Lecture2 Note

8/13/2019 Lecture2 Note

1/18

EE5530: Wireless Communications

2. Propagation Modeling

Radio propagation characteristics and physical mechanisms

Long-term fading: path loss modeling, shadowing

Short-term fading: statistical multipath modelEffects of motion and Doppler

Flat fading: envelop fading and fade duration

Selective fading: scattering function, delay spread and coherencebandwidth, Doppler spectrum and coherence time

Performance analysis in flat fading channelsSimulations of mobile radio channels

Impacts of radio channel impairments

Overview

Complex Radio Propagation Effect of mobility: channel varies with user location and time

Large scale long-term fades Attenuation effects from path loss: Main characteristics captured in

simple model Pr=PtK[d0/d]

Shadowing from dominate objects: modeled as log-normal (withempirical parameters) and affects cell coverage area

Small scale short-term fades Multipath scattering from nearby objects: leads to time-varying

Channel impulse response and rapid fluctuation of received power

Resulting channel impairments Time Delay spread: For cellular telephony: -30dB, 3s delay spread Frequency Doppler Spread

Average fade duration dictates performance measures


2/18

Radio Propagation Characteristics

Path Loss

Shadowing

Multipath Fading

Multiple Access Interference

Pr/Pt

d=vt

PrPt

d=vt

v

d

Path loss +

shadowing

MP fading

Radio medium

Active scattering region

~ 100

Propagation Mechanisms

Reflection Propagation wave impinges on an object which is large

compared to wavelength

E.g. Earth surface, building, walls, etc.

Diffraction Radio path between Tx and Rx obstructed by surface with

sharp irregular edges

Waves bend around the obstacle, even when no LOS

Scattering Objects smaller than the wavelength of the propagating wave

E.g. foliage, street signs, lamp posts


3/18

Longer-Term Fading

Long-term signal fading Describes the average signal strength

Mainly a function of the distance dbetween Tx and Rx

Received signal power in mobile radio channel

Pr=PtGT GR d-

d: distance between Tx and Rx

: propagation constant, depends on terrain, somewhatfrequency dependent

: adjustment factor, reflecting antenna heights, terrain,weather, foliage,

Typically, and are too complex (or non-predictableconsidering short-term fading) to be modeleddeterministically => statistical model

Path Loss Modeling

Maxwells equations Complex and impractical

Power falloff with distance Proportional to d2 in free space, d4 in two-path model

Ray tracing models General ray tracing computationally complex, used for site-

specific models

Simplified power falloff models Main characteristics of path loss captured in simple model

Pr=PtK[d0/d]

Models vary in complexity and accuracy

Statistical modelPr(dB) = 10log10Pr is Gaussian with meanPand variance

2

Pr is log-normal with pdf ~ (P, 2)

Path lossLp(dB) = 10log10(PtGTGR/P)


4/18

Free Space (LOS) Model

Path loss for unobstructed LOS path

Power falloff :

Proportional to d2, inversely proportional to 2 (fc-2)

Path lossLp(dB) = 20 log10(4d/) = 20log10d - 20log10(/4)

d=vt

2

4

=

d

GGP RTtP

Two Path Model

Path loss for flat reflecting surface One LOS path and one ground (or reflected) bounce

Ground bounce approximately cancels LOS path abovecritical distance

Power falloff Proportional to d2 (small d) Proportional to d4 (d>dc) Independent of (fc)

Path loss:Lp(dB) = 40log10d - 20log10(hb) - 20log10(hm)

2

2

=

d

hhGGP mbRTtP

hb

hm

hmd


5/18

General Ray Tracing

Models all propagation mechanisms Reflections, Scattering, Diffraction

Site specific

Requires detailed site geometry and dielectric properties: Represent wave-fronts as simple particles, and use geometry to

determine received signal from each signal component similar to Maxwell, but easier math

Computer packages often used

Simplified Path Loss Model

Detailed path loss models hard to factor into

overall system design.

