take advantage of easy implementation of equation (3.1.1). This, in turn, implies that the low pass Gaussian noise components are actually a series of frequency components (line spectrum from [pic] to[pic]), which are equally spaced and each have a complex Gaussian weight.

To implement the simulator shown in Figure 3.1 the following step are used [3]:

1- Specify the number of frequency domain points (N) used to represent [pic] and the maximum Doppler frequency shift ([pic]).The value used for N is usually a power of 2.

2- Compute the frequency spacing between adjacent spectral lines as [pic].This defines the time duration of a fading waveform, [pic]

3- Generate complex Gaussian random variables for each of the [pic] positive frequency component of the noise source.

4- Construct the negative frequency components of the noise source by conjugating positive frequency values and assigning these at negative frequency values.

5- Multiply the in-phase and quadrature noise sources by the fading spectrum [pic].

6- Perform an IFFT on the resulting frequency domain signals from the in-phase and quadrature arms to get two N-length time series, and add the squares of each signal point in time to create an N-point time series like under the radical of equation :

[pic][pic] (3.1.2)

7- Take the square root of the sum obtained in step 6 to obtain an N point time series

of a simulated Rayleigh fading signal with the proper Doppler spread and time

correlation.

In this project I used the MATLAB program to generate and simulate Rayleigh

fading.

The simulated rayleigh fading envelope at baseband is shown in Figure 3.2 .which shows the time varying nature of the received envelope of a flat fading signal, or the envelope of an individual multipath component. Figure 3.2 shows a Rayleigh distributed signal envelope as a function of time.

[pic]

Figure 3.2, A typical Rayleigh Fading Envelope at 900 MHz.

As mentioned before Rayleigh distribution has probability density function (pdf) given in equation (2.1). And the histogram of the Rayleigh fading envelopes takes the shape of probability density function of Rayleigh distribution, as shown in Figure 3.3.

[pic]

Figure 3.3:The Histogram of Rayleigh Fading Envelope.

Several Rayleigh fading simulators may be used in conjunction with variable gains and time delays to produce frequency selective fading. This is shown in Figure 3.4.

By making a single frequency component dominant in amplitude within[pic], the fading is changed from Rayleigh to Ricean .This can be used to alter the probability distributions of the individual multipath components in the simulator of Figure3.4.

To determine the impact of flat fading on an applied signal [pic] , one merely needs to multiply the applied signal by [pic],the output of the fading simulator .To determine the impact of more than one multipath component, a convolution must be performed as shown in Figure 3.4.

[pic]

Figure 3.4: A signal ma be applied to a Rayleigh fading simulator to determine performance in a

wide range of channel conditions.Both flat and frequency selective fading conditions may be

simulated,depending on gain and time delay settings.

By applying a test signal [pic] to a Rayleigh fading simulator as shown in Figure 3.4 to determine performance In a wide range of channel conditions. The impact of flat fading on [pic] is shown in Figure.3.5. It is clear that the received signal will suffer a rapid fluctuation in the amplitude and a phase shifts, Figure 3.5 shows the fading of a Sinusoidal test signal applied to a three paths Rayleigh simulator.

[pic]

Figure 3.5. The impact of multipath fading channels on a test signal.

3.2 Modeling and Simulation of the Channel Time-Variance for Fixed Wireless Communication

Indoor propagation channels are characterized be severe multipath propagation. As a signal is transmitted , a series of attenuated and delayed versions of the original signal is received leading to typical multipath channel response, Furthermore, this channel response changes over time. Two different time-varying propagation scenarios are possible. First, if the receiver (or the transmitter) is mobile, it moves through the interference pattern generated by the electromagnetic waves and a different channel response is observed at each location. This sort of time–variation has been studied extensively in the context of cellular communications and has been modeled stochastically by Jakes in [4]. Second, if the receiver and transmitter are stationary but reflectors in the indoor environment move, the interference pattern itself will change over time. This sort of time–variations has not been analyzed yet. In this section, I will discuss a new modeling approach by [1] which corresponds well to measurements of the Doppler spectrum for such channels described in literature [13]-[14].

