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

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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