Channel modelling repetition

Transcription

1 Channel Modelling ETIM10 Lecture no: 11 Channel modelling repetition Fredrik Tufvesson Department of Electrical and Information Technology Lund University, Sweden Fredrik Tufvesson - ETIM10 1

2 Why channel modelling? The performance of a radio system is ultimately determined by the radio channel The channel models basis for system design algorithm design antenna design etc. Trend towards more interaction system-channel MIMO UWB radio based positioning Without reliable channel models, it is hard to design radio systems that work well in real environments Fredrik Tufvesson - ETIM10

3 THE RADIO CHANNEL It is more than just a loss Some examples: behavior in time/place? behavior in frequency? directional properties? bandwidth dependency? behavior in delay? Fredrik Tufvesson - ETIM10 3

4 THE RADIO CHANNEL Some properties Path loss Roughly, received power decays exponentially with distance Received power Transmitted power Distance Propagation exponent Large-scale fading Large objects, compared to a wavelength, in the signal path obstruct the signal Small-scale fading Objects reflecting the signal causes multipath propagation from transmitter to receiver Fredrik Tufvesson - ETIM10 4

5 Free-space loss If we assume RX antenna to be isotropic: P RX λ = 4π d P TX d A RX Attenuation between two isotropic antennas in free space is (free-space loss): L free ( d ) = 4πd λ Fredrik Tufvesson - ETIM10 5

6 Large-scale fading Log-normal distribution Measurements confirm that in many situations, the large-scale fading of the received signal strength has a normal distribution in the db domain. POWER [db] pdf ( L db ) Note db scale P TX db L db P RX db pdf ( LdB ) Deterministic mean value of path loss, L 0 db 1 = exp ( L ) db L0 db πσfdb σ FdB db Standard deviation σ 4K 10 db FdB Fredrik Tufvesson - ETIM10 6

7 Small-scale fading Many incoming waves Many incoming waves with independent amplitudes and phases Add them up as phasors r1, φ1 r, φ r 3 φ 3 φ r φ r 1 φ 1 r3, φ3 r4, φ4 r, φ φ 4 r 4 r ( φ) = ( φ ) + ( φ ) + ( φ ) + ( φ ) rexp j r exp j r exp j r exp j r exp j Fredrik Tufvesson - ETIM10 7

8 Small-scale fading Rayleigh fading No dominant component (no line-of-sight) TX X RX Tap distribution D Gaussian (zero mean) Amplitude distribution 0.8 Rayleigh 0.6 Im( a ) Re( a) r = a No line-of-sight component ( ) pdf r r r = exp σ σ Fredrik Tufvesson - ETIM10 8

9 Small-scale fading Rice fading Tap distribution D Gaussian (non-zero mean) A Im( a ) Re( a) A dominant component (line of sight) r = α Amplitude distribution Rice k = 30 k = 10 k = 0 TX RX Line-of-sight (LOS) component with amplitude A. ( ) pdf r r r + A ra = exp I 0 σ σ σ Power in LOS component A k = = Power in random components σ Fredrik Tufvesson - ETIM10 9

10 Small-scale fading Nakagami distribution In many cases the received signal can not be described as a pure LOS + diffuse components The Nakagami distribution is often used in such cases m m pdf r r r Γ( m) Ω Ω Γ( m) Ω= m = m m 1 ( ) = ( ) exp( ) r is the gamma function Ω ( r Ω) with m it is possible to adjust the dominating power Fredrik Tufvesson - ETIM10 10

11 Both small-scale and large-scale fading Large-scale fading - lognormal fading gives a certain mean Small scale fading Rayleigh distributed given a certain mean The two fading processes adds up in a db-scale Suzuki distribution: log-normal mean 4σ pdf () r e e = 0 π r πr 0 1 σ σσ π ln(10) F 0log( σ ) µ σ log-normal std small-scale std for complex components F Fredrik Tufvesson - ETIM10 11

12 Small-scale fading Doppler shifts v r θ Receiving antenna moves with speed v r at an angle θ relative to the propagation direction of the incoming wave, which has frequency f 0. c Frequency of received signal: f = f0 + ν where the doppler shift is ν = v r f0 cos( θ) c The maximal Doppler shift is ν = f max 0 v c Fredrik Tufvesson - ETIM10 1

13 Small-scale fading The Doppler spectrum Uncorrelated scattering with uniform angular distribution SD ( ν f ) Doppler spectrum at center frequency f 0. 0 Doppler spectrum by Fourier transformation of the time correlation of the signal: D j ( ) ( ) πνδτ S ν = ρ Δτ e dδτ π ν 1 max ν for νmax < ν < νmax f 0 ν max f 0 f0 + ν max What does this mean in practice? Fredrik Tufvesson - ETIM10 13

