Journal of Engineering and Applied Sciences 15 (2): 444-451, 2020ISSN: 1816-949X© Medwell Journals, 2020

Fading Characteristics over Wireless Channels

Siriaksorn JakborvornphanDepartment of Engineering, Thai-Nichi Institute of Technology, 1771/1 Pattanakarn Road,

Suan Luang, 10250 Bangkok, Thailand

Abstract: Multipath fading is phenomena that may cause attenuation and distortion to the transmitted signal.The signal transmitted may be diffracted, refracted or reflected over a spread of times from obstacles such asground, hills, building that are located in the transmission path between the transmitter and receiver sides.Multipath fading, therefore, needs to be taken into consideration when designing wireless radio communicationsystems. This study presents the key characteristics and simulation modelling for various types of fadingchannels in the wireless transmission system. Besides, an effort has been made to illustrate the performancecomparison of different types of small-scale fading that are subjected to due to multipath delay spread in timeand a movement of mobility. The simulations of small-scale fading over the wireless channel that are dependenton Doppler spread and delay spread were determined using communication toolbox in MATLAB.

Key words: Mobile radio propagation, small-scale fading, multipath delay spread, frequency selective fading,fast fading, communication

INTRODUCTION

Wireless propagation can be served in distinctsize of service areas. The focuses here in this study are onthe propagation of transmitted signal over the wirelessradio channel through different types of fading. Thepropagation over open areas that are free from obstaclesis the simplest model to treat. On the other hand, thepropagation in urban areas is quite complex because thereare a number of obstacles on the way of transmission. Asignal propagating through a mobile radio channeldepends on the nature of the transmitted signal withrespect to the characteristics of the channel (Sklar, 2001). Also, a Line-of-Sight (LOS) transmission path betweenthe transmitter and the receiver is rarely found over thewireless communication systems. The propagationconditions over the wireless link are in general difficult tocharacterise because electromagnetic waves generated ateither ends will encounter obstacles during transmission.Due to reflection, diffraction and scattering from variousobstacle objects, the signal can take many different pathsfrom transmitter to receiver. The transmitted signal oftenreaches the receiver by more than one path, resulting inthe phenomenon known as multipath fading. The receivedsignals compose of signals from indirect paths and adirect path (if exists) at the receiver to give a distortedtransmitted signal. As a mobile terminal moves, signalamplitude will fluctuate randomly and the interactionbetween the electromagnetic waves results in a so-calledmultipath fading of signal.

The rate of fading is related to the relative speed ofthe mobile with respect to the base station and wavelengthof the signal that is being transmitted. This means that the

strengths of the signal decrease with the distance betweenthe transmitter and receiver. One of the difficulties inwireless propagation is maintaining good communicationssince, the field pattern of the transmitting signals aredisturbed and thereby diminishing the received signal fora long period of time (Rappaport, 2002).

Mobile radio propagations: As a mobile terminal movesaway from the transmitter over much larger distances, thelocal average received signal will gradually decrease. Themean signal strength for an arbitrary TransmissionReception (T-R) separation distance is predicted byslower large-scale propagation models. There arebasically two major types of fading in the wirelesscommunication systems, namely, small-scale andlarge-scale fading. The two models are useful inestimating the coverage area of a transmission over largeT-R separation distance (typically on the order ofhundreds of kilometres).

The rapid fluctuations of the received signal strengthover very short distances (a few wavelength) or shortduration of time (on the order of seconds) can becharacterised by small-scale fading model. The receivedsignal power is a sum of many contributions coming fromdifferent directions. On the other hand, large-scale fadingrepresents the average signal power attenuation over largeareas caused by terrain contours such as hills, forests orbuilding, located in the transmission path between thetransmitter and the receiver. Large-scale fading caused bypath loss and shadowing provides a way of estimating thepath loss as a function of propagation distance(Goldsmith, 2005).

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Small-scale fading

Time delay spreadcaused by multipath

Doppler spreadcaused by mobiilty

Flatfading

Fastfading

Frequencyselectivefading

Slowfading

Fig. 1: Types of small-scale fading

MATERIALS AND METHODS

Small-scale fading: Multipath in the radio channelcreates small-scale fading effects. The three mostimportant effects in small-scale multipath propagation arefading, random frequency modulation and timedispersion. The mobile receives the signals from differentdirections, paths with different propagation delays. Eachof the multipath components have randomly distributedamplitudes, phases and angles of arrival. They arecombined at the receiver antenna and cause the signalreceived by the mobile to be distorted.

