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l Without shadowingl With shadowingl Okumura Modell Okumura-Hata Path Loss Modell COST 231 Modell Lees Path Loss Model lEmpirical formulation to match Okumura modellSuitable for large celllThe path loss is represented as a function of The carrier frequency,150,1500MHzAntenna heights of base station and mobile station,hb30,200m,hm1,10mThe distance between the base station and mobile station,1,20KmlThe path loss in dB is given bywherela(hm)is the correction factor for mobile antenna height,and is given byFor a small and medium cityFor a large cityfc=900MHzhb=50mhm=3mlThe Hata model was extended by the European cooperative for scientific and technical research(EURO-COST)to 2GHzWhere a(hr)is the same correction factor as before and CM is 0 dB for medium sized cities and suburbs and 3dB for metropolitan areas.lThe COST 231 model is restricted to the following range of parameters:The carrier frequency,1.5,2GHzAntenna heights of base station and mobile station,hb30,200m,hm1,10mThe distance between the base station and mobile station,1,20KmlLees model can be used to predict area-to-area path loss.The model consists of two parts:Path loss prediction for a specified set of conditionsAdjustment factors for a set of conditions different from the specified onelThe model requires two parameters:The power at a 1.6km(1 mile)of interception P0 in dBmThe path-loss exponent k.lThe specified set of conditions is as follows:Carry frequency fc=900MHzBase station antenna height=30.48 m(100 ft)Base station power at the antenna=10 WBase station antenna gain=6 dB above dipole gainMobile station antenna height=3 m(10 ft)Mobile station antenna gain=0 dB above dipole gainro=1mil =1,6 kmrPoPrlThe received signal power in dBm is represented by:Where d0=1.6km,d(d0)is the distance between the mobile station and the base station in km,and n is a constant between 2 and 3 dependent on the geographical locations and the operating frequency ranges.n=2 is recommended for a suburban or open area with f 450MHz.lThe parameter a0(dB)is an adjustment factor for a different set of conditions:WherelThe parameter a0(dB)is an adjustment factor for a different set of conditions:WherelThe value v in a2 is obtained from empirical data and is given by:lA 2dB signal gain is provided by an actual 4dB gain antenna at the mobile unit in a suburban area,and less than 1dB gain received from the same antenna in an urban area for adjusting a5.terrainP0(dBm)kFree space-452.00Open area-494.35Suburban areas-61.73.84Urban area(Philadelphia)-703.68Urban area(Newark)-644.31Urban area(Tokyo)-843.05fc=900MHzhb=50mAntenna gain=6dBTransmitter power=10Whm=3ml Free-space propagationl Two-ray ground reflection modell Log-distance path loss modell Log-normal path loss modell Okumura Hata model,Lees modelReceived power reduces with propagation distance and terrain characteristics models lKeep in mind when studying section 2.4:The channel model is independent of signals,symbol rate,modulation,etc.Channel&signal:Different signals may see different aspect of channel.The channel fading can be classified as large-scale fading or small-scale fading.lLarge-scale fading:Due to the general terrain and the density and height of building and vegetation;characterized statistically by the median path loss and lognormal shadowing,varies relatively slowly with time.lSmall-scale fading:Due to the local environment,signal variability on a scale of,have been characterized statistically as instantaneously received signal level variations with the local average.Shadowing or lognormal fadingTime delay spreadTime-varyingIn this section,we made the assumption that the channel was linear,according to this assumption,all distortions can be characterized by the attenuation or superposition of different signals.In addition,we allow the possibility that the propagation channel may be time varying.As a consequence of these assumptions,the channel can be presented by a dual time time-varying impulse response,defined as Linear time-variant channel.2.2.2 Time-Variant Transfer Function 2.2.2 Time-Variant Transfer Function 2.2.4 Example on the Channel Functions 2.2.4 Example on the Channel Functions 2.2.1 Channel Impulse Response 2.2.1 Channel Impulse Response 2.2.3 Doppler Spread Function and 2.2.3 Doppler Spread Function and Delay-Doppler spread function Delay-Doppler spread function l Baseband Equivalent Channel Modell Linear Time-Variant(LTV)ChannelConsider a multipath propagation environment with N distinct scatters.The path associated with the nth distinct scatter is characterized by:l ,represents the amplitude fluctuation by the scatter at time tl ,associated propagation delayConsider a narrowband signal transmitted over the wireless channel at a carrier frequency fc,such that And the received signal at the channel output is The channel can be characterized equivalently by its impulse response at baseband.l Let us first review the impulse