3.2.1. Classical Jakes’ model for Moving Receiver

In conventional mobility modeling, it is assumed that the receiver moves at speed [pic]. As the receiver moves over a distance [pic] in the order of a few wavelengths, the amplitudes [pic] and the incident angels [pic] of the propagation paths stay quasi-unaltered. However, the phase [pic]of each path changes drastically as the electrical distance traveled by the wave alters significantly. The phase of the pth propagation path changes from [pic] with c the speed of light.

The channel correlation as a function of time offset Δ.t for the k-th discrete-time

channel tap can be computed as

[pic] (3.2.1)

[pic] (3.2.2)

A stochastic model for the time correlation is obtained by inserting the stochastic angular density [pic], which is independent of the channel tap index k , in the previous equation.

[pic] (3.2.3)

Where the Doppler frequency [pic] and J0(x) stands for the zeroth-order Bessel function of the first kind. This well known result, which was first derived by Jakes[4], corresponds to a bathtub-like Doppler spectrum [pic] given by:

[pic] (3.2.4)

Although this model only applies for a vary specific scenario of omni-directional scattering and a moving receiver, it has found widespread adoption for other scenarios as well, mainly due to its simplicity. However, the bathtub shape does not correspond to the Doppler spectra reported in [13]-[14], which were measured with a static transmitter and receiver and some moving objects.

3.2.2 Proposed model for Stationary receiver

The phase change of a propagation path p induced by a moving reflector as a function of time is given by

[pic] (3.2.5)

With [pic] the angle between the direction of movement and the direction orthogonal to the reflecting surface as only the movement of the reflector along the latter direction influences the path length. The angle [pic] denotes the reflection angle for the moving scatterer .Both the path from the preceding and the path to the next reflector are affected by the movement. Although in this project I will assume that maximally one moving reflector is encountered by each propagation path, multiple reflections off moving reflectors can be handled in a similar fashion. Assuming [pic].and the angles [pic]and[pic] to be uniformly distributed on [pic], the correlation function of time can be computed by following a similar reasoning as in equations (3.2.2) and (3.2.3).

[pic] (3.2.6)

[pic] (3.2.7)

It can be found that the Doppler spectrum for this model is given by :

[pic] (3.2.8)

Where K stands for the complete elliptic integral. The Doppler spectrum is this case has a bandwidth [pic] which is twice the bandwidth of Jakes’ model which equals [pic] . The derivation leading to equation(3.2.7) assumes that all reflectors move randomly at speed [pic] which is overly pessimistic. The motion of the reflectors can be modeled more accurately be altering the pdf of the speed v. Rather than assuming a pdf with an impulse at [pic],representing the maximum indoor speed, another model is used here which corresponds better to the physical reality. In indoor environments, most paths reflect off static objects such as walls. Only a small percentage of the paths actually encounters a moving objects such as a human being. Therefore, we assume that a factor [pic] of the paths are static and a factor [pic] of the paths are time-varying. Further more, it is highly unlikely that all moving objects are moving at exactly speed [pic].Hence, we assume that the speeds of the moving objects are distributed uniformly between 0 and [pic].Consequently. the correlation as a function of time is given by:

[pic] (3.2.9)

Unfortunately, no closed-form expression exists for this integral and we resort to numerical integration. Other models for pdf of the speed can be constructed dependent on the specific indoor propagation scenario.

The time correlation of the channels for different models is shown in Figure 3.6.The red line corresponds to the Jakes model described by equation (3.2.3).The green line represents the time correlation when all reflectors move exactly at speed [pic],corresponding to (3.2.7).The blue line represents the case where [pic]=0 such that all paths are time-varying. A more realistic value for the percentage of static paths in the indoor propagation environment is given by [pic]=0.9 which is plotted in dotted line. Clearly the correlation degrades only slowly with time.

The Doppler spectra for all models are shown in Figure 3.7.The jakes spectrum has a bandwidth of 2[pic]with a very high probability of high Doppler frequency, (Note: Jakes spectrum is added to Figure3.7, to realize this).In the cases mentioned before moving reflectors are considered, the band width of the fading process is twice as high or equal to 2[pic].The proposed model gives rise to more peaky Doppler spectra than Jakes’ Model..

