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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