Radio Propagation and Channel Modeling
Lecture 2 Outline Review of Last Lecture Radio Propagation Characteristics
Signal Propagation Overview Path Loss Models
• Free-space Path Loss• Ray Tracing Models• Simplified Path Loss Model• Empirical Models
Shadowing Combined Path Loss and Shadowing Multipath Channel Models
Channel modeling methods MIMO Channel Models
Standardized channel models An Example - WiNNER II Channel Model
Conclusions
Lecture 2 Outline Review of Last Lecture Radio Propagation Characteristics
Signal Propagation Overview Path Loss Models
• Free-space Path Loss• Ray Tracing Models• Simplified Path Loss Model• Empirical Models
Shadowing Combined Path Loss and Shadowing Multipath Channel Models
Channel modeling methods MIMO Channel Models
Standardized channel models An Example - WiNNER II Channel Model
Conclusions
Lecture 1 ReviewCourse InformationWireless VisionTechnical ChallengesMultimedia RequirementsCurrent Wireless SystemsSpectrum Regulation and Standards
Lecture 2 Outline Review of Last Lecture Radio Propagation Characteristics
Signal Propagation Overview Path Loss Models
• Free-space Path Loss• Ray Tracing Models• Simplified Path Loss Model• Empirical Models
Shadowing Combined Path Loss and Shadowing Multipath Channel Models
Channel modeling methods MIMO Channel Models
Standardized channel models An Example - WiNNER II Channel Model
Conclusions
Propagation Characteristics
Path Loss (includes average shadowing)Shadowing (due to obstructions)Multipath Fading
Pr/Pt
d=vt
PrPt
d=vt
v Very slow
SlowFast
Lecture 2 Outline Review of Last Lecture Radio Propagation Characteristics
Signal Propagation Overview Path Loss Models
• Free-space Path Loss• Ray Tracing Models• Simplified Path Loss Model• Empirical Models
Shadowing Combined Path Loss and Shadowing Multipath Channel Models
Channel modeling methods MIMO Channel Models
Standardized channel models An Example - WiNNER II Channel Model
Conclusions
Path Loss ModelingMaxwell’s equations
Complex and impracticalFree space path loss model
Too simpleRay tracing models
Requires site-specific informationEmpirical Models
Don’t always generalize to other environmentsSimplified power falloff models
Main characteristics: good for high-level analysis
Free Space (LOS) Model
Path loss for unobstructed LOS pathPower falls off :
Proportional to d2
Proportional to l2 (inversely proportional to f2)More references:
Herry L. Bertoni, Radio Propagation for Modern Wireless Systems, Publishing House of Electronics Industry.
d=vt
2
10 210log4l
LG
P dBdl
Ray Tracing Approximation
Represent wavefronts as simple particlesGeometry determines received signal from each
signal componentTypically includes reflected rays, can also
include scattered and defracted rays.Requires site parameters
GeometryDielectric properties
Softwares:WiSE, SitePlanner, Planet EV, et.al.
Two Path Model
Path loss for one LOS path and 1 ground (or reflected) bounce
Ground bounce approximately cancels LOS path above critical distance
Power falls off Proportional to d2 (small d)Proportional to d4 (d>dc) Independent of l (f)
General Ray Tracing
Models all signal componentsReflectionsScatteringDiffraction
Requires detailed geometry and dielectric properties of site
Similar to Maxwell, but easier math.Computer packages often used
Simplified Path Loss Model
82,0
ddKPP tr
Used when path loss dominated by reflections.
Most important parameter is the path loss exponent , determined empirically.
