1 / 70

860 likes | 1.72k Views

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

Download Presentation
## Radio Propagation and Channel Modeling

**An Image/Link below is provided (as is) to download presentation**
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.
Content is provided to you AS IS for your information and personal use only.
Download presentation by click this link.
While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

**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 Review**• Course Information • Wireless Vision • Technical Challenges • Multimedia Requirements • Current Wireless Systems • Spectrum 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**Slow**Fast Very slow Propagation Characteristics • Path Loss (includes average shadowing) • Shadowing (due to obstructions) • Multipath Fading Pr/Pt Pt Pr v d=vt d=vt**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 Modeling**• Maxwell’s equations • Complex and impractical • Free space path loss model • Too simple • Ray tracing models • Requires site-specific information • Empirical Models • Don’t always generalize to other environments • Simplified power falloff models • Main characteristics: good for high-level analysis**d=vt**Free Space (LOS) Model • Path loss for unobstructed LOS path • Power 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.**Ray Tracing Approximation**• Represent wavefronts as simple particles • Geometry determines received signal from each signal component • Typically includes reflected rays, can also include scattered and defracted rays. • Requires site parameters • Geometry • Dielectric 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 components • Reflections • Scattering • Diffraction • Requires detailed geometry and dielectric properties of site • Similar to Maxwell, but easier math. • Computer packages often used**Simplified Path Loss Model**• Used when path loss dominated by reflections. • Most important parameter is the path loss exponent g, determined empirically.**Empirical Models**• Okumura model • Empirically based (site/freq specific) • Awkward (uses graphs) • Hata model • Analytical 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]g • 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 obstructions • Random due to random # and type of obstructions • Typically follows a log-normal distribution • dB value of power is normally distributed • m=0 (mean captured in path loss), 4<s2<12 (empirical) • LLN used to explain this model • Decorrelated over decorrelation distance Xc Xc**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**Slow**Combined Path Loss and Shadowing • Linear Model: y lognormal • dB Model 10logK Pr/Pt (dB) Very slow -10g log d**Outage Probability and Cell Coverage Area**• Path loss: circular cells • Path loss+shadowing: amoeba cells • Tradeoff between coverage and interference • Outage probability • Probability received power below given minimum • Cell coverage area • % of cell locations at desired power • Increases as shadowing variance decreases • Large % indicates interference to other cells**K (dB)**2 sy 10g log(d0) Model Parameters from Empirical Measurements • Fit model to data • Path loss (K,g), d0 known: • “Best fit” line through dB data • K obtained from measurements at d0. • Exponent is MMSE estimate based on data • Captures mean due to shadowing • Shadowing variance • Variance of data relative to path loss model (straight line) with MMSE estimate for g Pr(dB) log(d)**Main Points**• Random attenuation due to shadowing modeled as log-normal (empirical parameters) • Shadowing decorrelates over decorrelation distance • Combined 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 with • Random amplitude • Random phase • Random Doppler shift • Random delay • Random components change with time • Leads 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 observed • t-t is time when impulse put into the channel • t is how long ago impulse was put into the channel for the current observation • path delay for MP component currently observed**Received Signal Characteristics**• Received signal consists of many multipath components • Amplitudes change slowly • Phases change rapidly • Constructive and destructive addition of signal components • Amplitude fading of received signal (both wideband and narrowband signals)**Narrowband Model**• Assume delay spread maxm,n|tn(t)-tm(t)|<<1/B • Then 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)=d(t)**In-Phase and Quadrature components under CLT Approximation**• In 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 jn(t) uniform, the in-phase/quad components are mean zero, indep., and stationary.**Auto and Cross Correlation**• Assume fn~U[0,2p] • Recall that qn is the multipath arrival angle • Autocorrelation of inphase/quad signal is • Cross Correlation of inphase/quad signal is • Autocorrelation of received signal is**Uniform AOAs**• Under uniform scattering, in phase and quad comps have no cross correlation and autocorrelation is • The PSD of received signal is Decorrelates over roughly half a wavelength Sr(f) Used to generate simulation values fc fc+fD fc-fD**Signal Envelope Distribution**• CLT approx. leads to Rayleigh distribution (power is exponential) • When LOS component present, Ricean distribution is used • Measurements support Nakagami distribution in some environments • Similar to Ricean, but models “worse than Rayleigh” • Lends itself better to closed form BER expressions**Level crossing rate and Average Fade Duration**• LCR: rate at which the signal crosses a fade value • AFD: 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 t1 t2 t3 R**Markov Models for Fading**• Model for fading dynamics • Simplifies performance analysis • Divides range of fading power into discrete regions Rj={g: Aj g < Aj+1} • Aj s and # of regions are functions of model • Transition probabilities (Lj is LCR at Aj): R2 A2 R1 A1 R0 A0**t**t Wideband Channels • Individual multipath components resolvable • True when time difference between components exceeds signal bandwidth Narrowband Wideband**Scattering Function**• Fourier transform of c(t,t) relative to t • Typically 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,Dt)=Ac(t,Dt) • Statistical scattering function: r s(t,r)=FDt[Ac(t,Dt)] t**Multipath Intensity Profile**• Defined as Ac(t,Dt=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(Df)=F[Ac(t)]>0 • Ac(Df)=0 implies signals separated in frequency by Df will be uncorrelated after passing through channel Ac(t) TM t Ac(f) f t Bc 0**Doppler Power Spectrum**• Sc(r)=F[Ac(t=0,Dt)]= F[Ac(Dt)] • Doppler spread Bd is maximum doppler for which Sc (r)=>0. • Coherence time Tc=1/Bd • Maximum time over which Ac(Dt)>0 • Ac(Dt)=0 implies signals separated in time by Dt will be uncorrelated after passing through channel Sc(r) 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 processes • Processes completely characterized by their mean, autocorrelation, and cross correlation. • Assuming uniform phase offsets, process is zero mean with joint expectation also zero.**Main Points**• Narrowband model has in-phase and quad. comps that are zero-mean stationary Gaussian processes • Auto and cross correlation depends on AOAs of multipath • Uniform scattering makes autocorrelation of inphase and quad follow Bessel function • Signal components decorrelate over half wavelength • Cross correlation is zero (in-phase/quadratureindep.) • The power spectral density of the received signal has a bowel shape centered at carrier frequency • PSD useful in simulating fading channels**Main Points**• Narrowband fading distribution depends on environment • Rayleigh, 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 Points**• Delay 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**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**Physical MIMO channel modeling**• Multidimensional channel modeling • The double-directional channel impulse response • Multidimensional correlation functions and stationarity • Channel fading, K-factor and Doppler spectrum • Power delay and direction spectra • From double-direction propagation to MIMO channels • Statistical properties of the channel matrix • Discrete channel modeling : sampling theorem revisited • Physical 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 methods • Multi-polarized channel • Geometry-based models • One-ring model • Two-ring model • Combined elliptical-ring model • Elliptical and circular models • Extension of geometry-based models to dual-polarized channels**Physical MIMO channel modeling(cont)**• Empirical models • ExtendenSaleh-Valenzuela model • Stanford university interim channel models • COST models**Analytical MIMO channel models**• General representations of correlated MIMO channels • Rayleigh fading channels • Ricean fading channels • Dual-polarized channels • Double-Rayleigh fading model for keyhole channels • Simplified representations of Guassian MIMO channels • The Kronecker model • Virtual channel representation • The eigenbeam model**Analytical MIMO channel models (cont)**• Propagation-motivated MIMO metrics • Comparing models and correlation matrices • Characterizing the multipath richness • Measuring the non-stationarity of MIMO channels

More Related