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单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,*,Mobile Radio Propagation:Small-Scale Fading and Multipath,8/8/2024,1,Mobile Radio Propagation:Smal,8/8/2024,2,8/20/20232,Fading(small-scale)is a more rapid fluctuation of signals,caused by,constructive and destructive interference between two or more versions of the same signal(,multipath,),Doppler effect,due to moving terminals or surroundings,signals wider than,coherence bandwidth,of radio channel,Small-Scale fading,8/8/2024,3,Fading(small-scale)is a more,Time-variant multipath channel,8/8/2024,4,Time-variant multipath channel,Doppler Shift,Example,Carrier frequency,f,c,=1850 MHz (i.e.,=16.2 cm),Vehicle speed,v,=60 mph=26.82 m/s,If the vehicle is moving directly towards the transmitter,If the vehicle is moving perpendicular to the angle of arrival of the transmitted signal,8/8/2024,5,Doppler ShiftExample8/20/20,Coherence Bandwidth&Coherence Time,8/8/2024,6,Coherence Bandwidth&Coherence,Characteristics of Radio Channel,(Large path loss),Multipath(reflection,scattering),Time-variant(time-varying,a consequence of the constantly changing physical characteristics of the media,e.g.moving of objects),It is reasonable to characterize the time-variant multipath channels statistically.,Fadingpath loss,slow fading,fast fading(multipath and time-variant),Time spread(multipath),Frequency spread(time-variant),8/8/2024,7,Characteristics of Radio Chann,Impulse response of wireless channels,The mobile channel can be modeled as a linear,time varying filter with impulse response,h,(,t,t,),where,t,is the channel multipath delay for a fixed,t,.,The impulse response,h,(,t,t,),completely characterizes the channel and is a function of both t and,t,The received signal can be expressed as a convolution of the channel impulse response,h,(,t,t,),with the transmitted signal x(t),8/8/2024,8,Impulse response of wireless c,8/8/2024,9,8/20/20239,Random Characteristics of wireless channels,The impulse response of the time-variant multipath channel is a random process,The signal passed through a time-variant multipath channel is a random process,describe multipath delay as the,excess delay,relative to the first arriving multipath component with excess delay t,0,=0,Discretize,excess delay in,N,equally spaced“bins”,such that all multipath wave components inside bin no.,i,are represented by,one,component with delay .,?,8/8/2024,10,Random Characteristics of wire,the time varying discrete-time impulse response model for a multipath,radio channel,8/8/2024,11,the time varying discrete-time,So far,we have channel model,Good:it gives every detail about the channel,Bad:it is hard to see any essential characteristics of channels,such as what signal can pass,what signal can not pass,We need a few major parameters for easy,Compare different channels(delay,bandwidth,spectrum,etc),Develop design guide lines for wireless signals,8/8/2024,12,So far,we have channel model8,Such parameters can be derived from channel model,Specifically,from“power delay profile”of the channel,Power delay profile is the spatial/time average over a local area,It is a function:power delay,i.e.,the average received power with some delay.,8/8/2024,13,Such parameters can be derived,Are measured by channel sounding techniques,Plots of relative received power as a function of excess delay,They are found by averaging,intantenous,power delay measurements over a local area,Local area:no greater than 6m outdoor,Local area:no greater than 2m indoor,Power Delay Profiles,8/8/2024,14,Are measured by channel soundi,Continuous Wave(CW),Signal,Highbandwidth,(Wideband),Signal,Received power for CW signals undergoes rapid fades over small distances,Received power for wideband signals changes very little of small distances.,However,the local area average of both signals are nearly identical.,Different,Baseband Signals,8/8/2024,15,Continuous Wave(CW)Highbandw,Parameters of Mobile Multipath Channels,Time Dispersion Parameters,Coherent bandwidth,Doppler Spread,Coherence Time,8/8/2024,16,Parameters