Empirical ModelsOkumura model
Empirically based (site/freq specific)Awkward (uses graphs)
Hata modelAnalytical approximation to Okumura model
Cost 136 Model: Extends Hata model to higher frequency (2 GHz)
Walfish/Bertoni:Cost 136 extension to include diffraction from rooftops
Commonly used in cellular system simulations
Main Points Path loss models simplify Maxwell’s equations
Models vary in complexity and accuracy Power falloff with distance is proportional to d2 in free space, d4 in two
path model General ray tracing computationally complex
Empirical models used in 2G simulations Low accuracy (15-20 dB std) Capture phenomena missing from formulas Awkward to use in analysis
Main characteristics of path loss captured in simple model Pr=PtK[d0/d]
Captures main characteristics of path loss
Lecture 2 Outline Review of Last Lecture Radio Propagation Characteristics
Signal Propagation Overview Path Loss Models
• Free-space Path Loss• Ray Tracing Models• Simplified Path Loss Model• Empirical Models
Shadowing Combined Path Loss and Shadowing Multipath Channel Models
Channel modeling methods MIMO Channel Models
Standardized channel models An Example - WiNNER II Channel Model
Conclusions
Shadowing
Models attenuation from obstructionsRandom due to random # and type of obstructionsTypically follows a log-normal distribution
dB value of power is normally distributedm=0 (mean captured in path loss), 4<s2<12 (empirical)LLN used to explain this modelDecorrelated over decorrelation distance Xc
Xc
210
2
(10 log )( ) exp
22dB
dBd
P
mss
B
Lecture 2 Outline Review of Last Lecture Radio Propagation Characteristics
Signal Propagation Overview Path Loss Models
• Free-space Path Loss• Ray Tracing Models• Simplified Path Loss Model• Empirical Models
Shadowing Combined Path Loss and Shadowing Multipath Channel Models
Channel modeling methods MIMO Channel Models
Standardized channel models An Example - WiNNER II Channel Model
Conclusions
Combined Path Loss and ShadowingLinear Model: lognormal
dB Model
ddK
PP
t
r 0
),0(~
,log10log10)(2
01010
s
NddKdB
PP
dB
dBt
r
Pr/Pt
(dB)
log d
Very slow
Slow10logK
-10
Outage Probability and Cell Coverage Area
Path loss: circular cellsPath loss+shadowing: amoeba cells
Tradeoff between coverage and interferenceOutage probability
Probability received power below given minimumCell coverage area
% of cell locations at desired powerIncreases as shadowing variance decreasesLarge % indicates interference to other cells
rP
Model Parameters from Empirical MeasurementsFit model to data
Path loss (K,), d0 known:“Best fit” line through dB dataK obtained from measurements at d0.Exponent is MMSE estimate based on dataCaptures mean due to shadowing
Shadowing varianceVariance of data relative to path loss model
(straight line) with MMSE estimate for
Pr(dB)
log(d)10
K (dB)
log(d0)
s2
Main PointsRandom attenuation due to shadowing modeled as
log-normal (empirical parameters)
Shadowing decorrelates over decorrelation distanceCombined path loss and shadowing leads to outage
and amoeba-like cell shapes
Cellular coverage area dictates the percentage of locations within a cell that are not in outage
Path loss and shadowing parameters are obtained from empirical measurements
Lecture 2 Outline Review of Last Lecture Radio Propagation Characteristics
Signal Propagation Overview Path Loss Models
• Free-space Path Loss• Ray Tracing Models• Simplified Path Loss Model• Empirical Models
Shadowing Combined Path Loss and Shadowing Multipath Channel Models
Channel modeling methods MIMO Channel Models
Standardized channel models An Example - WiNNER II Channel Model
Conclusions
Statistical Multipath Model
Random # of multipath components, each withRandom amplitudeRandom phaseRandom Doppler shiftRandom delay
Random components change with timeLeads to time-varying channel impulse response
Time Varying Impulse Response
Response of channel at t to impulse at t-t:
t is time when impulse response is observedt-t is time when impulse put into the channelt is how long ago impulse was put into the
channel for the current observation • path delay for MP component currently observed
))(()(),(1
)( tettc n
N
n
tjn
n ttt
Received Signal Characteristics
Received signal consists of many multipath components
Amplitudes change slowlyPhases change rapidly
Constructive and destructive addition of signal components
Amplitude fading of received signal (both wideband and narrowband signals)
Narrowband ModelAssume delay spread maxm,n|tn(t)-tm(t)|<<1/BThen u(t)u(t-t).Received signal given by
No signal distortion (spreading in time)Multipath affects complex scale factor in brackets.Characterize scale factor by setting u(t)=(t)
)(
0
)(2 )()()(tN
n
tjn
tfj nc etetutr
In-Phase and Quadrature components under CLT ApproximationIn phase and quadrature signal components:
For N(t) large, rI(t) and rQ(t) jointly Gaussian (sum of large # of random vars).
Received signal characterized by its mean, autocorrelation, and cross correlation.
If n(t) uniform, the in-phase/quad components are mean zero, indep., and stationary.
