radio propagation and channel modeling

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Radio Propagation and Channel Modeling

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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 - PowerPoint PPT Presentation

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Page 1: Radio Propagation and Channel Modeling

Radio Propagation and Channel Modeling

Page 2: 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

Page 3: 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

Page 4: Radio Propagation and Channel Modeling

Lecture 1 ReviewCourse InformationWireless VisionTechnical ChallengesMultimedia RequirementsCurrent Wireless SystemsSpectrum Regulation and Standards

Page 5: 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

Page 6: Radio Propagation and Channel Modeling

Propagation Characteristics

Path Loss (includes average shadowing)Shadowing (due to obstructions)Multipath Fading

Pr/Pt

d=vt

PrPt

d=vt

v Very slow

SlowFast

Page 7: 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

Page 8: Radio Propagation and Channel Modeling

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

Page 9: Radio Propagation and Channel Modeling

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

Page 10: Radio Propagation and Channel Modeling

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.

Page 11: Radio Propagation and Channel Modeling

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)

Page 12: Radio Propagation and Channel Modeling

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

Page 13: Radio Propagation and Channel Modeling

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.

Page 14: Radio Propagation and Channel Modeling

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

Page 15: Radio Propagation and Channel Modeling

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

Page 16: 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

Page 17: Radio Propagation and Channel Modeling

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

Page 18: 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

Page 19: Radio Propagation and Channel Modeling

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

Page 20: Radio Propagation and Channel Modeling

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

Page 21: Radio Propagation and Channel Modeling

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

Page 22: Radio Propagation and Channel Modeling

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

Page 23: 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

Page 24: Radio Propagation and Channel Modeling

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

Page 25: Radio Propagation and Channel Modeling

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

Page 26: Radio Propagation and Channel Modeling

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)

Page 27: Radio Propagation and Channel Modeling

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

Page 28: Radio Propagation and Channel Modeling

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

Page 29: Radio Propagation and Channel Modeling

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

Page 30: Radio Propagation and Channel Modeling

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

Page 31: Radio Propagation and Channel Modeling

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

Page 32: Radio Propagation and Channel Modeling

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

Page 33: Radio Propagation and Channel Modeling

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

Page 34: Radio Propagation and Channel Modeling

Wideband ChannelsIndividual multipath components resolvableTrue when time difference between

components exceeds signal bandwidth

uB/1t uB/1t

t t1t 2t

Narrowband Wideband

Page 35: Radio Propagation and Channel Modeling

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)]

Page 36: Radio Propagation and Channel Modeling

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

Page 37: Radio Propagation and Channel Modeling

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

Page 38: Radio Propagation and Channel Modeling

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.

Page 39: Radio Propagation and Channel Modeling

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

Page 40: Radio Propagation and Channel Modeling

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.

Page 41: Radio Propagation and Channel Modeling

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

Page 42: 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

Page 43: Radio Propagation and Channel Modeling

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

Page 44: 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

Page 45: Radio Propagation and Channel Modeling

Classification of MIMO channel models

Page 46: Radio Propagation and Channel Modeling

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.

Page 47: Radio Propagation and Channel Modeling

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

Page 48: Radio Propagation and Channel Modeling

Physical MIMO channel modeling(cont)

Empirical models Extenden Saleh-Valenzuela model Stanford university interim channel models COST models

Page 49: Radio Propagation and Channel Modeling

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

Page 50: Radio Propagation and Channel Modeling

Propagation-motivated MIMO metricsComparing models and correlation matricesCharacterizing the multipath richnessMeasuring the non-stationarity of MIMO channels

Analytical MIMO channel models (cont)

Page 51: Radio Propagation and Channel Modeling

Physical Models & Analytical Models

The Kronecker model paradoxNumerical examplesComparison between analytical models: a

system viewpoint

Page 52: 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

Page 53: Radio Propagation and Channel Modeling

Standardized Channel Models IEEE 802.11 TGn models IEEE 802.16d/e models 3GPP/3GPP2 spatial channel models WiNNER I/ WiNNER II Models

Page 54: 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

Page 55: Radio Propagation and Channel Modeling

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.

Page 56: Radio Propagation and Channel Modeling

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

Page 57: Radio Propagation and Channel Modeling

WiNNER II Channel Model

Page 58: Radio Propagation and Channel Modeling

M=20 :number of subpaths(rays) in a path

WiNNER II Channel Model

Page 59: Radio Propagation and Channel Modeling

WiNNER II Channel Modeling Approach

Page 60: Radio Propagation and Channel Modeling

Propagation scenarios

Page 61: Radio Propagation and Channel Modeling

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

Page 62: Radio Propagation and Channel Modeling

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:

Page 63: Radio Propagation and Channel Modeling

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

Page 64: Radio Propagation and Channel Modeling

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 )

Page 65: Radio Propagation and Channel Modeling

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.

Page 66: Radio Propagation and Channel Modeling

Table of parameters for generic models

Page 67: Radio Propagation and Channel Modeling

Channel coefficient generation

Figure: Channel coefficient generation procedure

Page 68: 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

Page 69: Radio Propagation and Channel Modeling

ConclusionsRadio propagation characteristicsWhy channel modeling?How to use channel models?

Page 70: Radio Propagation and Channel Modeling

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