Presented By :Presented By :Er. Rajesh KumarEr. Rajesh KumarINDIAINDIA
FADINGFADING““This is about the phenomenon ofThis is about the phenomenon ofloss of signal in telecommunicationsloss of si...
INDEXINDEXSMALL SCALE FADINGSMALL SCALE FADING1.1. Small scale multipath propagationSmall scale multipath propagation2.2. ...
FADINGFADINGSelective fading causes a cloudy pattern to appear onSelective fading causes a cloudy pattern to appear onanan...
 FadingFading refers to the time variation of therefers to the time variation of thereceived signal power caused by chang...
EXAMPLEEXAMPLE For example, consider the common experience ofFor example, consider the common experience ofstopping at tr...
FADING IN WIRELESS COMMUNICATIONSFADING IN WIRELESS COMMUNICATIONS In wireless communications, signal fading isIn wireles...
SMALL SCALE MULTIPATH PROPAGATIONSMALL SCALE MULTIPATH PROPAGATION Multipath in the radio channel creates smallMultipath ...
FACTORS INFLUENCING SMALL SCALE FADINGFACTORS INFLUENCING SMALL SCALE FADINGMany physical factors in the radio propagation...
(3) Speed of surrounding objects :If objects in the radio channel are in motion, they induced a timevarying Doppler Shift ...
DOPPLER SHIFTDOPPLER SHIFT
 Consider a mobile moving at aConsider a mobile moving at aconstant velocityconstant velocity vv, along a path, along a p...
The phase change in received signalThe phase change in received signaldue to difference in path lengths isdue to differenc...
TYPES OF SMALL SCALE FADINGTYPES OF SMALL SCALE FADINGFig. (2) : Types of small scale fading
FLAT FADINGFLAT FADING Flat fadingFlat fading, where the bandwidth of, where the bandwidth ofthe signal is less than thet...
Fig. (3):Fig. (3): Flat Fading channel characteristicsFlat Fading channel characteristics
FREQUENCY SELECTIVE FADINGFREQUENCY SELECTIVE FADING Frequency selective fadingFrequency selective fading, where, whereth...
Fig. (4) :Fig. (4) : Frequency selective fading channel characteristicsFrequency selective fading channel characteristics
FADING EFFECT DUE TO DOPPLER SPREADFADING EFFECT DUE TO DOPPLER SPREAD Due to Doppler Effect, if a transmitter isDue to D...
FASTFAST FADINGFADING Fast FadingFast Fading is a kind of fading occurring with smallis a kind of fading occurring with s...
SLOWSLOW FADINGFADING Slow FadingSlow Fading is a kind of fading caused by largeris a kind of fading caused by largermove...
Fig. (5) : Type of fading experienced by a signal as a functionFig. (5) : Type of fading experienced by a signal as a func...
STATISTICAL MODELS FOR MULTIPATHSTATISTICAL MODELS FOR MULTIPATHFADING CHANNELSFADING CHANNELS Several multipath models h...
CLARKE’S MODELCLARKE’S MODEL Clarke developed a model where the statisticalClarke developed a model where the statistical...
TWO-RAY RAYLEIGH FADING MODELTWO-RAY RAYLEIGH FADING MODEL Clarke’s model and the statistics for RayleighClarke’s model a...
The figure shows a block diagram of the two-rayThe figure shows a block diagram of the two-rayindependent Rayleigh fading ...
SALEH AND VALENZUELA INDOOR STATISTICAL MODEL Saleh and Valenzuela reported the results ofSaleh and Valenzuela reported t...
SIRCIM AND SMRCIM INDOOR AND OUTDOORSIRCIM AND SMRCIM INDOOR AND OUTDOORSTATISTICAL MODELSSTATISTICAL MODELS Rappaport an...
REFERENCESREFERENCES Wireless CommunicationWireless Communication(T. S. RAPPAPORT, EEE Pub.)(T. S. RAPPAPORT, EEE Pub.) ...
ANY QUERIES PLEASE ?ANY QUERIES PLEASE ?