14 Condensed parameters The time correlation A property closely related to the Doppler spectrun is the time correlation of the channel. It is in fact the inverse Fourier transform of the Doppler spectrum: t ( ) ( ) exp( ) ρ t P ν j πν t dν Δ = B Δ 1 measured theoretical Frequency resp (db) Time corr Position (m) Position (m) Compare 1/(*π*v max )=0.014 s Fredrik Tufvesson - ETIM10 14

15 Condensed parameters Coherence time Given the time correlation of a channel, we can define the coherence time T C : ρ t ( Δt ) ρ t ( 0) ρ t ( 0) What does the coherence time tell us? It shows us over how long time we can assume that the channel is fairly constant. T C Δt E.g. radio systems transmitting data in frames much shorter than T C will not experience any fading within a single frame Fredrik Tufvesson - ETIM10 15

16 Narrow- versus wide-band Channel impulse response The same radio propagation environment is experienced differently, depending on the system bandwidth. High BW Medium BW Low BW h( τ ) h( τ ) h( τ ) τ τ τ Fredrik Tufvesson - ETIM10 16

17 Narrow- versus wide-band Channel frequency response H ( f ) db A narrow-band system (bandwidth B 1 ) will not experience any significant frequency selectivity or delay dispersion. A wide-band system (bandwidth B ) will however experience both frequency selectivity and delay dispersion. B 1 B f Note that narrow- or wide-band depends on the relation between the channel and the system bandwidth. It is not an absolute measure Fredrik Tufvesson - ETIM10 17

18 Condensed parameters Power-delay profile (cont.) We can reduce the PDP into more compact descriptions of the channel: Total power (time integrated): ( τ) Pm = P dτ Average mean delay: T m S ( ) τp τ dτ = P Average rms delay spread: m ( ) τ P τ dτ = T P m For our tapped-delay line channel: N = σ Fredrik Tufvesson - ETIM10 18 P T m m = i= 1 N i= 1 i τ σ N τi σi i= 1 m S = Tm Pm i P m i

19 Condensed parameters Frequency correlation A property closely related to the power-delay profile (PDP) is the frequency correlation of the channel. It is in fact the Fourier transform of the PDP: ρ ( ) ( ) exp( ) f Δ f = P τ j πδfτ dτ Frequency resp (db) Freq corr based on PDP based on H(f) Frequency (Hz) x Frequency (Hz) x 10 7 Compare 1/(*π*τ rms )=9.8 MHz Fredrik Tufvesson - ETIM10 19

20 Condensed parameters Coherence bandwidth Given the frequency correlation of a channel, we can define the coherence bandwidth B C : B C ρ f ( Δf ) ρ f ( 0) ρ f ( 0) Δf What does the coherence bandwidth tell us? It shows us over how large a bandwidth we can assume that the channel is fairly constant. Radio systems using a bandwidth much smaller than B C will not notice the frequency selectivity of the channel Fredrik Tufvesson - ETIM10 0

21 Channel measures Fredrik Tufvesson - ETIM10 1

22 Complex dielectric constant conductivity i i j e,i f c dielectric constant Describes the dielectric material in one single parameter Fredrik Tufvesson - ETIM10

23 Reflection and transmission Θe Θr reflected angle ε 1 ε transmitted angle sin t 1 sin e. Θ t Fredrik Tufvesson - ETIM10 3

24 Diffraction Fredrik Tufvesson - ETIM10 4

25 Diffraction, Huygen s principle Each point of a wavefront can be considered as a source of a spherical wave Bending around corners and edges Fredrik Tufvesson - ETIM10 5

26 Diffraction Bullington s method tangent Replace all screens with one equivalent screen Height determined by the steepest angle Simple but a bit optimistic equivalent screen E total exp jk 0 x 1 exp j /4 F F F k d 1 d d 1 d Fredrik Tufvesson - ETIM10 6

27 Scattering Specular reflection Specular reflection Scattering Smooth surface Rough surface Fredrik Tufvesson - ETIM10 7

28 Kirchhoff theory scattering by rough surfaces calculate distribution of the surface amplitude assume no shadowing from surface calculate a new reflection coefficient for Gaussian surface distribution angle of incidence rough smoothexp k 0 h sin standard deviation of height Fredrik Tufvesson - ETIM10 8

29 Waveguiding Waveguiding effects often result in lower propagation exponents n=1.5-5 This means lower path loss along certain street corridors Fredrik Tufvesson - ETIM10 9