Most important characteristic is power falloff with

distance

Capture using simplified model:

Exponentdetermined by experiment

(*)82,

==

d

dKPP otrP

dL dBp 10)( log10+=


6/18

Empirical Path-Loss Models

Okumara-Hata Model Empirical data model for Tokyo

Accurate to within 1 dB for distances ranging 1---20km

Path loss for urban area withfc>400MHz

Lp(dB) = A + Blog10(d)

A = 69.55 + 26.16 log10(fc) -13.82 log10(hb) - a(hm)

B = 44.9 - 6.55 log10(hb)

a(hm) = 3.2(log10(11.75hm))2 - 4.97

Other empirical models

Lees area-to-area model for flat terrain

CCIR model

Outdoor Propagation

Macro versus Microcells

PCS Microcells 1800-2000 Hz frequency bands Path losses are about 10 dB higher than at the cellular bands Empicial models: COST231-Hata, COST231-Walfish-

Ikegami, two-slop model, etc.

1M bps0.3M bpsMax bit rate10-100 ns0.1-10 sDelay spread

RiceanRayleighFading

0.1-1 W1-10 WTx Power

0.1-1 km1-20kmCell radius

MicrocellMacrocell


7/18

Indoor Propagation

Physical effects Signal decays much faster Coverage contained by walls, etc. Walls, floors, furniture attenuate/scatter radio signals

Indoor measurements Received signal strength depends on open plan offices,

construction materials, density of personnel, furniture, etc.

Path loss formula

Lp(dB) =Lp(dB)(do) + 10log10(d) = k F + I WLp(dB)(do): reference power loss at do=1m distance (30dB)

k: number of floors the signal traversesF: loss per floor (1th:15dB; 2nd-5th: 6-10dB; >5th: 1-2dB)I: Number of walls the signal traverses W: loss per wall (I W= 10-15dB)


8/18

Shadowing

Models attenuation from obstructions

Log normal distribution typical model for randomattenuation

Random due to random number and type ofobstructions

Typically follows a log-normal distribution dB value of power is normally distributed

= 0 (mean captured in path loss), 4


9/18

Understanding Motion Effects: Doppler

Single-Path Doppler Effects Scenario: mobile at positionx, moving with velocity v, with signal

arriving at angle .

Doppler effects (assume carrier frequencyfc). Transmitted signal: s(t) = cos(2fct) = Re{exp[j 2fct]}

Path delay: (t) = x/c = v t cos/c

Received signal: r(t) =Re{A exp[j 2fc(t(t))]} Phase: (t) =2fc t -x cos= 2fc t-v t cos ( =2fc/c=2/c)

Resulting Doppler frequency shift: fD = v/c cos

Maximum Doppler frequency: fm = v/c

Often, v and vary with time, sofD vary correspondingly,causingDoppler spread, which characterizes the rate ofchannel variations.

Motion Effects: Amplitude Variation

Two-path Doppler Effects Scenario: two incoming waves arrive at the mobile at angles of 0 and

. Assume they are of equal amplitude. Received signal: r(t) =Aej2fct(e-jx+e- jx cos)

=Aej2fcte-jx(1+cos)/2. 2cos(x (1-cos)/2) Phase: (t) =2fc t -x (1+cos)/2 Doppler frequency:fD = v/c . (1+cos)/2

Signal amplitude: (t) = 2A cos(x(1+cos)/2) Amplitude fluctuates with frequency fA = v/c . (1- cos)/2

Key properties of multipath channels due to motion

Thefade level(amplitude) varies as a function ofposition. In thegeneral case when a large and random number of path exist, theresulting amplitude (envelop) is modeled as a r. v. (e.g. Rayleigh)

The rate of fading fluctuations depends on velocity. A rough measureof the fading rate is the Doppler spread.


10/18

Statistical Multipath Model

Random MP components change with time, each with Random amplitude Random phase Random Doppler shift Random delay

Leads to time-varying channel impulse response: Rapid changes in signal strength over a small area/time interval Time dispersions (echoes) caused by MP delays

Characterization of MP Fading Channels

Channel impulse response function

MP Effects Combined Doppler effect from MP result in amplitude and

phase variations Component amplitudes change slowly; A large change in

Cn(t) are necessary to change r(t) significantly Component phases change rapidly; Only small changes inn(t) are required to change r(t) dramatically (fc is very large)