Fadingseminar 100713035600-phpapp02
Upcoming SlideShare
Loading in …5
×

Fadingseminar 100713035600-phpapp02

816 views
776 views

Published on

Published in: Technology, Business
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
816
On SlideShare
0
From Embeds
0
Number of Embeds
9
Actions
Shares
0
Downloads
0
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Fadingseminar 100713035600-phpapp02

  1. 1. Presented By :Presented By :Er. Rajesh KumarEr. Rajesh KumarINDIAINDIA
  2. 2. FADINGFADING““This is about the phenomenon ofThis is about the phenomenon ofloss of signal in telecommunicationsloss of signal in telecommunications.“.“
  3. 3. INDEXINDEXSMALL SCALE FADINGSMALL SCALE FADING1.1. Small scale multipath propagationSmall scale multipath propagation2.2. Multipath fading channelMultipath fading channelFACTORS INFLUENCING SMALL SCALE FADINGFACTORS INFLUENCING SMALL SCALE FADINGDOPPLER SHIFTDOPPLER SHIFTTYPES OF SMALL SCALE FADINGTYPES OF SMALL SCALE FADING1.1. Fading effect due to multipath time delay spreadFading effect due to multipath time delay spread• Flat FadingFlat Fading• Frequency Selective FadingFrequency Selective Fading2. Fading effect due to Doppler Spread2. Fading effect due to Doppler Spread• Fast FadingFast Fading• Slow FadingSlow FadingSTATISTICAL MODELS FOR MULTIPATH FADINGSTATISTICAL MODELS FOR MULTIPATH FADING CHANNELSCHANNELS1.1. Clarke’s modelClarke’s model2.2. Two ray Rayleigh Fading modelTwo ray Rayleigh Fading model3.3. Saleh and Valenzuele Indoor statistical modelSaleh and Valenzuele Indoor statistical model4.4. SIRCIM AND SMRCIM Indoor and Outdoor statistical modelSIRCIM AND SMRCIM Indoor and Outdoor statistical model
  4. 4. FADINGFADINGSelective fading causes a cloudy pattern to appear onSelective fading causes a cloudy pattern to appear onanan FFTFFT display.display.FadingFading (or(or fading channelsfading channels) refers to mathematical) refers to mathematicalmodels for the distortion that a carrier-modulatedmodels for the distortion that a carrier-modulatedtelecommunication signal experiences over certaintelecommunication signal experiences over certainpropagation media. Short-term fading, also known aspropagation media. Short-term fading, also known asmultipathmultipath induced fadinginduced fading, is due to, is due to multipathmultipathpropagationpropagation. Fading results from the. Fading results from the superpositionsuperposition ofoftransmitted signals that have experienced differences intransmitted signals that have experienced differences inattenuationattenuation,, delaydelay andand phase shiftphase shift while traveling from thewhile traveling from thesource to the receiver. It may also be caused by attenuationsource to the receiver. It may also be caused by attenuationof a single signal.of a single signal.The most common types of fading, known as "slowThe most common types of fading, known as "slowfading" and "fast fading", as they apply to a mobile radiofading" and "fast fading", as they apply to a mobile radioenvironment, are explained below.environment, are explained below.
  5. 5.  FadingFading refers to the time variation of therefers to the time variation of thereceived signal power caused by changes in thereceived signal power caused by changes in thetransmission medium or path.transmission medium or path. Small scale fading or simply fading is used toSmall scale fading or simply fading is used todescribe the rapid fluctuations of the amplitude,describe the rapid fluctuations of the amplitude,phases or multipath delays of a radio signal overphases or multipath delays of a radio signal overa short period of time or travel distance, so thata short period of time or travel distance, so thatlarge scale path loss effects may be ignored.large scale path loss effects may be ignored.Fading is caused by interference between two orFading is caused by interference between two ormore versions of the transmitted signal whichmore versions of the transmitted signal whicharrives at the receiver at slightly different times.arrives at the receiver at slightly different times. These waves, called multipath waves, combine atThese waves, called multipath waves, combine atthe receiver antenna to give a resultant signal,the receiver antenna to give a resultant signal,which can vary widely in amplitude and phase,which can vary widely in amplitude and phase,depending on the distribution of the intensity anddepending on the distribution of the intensity andrelative propagation time of the waves and therelative propagation time of the waves and thebandwidth of the transmitted signal.bandwidth of the transmitted signal.
