Pathloss Modeling and Estimation for V2V Wireless ... · Pathloss Modeling and Estimation for V2V...

Pathloss Modeling and Estimation

for V2V Wireless Communications

Carl Gustafson

Department of Electrical and Information Technology,

Lund University,

Sweden

-

with contributions from

Taimoor Abbas, David Bolin and Fredrik Tufvesson

1 / 17

Introduction

In this talk, I will discuss the pathloss concept, applied tovehicle-to-vehicle (V2V) wireless communications.

I Pathloss - What is it?I Pathloss Models - How should we model pathloss for V2V

scenarios?I Censored and Truncated Data - What happens when there are

missing samples in the measurement data?I Estimation and Results

IEEE VTS Workshop, Halmstad, 2015-11-11 2/17

Introduction


I Pathloss - What is it?

I Pathloss Models - How should we model pathloss for V2Vscenarios?

I Censored and Truncated Data - What happens when there aremissing samples in the measurement data?

I Estimation and Results


Introduction



scenarios?

I Censored and Truncated Data - What happens when there aremissing samples in the measurement data?



Introduction




missing samples in the measurement data?



Introduction




missing samples in the measurement data?I Estimation and Results


What is Pathloss?

I In free space, the attenuation in received power due to theexpansion of the radio wave in space, between two isotropicantennas, is given by:

FSPL =

✓4⇡d

�

◆2

= 20 log10

✓4⇡d

�

◆[dB].

I FSPL / d

2, i.e., in free space, the pathloss exponent is n = 2.

I However, a realistic user will experience a multi-pathenvironment, with small-scale and large-scale fading.

Txy

x

z

2

1

3

4

L

Rx

y

x

z

2

13

4

L


What is Pathloss?

I In free space, the attenuation in received power due to theexpansion of the radio wave in space, between two isotropicantennas, is given by:

FSPL =

✓4⇡d

�

◆2

= 20 log10

✓4⇡d

�

◆[dB].

I FSPL / d

2, i.e., in free space, the pathloss exponent is n = 2.I However, a realistic user will experience a multi-path

environment, with small-scale and large-scale fading.

Txy

x

z

2

1

3

4

L

Rx

y

x

z

2

13

4

L


What is Pathloss?

I In a multi-path environment, pathloss typically describes theexpected loss in received power as a function Tx-Rx separationdistance and the effects of random large scale fading.

I The effects of small scale fading are averaged out of the data.I The variation of the antenna gain will influence the received

power. Mounted car antennas have gains that vary a lot.

Rx

y

x

z

2

13

4

L


What is Pathloss?


I The effects of small scale fading are averaged out of the data.

I The variation of the antenna gain will influence the receivedpower. Mounted car antennas have gains that vary a lot.

Rx

y

x

z

2

13

4

L


What is Pathloss?


I The effects of small scale fading are averaged out of the data.I The variation of the antenna gain will influence the received

power. Mounted car antennas have gains that vary a lot.

Rx

y

x

z

2

13

4

L


Pathloss Models for V2V

A number of pathloss models have been developed for a variety ofwireless communication systems. A common model for (some) V2Vscenarios is the log-distance power law model:

PL(d) = PL(d0) + 10nlog10

✓d

d0

◆

| {z }Mean pathloss, µ(d)

+ �|{z}Large-scale fading

, d � d0, (1)

I Parameters to be estimated for this model:

1. PL exponent: n

2. Pathloss at the reference distance d0: PL(d0)

3. Large-scale fading about the mean power: � ⇠ N (0,�

2)


Example - Synthetic Pathloss Data

PL(d) = PL(d0) + 10nlog10

✓d

d0

◆

| {z }Mean pathloss, µ(d)

+ �|{z}Large-scale fading

, d � d0, (2)

10

010

110

210

3

40

60

80

100

120

µ̂(d) + 2�

µ̂(d) - 2�

Distance [m]

Pat

hlos

s[d

B]

µ(d)


What happens if there are missing samples?

I The observation of the received signal power at the receiver islimited by the system noise. Signals with power below thenoise floor can therefore not be measured properly.

I In vehicle-to-vehicle measurements, this limitation due to thesystem noise is often present at longer distances.

10

010

110

210

3

-40

-60

-80

-100

�PL(d0)

µ

0(dl)

dl

N (µ

0(dl),�

2)

Noise floor

Distance [m]

Cha

nnel

gain

[dB

]

µ

0(d)


What happens if there are missing samples?

I The observation of the received signal power at the receiver islimited by the system noise. Signals with power below thenoise floor can therefore not be measured properly.

I In vehicle-to-vehicle measurements, this limitation due to thesystem noise is often present at longer distances.

10

010

110

210

3

-40

-60

-80

-100

�PL(d0)

dl

µ

0(dl)

N (µ

0(dl),�

2)

Noise floor

Distance [m]

Cha

nnel

gain

[dB

]

µ

0(d)


Censored and Truncated Samples

IY is censored when we observe X for all observations, but weonly know the true value of Y for a restricted range ofobservations.

IY is truncated when we only observe X for observations whereY is within a restricted range, i.e., there is no additionalinformation outside this range.

In pathloss measurements, the samples can be modeled as beingcensored, since we observe X (i.e. d) for all observations [1].[1] C. Gustafson, T. Abbas, D. Bolin and F. Tufvesson, "Statistical Modeling and Estimation

of Censored Pathloss Data" IEEE Wireless Comm. Letters, 2015.


