440.306 Kommunikationssysteme, Labor440.430 Advanced Telecommunications

Laboratory

Handout for lab session“Fading Channels”

Author: Katharina Hausmair

Supervisor: Dr. Klaus Witrisal

Graz University of Technology

Signal Processing and Speech Communication Lab

Inffeldgasse 12, 8010 Graz, Austria

http://www.spsc.tugraz.at - witrisal@tugraz.at

c©Graz University of Technology

June 8, 2008

Fading Channels

Contents

1 Introduction 3

2 Radio Propagation Mechanisms 4

3 The Mobile Multipath Channel 63.1 Physical Factors for Small-Scale Fading . . . . . . . . . . . . . . . . . . . . . . . 63.2 Channel Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.2.1 Impulse Response and Power Delay Profile . . . . . . . . . . . . . . . . . 73.2.2 Channel Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.3 Types of Small-Scale Fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.4 Stochastic description of Small-Scale Fading . . . . . . . . . . . . . . . . . . . . . 12

3.4.1 Rayleigh Fading Distribution . . . . . . . . . . . . . . . . . . . . . . . . . 123.4.2 Rice Fading Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4 Simulation of Transmission in a Multipath Environment using MATLAB 144.1 Channel Response Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144.2 Project Implementation in MATLAB . . . . . . . . . . . . . . . . . . . . . . . . . 14

4.2.1 Pulse Transmission Simulation . . . . . . . . . . . . . . . . . . . . . . . . 144.2.2 Signal Transmission Simulation . . . . . . . . . . . . . . . . . . . . . . . . 17

4.3 Simulation Results and Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

References 18

2

Fading Channels

1 Introduction

Among other physical challenges like spectrum and energy limitations or user mobility the mobileradio channel is a fundamental limiting factor for the performance of wireless communicationsystems.

In a wired system, where the medium is stable and has well-defined and time invariant prop-erties, the transmission channel is stationary and predictable. The signal in a wireless system onthe other hand can reach the receiver either over a simple line-of-sight connection or it can bereflected or diffracted by objects in the environment and reach the receiver over a non-line-of-sight path. As a consequence of this so-called multipath propagation the radio channel is veryrandom and predicting its parameters such as received power is very difficult and mostly doneby means of statistics [Rappaport, 2002], [Molisch, 2005].

The effects of multipath propagation cause a lot of problems in radio systems. The differentpropagation paths of a signal may vary in length and so the signals arriving over different pathswill reach the receiver at different times, from different directions with distinct phases and ampli-tudes. A simple receiver cannot distinguish between the different multipath components and soit adds them up. Depending on the phases of the multipath components the interference can beeither destructive or constructive. This effect is called fading [Molisch, 2005]. If receiver, trans-mitter or the obstacles are moving, interference and fading change with time [Rappaport, 2002].For example at a 2GHz carrier frequency a movement by less than 10cm can already effect achange from constructive to destructive interference [Molisch, 2005].

Figure 1: Multipath fading [Molisch, 2005].

The rapid fluctuations of the received signal strength over very short travel distances (lessthan wavelengths) are called small-scale fading. The changing of the mean signal strength overlarge distances is called large-scale fading. For an illustration of small-scale fading comparedto large-scale fading see Figure 2. The figure shows that the signal changes rapidly when thereceiver moves only small distances while the signal average changes only slowly with distance.

Propagation models that estimate the large-scale path loss try to predict the average receivedsignal strength at a certain distance and may therefore be useful for establishing the coveragearea of a transmitter. This article, however, concentrates on the small-scale effects of multipathpropagation, since this is the topic of the practical part of the project. The first two, theoretical,chapters therefore mainly concentrate on the description of the mobile radio channel and small-

3

Fading Channels

scale fading. The basic mechanisms of radio propagation are explained as well. In the thirdchapter, the practical part of the project is presented.

Figure 2: Small-scale and large-scale fading.

2 Radio Propagation Mechanisms

As already mentioned above, a signal can reach a receiver not only via the direct path. Radiowaves can be reflected, diffracted or scattered by obstacles on their way to the receiver. Thesemechanisms, which lead to multipath propagation, are shortly demonstrated in this chapter.