A radio wave propagation can be dispersed either intime or in frequency domain for any mobile radio channel.A small-scale fading leads to four distinct effects, asshown in Fig. 1. Fading effects due to multipath timedelay spread leads to “time dispersion” and “frequencyselective fading” whereas Doppler spread leads to“frequency dispersion” and “time selective fading”. Timedispersion due to multipath causes the transmitted signalto undergo either flat fading or frequency selective fading.On the other hand, a channel may be classified either asa fast fading or slow fading channels, depending on howrapidly the transmitted baseband signal changes ascompared to the rate of change of the channel(Molisch, 2011).

Types of small-scale fadingFrequency selective fading: If the channel possesses aconstant gain and linear phase response over a bandwidththat is smaller than the bandwidth of the transmittedsignal, then the channel creates frequency selective fadingon the received signal. The spectrum s(f) of thetransmitted signal has a bandwidth which is greater thanthe coherence bandwidth BC of the channel in frequencyselective fading. Frequency selective fading is caused bymultipath delays which approach or exceed the symbolperiod of the transmitted symbol. A multipath delayspread (στ) is greater than the reciprocal bandwidth of thetransmitted signal (TS). A common rule of thumb is thata channel is frequency selective if TS#10στ.

The received signal is distorted because multipleversions of the transmitted waveform are attenuated

(faded) and delayed in time. Frequency selective fading isdue to time dispersion and hence induces the Inter SymbolInterference (ISI). Frequency selective fading channelsare known as “wideband channels” since, the bandwidthof the signal is wider than the bandwidth of thechannel impulse response (Rappaport, 2002). A signal isconsidered to be frequency selective fading if:

C Bs>Bc

C TS<στC Inter Symbol Interference (ISI) and irreducible BER

Flat fading: If a mobile radio channel has a constant gainand linear phase response over a bandwidth is greaterthan the bandwidth of the transmitted signal, then thereceived signal will undergo flat fading. The spectrumcharacteristics of the transmitted signal are preserved atthe receiver. The strength of the received signal changeswith time due to fluctuation in the gain caused bymultipath. The reciprocal bandwidth of the transmittedsignal (TS) is much greater than the multipath time delayspread of the channel (στ). Flat fading channels are knownas “amplitude varying channels” or “narrowbandchannels” because the bandwidth of applied signal isnarrower than the channel flat fading bandwidth (Molisch,2005). A signal is considered to be flat fading if:

C Bs<Bc

C TS>στC Signal fits easily within the bandwidth of the channelC Loss in SNR

Slow fading: The channel impulse response changes at arate much slower than the transmitted baseband signal.The rate of change of the channel characteristics is muchsmaller than the rate of change of the transmitted signal.The doppler spread of the channel BD is much less thanthe bandwidth of the baseband signal BS. A signal isconsidered to be slow fading if:

C TS<Tc

C BS>Bd

C Low doppler spread and loss in SNR

Fast fading: The channel impulse response changesrapidly with the symbol duration. Fast fading deals withthe rate of change of the channel due to motion. The rateof change of the channel characteristics is larger than therate of change of the transmitted signal. The channelchanges during a symbol period because of receivermotion. The coherent Time of the channel (Tc) is smallerthan the symbol period of the Transmitted signal (Ts)causing “frequency dispersion” or “time selective fading”due to doppler spreading which leads to signal distortion.The effects of small-scale fading due to multipath delayspread in time and frequency domains are summarisedclearly in Fig. 2.

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Flat fading Frequencyselective fading

Fast fading Slow fading

B <<BS C

S<<TB>>BC

S>>T

B <<BS D

C ST <<TB <<BS D

C ST >>T

C High Doppler spread Channel variations faster thanC

baseband signal variations

C Low Doppler spread Channel variations slower thanC

baseband signal variations

Doppler spreadfrequency dispression

B = f is doppler spread/shiftD m

B is signal bandwidthS

B is coherence bandwidthS

T is reciprocal bandwidth of the transmitted signal (symbol period)S

is delay spread

Multipath delay spreadtime disprersion

Fig. 2: Condition of small-scale fading for multipath delay spread in time and frequency domains

A signal is considered to be fast fading if:

C Ts>Tc

C Bs<Bd

C High Doppler spread and irreducible in BER

RESULTS AND DISCUSSION

Parameters settingRMS delay spread: The RMS delay spread is the squareroot of the second central moment of the power delayprofile and is defined as:

(1) 22

where, the mean excess delay or the first moment of thepower delay profile is given by:

(2)

2k k k k

k k2k k

k k

a P( )

a P( )

and the second central moment of the power delay profileis defined as:

(3)

2 2 2k k k k

2 k k2k k

k k

a P( )

a P( )

These delays are measured relative to the firstdetectable signal arriving at the receiver at the value of

τ0 = 0. Typical values of RMS delay spread I Table 1 areon the order of microseconds (µsec) in outdoor mobileradio channels and on the order of nanoseconds (nsec) inindoor radio channels.

Coherent bandwidth: Coherent bandwidth is derivedfrom the RMS delay spread. It occurred because of anatural phenomenon caused by reflected and scatteredpropagation paths in the radio channel. Also, it is possibleto obtain an equivalent description of the channel in thefrequency domain using its frequency responsecharacteristics. If the delay spread parameters is used tocharacterise in the time domain, then coherencebandwidth is used to characterise the channel in thefrequency domain. Coherent Bandwidth (Bc) is astatistical measure of the range of frequencies over whichthe channel can be considered “flat”.

The RMS delay spread and coherence bandwidth areinversely proportional to one another. If the coherentbandwidth is defined as the bandwidth over which thefrequency correlation function is above 0.9, then thecoherent bandwidth is approximately equivalent to:

(4)C

1B

50

If the frequency correlation function is above0.5, then the coherent bandwidth is approximatelyequivalent to:

(5)C

1B

5

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Random integer BPSK Rayleigh fading

Random integergenerator

BPSKmodulatorbaseband

Multipath Rayleighfading channel

Table 1: Typical measured values of RMS delay spread (Rappaport, 2002)Environment Frequency (MHz) RMS delay spread (σt) NotesUrban 910 1300 nsec average 600 ns SD 3500 ns max New York CityUrban 892 10-25 μsec Worst case San FranciscoSuburban 910 200-310 nsec Averaged typical caseSuburban 910 1960-2110 nsec Averaged extreme caseIndoor 1500 10-50 nsec 25 nsec median Office buildingIndoor 850 270 nsec max Office building.Indoor 1900 70-94 nsec average 1470 nsec max Three San Francisco buildings

Table 2: Calculations for different types of fadingType of fading No. of paths Symbol period (Ts) (sec) Signal bandwidth (Bs) (Hz) RMS delay spread (στ) Coherence bandwidth (Be)Frequency 4 0.0001 10000 0 msec 0 HzSelective 0.2 msec 5 kHzFading 0.3 msec 333 Hz

0.4 msec 250 HzFlat fading 4 0.1 10 0 msec 0 Hz

0.2 msec 5 kHz0.3 msec 333 Hz0.4 msec 250 Hz

Slow fading 4 0.001 1000 2 sec 0.5 HzFast fading 4 0.001 1000 0.01 sec 100 Hz

Doppler spread: Doppler spread (Bd) is a measure of thespectral broadening caused by the time rate of change ofthe mobile radio channel. It is defined as the range offrequencies over which the received Doppler spectrum isessentially, non-zero and is defined as:

(6)cD m

vfvB f

c

where, fm is the maximum Doppler shift and is given by:

m

vf

Coherent time: Coherence Time (Tc) is the time domaindual of Doppler spread and is used to characterise thetime varying nature of frequency in the time domain. It isa statistically measure of the time duration over which thechannel response is invariant and quantifies the similarityof the channel response at different times. The Dopplerspread and coherence time are inversely proportional toone another and is expressed as:

(7)Cm

1T

f

Calculations and simulation resultsSimulation set up: A simple model was constructedusing a Simulink in MATLAB in order to generate dataSource, Binary PSK (BPSK) modulator and fadingchannel blocks. We use a random integer generator fromthe communications blockset, BPSK modulator fromcommunications blockset/modulation and the multipathrayleigh fading channel from the communicationsblockset/channels libraries in order to perform bothfrequency selective and flat fading as shown in Fig. 3.