Different n change in different, unpredictable ways

Conclusions r(t) is best described as a random process If a large number of paths contributes tor(t), then r(t) is well

modeled as a Gaussian random processg(t,) is a Gaussian random process

=

=)(

1

)()()(),(

tN

nn

tjn

netCtg


11/18

Characterization of Flat Fading

Flat frequency-non-selective fading Differential path delays are small than symbol period

All MP components differ only by amplitude and/orphase term (no data distortion/ISI)

Channel:g(t,)=g(t) (o), T (t, f ) =g(t)e-j2fo

LLN: forN(t) large, in-phase and quad signals rI(t) andrQ(t) are jointly Gaussian

Characterization of the received signal Correlation and PSD Envelop and phase distribution Envelop correlation and spectrum Envelop level crossing rate and average fade duration

Envelope Amplitude and Phase

Envelope signal g(t) =gI(t) + jgQ(t) g(t) is WSS complex Gaussian random process

Amplitude (t) = |g(t)|;

Phase (t) = tan-1(gQ(t)/gI(t))

Envelope power p = E[2(t)] = 2Pr (signal power) Squared-envelope 2(t) is proportional to instantaneous signal power

Fading distribution depends on environment NoLOS: Rayleigh distribution

Amplitude pdf: Rayleigh Power pdf: exponential Phase: uniformly distributed over [-, ]

LOS: Ricean distribution Amplitude pdf: Ricean Phase: not uniform, more complicated

Measurements support Nakagami distribution in some environments Similar to Ricean, but models worse than Rayleigh channels Lends itself better to closed form BER expressions


12/18

Flat Fading Channel Types

Channel

type

Environment

(see handout for probability density function)Rayleigh Mobile system with no LOS between Tx and RxRician

Nakagami-n Propagation paths with a LOS and random weaker components Related to Rician factor (n2=K) n=0: Rayleigh; n=inf: no fading

Nakagami-

m Land mobile, indoor mobile multipath m=1: Rayleigh; m=inf: no fading; m=1/2: one-side Gaussian

Nakagami-q

(Hoyt) Satellite links subject to strong ionospheric scintillation q=1: Rayleigh; q = 1: one-side Gaussian

Log-normal

shadowing

Urban land mobile, land mobile satellite systems; caused by terrain, buildings, trees

Composite

gamma/log-

normal

Congested downtown area with slow moving objectsNakagami-m multipath superimposed on log-normal shadowing

BER Analysis in Flat Fading

Generalized BER in digital comm:

: instantaneous SNR; a, c: constants related to modem

BER analysis No-fading channel: is deterministic,

No-fading channel: is r.v.

SNR distribution:obeys squared-envelop PDF of channel Average BER for an average SNR :

Example: BPSK in Rayleigh fading (pp. 244, Stuber)

Numerical Evaluation

( ) caQPe =)(

)(ee PP =

{ } { } ( )=== dpcaQPEPEP eee )()()(

=

os NE /=

=

=

2/

0 2

22

sin2exp

1

2exp

2

1)(

d

xdy

yxQ

x


13/18

Level Crossing and Fade Duration

Second-order statistics of envelope fading

Level crossing rate The rate at which the envelope crosses level R Rayleigh:

Average fade duration Average duration that the envelop level remains below R Depends on frequency, velocity, and fade depth Dictates performance measure Rayleigh: Inversely proportional to Doppler frequency

Deeper fades tend to occur less frequently and last shorterfc = 900M Hz, v = 60m/hr, fD = 88Hz, LR = 81/s, tR = 7.8ms for= 0dB LR = 2.2/s, tR = 45s for= -20dB

)2/()1(2

DR fet =

2

2 = efL DR


14/18

Frequency-Selective Fading

Frequency selective Time spread of the propagation path delays is large

compared to the inverse signal bandwidth

Frequency components in the transmitted signal willexperience different phase shifts along different paths,resulting in amplitude and phase distortions

Channel characterizing functions (Bello) MP channels modeled as time-variant linear filters Key elements: time t, time delay , freq.f, Doppler freq. Input delay spread function Output Doppler-spread function Time-variant transfer function Delay Doppler-spread function

Bello Transmission Functions

Input delay spread functiong(t,) Relates input-output time waveforms: r(t) =g(t,) *s(t)

Channel viewed as a transversal filter with tap spacing and time-varying tap gaing(t,m)

Output Doppler-spread functionH (f, ) Relates input-output spectra:R(f) =H (f, ) * S(f)

Channel viewed as a filter bank with transfer functionsH (f,m) followed by a frequency conversion chain producing the Doppler shifts

Time-variant transfer function T(f,t) Relates output time waveform to input spectrum: r(t) = IFFT{S(f)T(f, t)}

Delay Doppler-spread function S(,) Relates input-output time waveforms in terms of and

Fourier transform relations between the transmission functions


15/18

Wideband Channel Model

Channel Scattering Function S(,) Defined as Fourier transform of g(t,) with respect to t.