Free Space Loss When a signal is sent from a transmitting antenna to a receiving antennavia the direct line-of-sight path in free space, the received signal strength as a function of thedistance between transmitter and receiver, is predicted by the Friis free space equation (Friis’law),

PRX (d) =PTXGTXGRXλ

2

(4π)2 d2L

where d is the distance between transmitter and receiver in meters, PRX (d) is the received powerin watts, PTX is the transmitted power in watts, GTX is the transmitter antenna gain, GRXis the receiver antenna gain, λ is the wavelength in meters and L is the system loss factor notrelated to propagation (L ≥ 1) [Rappaport, 2002]. The system loss factor indicates losses dueto transmission line losses, filter losses and antenna losses.

Friis’ law shows that the received power falls off as the square of the distance between trans-mitter and receiver and also depends on the frequency.

Note that the Friis free space equation is restricted to the far field of the antenna.

Reflection and Transmission When a radio wave hits a perfectly dielectric object, a part of itsenergy will pass through the object (transmission or refraction, important for wave propagationinside buildings) and the other part of the energy will be reflected (see Figure 3). If the objectis a perfect conductor, all energy of the incident wave will be reflected, since electromagneticenergy cannot pass through [Rappaport, 2002].

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Fading Channels

Figure 3: Reflection and transmission from dielectrics.

Diffraction Diffraction refers to the bending of waves when they are obstructed by objectswith sharp irregularities (edges). This effect enables the bended secondary waves to propagateeven behind obstacles and thus reach a receiver even when no line-of-sight connection to thetransmitter exists (Figure 4). It also allows waves to propagate around the curved surface ofthe earth. Diffraction, like reflection, at high frequencies depends on the geometry of the object(size of the object compared to the wavelength), amplitude, phase and polarization of the wave[Rappaport, 2002].

Figure 4: Diffraction enables waves to propagate to a shadowed region.

Scattering When waves travel through or impinge onto a medium that consists of structuresthat are small compared to the wavelength, they get scattered [Rappaport, 2002]. Scatteringobjects, for example, can be street signs, street lamps, bookshelves or other objects that areusually not included in maps and building plans [Molisch, 2005]. Such rough surfaces scatterthe wave energy in all directions (Figure 5).

Figure 5: Scattering by a rough surface [Molisch, 2005].

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Fading Channels

3 The Mobile Multipath Channel

In a mobile radio channel small-scale fading is induced by the interference of one or more versionsof a signal, so-called multipath components, which arrive at the receiver at slightly differenttimes. The combination of these components results in a signal that can vary strongly in phaseand amplitude. The rapid changing of the signal strength, random frequency modulation due tothe Doppler shifts of different multipath components and time dispersion are the most importanteffects of small-scale multipath propagation [Rappaport, 2002].

3.1 Physical Factors for Small-Scale Fading

Multipath Propagation Especially in urban areas the received signal consists of a multitude ofmultipath components with random phases, amplitudes and angles of arrival that cause small-scale fading. A moving receiver can pass through different multipath scenarios (constructive ordestructive) in a small period of time. Even if the receiver and the mobile station stay put,moving objects like cars can cause variations in the received signal. As multipath propagationcan lengthen the time for the signal to reach the receiver, it can cause signal smearing due tointersymbol interference [Rappaport, 2002].

Speed of Mobile The relative motion between the base station and a mobile receiver resultsin random frequency modulation due to different Doppler shifts on each of the multipath com-ponents [Rappaport, 2002].

Consider the mobile in Figure 6, moving from A to B at a constant velocity ν while receivingsignals from a far away source S. Since the source is far away, θ is approximately the same at Aand B. The difference of path lengths for signals traveling to A and B is ∆l = d cos θ = ν∆t cos θ,where ∆t is the time required for the mobile to travel from A to B. Because of the difference inpath lengths the phase change in the received signal is

∆φ =2π∆lλ

=2πν∆tλ

cos θ

and the change in frequency, the Doppler shift, is given by

fd =1

2π∆φ∆t

=ν

λcos θ

If the mobile is moving towards the source the Doppler shift is positive, otherwise it is negative[Rappaport, 2002].

Speed of Surrounding Objects Moving objects in the radio channel induce time varyingDoppler shifts on multipath components. Fading induced by moving objects only needs tobe considered if the objects move at a greater rate than the mobile [Rappaport, 2002].