Estimation - Ordinary Least Squares

Ordinary least squares (OLS) is one of the standard estimationapproaches for the pathloss model in (1). Using (1), the data setfor L path loss measurements can be written as,

y = X↵+ ✏, where

y = [PL(d/d0)]L⇥1 ,

X = [1 10log10(d/d0)]L⇥2,

↵ = [PL(d0) n]T.

The OLS estimates are then given by:

ˆ↵ =

�X

TX

��1X

Ty

�̂

2=

1

L� 1

(y �X

ˆ↵)

T(y �X

ˆ↵)

I OLS estimation does not consider censored samples!


Estimation - Ordinary Least Squares

Ordinary least squares (OLS) is one of the standard estimationapproaches for the pathloss model in (1). Using (1), the data setfor L path loss measurements can be written as,

y = X↵+ ✏, where

y = [PL(d/d0)]L⇥1 ,

X = [1 10log10(d/d0)]L⇥2,

↵ = [PL(d0) n]T.

The OLS estimates are then given by:

ˆ↵ =

�X

TX

��1X

Ty

�̂

2=

1

L� 1

(y �X

ˆ↵)

T(y �X

ˆ↵)

I OLS estimation does not consider censored samples!IEEE VTS Workshop, Halmstad, 2015-11-11 9/17

Maximum-likelihood (ML) Estimation of Censored PathlossData

y = X↵+ ✏, only holds for the uncensored samples, so:I Samples that are dominated by noise are modeled as being

censored, and their PL values are set to c.I

I = 0 indicates that a sample is censored; otherwise I = 1.I The likelihood function for the model is then given by:

l(�,↵) =

NY

i=1

1

�

�

✓yi � xi↵

�

◆�Ii

| {z }Uncensored

1� �

✓c� xi↵

�

◆�1�Ii

| {z }Censored

Using the log-likelihood, the parameters � and ↵ are estimatedusing

[�̂,

ˆ↵] = argmin

�,↵{�L(�,↵)}. (3)


Estimation of Synthetic Censored Data

10

010

110

210

3

40

60

80

100

120

µ̂(d) + 2�

µ̂(d) - 2�

Distance [m]

Pat

hlos

s[d

B]

CensoredUncensoredML: µ̂(d)OLS: µ̂(d)

n̂ �̂

True 2 4ML 2.0 4.0

OLS 1.7 3.5

OLS is biased and inconsistent. It underestimates n and �.IEEE VTS Workshop, Halmstad, 2015-11-11 11/17

Estimation of Measured V2V Data that is Censored

10

110

210

3

60

80

100

120

µ̂(d) + 2�

µ̂(d) - 2�

Distance [m]

Pat

hlos

s[d

B]

UncensoredML: µ̂(d)OLS: µ̂(d)c

n̂ �̂

ML 2.2 7.6OLS 1.3 4.4

Measured V2V data for NLOS Highway scenarios at 5.6 GHz [2].


ML Framework for other Pathloss Models

I The presented ML method was developed based on thelog-distance power law model.

I It assumes that the LS fading is Gaussian, with zero mean anda variance that is independent of distance.

I However, the proposed ML framework can easily be extendedto include other pathloss models.

I The ML method is unbiased and consistent, given that theunderlying model is correct.

I In many V2V scenarios, such as highway and rural, thepathloss exhibits a clear two-ray behavior.

I For these cases, a proper two-ray pathloss model needs to beused instead.

I Currently, we are working on an estimator based on such amodel.


Estimated Two-ray Models based on V2V Measurements

10

110

210

3

60

70

80

90

100

110

Distance [m]

Pat

hlos

s[d

B]

XC70 to S60

MeasuredAverageML


Conclusions and Future Work

I We have shown, that if the effects of the noise floor are nottaken into account, the pathloss estimates will be biased.

I This can be solved by applying a ML estimator that takescensored samples into account.

I The approach can be extended to include other effects andalso works for different types of pathloss models.

I We will finalize the two-ray estimator.I Based on the results, Mikaels results for the convoy

measurements will be updated.


References

[1] C. Gustafson, T. Abbas, D. Bolin and F. Tufvesson, "StatisticalModeling and Estimation of Censored Pathloss Data" IEEE Wireless

Comm. Letters, 2015.[2] T. Abbas, K. Sjöberg, J. Karedal, and F. Tufvesson, "Ameasurement based shadow fading model for vehicle-to-vehiclenetwork simulations," International Journal of Antennas and

Propagation, 2015.[3] M. Nilsson, D. Vlastaras, T. Abbas, B. Bergqvist and F.Tufvesson, "On Multilink Shadowing Effects in Measured V2VChannels on Highway", EuCAP, 2015.[4] C. Gustafson, T. Abbas, D. Bolin, F. Tufvesson, "TobitMaximum-likelihood estimation of Censored Pathloss Data", LundUniversity, 2015.Code is available in [4], athttp://lup.lub.lu.se/luur/download?func=downloadFile&recordOId=7456326&fileOId=7456327


http://lup.lub.lu.se/luur/download?func=downloadFile&recordOId=7456326&fileOId=7456327

http://lup.lub.lu.se/luur/download?func=downloadFile&recordOId=7456326&fileOId=7456327

Thank You!

Questions?


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