A Novel Statistical AOA Model Pertinent to Indoor Geolocation

doi:10.4236/jgis.2010.21009

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Journal of Geographic Information System, 2010, 2, 45-48

doi:10.4236/jgis.2010.21009 Published Online January 2010 (http://www.scirp.org/journal/jgis)

A Novel Statistical AOA Model Pertinent to Indoor

Geolocation

F. O. AKGUL, K. PAHLAVAN

1Department of Electrical and Computer Engineering, Worcester Polytechnic Institute, Worcester, USA

Email: {ferit@wpi.edu, kaveh@wpi.edu}

Abstract: A novel statistical angle-of-arrival (AOA) model for indoor geolocation applications is presented.

The modeling approach focuses on the arrivals of the multipath components with respect to the line-of-sight

(LOS) path which is an important component especially when indoor geolocation applications are considered.

The model is particularly important for indoor applications where AOA information could be utilized for

tracking indirect paths to aid in precise ranging in harsh and dense multipath environments where LOS path

might be blocked due to obstructions. The results have been obtained by a measurement calibrated

ray-tracing (RT) tool.

Keywords: angle-of-arrival, indoor geolocation, statistical modeling, ray-tracing

1. Introduction

AOA modeling for indoor channel can be considered as a

relatively recent area compared to time-of-arrival (TOA),

since earlier systems were mainly omnidirectional and

hence did not exploit the direction of multipath compo-

nent (MPC) arrival. With advances in antenna technol-

ogy and signal processing techniques, AOA has gained

importance for MIMO systems employing spatial diver-

sity and beam-steering techniques.

Some previous works in AOA modeling include the

Geometrically Based Statistical Channel Models (GBS-

CMs) [1] and measurement fitted statistical models [2].

However, most of these studies are aimed at telecommu-

nications applications. Spencer’s Laplacian model [2] is

particularly useful for MIMO telecommunications appli-

cations in which data rate and coverage are important

factors hence relative positions of the transmitter and

receiver is not of primary concern. When indoor geolo-

cation applications are considered, AOA information can

be used to increase ranging and hence positioning accu-

racy coupled with additional information such as TOA

[3]. AOA information becomes particularly useful in

tracking certain indirect MPCs when these MPCs can be

used to aid in precise TOA ranging when the LOS path

gets blocked due to obstructions [4, 5]. For these appli-

cations, relative positions of transmitter and receiver gain

importance, since path arrivals will be affected accord-

ingly. In this paper, we propose a novel AOA model for

the arrival of MPCs with respect to the interconnection

line, or equivalently LOS, between the transmitter and

receiver based on an extensive set of RT results. The

outline of the paper is as follows: Section 2 presents the

data collection and simulation platform. Section 3 gives

the overall indoor propagation channel and the proposed

model. Section 4 presents the comparison results of the

model and empirical data and finally section 5 concludes

the paper.

2. Data Collection and Simulation Platform

Since exact modeling of indoor channel requires tedious

solution of Maxwell’s wave equations for complex

structures it is not time-efficient and requires high utili-

zation of computational resources. As an alternative there

exist RT solutions which are based on ray shooting prin-

ciples. In terms of speed and conformance to real-world

measurement data, RT techniques are preferred for most

indoor propagation prediction studies [6-8]. Given a

transmitter location, rays are shot in every possible di-

rection (with a certain discretization) and they interact

with the objects through either reflection or transmission.

The rays that can reach the receiver through geometric

propagation are considered to be the components of the

channel impulse response (CIR) if they are within the

detection threshold. For the purposes of our study a

measurement calibrated RT tool has been utilized to col-

lect CIR data [7].

For our simulations, we collected approximately

14000 CIRs for each of the three different transmitter

locations for a total of about 42000 CIRs on the 3rd floor

of Atwater Kent (AK) building at Worcester Polytechnic

F. O. AKGUL ET AL.

Figure 1. Simulation Environment

Institute, Worcester, MA as shown in figure 1. AK build-

ing, being a typical office environment, is representative

of a diversified RF propagation medium and has been

particularly chosen for this study.

The scale of the floorplan is 7pixels/m. RT tool gives

all relevant information for each MPC such as absolute

AOA, TOA and path gain. The anechoic RF chamber and

the elevator shaft are the metallic obstructions on this

floor hence LOS path cannot be detected if the receiver

is shadowed by these structures. In about 45% of the

receiver locations LOS path was blocked due to these

obstructions and in the remaining 55% of receiver loca-

tions LOS path was available. Since the percentages are

similar, our modeling is not biased towards LOS or

NLOS conditions. It is thus a joint modeling effort moti-

vated by the general fact that LOS and NLOS conditions

will be present at the same time in typical indoor scenar-

ios.