Transmission Bandwidth of the Signal The channel coherence bandwidth indicates the fre-quency range over which the channel can be considered flat. For signals with a narrow bandwidthcompared to the channel coherence bandwidth the signal amplitude will fade rapidly, but thesignal will not be distorted in time (see Figure 9). Signals with greater bandwidths than themultipath channel bandwidth will be distorted, but the received signal strength will fade lessover a local area (see Figures 11 and 10)(see also Capter 3.3).

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Fading Channels

Figure 6: Doppler effect [Rappaport, 2002].

3.2 Channel Description

3.2.1 Impulse Response and Power Delay Profile

The properties of a multipath channel can be modelled by its impulse response, as the impulseresponse contains all the necessary information for analyzing and simulating any type of radiotransmission through the channel. The different propagation delays of the multipath componentschange with moving to another spatial location. Therefore the impulse response of a multipathchannel may be modelled as h(t, τ) where t represents the time variations due to motion andτ represents the channel multipath delay for a fixed value of t [Rappaport, 2002]. The receivedsignal y(t) can be expressed by the convolution of the transmitted signal x(t) and the channelimpulse response h(t, τ)

y(t) = x(t) ∗ h(t, τ)

Assuming the channel to be a bandlimited bandpass channel, h(t, τ) can be equivalently de-scribed by a complex baseband impulse response hb(t, τ) so that

r(t) = c(t) ∗ 12hb(t, τ)

where c(t) and r(t) are the complex envelopes of x(t) and y(t)[Rappaport, 2002]

x(t) = Re{c(t)ej2πfct

}y(t) = Re

{r(t)ej2πfct

}To obtain a discrete-time impulse response model, the multipath delay axis τ is discretized intoequal segments, called excess delay bins, where τ0 is equal to 0, representing the first arrivingsignal, and τi = i∆τ for i = 0 to N − 1. The bin width ∆τ has to be chosen according tothe sampling theorem, considering the bandwidth of the transmitted signal. Any multipathcomponent received in the ith bin will then be represented by one single multipath componentat excess delay τi. Figure 7 gives an example of such a time varying discrete-time impulseresponse model. The last multipath component arrives with excess delay N∆τ . The timevarying discrete-time impulse response can then be expressed as

hb(t, τ) =N−1∑i=0

ai(t)ejθi(t)δ(τ − i∆τ)

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Fading Channels

where ai(t), i∆τ and θi(t) represent real amplitude, excess delay and phase term of the ithmultipath component [Rappaport, 2002].

Figure 7: Time Varying Discrete-Time Impulse Response [Rappaport, 2002].

For measuring the impulse response of the channel a probing pulse, which approximatesthe delta function is used as transmitted signal. After obtaining the impulse response, theinstantaneous multipath power delay profile for a specific location (time t0) |hb(t0; τ)|2 can bedetermined. The power delay profile P (τ) of the channel can be found by taking the spatialaverage of |hb(t0; τ)|2 over a local area.

P (τ) ≈ k |hb(t0; τ)|2

The gain k relates the transmitted power to the total received power.To determine the received power at a time t0 the power |r(t0)|2 is measured. For the probing

pulse, the value for |r(t0)|2 is found by summing up the multipath powers resolved in the instanta-neous multipath power delay profile |hb(t0; τ)|2, and is equal to the energy received over the timeduration of the multipath delay divided by the maximum excess delay τmax [Rappaport, 2002].For an example of a power delay profile see Figure 8.

|r(t0)|2 =N−1∑k=0

a2k(t0; τ)

By performing the Fourier transform the impulse response model can of course be transferredinto an equivalent model in the frequency domain. The Fourier transform of the impulse responseh(t, τ) with respect to the variable τ results in the time variant frequency response H(t, f). Thereceived frequency domain signal Y (f) may then be obtained by multiplication of the transmittedsignal X(f) and H(t, f) [Molisch, 2005].

This frequency domain interpretation suggests that the channel frequency response can bemeasured by sweeping a sine wave signal over a frequency range of interest and measuring theamplitude and phase gain of the channel. Indeed, this is an alternative way to measure radiochannels, which can be performed using a vector network analyzer. Compared with the pulse-based channel sounding method described above, the frequency domain technique has the greatadvantage that much more power can be transmitted in a continuous sine wave signal than witha short pulse signal. Hence it is often prefered in practice (cf. Section 4.1).

