TLCOM 612 Advanced Telecommunications Engineering II

Transcription

1 TLCOM 62 Advanced Telecommuncatons Engneerng II Wnter 2 Outlne Presentatons The moble rado sgnal envronment Combned fadng effects and nose Delay spread and Coherence bandwdth Doppler Shft Fast vs. Slow Fadng Frequency Selectve vs. Frequency Non-selectve fadng Equalzaton

2 Moble-Rado Sgnal long-term fadng attenuaton due to free-space loss attenuaton due to terran short-term fadng varatons n receved sgnal due to moble or statonary scatterers multpath many factors nfluence short-term fadng, such as, multpath, speed and bandwdth Moble-Rado Sgnal moble may be n moton or statonary, envronment may n moton or statonary moton wll cause changes n the scatterers and therefore changes n the receved sgnal f multple reflectors are present at dfferent dstances (or multple reflectons occur) then delay spread occurs can also cause correlaton between sgnals of neghborng frequences random frequency modulaton can occur because of dfferent Doppler shfts on dfferent multpaths 2

3 Moble-Rado Sgnal the reflectng objects or scatterers n envronment cause sgnal dsspaton n ampltude, phase and tme coherence bandwdth vs. delay spread fast vs. slow fadng frequency-selectve vs. frequencynonselectve fadng Moble-Rado Sgnal Multpath Fadng Transmtted Sgnal Representatons { ( ω φ )} ( ω φ ) ( ω φ ) s ( t) = a exp j t + { } { } s ( t) = R a exp j t + s ( t) = a cos t + a, φ constants 3

4 Moble-Rado Sgnal Multpath Fadng statonary moble and scatterers, can perhaps exactly calculate sgnal f there are few paths movng moble and/or scatterers typcally a statstcal analyss s performed τ = τ τ Moble-Rado Sgnal Multpath Fadng Receved Sgnal wth N paths N = ( τ ) s( t) = a s t, wth a complex propagaton tme of the th path τ = τ τ 4

5 Moble-Rado Sgnal Multpath Fadng (Statonary Scatterers) Rewrtng slghtly, { [ ] } s( t) = x( t τ )exp j 2 π f ( t τ ) + φ where the complex envelope of the receved sgnal s N x( t) = a a exp j2 f { π τ} = Moble-Rado Sgnal Multpath Fadng (Movng Scatterers) Wth a tme-varyng attenuaton and delay the receved sgnal becomes s( t) = x( t)exp( jφ )exp( j2 π f t) wth complex envelope N { π τ } x( t) = a a ( t)exp j2 f ( t) = 5

6 Moble-Rado Sgnal Multpath Fadng (Movng Scatterers) = = ( π τ ) 2 2 ( π τ ) Agan, to rewrte let R = a ( t)cos 2 f ( t) and N S = a ( t)sn 2 f ( t) then x( t) = a ( R js) = A( t)exp( jϒ( t)) where A( t) = a R + S and ϒ ( t) = tan N S R Moble-Rado Sgnal Doppler Shft Path dfference l = d cosθ = v t cos θ where d=path length v=constant velocty Phase dfference 2π l 2π v t φ = = cosθ λ λ 6

7 Moble-Rado Sgnal Doppler Shft Apparent change n frequency f d φ = = 2π t v λ c o s θ Observe that as moble moves toward basestaton the frequency ncreases and vce versa Moble-Rado Sgnal max Power Delay Profle Take a pulsed, RF sgnal where τ T p s(t)= R ( p(t)exp( j2πfct) ) p(t)=2 τ / T t T, elsewhere max = maxmum excess delay = pulse wdth p p 7

8 Moble-Rado Sgnal Power Delay Profle (from Rappaport) The lowpass channel output s N r( t) = a exp ( jθ ) p( t τ ) 2 = N τ T max p = a exp( jθ ) t τ = Tp 2 Moble-Rado Sgnal Power Delay Profle (from Rappaport) Instantaneous multpath power delay profle At tme t for resovable multpath components τmax 2 * r( t) = r( t) r ( t) dt τ = N = max a 2 ( t ) 8

