Example: Obstacle Modeling for Wireless Transmissions

Example: Obstacle Modeling for Wireless

TransmissionsAndy WangCIS 5930-03

Computer SystemsPerformance Analysis

2

Motivation• Typical studies of mobile wireless

networks assume an open field– No physical obstacles (e.g., no buildings)– Not reflective of urban settings

Goals• Validate the open-field wireless signal

attenuation model used in NS-2• Model the signal attenuation caused by

physical obstacles

3

Services• Wireless network signal transmissions

– Broadcast signals– Listen to signals

4

Outcomes• Sufficient signal strength for data

transmission– Successful transmissions– Unsuccessful transmissions (e.g., due to

interferences)• Insufficient signal strength for data

transmission– No service

5

Metric• Signal strength

– dBm (decibels relative to 1 mWatt)• Decibels are ratios (no units)

– Log transformed• 1 mW = 10log10(1mW/1mW) = 0 dBm

– Tricky unit conversions• (XWatts* 1000)mWatts

• (XdBW + 30)dBm

• Note: 30 = 10log10(1000mW/1mW)• Measured in electric power

6

Implicit Assumptions• Bandwidth, latency, and packet loss rate

are largely a function of signal strength• Not measured

7

Parameters• Open field

– Type of base station and receiver– Distance between sender and receiver– Presence of interference

• Self interference– Ground surface, signal reflections

• Other transmissions– Weather conditions– Height of transmission source

8

Parameters• With obstacles

– Location of obstacles– Type of obstacles

• Different building codes• Problem

– Difficult to quantify obstacles and their relationship to the base station and receiver

9

Factors and Evaluation Techniques

• Factors– Distance between sender and receiver– Presence of obstacles

• Evaluation techniques– Empirical measurements

10

Workloads• One sender, one receiver

– Continuous transmissions• Open field

– Mike Long Track on campus• With obstacles

– Around a block in downtown Tallahassee– Around Keen Building

11

Workloads• Problems

– No interferences– Only measured two scenarios

12

Experimental Settings• Base station

– 802.11b Linksys• Receiver

– Linux laptop with wireless PCI card– Used Wavemon to log transmission signals

13

Downtown Tallahassee

14

Keen Building GPS Coordinates

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30.445825, -84.301432 30.445806, -84.301347

30.446075, -84.301314 30.446056, -84.301239

30.446093, -84.301389

30.445973, -84.301486

30.445862, -84.301486

30.446010, -84.301143

30.445779, -84.301229

30.445880, -84.301175

30.445862, -84.300896

30.445723, -84.300939

30.445779, -84.301089

30.445917, -84.301035

1

3

2g f e

d

cba

h j

ki

Possible base station locations

Experimental Design• Ideally, start with 23r factorial design to

identify major factors and interactions

16

Experimental Design• What really happened

– 22 factorial design

– Had missing data points for temperature– Ground surfaces correlate to the presence

of obstacles17

Experimental Design• Problems

– Cumbersome setup• Needed portable battery• Network measurements drain batteries quickly

– Missing data points for temperature– Ground surfaces correlate to the presence

of obstacles

18

Experimental Design• Open-field model validation

– Simple design• Varied the distance between base station and

receiver• Obstacle model

– Simple design• Varied the distance between base station and

receiver

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Data Analysis• 22 factorial design (example 1)• Fractions of variations explained

* 36% due to the presence of obstacles* 60% due to distance* 4% due to the interaction between the two

• Okay to create separate models– With obstacles– Without obstacles

20

Open-field Data Analysis

• Simple linear regression (example 2)– Signal = -46 – 0.57(distance)– R2 = 0.78– Both coefficients are significant

21

0 10 20 30 40 50 60 70 80 90

-120

-100

-80

-60

-40

-20

0

yi y_hat90% confidence interval

distance (meters)

dBm

Open-field Data Analysis

• However, ANOVA not satisfactory

22

-100 -90 -80 -70 -60 -50 -40

-10

-5

0

5

10

15

20

25

y_hat

error residuals

0 2 4 6 8 10 12 14 16

-10

-5

0

5

10

15

20

25

experimental number

error residuals

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

-10

-5

0

5

10

15

20

25

f(x) = 6.46005695196675 x − 2.23503935841352E-15R² = 0.819196198781606

normal quantiles

observed error residual quan-

tiles

Try Transforms (Ex.3)• distance’ = 1/distance

– Signal = -91 + 682/distance– R2 = 0.98– Both coefficients are significant

23

20 30 40 50 60 70 80 90

-90-80-70-60-50-40-30-20-10

0

yi y_hat90% confidence interval

distance (meters)