3.2.2 Channel Parameters

Time Dispersion Parameters The effect, that the duration of the received signal is greaterthan the duration of the transmitted signal because of multipath is called time dispersion. In

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Fading Channels

the frequency domain this leads to frequency selective fading (see Figure 11). Mean excess delayτ , rms delay spread στ and excess delay spread τX can be derived from the power delay profileP (τ). The mean excess delay is the first moment of the power delay profile.

τ =

∑k

P (τk)τk∑k

P (τk)

The rms delay spread is defined as the second central moment of the power delay profile.

στ =√τ2 − τ2

where

τ2 =

∑k

P (τk)τ2k∑

k

P (τk)

The maximum excess delay or excess delay spread of the power delay profile is the timedelay during which the multipath energy falls to XdB below the maximum received multipathcomponent [Rappaport, 2002]. For an example of a power delay profile and the correspondingchannel parameters see Figure 8.

The values for the time dispersion parameters depend on the noise threshold that is chosen toprocess the power delay profile. The noise threshold defines the level for differentiating betweenmultipath components and thermal noise [Rappaport, 2002].

Figure 8: Power Delay Profile and Channel Parameters [Rappaport, 2002].

Coherence Bandwidth The coherence bandwidth Bc indicates the frequency range over whichthe channel frequency response can be considered flat. Frequency components which are sepa-rated by less than Bc pass the channel with equal gain and linear phase. If the frequency separa-tion is greater thanBc, the channel may affect the components quite differently [Rappaport, 2002].The coherence bandwidth is the corresponding frequency domain parameter for the rms delay

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Fading Channels

spread. It is defined as the frequency difference that is required so that the correlation coefficientof the channel gain (= frequency response) at two frequencies is smaller than a given value. Bctherefore depends on the chosen threshold for the correlation coefficient [Molisch, 2005]. If Bcfor example is the bandwidth over which the frequency correlation function is above 0.9, it canbe approximated by [Rappaport, 2002]

Bc ≈1

50στ

For a correlation function above 0.5, Bc is approximately

Bc ≈1

5στ

Doppler Spread and Coherence Time These parameters describe the time varying nature ofthe channel due to the relative motion between the mobile and the base station or movementof other objects in the channel. The Doppler spread Bd is a measure of the spectral broadeningof the received signal due to Doppler shifts. That means that the received signal bandwidthis greater than the bandwidth of the transmitted signal. This effect is also called frequencydispersion. Bd is the maximum Doppler shift and depends on the signal frequency fc and thevelocity ν of the mobile.

Bd =νfcc

where c is the speed of light [Rappaport, 2002].The coherence time Tc describes the effects of frequency dispersion in the time domain. Anal-

ogous to the coherence bandwidth it defines the time duration over which the channel impulseresponse can be considered time invariant [Rappaport, 2002]. If two arriving signals are sepa-rated by more than Tc they are affected differently by the channel. A popular rule of thumb forestimating the coherence time is [Rappaport, 2002]

Tc ≈0.423Bd

3.3 Types of Small-Scale Fading

The relation of the parameters of the transmitted signal, like bandwidth or symbol duration,and the channel parameters is determining as to which kind of fading the signal will suffer. Flatfading and frequency selective fading are induced by multipath time delay spread. Therefore thetransmitted signal bandwidth and the symbol period are determining as to whether the signalwill be distorted by the channel (frequency selective fading) or just delayed and attenuated(flat fading). Fast fading and slow fading are due to Doppler Spread. Note that fading due tomultipath delay spread and fading due to Doppler spread are independent from each other andtherefore a signal can undergo a combination of these two fading types.

