Channel Modelling ETI 085

Transcription

1 Channel Modellng ETI 85 Lecture no: Channel modellng repetton Fredrk Tufvesson Department of Electrcal and Informaton Technology Lund Unversty, Sweden Why channel modellng? The performance of a rado system s ultmately determned by the rado channel The channel models bass for system desgn algorthm desgn antenna desgn etc. Trend towards more nteracton system-channel MIMO UWB Wthout relable channel models, t s hard to desgn rado systems that work well n real envronments. 9-- Fredrk Tufvesson - ETI Fredrk Tufvesson - ETI 85 THE RADIO CHANNEL It s more than just a loss Some examples: behavor n tme/place? behavor n frequency? drectonal propertes? bandwdth dependency? behavor n delay? THE RADIO CHANNEL Some propertes ath loss Roughly, receved power decays exponentally wth dstance Receved power Transmtted power Dstance ropagaton exponent Large-scale fadng Large objects, compared to a wavelength, n the sgnal path obstruct the sgnal Small-scale fadng Objects reflectng the sgnal causes multpath propagaton from transmtter to recever 9-- Fredrk Tufvesson - ETI Fredrk Tufvesson - ETI 85 4

2 Free-space loss Large-scale fadng Log-normal dstrbuton If we assume RX antenna to be sotropc: RX λ = 4 π d TX Measurements confrm that n many stuatons, the large-scale fadng of the receved sgnal strength has a normal dstrbuton n the db doman. pdf ( L db OWER [db] Note db scale d A RX Attenuaton between two sotropc antennas n free space s (free-space loss: L free ( d 4πd = λ TX db L db Determnstc mean value of path loss, L db db πσ FdB σ FdB RX db ( L db L db pdf ( L db = exp Standard devaton σ 4K db F db 9-- Fredrk Tufvesson - ETI Fredrk Tufvesson - ETI 85 6 Small-scale fadng Many ncomng waves Many ncomng waves wth ndependent ampltudes and phases r, φ r3, φ3 r, φ r,φφ 4 4 Add them up as phasors r 3 φ 3 φ r, φ φ 4 r4 r φ r r φ ( φ = ( φ + ( φ + ( φ + ( φ rexp j r exp j r exp j r exp j r exp j r Small-scale fadng Raylegh fadng Tap dstrbuton D Gaussan (zero mean Im ( a Re( a No lne-of-sght component No domnant component TX X RX (no lne-of-sght r = a Ampltude dstrbuton Raylegh 3 r r pdf ( r = exp σ σ 9-- Fredrk Tufvesson - ETI Fredrk Tufvesson - ETI 85 8

3 Small-scale fadng Rce fadng A domnant component (lne of sght TX Tap dstrbuton Ampltude dstrbuton D Gaussan (non-zero mean Rce A Im ( a Re( a Lne-of-sght (LOS component wth ampltude A. r = α k = 3 k = k = 3 r r + A ra pdf ( r = exp I σ σ σ ower n LOS component A k = = ower n random components σ 9-- Fredrk Tufvesson - ETI 85 9 RX Small-scale fadng Nakagam dstrbuton In many cases the receved sgnal can not be descrbed as a pure LOS + dffuse components The Nakagam dstrbuton s often used n such cases m m pdf r = r r Γ( m Ω Ω Γ ( m s the gamma functon Ω= r Ω m = ( r Ω m m ( ( exp( wth m t s possble to adjust the domnatng power 9-- Fredrk Tufvesson - ETI 85 Both small-scale and large-scale fadng Small-scale fadng Doppler shfts Large-scale fadng - lognormal fadng gves a certan mean Small scale fadng Raylegh dstrbuted gven a certan mean The two fadng processes adds up n a db-scale Suzuk dstrbuton: π r π r 4σ ln( F pdf ( r = e e σ σσ π log( σ σ F log-normal mean log-normal std small-scale std for complex components μ θ v r Recevng antenna moves wth speed v r at an angle θ relatve to the propagaton drecton of the ncomng wave, whch has frequency f. c Frequency of receved sgnal: f = f + ν where the doppler shft s v r ν = f cos( θ c The mal Doppler shft s ν = f v c 9-- Fredrk Tufvesson - ETI Fredrk Tufvesson - ETI 85