Fig. 3: Simulation setup model for fading channel

The path of the block for a random integer generatoris set as follow (Fig. 4 and 5):

C Communications blockset»comm sources»randomdata sources»random integer generator

The path of the block for multipath Rayleigh fadingchannel is set as follow (Fig. 6 and 7):

C Communications blockset»channels»multipathRayleigh fading channel

Calculations: For a signal propagating over a wirelesschannel, symbol duration, system bandwidth, samplingperiod and the channel characteristics such as Dopplerspread, RMS delay spread, coherent bandwidth andcoherent time determine the type of fading that the signalcan experience. Table 2 indicates the lists of parametersused for the simulation of various types of fading.Frequency dispersion and time dispersion mechanism ina wireless communication channel have an influence onthe four different ways of small-scale fading dependingupon the channel characteristics, the velocity and thesignal parameters (Tang and Tang, 2005).

Simulation results: The channel impulse response forfrequency selective fading and flat fading are shown inFig. 8a and 9a, respectively. It can be seen that thechannel impulse response changed greatly compared tothe flat fading. A multipath delay spread and different

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Fig. 4: Sampling period for flat fading (Ts = 0.1sec)

Fig. 5: Sampling period for frequency selective fading(Ts = 0.0001sec)

frequency components can be easily seen in the case offrequency selective fading. As a result, the received signalis attenuated and distorted. Moreover, the frequencyresponses shown in Fig. 8b and 9b show that frequencyselective fading is worse than that of the flat fading.Therefore, an equalisation technique needs to beintroduced in the process in order to compensate for theunwanted signal.

Fig. 6: Maximum Doppler spread for slow fading (0.5Hz)

Fig. 7: Maximum Doppler spread for fast fading (100 Hz)

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Fig. 8 (a-b): (a) Impulse response and (b) Frequency response of frequency selective fading

Fig. 9 (a, b): Continue

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Fig. 9 (a, b): (a) Impulse response and (b) Frequency response of flat fading

Fig. 10: Multipath fading components of slow fading for four different paths

Fig. 11: Multipath fading components of fast fading for four different paths

The multipath fading curves for slow fading and fastfading channels are shown in Fig. 10 and 11, respectively.

It is clearly seen from the figures that the signal strengthchanges slowly over a period of time in that of the slow

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fading. This is because of a higher Doppler spread. Thechannel variations move faster than baseband signalvariations. In contrast, the channel impulse responsechanges at a rate much faster that the slow fading over theperiod of time. The reason for this is because the rate ofchange of the channel characteristics is much smaller thanthe rate of change of the transmitted signal.

CONCLUSION

Multipath fading is seen to be an issue in manyinstances since the transmitted signals can take multiplepaths to travel and as a result the received signal strengthsat the receiving end decreases. In this study, we havecharacterised several factors that contribute to small-scalefading models in wireless communication channels. Thecomparative study of small-scale fading was doneunder various channel fading conditions. Two majormanifestations (dispersion and fading rapidity) ofsmall-scale fading were studied in this work. Therespective channel impulse responses were studied andcompared between frequency selective fading and flatfading conditions. All the simulations of small-scalefading channels are based on BPSK modulation formatand were performed in MATLAB. We found that thesimulation results revealed a close agreement to thetheoretical frameworks. The fading caused by high speedof movement of the mobility shows much greaterdistortion of the received signal than the slow fading. The

impulse responses obtained showed that the differentfrequency components affected differently in that of afrequency selective fading.

ACKNOWLEDGEMENT

The researcher wishes to express her sincere thanksto the Department of Engineering, Thai-Nichi Institute ofTechnology for providing the MATLAB program toperform this study.

REFERENCES

Goldsmith, A., 2005. Wireless Communications.Cambridge University Press, Cambridge, UK.,ISBN-13:978-0-511-13315-2, Pages: 644.

Molisch, A.F., 2011. Wireless Communications. 2ndEdn., John Wiley & Sons Ltd, Chichester, England,UK., ISBN:9780470741870, Pages: 884.

Rappaport, T.S., 2002. Wireless Communications:Principles and Practice. 2nd Edn., Prentice Hall,Upper Saddle River, New Jersey, USA.,ISBN-13:978-0130422323, Pages: 736.

Sklar, B., 2001. Digital Communications: Fundamentalsand Applications. 2nd Edn., Prentice Hall, UpperSaddle River, New Jersey, USA., Pages: 1079.

Tang, K.W. and W.K.S. Tang, 2005. A chaos-basedsecure voice communication system. Proceedings ofthe 2005 IEEE International Conference on IndustrialTechnology, December 14-17, 2005, IEEE, HongKong, China, pp: 571-576.

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