30 The WSSUS model Assumptions A very common wide-band channel model is the WSSUS-model. Recalling that the channel is composed of a number of different contributions (incoming waves), the following is assumed: The channel is Wide-Sense Stationary (WSS), meaning that the time correlation of the channel is invariant over time. (Contributions with different Doppler frequency are uncorrelated.) The channel is built up by Uncorrelated Scatterers (US), meaning that the frequency correlation of the channels is invariant over frequency. (Contributions with different delays are uncorrelated.) Fredrik Tufvesson - ETIM10 30

31 Modelling methods Stored channel impulse responses realistic reproducible hard to cover all scenarios Deterministic channel models based on Maxwell s equations site specific computationally demanding Stochastic channel models describes the distribution of the field strength etc mainly used for design and system comparisons Fredrik Tufvesson - ETIM10 31

32 The Okumura-Hata model How to calculate prop. loss Metropolitan areas Small/mediumsize cities Suburban environments Rural areas ( ) km LO H= A+ Blog d + C ( 0 MHz ) ( b ) ( m ) A= log f 13.8 log h a h B= log ( ( hm )) ( ( hm )) ( h ) ah ( m ) = ( 1.1log( f0 MHz ) 0.7) ( f0 MHz ) h ( 1.56log 0.8) 8.9 log for f 00 MHz b 3. log for f 400 MHz m Fredrik Tufvesson - ETIM C = 0 0 ( f ) 0 MHz log /8 5.4 ( f ) 0 MHz ( f0 MHz ) h b and h m in meter 4.78 log log 40.94

33 The COST 31-Walfish-Ikegami model How to calculate prop. loss L= L0 + Lmsd + Lrts Free space Building multiscreen Roof-top to street BS MS d Details about calculations can be found in the textbook, Section Fredrik Tufvesson - ETIM10 33

34 Motley-Keenan indoor model For indoor environments, the attenuation is heavily affected by the building structure, walls and floors play an important rule PL PL 0 10nlog d/d 0 F wall F floor distance dependent path loss sum of attenuations from walls, 1-0 db/wall sum of attenuation from the floors (often larger than wall attenuation) site specific, since it is valid for a particular case Fredrik Tufvesson - ETIM10 34

35 Power delay profile Often described by a single exponential decay P sc () τ exp( τ / Sτ ) τ 0 = 0 otherwise log( Psc( τ )) τ delay spread though often there is more than one cluster P() τ = k P S c k c τ, k P sc 0 ( τ τ ) τ 0 c 0, k otherwise log( Psc( τ )) τ Fredrik Tufvesson - ETIM10 35

36 arrival time If the bandwidth is high, the time resolution is large so we might resolve the different multipath components Need to model arrival time The Saleh-Valenzuela model: The Δ-K-model: S1 S arrival rate: λ () t 0 Kλ () t Fredrik Tufvesson - ETIM10 36

37 Saleh-Valenzuela Model Originally not for UWB [A.M. Saleh, R.A. Valenzuela, 1987] MPCs arrive in clusters Impulse responses given by Path interarrival times given by Poisson-distributed arrival process Different occurance rates for clusters (L) and rays (l) Fredrik Tufvesson - ETIM10 37

38 Saleh-Valenzuela Model (cont d) Typical inter-cluster decay: ns Typical intra-cluster decay: 1-60 ns Fredrik Tufvesson - ETIM10 38

39 Wideband models COST 07 model for GSM Four specified power-delay profiles P [ db] RURAL AREA P [ db] 30 τ [ µs ] τ [ µs] TYPICAL URBAN P [ db] BAD URBAN P [ db] 30 τ [ µs ] τ [ µs] Fredrik Tufvesson - ETIM HILLY TERRAIN

40 Wideband models COST 07 model for GSM Four specified Doppler spectra P ντ, s ( ) i (, ) P ντ s i CLASS GAUS1 τ 0.5 µ s 0.5 µ s < τ µ s i i ν max 0 (, ) P ντ s +ν max i ν max 0 (, ) P ντ s +ν max i GAUS τ µ s i RICE > Shortest path in rural areas ν max 0 +ν max ν max 0 +ν max Fredrik Tufvesson - ETIM10 40

41 Narrowband vs. UWB Channel Models Assumptions about standard wireless channels: Narrowband in the RF sense (bandwidth much smaller than carrier frequency WSSUS assumption Complex Gaussian fading (Rayleigh or Rice) in each delay tap Specialties of UWB channel: Bandwidth comparable to carrier frequency Different frequency components can see different reflection/ diffraction coefficients of obstacles Few components per delay bin central limit theorem (Gaussian fading) not valid anymore ð New channel models are needed!! Fredrik Tufvesson - ETIM10 41