4 Small-scale fadng The Doppler spectrum Uncorrelated scatterng wth unform angular dstrbuton Doppler spectrum by Fourer transformaton of the tme correlaton of the sgnal: SD Doppler spectrum at center frequency f. ( ν f Condensed parameters The tme correlaton A property p closely related to the Doppler spectrun s the tme correlaton of the channel. It s n fact the nverse Fourer transform of the Doppler spectrum: ρ Δ t = ν exp j πνδ t d ν -4 t ( ( ( B measured theoretcal ( ( j πν Δ τ SD Δ e d ν = ρ Δτ Δτ π ν for ν < ν < ν ν for f ν f f + ν What does ths mean n practce? Frequency resp (db oston (m corr Tme oston (m Compare /(*π*v π =.44 s 9-- Fredrk Tufvesson - ETI Fredrk Tufvesson - ETI 85 4 Condensed parameters Coherence tme Gven the tme correlaton of a channel, we can defne the coherence tme T C : ρt ( Δt ρ t ( What does the coherence tme tell us? T C ρ t ( Δt It shows us over how long tme we can assume that the channel s farly constant. E.g. rado systems transmttng data n frames much shorter than T C wll not experence any fadng wthn a sngle frame. Narrow- versus wde-band Channel mpulse response The same rado propagaton envronment s experenced dfferently, dependng on the system bandwdth. Hgh BW Medum BW Low BW h ( τ h ( τ h ( τ τ τ τ 9-- Fredrk Tufvesson - ETI Fredrk Tufvesson - ETI 85 6

5 Narrow- versus wde-band Channel frequency response H( f db B B A narrow-band system (bandwdth B wll not experence any sgnfcant frequency selectvty or delay dsperson. A wde-band d system (bandwdth B wll however experence both frequency selectvty and delay dsperson. f Note that narrow- or wde-band depends on the relaton between the channel and the system bandwdth. It s not an absolute measure. 9-- Fredrk Tufvesson - ETI 85 7 Condensed parameters ower-delay profle (cont. We can reduce the D nto more compact descrptons of the channel: Total power (tme ntegrated: ( τ m = dτ Average mean delay: ( For our tapped-delay lne channel: N m = σ τ τ dτ τ σ Tm = = Tm = m m Average rms delay spread: N τ ( τ dτ τ σ = S = T m S = T m m 9-- Fredrk Tufvesson - ETI 85 8 = N m Condensed parameters Frequency correlaton A property p closely related to the power-delay yp profle (D s the frequency correlaton of the channel. It s n fact the Fourer transform of the D: Frequency resp (db ( Δ = ( exp ( Δ ρf f τ j π f τ d τ Frequency (Hz x 8 Freq corr based on D based on H(f ( Frequency (Hz x 7 Compare /(*π*τ rms =9.8 MHz 9-- Fredrk Tufvesson - ETI 85 9 Condensed parameters Coherence bandwdth Gven the frequency correlaton of a channel, we can defne the coherence bandwdth B C : ρ B C f ( Δf ρ ( What does the coherence f bandwdth tell us? It shows us over how large a bandwdth we can assume ρ f ( that the channel s farly constant. Rado systems usng a bandwdth much smaller than B C wll not notce Δf the frequency selectvty of the channel. 9-- Fredrk Tufvesson - ETI 85

6 Channel measures Complex delectrc constant conductvty j e, ff c delectrc constant Descrbes the delectrc materal n one sngle parameter 9-- Fredrk Tufvesson - ETI Fredrk Tufvesson - ETI 85 Reflecton and transmsson Dffracton Θe Θr reflected angle Θ e Θ r. ε ε transmtted tted angle snθ t snθ e snθ t snθ Θ e. Θ t 9-- Fredrk Tufvesson - ETI Fredrk Tufvesson - ETI 85 4