response of a linear time-invariant(LTI)channelLTIThe time variable t in the impulse response actually represents the propagation delay of the channel LTVTime-varying Discrete Impulse Response Model for multipath channelh(t,)(t0)(t1)(t2)t1t2t3t0t0 1 2 3 4 N-2 N-1(t3)delayed multipath componentstimeamplitudeDefinition 2.1 The impulse of an LTV channel,h(,t),is the channel output at t in response to an impulse applied to the channel at t -.In definition 2.1,the variable represents the propagation delay.Thus,the channel output can be represented in terms of the impulse response and the channel input byThe Channel impulse response for the channel with N distinct scatters is thenExample 2.9Example 2.10Same as 2.9,but receiver move at v=10m/s toward path#1 while away from path#2.What is the channel at time t=0.1 s?Carrier is 1 GHz.l Free-space propagationl Two-ray ground reflection modell Log-distance path loss modell Log-normal path loss modell Okumura Hata model,Lees modelLTILTVChannel impulse responseFourier transformChannel Transfer Functionh(t)H(f)h(,t)Definition 2.2 The time-variant transfer function of an LTV channel is the Fourier transform of the impulse response,h(,t),with respect to the delay variable.Where the time variable t can be viewed as a parameter.At any instant,say t=t0,the transfer function H(f,t0)characterizes the channel in the frequency domain.As the channel changes with t,the frequency domain representation also changes with t.Therefore,we have the channel time-varying transfer function.lIn general,the output signal of an LTI system does not have frequency components different from those of the input signallOn the other hand,both nonlinear and time-varying systems introduce new frequency components other than those existing in the input signal.Linear Time-Variant ChannelDoppler effectDoppler shiftsDoppler Shift in frequency:where v is the moving speed,is the wavelength of carrier.XYdVSAs a wireless channel can be characterized equivalently in both time and frequency domains,a channel being time varying in the time domain means a channel introducing Doppler shifts in the frequency domain.AssumelThat the delay spread is negligible as compared with the symbol interval of the transmitted signal.lThat this mean delay does not change with timeThe time-variant impulse response of the channel can be approximately described in the form:Where TsGiven that the transmitted signal is x(t),the received signal is In frequency domain,the received signal is Has a finite but nonzero pulse width in the frequency domainThis means that the channel indeed broadens the transmitted signal spectrum by introducing new frequency components,a phenomenon referred to as frequency dispersion.Definition:The Doppler spread function is defined by the following function:where:v is a variable describing the Doppler shift introduced by the channel.H(f,v)is the channel gain associated with Doppler shift v to the input signal component at frequency f.Since both the time-variant transfer function H(f,t)and the Doppler spread function H(f,v)can be used to describe the same channel,there exists a relation between the two channel functions.It can be sown that Where the frequency variable f can be viewed as a parameter.The preceding Fourier transform relation verifies that being time-variant in the time domain can be equivalently described by having Doppler shifts in the frequency domain.Definition:Delay-Doppler spread function defined as the Fourier transform of the channel impulse response with respect to t,as follows:Given the channel input signal x(t),it can be shown that the channel output signal isImpulse responseDoppler spreadTransfer functionDelay-Doppler spreadExample 2.11 LTV Channel ModelConsider an LTV channel with impulse response given byWhere T=0.1 ms,and .(a)Find the channel time-variant transfer function and the Doppler spread function(b)Given that the transmitted signal is Where T0=0.025ms,find the received signal in the absence of background noise.(c)Repeat part(b)if the transmitted signal isWhere T1=0.05ms(d)What do you observe from the results of parts(b)and(c)?Consider an LTV channel with impulse response given byWhere T=0.1 ms,and .Example 2.11 LTV Channel Model(a)Example 2.11 LTV Channel ModelConsider an LTV channel with impulse response given byWhere T=0.1 ms,and .(b)(c)(d)The received signals have a larger pulse width because the channel is time dispersive,and the received signal r2(t)is not r1(t)delayed by T1.Example 2.11 LTV Channel ModelConsider an LTV channel with impulse response given byWhere T=0.1 ms,and .2.2.2 Time-Variant Transfer Function2.2.2 Time-Variant Transfer Function2.2.4 Example on the Channel Functions2.2.4 Example on the Channel Functions2.2.1 Channel Impulse Response2.2.1 Channel Impulse Response2.2.3 Doppler Spread Function and 2.2.3 Doppler Spread Function and Delay-Doppler spread function Delay-Doppler spread 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