  6. 6. EXAMPLEEXAMPLE For example, consider the common experience ofFor example, consider the common experience ofstopping at traffic lights and hearing a lot of staticstopping at traffic lights and hearing a lot of staticon your FM broadcast radio, which is immediatelyon your FM broadcast radio, which is immediatelycorrected if you move less than a meter. Cellularcorrected if you move less than a meter. Cellularphones also exhibit similar momentary fades. Thephones also exhibit similar momentary fades. Thereason for these losses of signal is the destructivereason for these losses of signal is the destructiveinterference that multiple reflected copies of theinterference that multiple reflected copies of thesignal make with itself. To understand how asignal make with itself. To understand how asignal can destructively interfere with itself,signal can destructively interfere with itself,consider the sum of twoconsider the sum of two sinusoidalsinusoidal waveformswaveforms(which are similar to modulated carrier signals)(which are similar to modulated carrier signals)with different phases.with different phases.
  7. 7. FADING IN WIRELESS COMMUNICATIONSFADING IN WIRELESS COMMUNICATIONS In wireless communications, signal fading isIn wireless communications, signal fading iscaused by multi-path effect. Multi-path effectcaused by multi-path effect. Multi-path effectmeans that a signal transmitted from ameans that a signal transmitted from atransmitter may have multiple copies traversingtransmitter may have multiple copies traversingdifferent paths to reach a receiver.different paths to reach a receiver. At the receiver, the received signal should be theAt the receiver, the received signal should be thesum of all these multi-path signals. Because thesum of all these multi-path signals. Because thepaths traversed by these signals are different;paths traversed by these signals are different;some are longer and some are shorter.some are longer and some are shorter. The one at the direction of light of signal (LOS)The one at the direction of light of signal (LOS)should be the shortest. These signals interactshould be the shortest. These signals interactwith each other. If signals are in phase, theywith each other. If signals are in phase, theywould intensify the resultant signal; otherwise,would intensify the resultant signal; otherwise,the resultant signal is weakened due to out ofthe resultant signal is weakened due to out ofphase. This phenomenon is called channel fading.phase. This phenomenon is called channel fading.
  8. 8. SMALL SCALE MULTIPATH PROPAGATIONSMALL SCALE MULTIPATH PROPAGATION Multipath in the radio channel creates smallMultipath in the radio channel creates smallscale fading effects. The three mostscale fading effects. The three mostimportant effects are :important effects are : Rapid changes in signal strength over aRapid changes in signal strength over asmall travel distance or time interval.small travel distance or time interval. Random frequency distribution due toRandom frequency distribution due tovarying Doppler shifts on differentvarying Doppler shifts on differentmultipath signals.multipath signals. Time dispersion (Echoes) caused byTime dispersion (Echoes) caused bymultipath propagation delays.multipath propagation delays.
  9. 9. FACTORS INFLUENCING SMALL SCALE FADINGFACTORS INFLUENCING SMALL SCALE FADINGMany physical factors in the radio propagation channelMany physical factors in the radio propagation channelinfluence small-scale fading. These include the following :influence small-scale fading. These include the following :(1)(1) Multipath PropagationMultipath Propagation ::The presence of reflecting objects and scatters in the channelThe presence of reflecting objects and scatters in the channelcreates a constantly changing environment that dissipates the signalcreates a constantly changing environment that dissipates the signalenergy in amplitude, phase and time. These effects results in multipleenergy in amplitude, phase and time. These effects results in multipleversions of the transmitted signal that arrive at the receivingversions of the transmitted signal that arrive at the receivingantenna, displaced with respect to one another in time and spatialantenna, displaced with respect to one another in time and spatialorientation. The random phase and amplitude of the differentorientation. The random phase and amplitude of the differentmultipath components caused fluctuations in signal strength, therebymultipath components caused fluctuations in signal strength, therebyinducing Small scale fading, Signal distortion, or both. Multipathinducing Small scale fading, Signal distortion, or both. Multipathpropagation often lengthens the time required for the base bandpropagation often lengthens the time required for the base bandportion of the signal to reach the receiver which can cause signalportion of the signal to reach the receiver which can cause signalsmearing due to inter symbol interference.smearing due to inter symbol interference.(2)(2) Speed of the mobileSpeed of the mobile ::The relative motion between the base station and the mobileThe relative motion between the base station and the mobileresults in random frequency modulation due to different Dopplerresults in random frequency modulation due to different DopplerShifts on each of the multipath components. Doppler Shift will beShifts on each of the multipath components. Doppler Shift will bepositive or negative depending on whether the mobile receiver ispositive or negative depending on whether the mobile receiver ismoving towards or away from the base station.moving towards or away from the base station.