7 Dffracton, Huygen s prncple Dffracton Bullngton s method Each pont of a wavefront can be consdered as a source of a sphercal wave Bendng around corners and edges tangent Replace all screens wth one equvalent screen Heght determned by the steepest angle Smple but a bt optmstc equvalent screen E total exp jk x exp j /4 F F F k d d d d 9-- Fredrk Tufvesson - ETI Fredrk Tufvesson - ETI 85 6 Scatterng Krchhoff theory scatterng by rough surfaces Smooth surface Specular reflecton Rough surface Specular reflecton Scatterng calculate dstrbuton of the surface ampltude assume no shadowng from surface calculate l a new reflecton coeffcent for Gaussan surface dstrbuton angle of ncdence rough smooth exp k h sn standard d devaton of heght ht 9-- Fredrk Tufvesson - ETI Fredrk Tufvesson - ETI 85 8

8 Wavegudng The WSSUS model Assumptons Wavegudng effects often result n lower propagaton exponents n=.5-5 Ths means lower path loss along certan street corrdors A very common wde-band channel model s the WSSUS-model model. Recallng that the channel s composed of a number of dfferent contrbutons (ncomng waves, the followng s assumed: The channel s Wde-Sense Statonary (WSS, meanng that t the tme correlaton of the channel s nvarant over tme. (Contrbutons wth dfferent Doppler frequency are uncorrelated. The channel s bult up by Uncorrelated Scatterers (US, meanng that the frequency correlaton of the channels s nvarant over frequency. (Contrbutons wth dfferent delays are uncorrelated. 9-- Fredrk Tufvesson - ETI Fredrk Tufvesson - ETI 85 3 Modellng methods Stored channel mpulse responses realstc reproducble hard to cover all scenaros Determnstc channel models based on Maxwell s equatons ste specfc computatonally demandng Stochastc channel models descrbes the dstrbuton of the feld strength etc manly used for desgn and system comparsons 9-- Fredrk Tufvesson - ETI 85 3 The Okumura-Hata model How to calculate prop. loss Metropoltan areas Small/medumsze ctes Suburban envronments ( km L = A+ Blog d + C h b and h m O H n meter ( MHz ( b ( m ( h A = log f 3.8log h a h B= log b ( ( hm ( ( hm a( h m = C = 8.9 log.54. for f MHz 3. log for f 4 MHz (.log ( f.7 MHz h m (.56log ( f.8 MHz ( f MHz Rural areas ( f MHz ( f MHz log / log log Fredrk Tufvesson - ETI 85 3

9 The COST 3-Walfsh-Ikegam model How to calculate prop. loss Motley-Keenan ndoor model Free space L= L + L + L msd rts Buldng multscreen Roof-top to street For ndoor envronments, the attenuaton s heavly affected by the buldng structure, walls and floors play an mportant rule L L nlog d/d F wall F floor BS MS dstance dependent sum of attenuatons path loss from walls, - db/wall sum of attenuaton from the floors (often larger than wall attenuaton d ste specfc, snce t s vald for a partcular case Detals about calculatons can be found n the textbook, Secton Fredrk Tufvesson - ETI Fredrk Tufvesson - ETI ower delay profle arrval tme Often descrbed by a sngle exponental decay log( sc ( τ exp( τ / Sτ τ sc ( τ = otherwse delay spread τ If the bandwdth s hgh, the tme resoluton s large so we mght resolve the dfferent multpath th components Need to model arrval tme The Saleh-Valenzuela l l model: The Δ-K-model: K though often there s more than one cluster ( τ = log( sc ( τ c k c sc(, k c τ τ τ = k Sτ, k otherwse τ arrval rate: S S λ ( t Kλ ( t 9-- Fredrk Tufvesson - ETI Fredrk Tufvesson - ETI 85 36

10 Saleh-Valenzuela Model Saleh-Valenzuela Model (cont d Orgnally not for UWB [A.M. Saleh, R.A. Valenzuela, 987] MCs arrve n clusters Impulse responses gven by Typcal nter-cluster decay: -3 ns Typcal ntra-cluster decay: -6 ns ath nterarrval tmes gven by osson-dstrbuted arrval process Dfferent occurance rates for clusters (Λ and rays (λ 9-- Fredrk Tufvesson - ETI Fredrk Tufvesson - ETI Wdeband models COST 7 model for GSM Four specfed power-delay profles [ db] 3 [ db] RURAL AREA BAD URBAN τ [ μs] [ db] TYICAL URBAN [ db] HILLY TERRAIN τ [ μs] τ [ μs] τ [ μs] 9-- Fredrk Tufvesson - ETI Wdeband models COST 7 model for GSM Four specfed Doppler spectra ( ν, τ ( ν, τ s CLASS GAUS τ.5 μs.5 μs < τ μs GAUS τ μs ν +ν ν (, ν τ s RICE > Shortest path n rural areas ν +ν ν s s (, ν τ +ν 9-- Fredrk Tufvesson - ETI ν