Flat Fading in Narrowband Systems When a signal suffers from flat fading, the received signalamplitude will change with time but the spectrum will not. This is the case when the signalbandwidth is smaller than the channel coherence bandwidth and the symbol period of the signalis greater than the delay spread of the channel. The channel frequency response is flat over thewhole signal bandwidth [Rappaport, 2002]. In a flat fading channel the inverse of the signalbandwidth is much larger than the maximum excess delay. Signals that may be characterized

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Fading Channels

by this constraint are called narrowband [Molisch, 2005]. Figure 9 gives an example for flatfading in narrowband system with a signal bandwidth of 1MHz. The time domain graph clearlyshows that the received signal is not distorted, but its amplitude is only a thousandth part ofthe transmitted signal amplitude. It also shows that the symbol period is by far larger thanthe delay spread. The frequency domain view shows that the signal bandwidth is very smallcompared to the variations of the channel response and therefore the signal does not sufferfrom frequency selective fading. A comparison of Figure 9 with Figures 10 and 11 shows howincreasing the signal bandwidth influences the effects of the channel on the transmitted signal.

Frequency Selective Fading in Wideband Systems If the channel frequency response is notflat over the whole signal bandwidth, the signal will undergo frequency selective fading. Forthis type of fading the delay spread of the impulse response is greater than the inverse of thesignal bandwidth. As a consequence the received signal is stretched in time and the channelinduces intersymbol interference. Since the bandwidth of the transmitted signal is wider thanthe channel coherence bandwidth, signals that suffer from frequency selective fading are calledwideband [Rappaport, 2002].

Frequency selective fading can be seen in Figures 10 and 11. The frequency domain view inthese figures shows that the channel gain varies for different frequencies. In the time domainview it is obvious that the symbol period of the transmitted signal is small compared to theimpulse response delay spread and the received signal therefore is stretched in time.

All fading channel examples in Figures 9, 10 and 11 are created for the same channel andsignal center frequency. A comparison of the figures shows how changing the signal bandwidthinfluences the effects of the channel on the transmitted signal.

Figure 9: Flat Fading in a Narrowband System (Bandwidth = 1MHz).

Fast Fading and Slow Fading These two types of fading are due to Doppler spread. A channelis called fast fading if its characteristics change at a faster rate than the signal (within onesymbol period). The coherence time is smaller than the symbol period of the signal, thus thesignal is distorted because of frequency dispersion.

A channel is called slow fading if the changing rate of channel characteristics due to Doppler

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Fading Channels

Figure 10: Frequency Selective Fading in a Wideband System (Signal Bandwidth = 100MHz).

Figure 11: Frequency Selective Fading in a Wideband System (Signal Bandwidth = 1000MHz).

spread is slower than the signal rate. The Doppler spread in this case is less than the signalbandwidth [Rappaport, 2002].

3.4 Stochastic description of Small-Scale Fading

In realistic scenarios a radio channel usually consists of a large number of obstacles and movingreceivers. Therefore, a deterministic description of the channel is not efficient, in stead stochasticmethods are used to describe wireless communication channels.

3.4.1 Rayleigh Fading Distribution

The behaviour of most receivers is determined by the amplitude of the received signal. Whenanalyzing the channel, the distribution of the envelope of the received signal (magnitude of

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Fading Channels

the field strength phasor) has to be investigated. As the received phases vary strongly, theycan be approximated as uniformly distributed random variables. Thus the in-phase and thequadrature-phase component of the received fieldstrength are both the sum of many randomvariables. The pdf of such a sum is a Gaussian distribution [Molisch, 2005]. The distributionof complex numbers whose real and imaginary parts follow a Gaussian distribution obey aRayleigh distribution. Therefore the Rayleigh distribution can be used to describe the timevarying nature of the received envelope of a flat fading signal for scenarios where no dominantsignal component (LOS signal) is received. For these cases it is an excellent approximation[Molisch, 2005]. The probability density function of the received signal amplitude r is given bythe Rayleigh distribution

pdf(r) =

{rσ2 e

− r2

2σ2 0 ≤ r ≤ ∞0 r < 0

where σ2 is the time-average received power and σ is the rms value of the received voltage signal[Rappaport, 2002]. The mean value of the Rayleigh distribution is

r = σ

√π

2

the variance isσr = σ2

(2− π

2

)and the median value is given by [Molisch, 2005]

rmedian = σ√

2ln2

Figure 12: PDFs of a Rayleigh Distribution and Two Rice Distributions for Different Kr.