  10. 10. (3) Speed of surrounding objects :If objects in the radio channel are in motion, they induced a timevarying Doppler Shift on multipath components. If the surroundingobjects move at a greater rate than the mobile, then this effectdominates the Small scale Fading. Otherwise, motion of surroundingobjects may be ignored and only the speed of the mobile need beconsidered. The coherence time defines the “static ness” of thechannel, and is directly impacted by the Doppler shift.(4) The transmission bandwidth of the signal :If the transmitted radio signal bandwidth is greater than the“bandwidth” of the multipath channel, the received signal will bedistorted, but the received signal strength will not fade much over alocal area (i.e., the small scale signal fading will not be significant). Aswill be shown, the bandwidth of the channel can be quantified by thecoherence bandwidth which is related to the specific multipath structureof the channel. The coherence bandwidth is a measure of the maximumfrequency difference for which signals are still strongly correlated inamplitude. If the transmitted signal has a narrow bandwidth ascompared to the channel, the amplitude of the signal change rapidly,but the signal will not be distorted in time.
  11. 11. DOPPLER SHIFTDOPPLER SHIFT
  12. 12.  Consider a mobile moving at aConsider a mobile moving at aconstant velocityconstant velocity vv, along a path, along a pathsegment having lengthsegment having length dd betweenbetweenpoints X and Y, while it receivespoints X and Y, while it receivessignals from a remote source assignals from a remote source asillustrated in Fig (1) in previous slide :illustrated in Fig (1) in previous slide : The difference in path length traveledThe difference in path length traveledby the wave from source S to theby the wave from source S to themobile at points X and Y ismobile at points X and Y is∆∆l = dcosθ = v∆tcosθl = dcosθ = v∆tcosθ
  13. 13. The phase change in received signalThe phase change in received signaldue to difference in path lengths isdue to difference in path lengths istherefore,therefore,∆∆ Φ =Φ = 2 π ∆2 π ∆ ll == 2 π v ∆2 π v ∆ tt cos θcos θλ λλ λand hence the apparent change inand hence the apparent change infrequency or Doppler shift, is givenfrequency or Doppler shift, is givenbyby fdfd, where, wherefdfd == 11 .. ∆Φ∆Φ == vv . cosθ. cosθ2π ∆ t λ2π ∆ t λ
  14. 14. TYPES OF SMALL SCALE FADINGTYPES OF SMALL SCALE FADINGFig. (2) : Types of small scale fading
  15. 15. FLAT FADINGFLAT FADING Flat fadingFlat fading, where the bandwidth of, where the bandwidth ofthe signal is less than thethe signal is less than thecoherence bandwidthcoherence bandwidth of the channelof the channelor theor the delay spreaddelay spread is less than theis less than thesymbol periodsymbol period..
  16. 16. Fig. (3):Fig. (3): Flat Fading channel characteristicsFlat Fading channel characteristics
  17. 17. FREQUENCY SELECTIVE FADINGFREQUENCY SELECTIVE FADING Frequency selective fadingFrequency selective fading, where, wherethe bandwidth of the signal is greaterthe bandwidth of the signal is greaterthan the coherence bandwidth of thethan the coherence bandwidth of thechannel or the delay spread ischannel or the delay spread isgreater than the symbol period.greater than the symbol period.
  18. 18. Fig. (4) :Fig. (4) : Frequency selective fading channel characteristicsFrequency selective fading channel characteristics
  19. 19. FADING EFFECT DUE TO DOPPLER SPREADFADING EFFECT DUE TO DOPPLER SPREAD Due to Doppler Effect, if a transmitter isDue to Doppler Effect, if a transmitter ismoving away from a receiver, themoving away from a receiver, thefrequency of the received signal is lowerfrequency of the received signal is lowerthan the one sent out from the transmitter;than the one sent out from the transmitter;otherwise, the frequency is increased.otherwise, the frequency is increased. In wireless communications, there areIn wireless communications, there aremany factors that can cause relativemany factors that can cause relativemovement between a transmitter and amovement between a transmitter and areceiver.receiver. It can be the movement of a mobile suchIt can be the movement of a mobile suchas a cell phone.as a cell phone. It can be the movement of someIt can be the movement of somebackground objectives, which causes thebackground objectives, which causes thechange of path length between thechange of path length between thetransmitter and the receiver.transmitter and the receiver.