9 Moble-Rado Sgnal Power Delay Profle (from Rappaport) plotted as relatve receved power as a functon of excess delay average nstantaneous power delay profle measurements over a gven area Moble-Rado Sgnal Delay parameters Mean excess delay τ = rms delay spread σ τ τ τ a τ 2 a τ = where = a τ 2 a 2 2 9

10 Moble-Rado Sgnal Typcal Values of rms Delay Spread (from Rappaport) Area Freq spread locaton (MHz) mcrosec. Urban 9.3 NYC Urban SanFran Suburb typcal Indoor offce Moble-Rado Sgnal Delay parameters (contnued) Def: maxmum excess delay (X db) s the tme at whch the multpath energry falls below X db of the strongest multpath

11 Moble-Rado Sgnal Coherence Bandwdth the range of frequences over whch the channel s consdered flat all frequences n ths range have equal attenuaton and lnear phase derved from the delay spread Moble-Rado Sgnal Coherence Bandwdth estmates based on correlaton General: B AM: B C FM,PM: B C C = 8σ = 2πσ τ τ = 4πσ τ

12 Moble-Rado Sgnal Doppler Spread we prevously saw how to calculate Doppler shft for a multpath B d Doppler spread,, s defned as the maxmum Doppler shft f the sgnal bandwdth s sgnfcantly larger than the Doppler spread the effects of Doppler spread are neglgble Moble-Rado Sgnal Coherence tme measures the tme-nvarance of the channel mpulse response tme duraton over whch two sgnals are lkely to be strongly ampltude correlated T C B d 2

13 Moble-Rado Sgnal Classfcaton of Fadng Channels Flat Fadng (frequency non-selectve) sgnal BW < channel BW delay spread < symbol perod Frequency Selectve Fadng sgnal BW > channel BW delay spread > symbol perod Moble-Rado Sgnal Classfcaton of Fadng Channels Fast Fadng large Doppler spread coherence tme < symbol perod channel vares faster than baseband sgnal Slow Fadng lttle Doppler spread coherence tme > symbol perod channel vares slower than baseband sgnal 3

14 Moble-Rado Sgnal A Closer Look At Classfcaton of Fadng Channels nondspersve channels channels dspersve n tme channels dspersve n frequency doubly dspersve channels Much of the followng materal on channel classfcaton s adopted from R.S. Kennedy, Fadng Dspersve Communcatons Channels, Wley,969, An excellent and comprehensve reference. Moble-Rado Sgnal Nondspersve Channels Raylegh Nakagam-Rce The receved sgnal for a Raylegh channel looks lke y( t) = a ( t) s ( t) where a ( t) s a complex random process representng statstcally ndependent ampltude and phase. The ampltude s Raylegh dstrbuted, whle the phase s unformly dstrbuted. Note that t s assumed that there are no path length dfferences. 4

15 Moble-Rado Sgnal Nondspersve Channels (contnued) Ths can be derved as follows: N ( π π θ φ ) E = E c cos 2 f t + 2 f cos t + Z n c d n n n= where f s the max. Doppler shft, θ s the ncdent angle of d each path n, and φ s the phase of each path. We assume θ are n random, unformly dstrbuted over +[- π, π ]. n n Moble-Rado Sgnal Nondspersve Channels (contnued) We can wrte the prevous n quadrature-carrer form E = T ( t)cos ω ( t) T ( t)sn ω ( t) where and z c c s c N ( π θ φ ) T ( t) = E c cos 2 f cos t + c n d n n n= N ( π θ φ ) T ( t) = E c sn 2 f cos t + s n d n n n= 5

16 Moble-Rado Sgnal Nondspersve Channels (contnued) These n-phase and quadrature components are Gaussan RPs wth propertes: and T c = T = c = s = z = s c p( T ) = s T T E E T T = e 2 2πσ 2 2 T / 2σ 2 2 for T = Tc, Ts and σ = E / 2. / 2 Moble-Rado Sgnal Nondspersve Channels (contnued) 2 2 Thus, the envelope of Ez s r Tc Ts and obvously from before r 2 2 r / 2σ p( r) = e for r > 2 σ and p( θ ) = over [ π, π ]. 2π = + 6

