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ECE 5221 Personal Communication Systems. Prepared by: Dr . Ivica Kostanic Lecture 4: Estimation of coverage reliability. Spring 2011. Outline . Macroscopic propagation modeling Edge reliability Area reliability Reudnik curves and fade margin calculations Examples.

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ece 5221 personal communication systems
ECE 5221 Personal Communication Systems

Prepared by:

Dr. Ivica Kostanic

Lecture 4: Estimation of coverage reliability

Spring 2011

  • Macroscopic propagation modeling
  • Edge reliability
  • Area reliability
  • Reudnik curves and fade margin calculations
  • Examples

Important note: Slides present summary of the results. Detailed derivations are given in notes.

macroscopic propagation modeling
Macroscopic propagation modeling

Log distance path loss model

  • More input descriptors – more accurate models
  • As the models become more accurate, the standard deviation of the unexplained portion of path loss becomes smaller
  • The unexplained portion still retains log normal character

More general models

  • Macroscopic models predict median path loss at some distance d
  • As one measures the actual path loss, its value will always be different than predicted
  • The difference is a log normal random variable with zero mean and variance that depends on environment
expected accuracy of propagation model
Expected accuracy of propagation model
  • Macroscopic propagation models – limited accuracy
  • Accuracy depends:
    • Input data accuracy
    • Type of the environment
    • Computational time
    • Model limitations
  • The accuracy is quantified through standard deviation of prediction error
  • For a well tuned model, standard deviation of prediction error is 6-8dB
  • Note: the error is relatively large
  • GOAL: coverage design using imperfect tools

Comparison of measurements and predictions

Distribution of prediction error

edge reliability
Edge reliability
  • RSLT – Coverage threshold that needs to be met by the network. The threshold determined from coverage objectives
  • RSLT – contour provides 50% reliability (i.e. if one walks around the contour the threshold is met only 50% of locations)
  • RSLP – contour that provides required reliability for meeting the threshold RSLT
  • RSLP=RSLT + D, where D is the value that needs to be determined based on required edge reliability
  • Mathematically:

Goal: determine RSLP contour that meets edge reliability requirements

edge reliability example
Edge reliability - example

Assume that one needs to perform design for RSLT = -90dBm. The area is characterized with standard deviation of s=8dB. What contour RSLP provides 70% edge reliability.

Answer: RSLP = -85.2dBm, D=4.8dB

Following the same approach one obtains the table

concept of area reliability
Concept of area reliability
  • Coverage is an areal phenomenon
  • Design needs to guarantee specified area reliability
  • One needs to find RSLP contour such that

Where Rais the area reliability.

Typical values for area reliability are 90-95%

Note: there is tradeoff between coverage reliability and cell count

Illustration of cell coverage area

calculation of area reliability result
Calculation of area reliability (result)

Area reliability

  • Notes:
    • Equation – to complicated for day to day use
    • Gives the answer
    • Need for easier way to calculate

Based on log-distance path model


reudnik curves
Reudnik curves

Edge reliability

Area reliability calculations – complicated

Edge reliability calculations – easy

Reudnik curves relate area and edge reliabilities

Area reliability

Properties of environments

area reliability examples
Area reliability - examples

Example 1: Consider environment with s/n = 3. Determine reliability over the area bounded with a contour having edge reliability of 70%

Answer: 85%

Example 2: Consider the following design task

Design threshold: -95dBm

Area reliability: 90%

Path loss exponent: 3.84

Standard deviation of the modeling accuracy: 8dB


  • Edge reliability requirement Answer: 75%
  • Required prediction contour Answer: -89.4dBm
fade margin calculations direct method
Fade margin – calculations (direct method)
  • Fade margin – difference between RSLP and RSLT
  • Can be calculated directly from area reliability requirement, s and n
  • Process:
    • Calculate s/n
    • Determinez-score (table lookup)
    • Fade margin is calculated as z-score x s
  • Calculate the fade margin for the following scenario
    • Area reliability requirement: 95%
    • Model uncertainty: 8dB
    • Slope: 35dB/dec


s/n = 2.29

z-score: 1.10

FM = 1.10 x 8 = 8.8 dB