  20. 20. FASTFAST FADINGFADING Fast FadingFast Fading is a kind of fading occurring with smallis a kind of fading occurring with smallmovements of a mobile or obstacle.movements of a mobile or obstacle. Depending upon how rapidly the transmitted base bandDepending upon how rapidly the transmitted base bandsignal changes as compared to the rate of change of thesignal changes as compared to the rate of change of thechannel.channel. The channel may be classified either as aThe channel may be classified either as a Flat fadingFlat fading ororSlow fadingSlow fading channel.channel. In aIn a Fast fadingFast fading channel, the impulse response changeschannel, the impulse response changesrapidly within the symbol duration. That is, the coherencerapidly within the symbol duration. That is, the coherencetime of the channel is smaller than the symbol period of thetime of the channel is smaller than the symbol period of thetransmitted signal. This causes frequency dispersion (alsotransmitted signal. This causes frequency dispersion (alsocalled the selective fading) due to Doppler spreading, whichcalled the selective fading) due to Doppler spreading, whichleads to signal distortion.leads to signal distortion.
  21. 21. SLOWSLOW FADINGFADING Slow FadingSlow Fading is a kind of fading caused by largeris a kind of fading caused by largermovements of a mobile or obstructions within themovements of a mobile or obstructions within thepropagation environment. This is often modeledpropagation environment. This is often modeledasas log-normal distributionlog-normal distribution with a standardwith a standarddeviation according to thedeviation according to theLog Distance Path Loss ModelLog Distance Path Loss Model.. In a slow fading channel, the channel impulseIn a slow fading channel, the channel impulseresponse changes at a rate much slower than theresponse changes at a rate much slower than thetransmitted base band signal s(t). In this case,transmitted base band signal s(t). In this case,channel may be assumed to be static over one orchannel may be assumed to be static over one orseveral reciprocal bandwidth intervals.several reciprocal bandwidth intervals.
  22. 22. Fig. (5) : Type of fading experienced by a signal as a functionFig. (5) : Type of fading experienced by a signal as a function(a) Symbol period(a) Symbol period (b) Base band signal bandwidth(b) Base band signal bandwidth
  23. 23. STATISTICAL MODELS FOR MULTIPATHSTATISTICAL MODELS FOR MULTIPATHFADING CHANNELSFADING CHANNELS Several multipath models have been suggested toSeveral multipath models have been suggested toexplain the observed statistical nature of a mobileexplain the observed statistical nature of a mobilechannel.channel. The first model presented by ossana was based onThe first model presented by ossana was based oninterference of waves incident and reflected from theinterference of waves incident and reflected from theflat sides of randomly located buildings.flat sides of randomly located buildings. Ossana’s model is therefore rather inflexible andOssana’s model is therefore rather inflexible andinappropriate for urban areas where the direct path isinappropriate for urban areas where the direct path isalmost always blocked by buildings or other obstacles.almost always blocked by buildings or other obstacles.Clarke’s model is based on scattering and is widelyClarke’s model is based on scattering and is widelyused.used.
  24. 24. CLARKE’S MODELCLARKE’S MODEL Clarke developed a model where the statisticalClarke developed a model where the statisticalcharacteristics of the electromagnetic fields of thecharacteristics of the electromagnetic fields of thereceived signals of the mobile are deduced fromreceived signals of the mobile are deduced fromscattering.scattering. The model assumes a fixed transmitter with aThe model assumes a fixed transmitter with avertically polarized antenna. The field incident on thevertically polarized antenna. The field incident on themobile antenna is assumed to be comprised of Nmobile antenna is assumed to be comprised of Nazimuthal plane waves with arbitrary carrier phases,azimuthal plane waves with arbitrary carrier phases,arbitrary azimuthal angles of arrival, and each wavearbitrary azimuthal angles of arrival, and each wavehaving equal average amplitude.having equal average amplitude. It should be noted that the equal average amplitudeIt should be noted that the equal average amplitudeassumption is based on the fact that in the absence ofassumption is based on the fact that in the absence ofa direct line-of-sight path, the scattered arriving at aa direct line-of-sight path, the scattered arriving at areceiver will experience similar attenuation overreceiver will experience similar attenuation oversmall-scale distances.small-scale distances.