3.4.2 Rice Fading Distribution

In a scenario where a dominant non fading component (LOS connection) is present, the envelopedistribution changes into a Ricean distribution. The probability density function of the receivedsignal amplitude is given by the Rice distribution

pdf(r) =

rσ2 e

−(r2+A2)2σ2 I0

(Arσ2

)A > 0, r > 0

0 r < 0

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Fading Channels

where A denotes the peak amplitude of the dominant component and I0 is the modified Besselfunction of the first kind, zero order. The ratio of the power in the LOS component to the powerin the diffuse component is called the Rice factor Kr [Molisch, 2005]:

Kr =A2

2σ2

For a weak LOS component (small A) and therefore a small Rice factor Kr the Ricean distribu-tion becomes a Rayleigh distribution. For a strong LOS component the Rayleigh distributionapproximates a Gaussian distribution with a mean value A [Molisch, 2005].

4 Simulation of Transmission in a Multipath Environment usingMATLAB

The theory explained in the previous chapters is applied in the practical part of the projectthat will be introduced in this chapter. Based on multipath channel response measurements,the transmission of pulses of different bandwidths and center frequencies, chosen by the uservia a graphical user interface, is computed in both time and frequency domain. The results arevisualized in the GUI and there is also an option for saving the computed data. Furthermore thetransmission of different PAM and QPSK signals is simulated and then visualized in a GUI. Theproject is implemented in MATLAB, using GUIDE, the MATLAB development environmentfor graphical user interface, for the layout of the GUIs [MathWorks].

4.1 Channel Response Data

The implementation of the project application is based upon a subset of ultra wideband (UWB)channel measurements that were performed by IMST GmbH within the ”whyless.com” projectto determine the characteristics of an indoor UWB radio channel [IMST] [whyless.com]. Themeasurements were performed in the frequency domain, using a vector network analyzer toobtain the complex channel transfer functions [whyless.com]. For the measurement subset usedin this project the UWB data was taken for a frequency range from 1GHz to 11GHz with afrequency resolution of ∆f = 6.25MHz (N = 1601 frequency points). The measuring systemwas set up in an office of about 5m x 5m in size and 2.75m height (see Figure 13).

The data was measured for three different scenarios (LOS, NLOS and transition between LOSand NLOS conditions). In each scenario the receiver antenna was placed in a fixed position at1.5m height and the transmitter antenna was moved along 30 parallel tracks at 1.5m height,spaced 1cm apart, in 150 steps of 1cm which makes a total of 4500 transfer functions for each ofthe three scenarios. Each transfer function represents a time-invariant channel response H(f)and the combined 4500 transfer functions of one scenario measurement can be considered as thetime-varying channel transfer function H(t, f). For the NLOS and the transition between LOSand NLOS scenarios a metal cabinet of size 1.78m x 0.42m x 1.96m obstructs the direct pathbetween transmitter and receiver (see Figure 14) [Kunisch and Pamp, 2002]. The data is storedin .mat-files for further processing.

4.2 Project Implementation in MATLAB

4.2.1 Pulse Transmission Simulation

The layout of the GUI for the simulation of pulse transmission is shown in Figure 15. The usercan pick one of the three scenarios (LOS, NLOS, or (N)LOS which stands for the scenario with

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Fading Channels

Figure 13: Measurment Environment [whyless.com].

Figure 14: Measurement Setup [whyless.com].

transition between LOS and NLOS) and a specific transmitter position in the 150cm x 30cmgrid. The transmitted signal bandwidth and center frequency can also be chosen by the userwithin the predetermined limits of 0.1MHz to 10000MHz for the bandwidth and 1000MHz to11000MHz for the center frequency. According to the user’s choice the simulation of a raised-cosine pulse transmission is computed every time the user changes the specifications. The results(channel response, transmitted and received pulse) are plotted in the GUI, in the (delay) timeand the frequency domain.

For the simulation computation at first the channel frequency response which is specified bythe user’s choice of scenario and transmitter position has to be loaded from the .mat file. Toachieve a representation where the LOS multipath component arrives at an excess delay timeequal to zero the delay of the direct path is compensated by

Hc(f) = H(f)ej2πftd

whereH(f) is the channel frequency response, Hc(f) is the corrected channel frequency response,

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Fading Channels

Figure 15: GUI for Pulse Transmission Simulation.

f is the frequency and td is the delay given by

td =d

c

where d is the distance between transmitter and receiver and c is the speed of light. By applyingthe inverse Fourier transform on the channel frequency response Hc(f), the impulse response iscomputed.