),2cos()()()(
0
)( tfettr c
tN
n
tjnI
n
)2sin()()()(
0
)( tfettr c
tN
n
tjnQ
n
Auto and Cross CorrelationAssume n~U[0,2]Recall that qn is the multipath arrival angleAutocorrelation of inphase/quad signal is
Cross Correlation of inphase/quad signal is
Autocorrelation of received signal is
lqttt q /cos],2[cos)()( nDDrr vffPEAAnnnQI
)(]2[sin)( ,, ttt q QInnQI rrDrr AfPEA
)2sin()()2cos()()( , ttttt crrcrr fAfAAQII
Uniform AOAs
Under uniform scattering, in phase and quad comps have no cross correlation and autocorrelation is
The PSD of received signal is
)2()()( 0 ttt Drr fPJAAQI
Decorrelates over roughly half a wavelength
)]2([)(
)]()([25.)(
0 t Dr
crcrr
fPJfS
ffSffSfS
I
II
F
fc+fDUsed to generate simulation values fc
Sr(f)
fc-fD
Signal Envelope DistributionCLT approx. leads to Rayleigh distribution (power is
exponential)
When LOS component present, Ricean distribution is used
Measurements support Nakagami distribution in some environmentsSimilar to Ricean, but models “worse than Rayleigh”Lends itself better to closed form BER expressions
Level crossing rate and Average Fade DurationLCR: rate at which the signal crosses a fade valueAFD: How long a signal stays below target R/SNR
Derived from LCR
For Rayleigh fading
Depends on ratio of target to average level (r) Inversely proportional to Doppler frequency
)2/()1(2
rrDR fet
Rt1 t2 t3
Markov Models for FadingModel for fading dynamics
Simplifies performance analysis
Divides range of fading power into discrete regions Rj={: Aj < Aj+1}Aj s and # of regions are functions of model
Transition probabilities (Lj is LCR at Aj):1,1,,1,
11, 1,,
jjjjjj
j
jjj
j
jjj ppp
TLp
TLp
A0A1
A2
R0
R1
R2
Wideband ChannelsIndividual multipath components resolvableTrue when time difference between
components exceeds signal bandwidth
uB/1t uB/1t
t t1t 2t
Narrowband Wideband
Scattering FunctionFourier transform of c(t,t) relative to tTypically characterize its statistics, since c(t,t)
is different in different environments
Underlying process WSS and Gaussian, so only characterize mean (0) and correlation
Autocorrelation is Ac(t1,t2,t)=Ac(t,t)Statistical scattering function:
t
rs(t,r)=Ft[Ac(t,t)]
Multipath Intensity Profile
Defined as Ac(t,t=0)= Ac(t)Determines average (TM ) and rms (st) delay spread Approximate max delay of significant m.p.
Coherence bandwidth Bc=1/TM
Maximum frequency over which Ac(f)=F[Ac(t)]>0Ac(f)=0 implies signals separated in frequency by f
will be uncorrelated after passing through channel
t
Ac(t)TM
um BT /1
t1t 2t f
cu BB
Ac(f)
0 Bc
Doppler Power Spectrum
Sc(r)=F[Ac(t0,t)]= F[Ac(t)]
Doppler spread Bd is maximum doppler for which Sc (r)=>0.
Coherence time Tc=1/Bd
Maximum time over which Ac(t)>0Ac(t)=0 implies signals separated in time by t will be
uncorrelated after passing through channel
r
Sc(r)
Bd
Main Points
Statistical multipath model leads to a time-varying channel impulse response
Received signal has random amplitude fluctuations
Narrowband model and CLT lead to in-phase/quad components that are stationary Gaussian processesProcesses completely characterized by their mean,
autocorrelation, and cross correlation.
Assuming uniform phase offsets, process is zero mean with joint expectation also zero.
Main PointsNarrowband model has in-phase and quad. comps that
are zero-mean stationary Gaussian processesAuto and cross correlation depends on AOAs of multipath
Uniform scattering makes autocorrelation of inphase and quad follow Bessel functionSignal components decorrelate over half wavelengthCross correlation is zero (in-phase/quadrature indep.)
The power spectral density of the received signal has a bowel shape centered at carrier frequencyPSD useful in simulating fading channels
Main PointsNarrowband fading distribution depends on
environmentRayleigh, Ricean, and Nakagami all common
Average fade duration determines how long a user is in continuous outage (e.g. for coding design)
Markov model approximates fading dynamics.
Scattering function characterizes rms delay and Doppler spread. Key parameters for system design.
