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Florida Institute of technologies ECE 5221 Personal Communication Systems Prepared by: Dr. Ivica Kostanic Lecture 4: Estimation of coverage reliability Spring 2011
Florida Institute of technologies
ECE 5221 Personal Communication Systems Prepared by:
Dr. Ivica Kostanic
Lecture 4: Estimation of coverage reliability
Spring 2011
Florida Institute of technologies
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Macroscopic propagation modelingEdge reliabilityArea reliabilityReudnik curves and fade margin calculationsExamples
Outline
Important note: Slides present summary of the results. Detailed derivations are given in notes.
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Macroscopic propagation modeling 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
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Log distance path loss model
shadowing normal log
meandependent Distance
00 logPLPL X
ddm
More general models
losspath ofportion dUnexplainemeandependent Distance
ns,obstructio clutter,,,,,PL XfhhdF RxTX
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
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Expected accuracy of propagation model
Macroscopic propagation models – limited accuracy
Accuracy depends:o Input data accuracyo Type of the environmento Computational timeo 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
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Comparison of measurements and predictions
Distribution of prediction error
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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:
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yreliabilit edge requiredthreshold known
TP RSLRSL er RXP
,0~
Goal: determine RSLP contour that meets edge reliability requirements
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Edge reliability - example
Assume that one needs to perform design for RSLT = -90dBm. The area is characterized with standard deviation of =8dB. What contour RSLP provides 70% edge reliability.
Answer: RSLP = -85.2dBm, D=4.8dB
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D/ Edge reliability(%)0 50
0.6 701 84
1.28 901.64 95
2 982.33 99
Following the same approach one obtains the table
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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 Ra is the area reliability.
Typical values for area reliability are 90-95%
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aR Tarea the in RSLRSLPr
Illustration of cell coverage area
Note: there is tradeoff between coverage reliability and cell count
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Calculation of area reliability (result)
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Area reliability
bab
babaU -1erf121experf1
21RSL 2T
Where
2/log emb 2//log 00 dRmPLPRSLa TXT
Z
dxx0
2exp2zerf
Notes:o Equation – to complicated for
day to day useo Gives the answer o Need for easier way to calculate
Based on log-distance path model
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Reudnik curves
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Area reliability calculations – complicated Edge reliability calculations – easy Reudnik curves relate area and edge
reliabilities
Edge reliability
Area reliability
Properties of environments
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Area reliability - examples
Example 1: Consider environment with /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
Determine:
a) Edge reliability requirement Answer: 75%
b) Required prediction contour Answer: -89.4dBm
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Fade margin – calculations (direct method) Fade margin – difference between RSLP and RSLT
Can be calculated directly from area reliability requirement, and n Process:
o Calculate /n
o Determine z-score (table lookup)o Fade margin is calculated as z-score x
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sigma/n 85% 86% 87% 88% 89% 90% 91% 92% 93% 94% 95% 96% 97% 98% 99%0 - - - - - - - - - - - - - - -
0.1 - - - - - - - - - - - - - 0.00 0.670.2 - - - - - - - - - - - 0.00 0.17 0.50 0.830.3 - - - - - - - - - 0.00 0.11 0.22 0.44 0.67 1.110.4 - - - - - - - - 0.00 0.08 0.25 0.42 0.58 0.83 1.250.5 - - - - - - 0.00 0.07 0.13 0.27 0.40 0.53 0.73 0.93 1.330.6 - - - - - 0.00 0.06 0.17 0.28 0.39 0.50 0.67 0.83 1.06 1.390.7 - - - - 0.00 0.10 0.14 0.24 0.33 0.48 0.57 0.71 0.90 1.10 1.430.8 - - - 0.00 0.08 0.17 0.25 0.33 0.42 0.54 0.67 0.79 0.96 1.17 1.500.9 - 0.00 0.04 0.07 0.15 0.22 0.30 0.41 0.48 0.59 0.70 0.85 1.00 1.22 1.561 0.00 0.03 0.10 0.17 0.23 0.30 0.37 0.47 0.53 0.63 0.77 0.90 1.03 1.27 1.57
1.1 0.03 0.09 0.15 0.21 0.27 0.33 0.42 0.52 0.61 0.70 0.79 0.94 1.09 1.30 1.611.2 0.08 0.14 0.19 0.25 0.33 0.39 0.47 0.56 0.64 0.72 0.83 0.97 1.11 1.33 1.641.3 0.13 0.18 0.23 0.31 0.36 0.44 0.51 0.59 0.67 0.77 0.87 1.00 1.15 1.36 1.671.4 0.17 0.21 0.29 0.33 0.40 0.48 0.55 0.62 0.71 0.81 0.90 1.02 1.19 1.38 1.691.5 0.20 0.27 0.31 0.38 0.44 0.51 0.58 0.64 0.73 0.82 0.93 1.07 1.20 1.40 1.711.6 0.23 0.29 0.35 0.42 0.48 0.54 0.60 0.69 0.77 0.85 0.96 1.08 1.23 1.44 1.731.7 0.27 0.31 0.37 0.43 0.49 0.57 0.63 0.71 0.78 0.88 0.98 1.10 1.25 1.45 1.751.8 0.30 0.35 0.41 0.46 0.52 0.59 0.65 0.74 0.81 0.91 1.00 1.13 1.28 1.46 1.781.9 0.33 0.37 0.44 0.49 0.54 0.61 0.68 0.75 0.84 0.93 1.04 1.14 1.30 1.49 1.792 0.35 0.40 0.45 0.52 0.57 0.63 0.70 0.78 0.85 0.95 1.05 1.17 1.32 1.50 1.80
2.1 0.37 0.43 0.48 0.54 0.59 0.65 0.71 0.79 0.87 0.97 1.06 1.19 1.33 1.52 1.812.2 0.39 0.44 0.50 0.55 0.61 0.67 0.74 0.82 0.89 0.98 1.08 1.20 1.35 1.53 1.832.3 0.41 0.46 0.52 0.57 0.62 0.70 0.75 0.83 0.91 1.00 1.10 1.22 1.36 1.55 1.842.4 0.43 0.49 0.53 0.58 0.65 0.71 0.78 0.85 0.93 1.01 1.11 1.22 1.38 1.56 1.852.5 0.45 0.49 0.55 0.60 0.67 0.72 0.79 0.87 0.93 1.03 1.12 1.24 1.39 1.57 1.872.6 0.46 0.51 0.56 0.62 0.68 0.74 0.81 0.87 0.95 1.04 1.14 1.26 1.40 1.58 1.872.7 0.48 0.53 0.58 0.63 0.69 0.75 0.81 0.89 0.96 1.05 1.15 1.27 1.41 1.59 1.892.8 0.50 0.55 0.60 0.64 0.70 0.76 0.83 0.90 0.98 1.06 1.17 1.27 1.42 1.61 1.892.9 0.51 0.55 0.61 0.67 0.71 0.78 0.84 0.91 0.99 1.08 1.17 1.29 1.43 1.61 1.913 0.52 0.57 0.62 0.68 0.73 0.79 0.86 0.92 1.00 1.09 1.19 1.30 1.43 1.62 1.91
Area Reliability
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Example
Calculate the fade margin for the following scenarioo Area reliability requirement: 95%o Model uncertainty: 8dBo Slope: 35dB/dec
Answers:
/n = 2.29
z-score: 1.10
FM = 1.10 x 8 = 8.8 dB
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