11 Narrowband vs. UWB Channel Models Assumptons about standard wreless channels: Narrowband n the RF sense (bandwdth much smaller than carrer frequency WSSUS assumpton Complex Gaussan fadng (Raylegh or Rce n each delay tap Specaltes of UWB channel: Bandwdth comparable to carrer frequency Dfferent frequency components can see dfferent reflecton/ dffracton coeffcents of obstacles Few components per delay bn central lmt theorem (Gaussan fadng not vald anymore New channel models are needed!! Why drectonal channel models? The spatal doman can be used to ncrease the spectral effcency of the system Smart antennas MIMO systems Need to know drectonal propertes How many sgnfcant reflecton ponts? Whch drectons? Model ndependent on specfc antenna pattern 9-- Fredrk Tufvesson - ETI Fredrk Tufvesson - ETI 85 4 Double drectonal mpulse response Angular spread TX poston RX poston number of multpath components for these postons N r h t, r TX, r RX,,,, h l t, r TX, r RX,,,, l E s,,, s,,, s,,, double drectonal delay power spectrum DDDS,, s,,, d delay drecton-of-departure drecton-of-arrvalof angular delay power spectrum ADS, DDDS,, G MS d h l t, r TX, r RX,,, a l e j l l l l l angular power spectrum τl l AS ADS, d power AS d 9-- Fredrk Tufvesson - ETI Fredrk Tufvesson - ETI 85 44

12 Goals of MIMO Sgnal model Array gan ncrease power beamformng Transmtter ower Recever Antenna Dversty mtgate fadng space-tme codng TX Antenna Antenna H, H, H n, T Antenna RX H,n R Spatal multplexng l multply data rates spatally orthogonal channels H, n R H n, T n R Antenna n T H...transfer functon Antenna n R γ...snr at each recever branch 9-- Fredrk Tufvesson - ETI Fredrk Tufvesson - ETI Capacty formula Instantaneous channel characterzed by matrx H Shannon s formula (for two-dmensonal symbols: Foschn s formula: C = log ( + H bts / s / Hz γ γ C = log det I + HH nt bts / s / Hz H / n R Channel measurements In order to model the channel behavor we need to measure ts propertes Tme doman measurements mpulse sounder correlatve sounder Frequency doman measurements Vector network analyzer Drectonal measurements drectonal antennas real antenna arrays multplexed arrays vrtual arrays 9-- Fredrk Tufvesson - ETI Fredrk Tufvesson - ETI 85 48

13 Real, multplexed, and vrtual arrays Real array: smultaneous measurement at all antenna elements RX RX RX Multplexed array: short tme ntervals between measurements at dfferent elements Dgtal Sgnal rocessng RX Drectonal analyss The DoA can, e.g., be estmated by correlatng the receved sgnals wth steerng φ vectors. d a exp jk dcos exp jk k dcos d exp j M k dcos Vrtual array: long delay no problem wth mutual couplng Dgtal Sgnal rocessng RX Dgtal Sgnal rocessng An element spacng of d=5.8 cm d sn φ and an angle of arrval of φ = degrees gves a tme delay of s between neghborng elements 9-- Fredrk Tufvesson - ETI Fredrk Tufvesson - ETI 85 5 Important antenna parameters Drectvty Total power n a certan drecton compared to total t transmtted power Effcency R rad η = R + R + R rad ohmc match Q-factor Stored energy compared to dsspated energy Mean effectve gan Include nfluence of random channel Average receved power compared to average receved power by sotropc antenna n real envronment olarzaton Bandwdth 9-- Fredrk Tufvesson - ETI 85 5