17 Moble-Rado Sgnal Nondspersve Channels (contnued) Smlarly, for a Rcan channel we defne the receved sgnal to be y( t) = z( t) s( t) where z( t) s gven as jϕ z( t) = Γ e + a( t). Note that we have a dffuse and a specular component. Ths model s useful where there s a strong LOS component as may occur n a mcrocell system. Moble-Rado Sgnal Nondspersve Channels (contnued) Recall that the envelope of the receved sgnal s gven as 2 2 r r Γ Γr p( r) = exp I 2 2 for r 2 > σ 2σ σ K = Γ σ K 2 2 Lettng / 2 then as we have the AWGN channel and as K we have the Raylegh channel. The Rcan channels are lkewse a subset of the Nakagam channel. 7

18 Moble-Rado Sgnal Channels Dspersve n Tme path length dfferences, but no Doppler shft for scatterers termed tme-flat fadng channel Assume the transmtted sgnal s( t) s tmelmted to [ T / 2, T / 2] and s bandlmted to [ W / 2, W / 2]. Gven a delay spread n Lee's notaton of, the receved sgnal y( t) = a s( t τ ) s then spread over the range T+ sec. Moble-Rado Sgnal Channels Dspersve n Tme (contnued) If << T then there s no apparent spreadng of the sgnal, but t may be dstorted. Example: Assume << / W. Recall that Bc, ths means that W << B. We can assume a sgnal of bandwdth W does c not change much n ntervals of duraton <<. W 8

19 Moble-Rado Sgnal Channels Dspersve n Tme (contnued) Then f W / Bc << s ( t τ ) s ( t) for τ < 2 so that y(t) s(t) a Therefore, the dstorton s due to attenuatons and phase shfts. Ths looks lke Raylegh fadng! Concluson: If W << B c ths channel looks nondspersve. Moble-Rado Sgnal Channels Dspersve n Tme (contnued) But, as W ncrease so that W / B the assumpton that s( t τ ) s( t) no longer holds. Then the scatterers can combne destructvely even f T >>. Thus, f / W << << T there s lttle tme spreadng n the receved waveform, but the receved waveform may be severely corrupted. c 9

20 Moble-Rado Sgnal Channels Dspersve n Tme Summary << W / B c /T << Dstorted? no Dspersed? no >> << yes no >> >> yes yes Moble-Rado Sgnal Channels Dspersve n Frequency dual of tme-dspersve channel exchange tme-sgnal for frequency-sgnal n the prevous dscusson and replace the delay spread wth the Doppler spread Gven the same tme and bandlmted sgnal, f W << B then the bandwdth of the receved sgnal s much greater than W,.e. we get frequency spread. Also, f B non-dspersve. d << the channel appears T d 2

21 Moble-Rado Sgnal Channels Dspersve n Frequency Summary TB B / W d << << d Dstorted? no Dspersed? no >> << yes no >> >> yes yes Moble-Rado Sgnal Tme-Selectve Fadng Channel fast fadng = Doppler spread and short coherence tme slow fadng = low Doppler spread and large coherence tme 2

22 Moble-Rado Sgnal Doubly Dspersve Channels combne the effects of the tme and frequency dsperson Moble-Rado Sgnal Classfcaton of Fadng Channels Flat Fadng (frequency non-selectve) sgnal BW < channel BW delay spread < symbol perod Frequency Selectve Fadng sgnal BW > channel BW delay spread > symbol perod 22

23 Moble-Rado Sgnal Classfcaton of Fadng Channels Fast Fadng large Doppler spread coherence tme < symbol perod channel vares faster than baseband sgnal Slow Fadng lttle Doppler spread coherence tme > symbol perod channel vares slower than baseband sgnal 23