42 Why directional channel models? The spatial domain can be used to increase the spectral efficiency of the system Smart antennas MIMO systems Need to know directional properties How many significant reflection points? Which directions? Model independent on specific antenna pattern Fredrik Tufvesson - ETIM10 4

43 Double directional impulse response TX position RX position number of multipath components for these positions h t, r TX, r RX,,, N r 1 h t, r TX, r RX,,, delay direction-of-departure direction-of-arrival h t, r TX, r RX,,, a e j Fredrik Tufvesson - ETIM10 43

44 Angular spread E s,,, s,,, P s,,, double directional delay power spectrum DDDPS,, P s,,, d angular delay power spectrum ADPS, DDDPS,, G MS d τ l angular power spectrum APS APDS, d power P APS d Fredrik Tufvesson - ETIM10 44

45 Goals of MIMO Array gain increase power beamforming Diversity mitigate fading space-time coding Spatial multiplexing multiply data rates spatially orthogonal channels Fredrik Tufvesson - ETIM10 45

46 Signal model Transmitter Power P Receiver Antenna 1 TX Antenna 1 Antenna H 1,1 H,1 H n,1 T Antenna RX H 1, n R H, n R Antenna n R H n, T n R Antenna n T H...transfer function γ...snr at each receiver branch Fredrik Tufvesson - ETIM10 46

47 Capacity formula Instantaneous channel characterized by matrix H Shannon s formula (for two-dimensional symbols): C = log (1 + H ) bits / s / γ Hz Foschini s formula: C H log det n R bits / s / n γ = I + HH T Hz Fredrik Tufvesson - ETIM10 47

48 Channel measurements In order to model the channel behavior we need to measure its properties Time domain measurements impulse sounder correlative sounder Frequency domain measurements Vector network analyzer Directional measurements directional antennas real antenna arrays multiplexed arrays virtual arrays Fredrik Tufvesson - ETIM10 48

49 Real, multiplexed, and virtual arrays Real array: simultaneous measurement at all antenna elements RX RX RX Multiplexed array: short time intervals between measurements at different elements Digital Signal Processing RX Digital Signal Processing Virtual array: long delay no problem with mutual coupling RX Digital Signal Processing Fredrik Tufvesson - ETIM10 49

50 Directional analysis d φ The DoA can, e.g., be estimated by correlating the received signals with steering vectors. a exp exp 1 jk 0 dcos jk 0 dcos d sin φ exp j M 1 k 0 dcos An element spacing of d=5.8 cm and an angle of arrival of φ =0 degrees gives a time delay of s between neighboring elements Fredrik Tufvesson - ETIM10 50

51 Important antenna parameters Directivitiy Total power in a certain direction compared to total transmitted power Efficiency Rrad η = R + R + R Q-factor Stored energy compared to dissipated energy Mean effective gain Include influence of random channel Average received power compared to average received power by isotropic antenna in real environment Polarization Bandwidth rad ohmic match Fredrik Tufvesson - ETIM10 51

52 Techniques for wireless positioning Three main measurement principles: Angle-of-arrival (AOA) Received signal strength (RSS) Propagation-time: Time-of-arrival (TOA) Roundtrip-time-of-flight (RTOF) Time-difference-of-arrival (TDOA) These differ both in terms of system requirements and in accuracy Fredrik Tufvesson - ETIM10 5

53 Angle-of-arrival (AOA) based positioning Fixed unit Fixed unit α β Mobile unit Based on bearing estimation followed by intersection of different direction pointers Requires antenna arrays or directive antennas at measuring side: requires complex hardware Accuracy limited by size of antenna array or directivity No requirements on synchronization Fredrik Tufvesson - ETIM10 53

54 Received signal strength (RSS) based positioning Fixed unit P(d 1 ) P(d ) Fixed unit Based on propagation-loss equations Propagation-loss is often more complex than free-space (1/d^) loss, e.g., indoors: Advanced models required Mobile unit Fingerprinting (learn actual field strength from measuerements) Feasible implementation: Most radio modules already provide an RSS indicator Fredrik Tufvesson - ETIM10 54

55 Time-based positioning: Time-of-arrival (TOA) Fixed unit τ 1 τ Fixed unit Mobile unit Based on one-way propagation time Requires precise synchronization of all involved units (time synchronization directly affects accuracy) Ex. A 1 ns clock drift implies a distance error of 0.3 m Bandwidth dependent (accuracy inversely proportional to bandwidth) Can provide higher accuracy than AOA and RSS methods In practice, very expensive or less inaccurate Fredrik Tufvesson - ETIM10 55