  25. 25. TWO-RAY RAYLEIGH FADING MODELTWO-RAY RAYLEIGH FADING MODEL Clarke’s model and the statistics for RayleighClarke’s model and the statistics for Rayleighfading are for that fading conditions and do notfading are for that fading conditions and do notconsider multipath time delay.consider multipath time delay. In modern mobile communication systems withIn modern mobile communication systems withhigh data rates, it has become necessary tohigh data rates, it has become necessary tomodel the effects of multipath delay spread asmodel the effects of multipath delay spread aswell as fading.well as fading. A commonly used multipath model is anA commonly used multipath model is anindependent Rayleigh fading two-ray modelindependent Rayleigh fading two-ray model(which is a specific implementation of the(which is a specific implementation of thegeneric fading simulator shown in figuregeneric fading simulator shown in figurebelow).below).
  26. 26. The figure shows a block diagram of the two-rayThe figure shows a block diagram of the two-rayindependent Rayleigh fading channel model.independent Rayleigh fading channel model.INPUTINPUT OUTPUTOUTPUT
  27. 27. SALEH AND VALENZUELA INDOOR STATISTICAL MODEL Saleh and Valenzuela reported the results ofSaleh and Valenzuela reported the results ofindoor propagation measurements between twoindoor propagation measurements between twovertically polarized omni directional antennasvertically polarized omni directional antennaslocated on the same floor of a medium sizedlocated on the same floor of a medium sizedoffice building. Measurements were made usingoffice building. Measurements were made using10 ns, 1.5 GHz, radar-like pulses.10 ns, 1.5 GHz, radar-like pulses. The method involved averaging the square lawThe method involved averaging the square lawdetected pulse response while sweeping thedetected pulse response while sweeping thefrequency of the transmitted pulse. Using thisfrequency of the transmitted pulse. Using thismethod, multipath components within 5 ns weremethod, multipath components within 5 ns wereresolvable.resolvable.
  28. 28. SIRCIM AND SMRCIM INDOOR AND OUTDOORSIRCIM AND SMRCIM INDOOR AND OUTDOORSTATISTICAL MODELSSTATISTICAL MODELS Rappaport and Seidel reported measurement at 1300 MHz in fiveRappaport and Seidel reported measurement at 1300 MHz in fivefactory buildings and carried out subsequent measurements infactory buildings and carried out subsequent measurements inother types of buildings. The authors developed an elaborate,other types of buildings. The authors developed an elaborate,empirically derived statistical model to generate measuredempirically derived statistical model to generate measuredchannels based on the discrete impulse response channel modelchannels based on the discrete impulse response channel modeland wrote a computer program calledand wrote a computer program called SIRCIM (simulation ofSIRCIM (simulation ofindoor radio channel impulse-response models)indoor radio channel impulse-response models).. SIRCIM generates realistic samples of small-scale indoor channelSIRCIM generates realistic samples of small-scale indoor channelimpulse response measurements. Subsequent work by Huangimpulse response measurements. Subsequent work by Huangproducedproduced SMRCIM (simulation of mobile radio channelSMRCIM (simulation of mobile radio channelimpulse response models)impulse response models), a similar program that generates, a similar program that generatessmall-scale urban cellular and microcellular channel impulsesmall-scale urban cellular and microcellular channel impulseresponses.responses. These programs are currently in use at over 100 institutionsThese programs are currently in use at over 100 institutionsthroughout the world, and have been updated to include angle ofthroughout the world, and have been updated to include angle ofarrival information for micro cell, indoor, and macro cell channels.arrival information for micro cell, indoor, and macro cell channels.
  29. 29. REFERENCESREFERENCES Wireless CommunicationWireless Communication(T. S. RAPPAPORT, EEE Pub.)(T. S. RAPPAPORT, EEE Pub.) Wikipedia, the free encyclopediaWikipedia, the free encyclopedia Google.co.inGoogle.co.in
  30. 30. ANY QUERIES PLEASE ?ANY QUERIES PLEASE ?

×