The dB values of the spectrum in Figure 3.7 are not normalized.

[pic]

Fig 3.6.Time correlation of the propagation channel.

[pic]

Figure 3.7. Doppler spectrum of the propagation channels.

5. CONCLUSION

The mobile radio channel places fundamental limitations on the performance of wireless communication system. The transmission path between the transmitter and the receiver can vary from simple line-of-sight to one that is severely obstructed by buildings, mountains, and foliage. Unlike wired channels that are stationary and predictable, radio channels are extremely impacts how rapidly the signal level fades as a mobile terminal moves in space.

As a mobile moves over very small distances, the instantaneous received signal strength may fluctuate rapidly giving rise to small-scale fading. The reason for this is that the received signal is a sum of much contribution coming form different direction.

As a mobile moves away form the transmitter over much larger distances, the local average received signal will gradually decrease, and it is the local average signal level that is predicted by large-scale propagation models.

Due to the relative motion between the mobile and the base station, each multipath wave experiences as apparent shift in frequency. The shift in received signal frequency due to motion is called the Doppler shift, and is directly proportional to the velocity and direction of motion of the mobile with respect to the direction of arrival of the received multipath wave.

References

[1] S.Theon,”Modeling the Channel Time-Variance for Fixed Wireless

Communications” ,IEEE Communication Mag.,vol.6,NO.8, AUGUST 2002 ,pp

331-333.

[2] B. Skler .,”Rayleigh Channels in Mobile Digital Communication Systems,”IEEE

Communication Mag.,vol.29,no 4,July 1997,pp 90-100.

[3] T. S. Rappaport, Wireless Communication, Chapters. 3 and 4,Upper Saddle River,

NJ: Prentice Hall, 1996.

[4] W.C. Jakes, microwave Mobile Communications, IEEE Press, 1994.

[5] D. C. Cox, R. R. Murray,and A W. Norris, “Measurements of 800 MHz Radio

Transmission into Buildings with Metallic Walls,” Bell System Technical

Journal,Vol. 62, pp. 2695~2717,November 1983.

[6] D. C. Cox, R. R. Murray,and A W. Norris, “Measurements of 800 MHz

Attenuation Measured In and Around Suburban Houses,”Bell System Technical

Journal,Vol. 63, pp. 921~954,November 1984.

[7] R. J. C. Bultitude and G. K. Bedal, “Propagation Characteristics on Microcellular

Urban Mobile Radio Channels at 910 MHz,” IEEE Journal on Selected Areas

in Communications, Vol. 7, No. 1, pp. 31_39, January 1989.

[8] T. S. Rappaport, “Characterization of UHF Multipath Radio Channels in Factory

Buildings,” IEEE Transactions on Antennas and Propagation, Vol. 37, No. 8, pp.

1058~1069, August 1989.

[9] D. C. Cox, “Universal Digital Portable Radio Communications,” IEEE

Proceedings,Vol 75, No. 4, pp. 436~ 477, April 1987.

[10] H. Hashemi, “Impulse Response Modeling of Indoor Radio Propagation

Channels,”IEEE Journal on Selected Areas in Communications, Vol 11, No. 7, pp.

967_978, September 1993.

[11] J. C.-I. Chuang, “The Effects of Time Delay Spread on Portable Radio

Communications Channels with Digital Modulation," IEEE Journal on Selected

Areas in Communications, Vol. 5, No. 5, pp. 879_889, June 1987.

[12] put reference for dopller filter

[13] R.J.C Bultitude,R.F.Hahn.and R.J.Davies,”Propagation consideration for the

design of an indoor broad-brand communication system at EHF,”IEEE Trans,

Veh. Technol.,vol. 47,pp.235-245,Feb.1998.

[14] H.Hashemi, M.McGuire,and D.Tholl,”Measurements and modeling of temporal

variation of indoor radio propagation channel.”IEEE Trans.Veh.

Technol.,vol.43,pp 733-737,Aug.1994.

Note: All MATLAB codes used for the simulation in this projects are included in a CD with each copy.

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