EE359 – Lecture 3 Outline

Announcements HW posted, due Friday 5pm Discussion section starts tomorrow, 4-5pm, 364

Packard TA OHs start this week

mmWave Signal PropagationLog Normal ShadowingCombined Path Loss and

ShadowingOutage ProbabilityModel Parameters from

Measurements

Lecture 2 Review Signal Propagation Overview Ray Tracing Models Free Space Model

Power falloff with distance proportional to d-2

Two Ray ModelPower falloff with distance proportional

to d-4

Simplified Model: Pr=PtK[d0/d]g, 2g8.Captures main characteristics of path

lossEmpirical Models

mmWave Propagation (60-100GHz)

Channel models immatureBased on measurements, few accurate

analytical models Path loss proportion to l2 (huge) Also have oxygen and rain absorbtion

l is on the order of a water molecule

mmWave systems will be short range or require “massive MIMO”

mmWMassiveMIMO

Shadowing

Models attenuation from obstructions Random due to random # and type of

obstructions Typically follows a log-normal

distributiondB value of power is normally distributedm=0 (mean captured in path loss), 4<s<12

(empirical)CLT used to explain this modelDecorrelates over decorrelation distance

Xc

Xc

Combined Path Loss and Shadowing

Linear Model: y lognormal

dB Model

yg

ddK

PP

t

r 0

,log10log10)(0

1010 dBt

r

ddKdB

PP yg

Pr/Pt

(dB)log d

Very slow

Slow10logK

-10g

),0(~ 2ysy NdB

Outage ProbabilityPath loss only: circular “cells”;

Path loss+shadowing: amoeba-shaped cells

Outage probability: probability received power falls below given minimum:

For log-normal shadowing model

rP

Model Parameters from

Empirical Measurements

Fit model to dataPath loss (K,g), 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 g

Pr(dB)

log(d)10g

K (dB)

log(d0)

sy2

Main Points mmWave propagation models still

immaturePath loss large due to frequency, rain, and

oxygen

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

Path loss and shadowing parameters are obtained from empirical measurements