Main PointsDelay spread defines maximum delay of significant
multipath components. Inverse is coherence bandwidth of channel
Doppler spread defines maximum nonzero doppler, its inverse is coherence time
Lecture 2 Outline Review of Last Lecture Radio Propagation Characteristics
Signal Propagation Overview Path Loss Models
• Free-space Path Loss• Ray Tracing Models• Simplified Path Loss Model• Empirical Models
Shadowing Combined Path Loss and Shadowing Multipath Channel Models
Channel modeling methods MIMO Channel Models
Standardized channel models An Example - WiNNER II Channel Model
Conclusions
Channel Modeling Methods建模方法 优点 缺点
确定性
双向信道模型 收、发端的延时、角度等信息精确 计算量大、实现困难
存储信道冲激响应 数据可以无限期地再利用,甚至可用于不同系统的仿真
获取和存储数据需要大量的工作;数据只能表征某个区域
射线跟踪法 模拟空间信道的信息较准确需要与实际地理环境相
符的地图,计算量大、实现较困难FDTD法 准确;可同时提供地图中所有点
的完整信息,可以用做检查和验证需要大量的存储空间和巨大的运算量
随机性
基于几何随机信道模型几何概念简单,重点考虑内部参数的相关性,参数可变性强,易于简
化,便于参数的提取与信道的仿真实现只能反映信道的长期统
计特性
基于相关性随机模型 变量相对少;计算量小 仿真量大;无法对信道进行动态建模
参数随机模型 复杂度较低,具有移动的通用性 和实际信道有较大的偏差,随机生成的参数和实际可能有很大差别
Lecture 2 Outline Review of Last Lecture Radio Propagation Characteristics
Signal Propagation Overview Path Loss Models
• Free-space Path Loss• Ray Tracing Models• Simplified Path Loss Model• Empirical Models
Shadowing Combined Path Loss and Shadowing Multipath Channel Models
Channel modeling methods MIMO Channel Models
Standardized channel models An Example - WiNNER II Channel Model
Conclusions
Classification of MIMO channel models
Physical MIMO channel modelingMultidimensional channel modeling
The double-directional channel impulse responseMultidimensional correlation functions and stationarityChannel fading, K-factor and Doppler spectrumPower delay and direction spectraFrom double-direction propagation to MIMO channelsStatistical properties of the channel matrixDiscrete channel modeling : sampling theorem revisitedPhysical versus analytical models
•1. C. Oestges and B. Clerckx, MIMO Wireless Communications: From Channel Models to Space-Time Code Design. Academic Press, 2007.
Physical MIMO channel modeling(cont)Electromagnetic models
Ray-based deterministic methodsMulti-polarized channel
Geometry-based modelsOne-ring modelTwo-ring modelCombined elliptical-ring modelElliptical and circular modelsExtension of geometry-based models to dual-polarized
channels
Physical MIMO channel modeling(cont)
Empirical models Extenden Saleh-Valenzuela model Stanford university interim channel models COST models
Analytical MIMO channel modelsGeneral representations of correlated MIMO
channelsRayleigh fading channelsRicean fading channelsDual-polarized channelsDouble-Rayleigh fading model for keyhole channels
Simplified representations of Guassian MIMO channelsThe Kronecker modelVirtual channel representationThe eigenbeam model
Propagation-motivated MIMO metricsComparing models and correlation matricesCharacterizing the multipath richnessMeasuring the non-stationarity of MIMO channels
Analytical MIMO channel models (cont)
Physical Models & Analytical Models
The Kronecker model paradoxNumerical examplesComparison between analytical models: a
system viewpoint
Lecture 2 Outline Review of Last Lecture Radio Propagation Characteristics
Signal Propagation Overview Path Loss Models
• Free-space Path Loss• Ray Tracing Models• Simplified Path Loss Model• Empirical Models
Shadowing Combined Path Loss and Shadowing Multipath Channel Models
Channel modeling methods MIMO Channel Models
Standardized channel models An Example - WiNNER II Channel Model
Conclusions
Standardized Channel Models IEEE 802.11 TGn models IEEE 802.16d/e models 3GPP/3GPP2 spatial channel models WiNNER I/ WiNNER II Models
Lecture 2 Outline Review of Last Lecture Radio Propagation Characteristics
Signal Propagation Overview Path Loss Models
• Free-space Path Loss• Ray Tracing Models• Simplified Path Loss Model• Empirical Models
Shadowing Combined Path Loss and Shadowing Multipath Channel Models
Channel modeling methods MIMO Channel Models
Standardized channel models An Example - WiNNER II Channel Model
Conclusions
WiNNER II
M.2135 —— Channel model for IMT-AdvancedContractual Date of Delivery to the CEC: 30/09/2007Participants: EBITG, TUI, UOULU, CU/CRC, NOKIAEstimated person months: 62 WINNER II channel models for link and system level
simulations. Both generic and clustered delay line models are
defined for selected propagation scenarios. The channel models are based on a literature survey
and measurements performed during this project.
