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 Propagation Log Normal Shadowing Combined Path Loss and Shadowing Outage Probability Model 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 Model Power falloff with distance proportional to d -4 Simplified Model: P r =P t K[d 0 /d]   Captures main characteristics of path loss Empirical Models

mmWave Propagation (60-100GHz) Channel models immature Based on measurements, few accurate analytical models Path loss proportion to 2 (huge) Also have oxygen and rain absorbtion is on the order of a water molecule mmWave systems will be short range or require “massive MIMO” mmW Massive MIMO

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  =0 (mean captured in path loss), 4<  <12 (empirical) CLT used to explain this model Decorrelates over decorrelation distance X c XcXc

Combined Path Loss and Shadowing Linear Model:  lognormal dB Model P r /P t (dB) log d Very slow Slow 10 log  -10 

Outage Probability

Model Parameters from Empirical Measurements Fit model to data Path loss (K,  ), d 0 known: “Best fit” line through dB data K obtained from measurements at d 0. 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  P r (dB) log(d) 10  K (dB) log(d 0 )  2

Main Points mmWave propagation models still immature Path 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