dBm

Try Transforms (Ex.3)• distance’ = 1/distance

– R2 = 0.98– Weird error patterns

24

-85 -80 -75 -70 -65 -60

-1.5

-1

-0.5

0

0.5

1

1.5

2

y_hat

error residuals

0 2 4 6 8 10 12 14

-1.5

-1

-0.5

0

0.5

1

1.5

2

experimental number

error residuals

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

-1.5

-1

-0.5

0

0.5

1

1.5

2

f(x) = 0.800580814768194 x − 1.43585620348543E-15R² = 0.892946654243968

normal quantiles

observed error residual quan-

tiles

Try Transforms (Ex. 4)• distance’ = 1/distance2

– Signal = -84 + 12925/distance2

– R2 = 0.92– Both coefficients are significant

25

20 30 40 50 60 70 80 90

-90-80-70-60-50-40-30-20-10

0

yi y_hat90% confidence interval

distance (meters)

dBm

Try Transforms (Ex. 4)• distance’ = 1/distance2

– R2 = 0.92– Weird error patterns

26

-85 -80 -75 -70 -65 -60

-3

-2

-1

0

1

2

3

y_hat

error residuals

0 2 4 6 8 10 12 14

-3

-2

-1

0

1

2

3

experimental number

error residuals-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

-3

-2

-1

0

1

2

3f(x) = 1.62457905305534 x − 2.15805052769733E-15R² = 0.969811539510596

normal quantiles

observed error residual quan-

tiles

Try Transforms (Ex. 5)• distance’ = 1/sqrt(distance)

– Signal = -107 + 211/sqrt(distance)– R2 = 0.99– Both coefficients are significant

27

20 30 40 50 60 70 80 90

-100-90-80-70-60-50-40-30-20-10

0

yi y_hat90% confidence interval

distance (meters)

dBm

Try Transforms (Ex. 5)• distance’ = 1/sqrt(distance)

– R2 = 0.99– Errors not normally distributed

28

-85 -80 -75 -70 -65 -60

-1

-0.5

0

0.5

1

1.5

y_hat

error residuals

0 2 4 6 8 10 12 14

-1

-0.5

0

0.5

1

1.5

experimental number

error residuals

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

-1

-0.5

0

0.5

1

1.5

f(x) = 0.472267862672277 x + 7.55722898312044E-15R² = 0.758206423633563

normal quantiles

observed error residual quan-

tiles

Try Transforms (Ex. 6)• distance’ = log10(distance)

– Signal= -18 – 35*log(distance)– R2 = 0.99

29

0 10 20 30 40 50 60 70 80 90

-100-90-80-70-60-50-40-30-20-10

0

yi y_hat90% confidence interval

distance (meters)

dBm

Try Transforms (Ex. 6)• distance’ = log10(distance)

– R2 = 0.99

30

-90 -85 -80 -75 -70 -65 -60 -55 -50

-1

-0.5

0

0.5

1

1.5

2

y_hat

error residuals

0 2 4 6 8 10 12 14 16

-1

-0.5

0

0.5

1

1.5

2

experimental number

error residuals

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

-1

-0.5

0

0.5

1

1.5

2

f(x) = 0.617459319587706 x + 1.40861403359254E-15R² = 0.920293187741683

normal quantiles

observed error residual quan-

tiles

Validate Open-field Model

• dBmr = -18 – 35*log(distance)• NS-2 model

* Wattr = Watts*α/distance2

* dBmr = 10*log(Powers*α/distance2) + 30= dBms + 10*log(α) – 20*log(distance)

= (dBms + A) – B*log(distance)

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Obstacle Data Analysis• Simple linear regression

– Signal = -50 – 0.64(distance)– R2 = 0.48– The second coefficient is not significant

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Obstacle Data Analysis (Ex. 7)

• ANOVA– Weird error patterns

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-110 -100 -90 -80 -70 -60 -50 -40