Channel realizations are generated by summing contributions of rays with specific channel parameters like delay, power, angle-of-arrival and angle-of-departure. Different scenarios are modeled by using the same approach, but different parameters. A number of rays constitute a cluster. In Winner II we equate the cluster with a propagation path diffused in space, either or both in delay and angle domains.
WiNNER II Channel Model
WiNNER II Channel Model
M=20 :number of subpaths(rays) in a path
WiNNER II Channel Model
WiNNER II Channel Modeling Approach
Propagation scenarios
Supported Parameters Large Scale Parameters
* Delay spread and distribution * Angle of Departure spread and distribution * Angle of Arrival Spread and distribution * Shadow Fading standard deviation * Ricean K-factor
Support Parameters * Scaling parameter for Delay distribution * Cross-polarization power ratios * Number of clusters * Cluster Angle Spread of Departure * Cluster Angle Spread of Arrival * Per Cluster Shadowing * Auto-correlations of the LS parameters * Cross-correlations of the LS parameters * Number of rays per cluster
Comparisons between scenarios
indoor &indoor related:
indoor (office/residential) A1
indoor to outdoor (indoor A1, outdoor B1) A2
outdoor to indoor(outdoor B1, indoor A1)
C4
B4
(outdoor C2, indoor A1)
reciprocity
+B3 (large indoor hall)
B1 refers to typical urban microcell.C2 refers to typical macrocell. continued
Note:
Comparisons between scenarios
microcell
typical urban microcell (regular street grid environment)
B3
B2
B1
bad urban microcell (same layout as B1, but with excess long delays )
large indoor hall/ indoor hotspot(conference hall/ industrial hall)
+B4 (outdoor B1, indoor A1)
Note: B2 same asB1+ long delays
continued
Comparisons between scenarios (cont)
macrocell
suburban macrocell
urban macrocell
bad urban macrocell
D2b
D2a
C3
C2
C1
C2:data based on B1 and C1
C3:same as C2+long delays
+C4 (outdoor C2, indoor A1)
D1rural macrocell
rural moving networks
a) moving networks: BS---MRS
b) moving networks: MRS---MSNote:
MRS: mobile relay stationD2a: very large Doppler variabilityD2b: same as A1 NLOS
(车站 ) (车 )
(车 ) (车内人 )
Comparisons between scenarios
stationary feeder models
LOS stat. feeder, rooftop to rooftop B5a
B5f
B5d
B5c
B5bLOS stat. feeder, street-level to street-level
LOS stat. feeder, below rooftop to street-level
NLOS stat. feeder, above rooftop to street-level
Feeder link BS ->FRS. Approximately RT to RT level.
B5c: LOS of B1
B5d: NLOS of C2
B5f: NLOS of B5a
for feeder scenarios , modeling is based entirely on literature.
Table of parameters for generic models
Channel coefficient generation
Figure: Channel coefficient generation procedure
Lecture 2 Outline Review of Last Lecture Radio Propagation Characteristics
Signal Propagation Overview Path Loss Models
• Free-space Path Loss• Ray Tracing Models• Simplified Path Loss Model• Empirical Models
Shadowing Combined Path Loss and Shadowing Multipath Channel Models
Channel modeling methods MIMO Channel Models
Standardized channel models An Example - WiNNER II Channel Model
Conclusions
ConclusionsRadio propagation characteristicsWhy channel modeling?How to use channel models?
References Herry L. Bertoni, Radio Propagation for Modern Wireless Systems,
Publishing House of Electronics Industry.Andrea GoldSmith, Wireless Communications, Posts & Telecom
Press. F. Perez Fontan and P. Marino Espineira, Modelling the Wireless
Propagation Channel : A simulation approach with Matlab , Sep.2008, Wiley.
Claude Oestges and Bruno Clerckx, MIMO Wireless Communications From Real World Propagation to Space Time Code Design, Acdamic Press.
IST-4-027756 WINNER II, D1.1.2 V1.1, WINNER II Channel Models IST-4-027756 , Matlab SW documentation of WIM2 model