3. Indoor Propagation and the Proposed

AOA Model

Indoor multipath propagation is dictated by various in-

teractions of the MPCs by the various types of objects

such as furniture, walls, doors and windows which have

varying degrees of effect on signal propagation. The two

main interactions are the reflection and transmission.

Diffraction and diffuse scattering can be ignored for in-

door environments [9]. Based on the material properties,

these objects will have different reflection and transmis-

sion coefficients. Metal and steel surfaces, for instance,

can be considered as specular reflectors but no or very

little transmission will take place. On the other hand,

materials such as wood or brick will both reflect and

transmit the incoming ray after a certain loss. Each re-

flection and transmission has a corresponding loss coef-

ficient and will decrease the path power accordingly. In

RT techniques, each ray is considered to be an infinite

bandwidth optical ray. This representation of MPCs is

also in line with the channel model that was first pro-

posed by Turin [10] and is well suited to describe RF

propagation in multipath-rich indoor environments. The

general multipath channel can be given as

(,)() ()

iii

hte t





 



 

 (1)

where N is the number of MPCs, and βi, τi, θi and φi

represent the path gain, TOA, AOA and phase, given by

φi = −2πτi / λ, of the ith path, respectively. In this paper

our focus will be on the AOA component or equivalently

θi.

Based on the collected database of CIRs, we observed

strong dependence of the MPC AOAs on the intercon-

nection line between the transmitter and the receiver. In

other words, the MPCs tend to arrive close to LOS path.

We should point out that actual LOS path might not be

available due to obstructions, however the arrival of

MPCs were still observed to be in the vicinity of trans-

mitter-receiver interconnection line. In order to describe

this behavior, we define the MPC AOA relative to the

AOA of the LOS path which is a deterministic value

given the locations of the transmitter and the receiver.

This is depicted in figure 2. Expression of MPC AOAs

MPC

θk

θi

TX θLOS

III IV

Universal

Reference

(X-axis)

Figure 2. Illustration of MPC arrivals

F. O. AKGUL ET AL.

relative to the LOS path takes into account the receiver

and transmitter locations with respect to each other and

hence allows for a more descriptive model. As a matter

of fact, the placement of transmitter and receivers are

generally done according to the building layout and the

uniform assumption of transmitter and/or receiver loca-

tions inside a building may not be always be a realistic

assumption. Hence dependence of the AOA on transmit-

ter/receiver placement should not be included in the

modeling approach; nonetheless, its effect should be ex-

plicitly given as a separate variable.

MPC AOAs can be uniquely identified in the range [-π,

π] with respect to the LOS path which is assumed to be

the reference axis for all MPC arrivals. Our observations

indicated strong angle components at -π, 0, and π finally

leading to a distribution model that is in the form of a

classic “bathtub” model similar to Doppler power spec-

tral density. We have found this model to show an accu-

rate representation of AOA distribution around the LOS

component.

The proposed model for the relative AOA can thus be

given as

1/2

() 0

1/2

otherwise















 



























(2)

The piecewise integration of (2) gives the CDF as

sin11/ 40

()sin13/4 0

otherwise

















 



















(3)

The distribution presented in (2) is the relative AOA.

The absolute AOA of a certain path with respect to a

certain universal reference is thus given by

()

abs LOSLOS





 (4)

where θLOS is the LOS angle expressed as

atan2( ,)

OSyy xx

TXRX TXRX



 (5)

with respect to a certain universal reference.

In (5), atan2 is the 4-quadrant inverse tangent and TXx,

TXy, RXx, RXy denote the x,y coordinates of the transmit-

ter and receiver respectively. 4-quadrant inverse tangent

takes on values from [-π, π] and is particularly useful for

identifying angles with respect to a certain reference axis

such as X-axis. Its formal definition is given by

tan (/ )0

tan (/ )0,0

atan2(y,x) /20, 0

/20, 0

0, 0

yx x

yxx y

undefinedx y





























(6)

4. Model Evaluation

The comparison of the proposed model and empirical

data can be seen in figures 3 and 4 which are the PDF

and CDF graphs for the relative AOAs of MPCs respec-

tively. We can see a very good match between the ex-

perimental data and the proposed model and the confor-

mance of data to our model shows the feasibility of this

multipath arrival modeling approach for indoor envi-

ronments.

Figure 3. PDF Plot for the proposed AOA model vs RT data

Figure 4. CDF Plot for the proposed AOA model vs RT data

F. O. AKGUL ET AL.

5. Conclusion

In this paper, we have proposed a novel statistical indoor

AOA model. The main difference of this model from

previous models is the relative modeling of multipath

arrivals with respect to the interconnection line between

the transmitter and the receiver. Hence a more descrip-

tive distribution of arrival angles is obtained given the

transmitter and receiver locations. This model is particu-

larly useful in situations where direct path is blocked due

to certain obstructions and multipath AOA information

can be utilized together with TOA for high precision

ranging.

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