-30

-20

-10

0

10

20

30

40

y_hat

error residuals

0 10 20 30 40 50 60 70 80

-30

-20

-10

0

10

20

30

40

experiment number

error residuals

-3 -2 -1 0 1 2 3

-30

-20

-10

0

10

20

30

40

f(x) = 13.3362552680386 x − 2.73649712017034E-15R² = 0.947276427868547

normal quantiles

observed error residual quan-

tiles

Try Log Transform (Ex. 10)

• R2 = 0.24• ANOVA shows patterns

34

-92 -90 -88 -86 -84 -82 -80 -78 -76 -74 -72

-20

-15

-10

-5

0

5

10

15

20

25

y_hat

error residuals

0 10 20 30 40 50 60 70 80

-20

-15

-10

-5

0

5

10

15

20

25

experiment number

error residuals

-3 -2 -1 0 1 2 3

-20

-15

-10

-5

0

5

10

15

20

25

f(x) = 9.43169204430789 x + 2.23760437095676E-14R² = 0.919889934362008

normal quantiles

observed error residual quan-

tiles

Analyze a Subset of Data

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30.445825, -84.301432 30.445806, -84.301347

30.446075, -84.301314 30.446056, -84.301239

30.446093, -84.301389

30.445973, -84.301486

30.445862, -84.301486

30.446010, -84.301143

30.445779, -84.301229

30.445880, -84.301175

30.445862, -84.300896

30.445723, -84.300939

30.445779, -84.301089

30.445917, -84.301035

1

3

2g f e

d

cba

h j

ki

Possible base station locations

Focus on this data set

Keen Building Location 1 (Ex. 13)

• Signal = -27 – 36*log10(distance)• R2 = 0.70• Both coefficients are significant

36

20 30 40 50 60 70 80

-140

-120

-100

-80

-60

-40

-20

0

yi y_hat90% confidence interval

distance (meters)

dBm

Keen Building Location 1

• ANOVA so so• Errors not quite normally distributed

37

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

-10

-8

-6

-4

-2

0

2

4

6

8f(x) = 3.74974884853963 x − 3.52240445076884E-15R² = 0.945171955778447

normal quantiles

observed error residual quan-

tiles

-96 -94 -92 -90 -88 -86 -84 -82 -80 -78 -76

-10

-8

-6

-4

-2

0

2

4

6

8

y_hat

error residuals

0 5 10 15 20 25

-10

-8

-6

-4

-2

0

2

4

6

8

experiment number

error residuals

Downtown Data Set (Ex. 15)

• Signal = -16 – 39*log10(distance)• R2 = 0.71• Only the second coefficient is significant

38

30 40 50 60 70 80 90

-250

-200

-150

-100

-50

0

50

yi y_hat90% confidence interval

distance (meters)

dBm

Downtown Data Set• ANOVA

39

-94 -92 -90 -88 -86 -84 -82 -80 -78 -76 -74

-6

-4

-2

0

2

4

6

8

y_hat

error residuals

0 1 2 3 4 5 6 7

-6

-4

-2

0

2

4

6

8

experiment number

error residuals

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

-6

-4

-2

0

2

4

6

8

f(x) = 4.15328384563262 x + 4.736951571734E-15R² = 0.859261278629964

normal quantiles

observed error residual quan-

tiles

Unified Model (Ex. 17)• Signal = -22 - 5.3*(if ob) – 33*log10(dist)• R2 = 0.32• All coefficients are significant• Passed F test

• The presence of obstacles costs 5.3 dBm

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Unified Model (Ex. 17)• Signal = -22 - 5.3*(if ob) – 33*log10(dist)• R2 = 0.32• All coefficients are significant

41

0 10 20 30 40 50 60 70 80 90 100

-140

-120

-100

-80

-60

-40

-20

0

yi y_hati90% confidence interval

distance (meters)

dBm

Unified Model• ANOVA not so good…

42

-95 -90 -85 -80 -75 -70 -65 -60 -55

-20

-15

-10

-5

0

5

10

15

20

25

y_hat

error residuals

0 10 20 30 40 50 60 70 80 90

-20

-15

-10

-5

0

5

10

15

20

25

experiment number

error residuals

-3 -2 -1 0 1 2 3

-20

-15

-10

-5

0

5

10

15

20

25

f(x) = 8.56394129011418 x − 1.96936779102633E-12R² = 0.935379159161522

normal quantiles

observed error residual quan-

tiles

Problems• Need better ways to describe the

relationship between obstacles, sender, and receiver

43

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White Slide