Denotes average power output of the channel as functionof and

Easy to measure in practice; Wheng(t,) unknown takeexpected value

Used to find key channel parameters

Multipath Intensity Profile: g()

Delay spread and Coherence bandwidth Doppler Spectrum: ()

Doppler spread and Coherence time

S(, )

Multipath Intensity Profile

Multipath intensity profile/Power delay profile

Average output of the channel as a function of the delay

Delay spread Tm The range of values for which g() is essentially non-zero

Typical Tm values: indoors < 1s, outdoor > 1s (1-10s)

Coherence bandwidth fc g(f): Fourier transform of g(); auto-correlation in f fc denotes the range of frequencies where g(f) is non-zero Two sinusoids with frequencies separated by more than will

be affected very differently by the channel;

Therefore severe distortion if BWs > fc, but also providesleverage for frequency diversity


16/18

Doppler Spectrum

Objective

Quantify the time-varying nature of the channel

Doppler power spectral density H()

Average power at the channel output as a function of

the Doppler frequency

Coherence time Tc Doppler spreadBd

Tc = 1/Bd indicates the length of time over whichchannel is approximately constant

Data rate and Channel characteristics

Ts >> Tm (Symbol period > Delay spread) ISI is no concern; equivalent to BWs > Tm => Ts ~ 50s, max rateR = 20Ksymbols/second ~ 1 voice channel

Ts < Tm (Symbol period < Delay spread) Frequency selective fading

ISI exists, equalization required E.g. GSMRb ~ 4 s

Ts Coherence time) Higher Doppler spread, equivalently toBd> 1/Ts; Fast fading


17/18

Channel Impairments and Mitigation

Multipath dispersion/Delay spread Time dispersion, frequency-selective fading

Rapid changes in signal strength over a small time/distance

MP spreads/smears the signal, causing ISI

Limits max. symbol rate: Transmission rate < coherence BW

Errors increase as bit period approaches delay spread

Doppler spread Frequency dispersion, time selective fading

Random frequency modulation on different MP signals

Loss of synchronization due to Doppler induced frequency/phase shifts

Error Burst resulted from fades in radio channels

Strategies for overcoming errors

Antenna diversity (+10dB) Forward error correction (FEC) through coding gain Equalization for frequency selective fading Automatic Repeat Request (ARQ)

Propagation Channel Summary

Complex Radio Propagation Channel varies with user location and time

Large scale Long-term fades Simplified pass loss model

Log-normal shadowing and coverage

Small scale short-term fades

Multipath scattering leads to time-varying Channel impulse responseand rapid fluctuation of received power

Statistical analysis: signal/envelope correlation & PSD

Rice factor

Resulting channel impairments Multipath dispersion/Delay spread

Rayleigh fading/Frequency Spread

Average fade duration dictates performance measures


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Simulating Short-Term Fading

Jakes method: sum of sinusoids

Discrete-time equivalent channel

Input delay spread functiong(t,), channels are viewed as a transversalfilter with tap spacing and time-varying tap gaingn(t) =g(t,m)

-spaced tapped delay line model (Figure 2.38)

The filter coefficientsgn(t) are typically modeled as complex-valuedGaussian random process. The parameters ofgn(t) are

fractional power: expected value E[|gn(t)|2]

PSD ofgn(t): Doppler spectrum Sg(f) (e.g. CLASS, RICE, etc.) gn(t) =IFFT{Gn(f) FFT(white Gaussian r.p)}, where |Gn(f)|

2 = Sg(f)

==

==N

nnn

N

nnn ttstgtrtttgtg

11

)(~)()(~,)()(),(

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