Channel model. Free space propagation

Transcription

1 //06 Channel model Free spae rado propagaton Terrestral propagaton - refleton, dffraton, satterng arge-sale fadng Empral models Small-sale fadng Nose and nterferene Wreless Systems 06 Free spae propagaton P T P PT p 4π P A T e π 4 eeve antenna aperture (effetve area) : A e eeve antenna aperture: A e Isotrop antenna A e, so λ 4π PT 4π p P ( 4π / λ) λ oss n free spae

2 //06 Transmtter range Assume Tx and x wth sotrop antennas x senstvty S -90 dbm P T 00 mw, f 800 MHz S 0log S dbm P 00 mw 0 9 S 0 mw T p mw p 4π λ 4π / f 4πf p π m 3 Dretonal antenna Antenna man lobe Pea gan 3 db beamwdth power densty at ( θ, φ) G T ( θ, φ) power densty of sotrop antenna effetve area at ( θ, φ) G ( θ, φ) effetve area of sotrop antenna Transmttng antenna πd A e η 4 G pea π η D λ Parabol antenna wth dameter D 4πAe ( θ, φ) G T ( θ, φ) G ( θ, φ) λ eproty 4

3 //06 Non-sotrop antennas Frs equaton PT GT G P p Assume a mrowe lne-of-sght ln Tx and x are spaed by 40m P T 00 mw, f 4 GHz A e 0.5 m Ae Ae f G GT λ / 4π / 4π p 4π λ 4π / f -6 Ae f 0 P PT 00mW 36 P 0dBm 60dB 5.5dB -55.5dBm where G G T 43.5dB 5 Terrestral propagaton efleton Dffraton Satterng Multpath transmsson Fadng Fadng arge sale (Shadow fadng) Small sale (Multpath fadng) 6 3

4 //06 efleton Fadng ours h T efletons. Frequeny ndependent transmsson. oss 4 (40dB/de) 3. Dependent on antenna heghts h E E tot tot Two-ray model >> h, h T E E00 φ and P Etotλ φ d refl ht h π λ λ P OS + E P G G T T refl ( h h ) T 4 7 Dffraton Huygen s prnple rado wes bend over obstales and reah shadow areas Fresnel zones Path length dfferene nλ/ (onstrutve or destrutve) 8 4

5 //06 Knfe-edge dffraton model Phase dfferene between OS and beam at the edge h ν r Obstruton of st Fresnel zone: 7dB Obstruton of half of st zone (h0) : 6dB For h>0 large λresults n less dffraton loss 9 Satterng efleted energy s spread n all dretons Crtal heght of surfae protuberanes Smooth surfae ough surfae h λ 8snθ h < h h > h Satterng results n a multtude of sgnal paths Usually elevates sgnal level predted by refleton and dffraton 0 5

6 //06 arge sale fadng eeved.power [dbm] -40 db/de -0 db/de Free spae Urban area Terran obstales Suburban area log(dstane) Usual loss db/de arge sale fadng (ont d) eeved Power [dbm] Gaussan dstrbuton wth std devaton of 6 0 db X σ P ( d ) P ( d ) T ( d ) ( d0) + 0n log [ dbm] d d 0 + X σ log(dstane) og-normal dstrbuton 6

7 //06 Empral models Varety of models for outdoor and ndoor appl. - ongley-e, Omura, Hata, - Cox, Alexander, Ersson, Oumura outdoor model (968) useful for urban areas 50MHz GHz m 00m Antenna heght > 30m Medan of loss 50 (db) F + A mu (f, d) - G(h te ) - G(h re ) - G area Free spae loss Medan attenuaton Correton for antenna gans and envronment 3 Oumura model (ont d) Base staton and moble antenna heghts 4 7

8 //06 Small sale fadng P α P s( t) s osω t v( t) 0 a os Multple rays by refleton and satterng ( ω ( t t τ ) + θ ) Small sale fadng effet (random) Average power due to large sale fadng Average delay due to large sale fadng andom phase andom nremental delay 5 v( t) a os Small sale fadng (ont d) ( ω ( t t τ ) + θ ) ( ω ( t t +φ) v t) a os ) ( aylegh PDF andom envelope wth aylegh dstrbuton (no lne of sght) f ( a) a a exp σ σ Exponental PDF of nstantaneous power Sne P a then also α aylegh dstrbuted f ( α) dα f ( P) dp f ( P) and P α P ( ) P σ P exp σ P 6 8

9 //06 Small sale fadng wth dret ray v( t) V os ( t t ) + a ( ω ( t t τ ) θ ) ω os + an PDF ne of sght ray ( ω ( t t +φ) v t) a os ) ( andom envelope wth e dstrbuton f dret ray (lne of sght) s sgnfant f ( a) a a V exp σ σ I av σ 0 Sne P a then also α e (an) dstrbuted For V >> σ anpdf s smlar to Gaussan PDF 7 Doppler effet β υ β υ os β υ f f os β λ λ υ υ f max f Max Doppler shft λ Extra effet on fadng a ( πf ( t t ) + φ f t) v( t) os π Typal fadng envelope, f 900 MHz Effet of tme delay and Doppler Doppler ontrbuton Average fade duraton < f ~ fmax 00 fades / se max 0 mse ate of Doppler fadng ~ fmax 8 9

10 //06 Multpath propagaton Two-tone model of WB sgnal s ( t) a os Inremental delay model f τ ) τ ( ω ( t t τ ) + ω t + θ ) τ exp τ ( τ σ τ s ( t) a os d ( ω t + θ ) τ arge sale fadng Small sale nl. Doppler and random nose s also std devaton alled delay spread τ ~a few µse or less Envelope orrelaton funton E a, a) E( a) E( a) ρa, σ E( a σ σ ( ) E ( a ) 9 Multpath propagaton (ont d) ρ a (0,) ρa ρa 0 Both omponents fade n the same way Fadng s not dstortng (flat fadng) Channel s dstortng or f BW large enough dstnt ehos may appear whh an be resolved le n CDMA systems aylegh fadng and exp. dstrbuton of τ Doppler Dfferene n arrval tme I0 ( ωm τ ) ρa + ( ωτ ) Bandwdth 0 0

11 //06 Coherene bandwdth ω m τ 0 ow orrelaton ρa + ( ωτ ) ρ a 0.5 ωτ > < π Bτ > Coherene bandwdth B oh πτ For ω τ > 0 m B oh B > B oh B >, BT πτ Frequeny seletve fadng ow orrelaton between the sgnal omponents Symbol tme T < πτ Seletve fadng results n ISI (Inter-Symbol Interferene) Power delay profle P(τ) eeved as mpulse response (statonary hannel) τ τ τ 3 τ 4 τ ( τ ) P( τ ) τ P( τ ) P( τ ) τ P( τ ) Delay spread σ τ τ τ ) ( ) ( 5σ τ B for freq. orrelaton funton 0.5 oh

12 //06 Coherene tme Assume ω 0 ρ I ( ω ) a 0 m τ Channel nvarant statstally f ρ a ρ a 0. 5 τ oh 0.8 f m Dstorton due to Doppler: T 0.8 > Tme seletve fadng f m Example: v 00 m/h, f GHz ν f fm 90Hz τ oh 0.8/ 90 ms - T < ms f > 500s requred to od Doppler dstorton symbol 3 Multpath propagaton (summary) Two nds of dstorton: B > T < B oh B oh Frequeny seletve fadng and ISI T > τ oh Tme seletve fadng f due to moblty m 4

13 //06 Nose and nterferene Envronmental nose (man made) Sy nose Eletron deves nose Multple aess nterferene External nterferene 5 3