of Mobile Multipath,Time Dispersion Parameters,Mean excess delay,RMS delay spread,where,8/8/2024,17,Time Dispersion ParametersMean,Power delay Profile,Received Signal Level(dBm),-105,-100,-95,-90,0,50,100,150,200,250,300,350,400,450,RMS Delay Spread(,)=46.4 ns,Mean Excess delay(,)=45 ns,Maximum Excess delay 10 dB=110 ns,Noise threshold,8/8/2024,18,Power delay ProfileReceived Si,-30 dB,-20 dB,-10 dB,0 dB,0,1,2,5,(s),1.37 s,Example,8/8/2024,19,-30 dB-20 dB-10 dB 0 dB0125,Coherence Bandwidth,Coherence bandwidth is a statistical measure of the range of frequencies over which the channel can be consider“flat”(i.e.,a channel which passes all spectral components with approximately equal gain and linear phase),Two frequencies separated greater than,B,c,have different channel response,If the coherence bandwidth is defined as the bandwidth over which the frequency correlation function is above 0.5,then the coherence bandwidth is approximately,Where,RMS delay spread,RMS delay spread(time dispersion parameters)and coherence bandwidth are parameters which describe multipath nature of the radio channel,8/8/2024,20,Coherence BandwidthCoherence b,Since,B,c,is greater than 30 kHz,AMPS will work without an equalizer.However,GSM requires 200 kHz bandwidth which exceeds,B,c,thus an equalizer would be needed for this channel.,8/8/2024,21,Since Bc is greater than 30 kH,Doppler Spread and Coherence,Time,Coherence time is actually a statistical measure of the time duration over which the channel impulse response is essentially invariant,and quantifies the similarity of the channel response at different times.,A popular definition of coherence time for digital communications is,Doppler Spread and Coherence Time are parameters which describe the time varying nature of the channel in a small-scale region.,8/8/2024,22,Doppler Spread and Coherence T,Example,The spatial sampling interval required to make small-scale propagation measurements is Tc/2.How many samples will be required over 10m travel distance if,f,c,=1900 MHz and,v,=50 m/s.How long would it take to make these measurements,assuming they could be made in real time from a moving vehicle?,Solution,8/8/2024,23,ExampleThe spatial sampling in,Fading Effects Due to Multipath Time Delay Spread,8/8/2024,24,Fading Effects Due to Multipa,8/8/2024,25,8/20/202325,Due to Doppler Spread,Rate of change of the,channel characteristics,is,larger,than theRate of change of the,transmitted signal,The channel changes during a symbol period.,The channel changes because of receiver motion.,Coherence time,of the channel is smaller than the,symbol period,of the transmitter signal,B,S,:Bandwidth of the signalB,D,:Doppler Spread,T,S,:Symbol PeriodT,C,:Coherence Bandwidth,Occurs when:,B,S,T,C,Fast Fading,8/8/2024,26,Due to Doppler SpreadBS:Bandw,Due to Doppler Spread,Rate of change of the,channel characteristics,is,much smaller,than theRate of change of the,transmitted signal,Occurs when:,B,S,B,D,and,T,S,T,C,B,S,:Bandwidth of the signalB,D,:Doppler Spread,T,S,:Symbol PeriodT,C,:Coherence Bandwidth,Slow Fading,8/8/2024,27,Due to Doppler SpreadOccurs wh,Fast fading&Slow fading,8/8/2024,28,Fast fading&Slow fading8/20/,Types of Small-Scale Fading,8/8/2024,29,Types of Small-Scale Fading 8/,8/8/2024,30,8/20/202330,Small scale fading and multipath,Impulse response model of channel,Discrete channel model,Parameters of channels,rms delay spread,Coherence bandwidth,Doppler Spread,Coherence Time,Relationship to signal bandwidth and symbol rate,8/8/2024,31,Small scale fading and multipa,Equalization,Compensates for intersymbol interference(ISI)created by multipath within time dispersive channels.,An equalizer within a receiver compensates for average range of expected channel amplitude and delay characteristics.,Equalizers are generally adaptive since channel is unknown and time varying,for example GSM.,Channel must be learned through training and tracked during data transmission.,Some techniques to mitigate fading,8/8/2024,32,Equalization Some techniques t,The intersymbol interference of received symbols(bits)must