Lecture 3 Outline l Log Normal Shadowing l

Lecture 3 Outline l Log Normal Shadowing l Combined Path Loss and Shadowing l Cell Coverage Area l Model Parameters from Measurements

Lecture 2 Review l l Ray Tracing Models Free Space Model l l Two Ray Model l l Power falloff with distance proportional to d-2 Power falloff with distance proportional to d-4 General Ray Tracing l Used for site-specific models l Empirical Models l Simplified Model: Pr=Pt. K[d 0/d]g, 2 g 8. l Captures main characteristics of path loss

Shadowing Xc l l l Models attenuation from obstructions Random due to random # and type of obstructions Typically follows a log-normal distribution d. B value of power is normally distributed l m=0 (mean captured in path loss), 4<s<12 (empirical) l LLN used to explain this model l

Combined Path Loss and Shadowing l Linear Model: y lognormal 10 log. K Pr/Pt (d. B) l d. B Model Slow Very slow -10 g log d

Outage Probability and Cell Coverage Area l Path loss: circular cells l Path loss+shadowing: amoeba cells l Tradeoff l between coverage and interference Outage probability l Probability minimum l received power below given Cell coverage area l % of cell locations at desired power l Increases as shadowing variance decreases l Large % indicates interference to other cells

Model Parameters from Empirical Measurements K (d. B) l l Fit model to data Pr(d. B) sy 2 10 g log(d 0) Path loss (K, g), d 0 known: log(d) l “Best fit” line through d. B data l K obtained from measurements at d 0. l Exponent is MMSE estimate based on data l Captures mean due to shadowing l Shadowing variance l Variance of data relative to path loss model (straight line) with MMSE estimate

Main Points l Random attenuation due to shadowing modeled as log-normal (empirical parameters) l Shadowing decorrelates over decorrelation distance l Combined path loss and shadowing leads to outage and amoeba-like cell shapes l Cellular coverage area dictates the percentage of locations within a cell that are not in outage l Path loss and shadowing parameters are