The raised-cosine pulse x(t) is defined by the user’s choice of the total required bandwidthand is computed by

x(t) = sinc(BN t)cos(πBNβt)

1− (2BNβt)2

where t is the time, β is the roll-off factor, and BN is the −6 dB bandwidth of the raised-cosinespectrum (Nyquist minimum bandwidth) given by

BN =B

1 + β

where B is the total required bandwidth [Proakis and Salehi, 2004].For the computation of the received pulse, the raised-cosine pulse is transferred into frequency

domain by the Fourier transform and shifted to the desired center frequency. The received pulseis obtained via multiplication of the transmitted pulse and the channel frequency response. Thetime domain version of the received pulse is computed with the inverse Fourier transform.

The simulation results are handed back to the GUI where they are plotted. For a betterpresentation some additional plot options are provided. All plots can be viewed in linear orlogarithmic scale, with or without zoom. When using the zoom option in time domain the

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Fading Channels

sampled received and transmitted pulses are shown additionally. For the time domain viewmagnitude or real/imaginary part representation can be selected.

For further processing it is possible to save the sampled received pulse data of one or moretransmitter positions to a .mat-file. The saving options (transmitter positions and time interval)can be selected in an extra window (Figure 16).

Figure 16: GUI for Saving Option.

4.2.2 Signal Transmission Simulation

The layout of the GUI for the simulation of signal transmission is shown in Figure 17.Similar to the pulse transmission GUI the user can choose transmitter position, scenario,

signal bandwidth and center frequency. The user can also decide between PAM and QPSKmodulation and it is possible to select the number of symbols that will be transmitted.

Figure 17: GUI for Signal Transmission Simulation.

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Fading Channels

According to the description in Chapter 4.2.1 the channel response data is loaded, corrected forLOS delay, and if necessary interpolated. Also the transmitted and received pulse are computedsimilarly. To obtain the received signal the time domain received pulse is convolved with asymbol sequence. For PAM the sequence consists of the randomly chosen values 1 and -1. ForQPSK a random sequence of 1, -1, j and -j is created.

The transmitted and the received signal and their sample values are plotted in the GUI in timedomain. Both plots can be viewed in either magnitude or real/imaginary part representation

4.3 Simulation Results and Theory

To compare the results of the transmission simulation with the theory explained in Chapter 3 afew examples are presented. The examples are all taken from the pulse transmission simulationbecause it provides not only time domain, but also frequency domain plots and therefore offersbetter options for discussion.

Impulse Response and Power Delay Profile Since the difference of the impulse responses ofthe three scenarios can be observed best when comparing the LOS and the NLOS scenario,examples of these two are shown in Figure 18. While in the LOS scenario the first and strongestmultipath component, namely the direct path component, arrives at time zero, in the NLOSscenario the first multipath component takes more time to arrive at the receiver and it also byfar isn’t the strongest component. The same can be observed when comparing the power delayprofiles computed from the complete LOS and NLOS measurement data in Figure 19.

Figure 18: LOS and NLOS Impulse Responses.

References

[IMST] IMST GmbH, Carl-Friedrich-Gau-Str. 2, 47475 Kamp-Lintfort,Germany, http://www.imst.com

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Fading Channels

Figure 19: LOS and NLOS Power Delay Profiles.

[Kunisch and Pamp, 2002] J. Kunisch and J. Pamp, ”Measurement results and modeling as-pects for the UWB radio channel”, in Proc. UWBST 2002, Balti-more, 2002.

[MathWorks] The MathWorks Headquarters, 3 Apple Hill Drive, Natick, MA01760-2098, USA, http://www.mathworks.com

[Molisch, 2005] Andreas F. Molisch, ”Wireless Communications”, John Wiley &Sons Ltd, 2005.

[Proakis and Salehi, 2004] John G. Proakis and Masoud Salehi, ”Grundlagen der Kommu-nikationstechnik”, 2. Auflage, Pearson Studium, 2004.

[Rappaport, 2002] Theodore S. Rappaport, ”Wireless Communications - Principlesand Practice”, Second Edition, Prentice Hall PTR, 2002.

[whyless.com] ”whyless.com the open mobile access network”, IST-2000-25197,http://www.whyless.org.

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