be removed,before,decision making(the case is illustrated below for a binary signal,where symbol=bit):,Decision,circuit,Adaptive,equalizer,Symbols with ISI,Symbols with ISI removed,“Clean”symbols,Decision time instant,Decision threshold,8/8/2024,33,The intersymbol interference o,Z,-1,Z,-1,Z,-1,w,0k,w,1k,w,2k,w,Nk,Adaptive Algorithm,+,-,Time Domain Equalization,8/8/2024,34,Z-1Z-1Z-1w0kw1kw2kwNkAdaptive,Powerful communications technique that provides wireless link improvement at relatively low cost.,Unlike equalization,diversity requires no training overhead.,Send bits over independent fading paths,Combine paths to mitigate fading effects.,Independent fading paths,Space,time,frequency,polarization diversity.,Diversity,8/8/2024,35,Diversity 8/20/202335,Space diversity,8/8/2024,36,Space diversity8/20/202336,x,x,s,c,(t),s,c,(t-iT,c,),x,s,c,(t-NT,c,),Demod,Demod,Demod,y(t),Diversity,Combiner,d,k,CDMA RAKE Receiver,8/8/2024,37,xxsc(t)sc(t-iTc)xsc(t-NTc)Demo,improves the small-scale link performance by adding redundant data bits in the transmitted message so that if an instantaneous fade occurs in the channel,the data may still be recovered at the receiver.,Channel coding are used to detect errors and correct errors.,Block codes,convolutional codes,Channel coding,8/8/2024,38,Channel coding8/20/202338,Divides bit stream into N substreams,Modulates substream with bandwidth B/N,Separate subcarriers,B/NBc flat fading(no ISI),OFDM is a transmission technique that is inherently resistant to ISI.,OFDM will no doubt play a large role in the emerging wireless LAN/MAN standards and 4G network deployments.,OFDM,8/8/2024,39,OFDM8/20/202339,Fading Distributions,Describes how the received signal amplitude changes with time.,Remember that the received signal is combination of multiple signals arriving from different directions,phases and amplitudes.,With the received signal we mean the baseband signal,namely the,envelope,of the received signal(i.e.r(t).,Its is a,statistical,characterization of the multipath fading.,Two distributions,Rayleigh Fading,Ricean Fading,8/8/2024,40,Fading DistributionsDescribes,Rayleigh fading,8/8/2024,41,Rayleigh fading8/20/202341,8/8/2024,42,8/20/202342,0,.,0,0,0,0,1,0,.,0,0,0,1,0,.,0,0,1,0,.,0,1,0,.,1,1,0,1,0,2,0,3,0,G,A,U,S,S,I,A,N,C,H,A,N,N,E,L,R,A,Y,L,E,I,G,H,F,A,D,I,N,G,s,i,g,n,a,l,-,t,o,-,n,o,i,s,e,r,a,t,i,o,(,d,B,),b,i,t,e,r,r,o,r,p,r,o,b,a,b,i,l,i,t,y,b,i,n,a,r,y,a,n,t,i,p,o,d,a,l,s,i,g,n,a,l,s,EFFECT OF FADING ON ERROR PROBABILITIES,8/8/2024,43,0.000010.00010.0010.010.110102,Ricean fading,When there is a dominant stationary(nonfading)signal component present,such as a line-of sight propagation path,the small-scale fading envelope distribution is Ricean.,8/8/2024,44,Ricean fadingWhen there is a d,Statistical Models for Flat Fading Channel,The Ricean distribution degenerates to a Rayleigh distribution when the dominant component fades away.,8/8/2024,45,Statistical Models for Flat Fa,1.,For the power delay profiles in Figure,estimate the 90%correlation and 50%correlation coherence bandwidths.,8/8/2024,46,1.For the power delay profile,2.If a baseband binary message with a bit rate,Rb,=100 kbps is modulated by an RF carrier using BPSK,answer the following:,(a)Find the range of values required for the rms delay spread of the channel such that the received signal is a flat-fading signal.,(b)If the modulation carrier frequency is 5.8 GHz,what is the coherence time of the channel,assuming a vehicle speed of 50 kilometers per hour?(use 4.40b),(c)For your answer in(b),is the channel fast or slow fading?,(d)Given your answer in(b),how many bits are sent while the channel appears static?,(e)A CDMA Rake receiver is able to exploit multipath when the channel is(a)flat;(b)slow;(c)fast;(d)frequency selective,8/8/2024,47,2.If a baseband binary message,3.Try to explain the meaning of the following:,(i),the channel is frequency-nonselective;,(ii),the channel is slowly fading;,(iii),the channel is frequency-selective.,8/8/2024,48,3.Try to explain the meaning o,
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