Journal of Geographic Information System, 2010, 2, 45-48
doi:10.4236/jgis.2010.21009 Published Online January 2010 (
Copyright © 2010 SciRes JGIS
A Novel Statistical AOA Model Pertinent to Indoor
1Department of Electrical and Computer Engineering, Worcester Polytechnic Institute, Worcester, USA
Email: {,}
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
Copyright © 2010 SciRes JGIS
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-
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
(,)() ()
hte t
 
 
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
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
Figure 2. Illustration of MPC arrivals
Copyright © 2010 SciRes JGIS
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
The proposed model for the relative AOA can thus be
given as
() 0
 
The piecewise integration of (2) gives the CDF as
sin11/ 40
()sin13/4 0
 
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
 (4)
where θLOS is the LOS angle expressed as
atan2( ,)
OSyy xx
 (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
tan (/ )0,0
atan2(y,x) /20, 0
/20, 0
0, 0
yx x
yxx y
yxx y
undefinedx y
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-
Figure 3. PDF Plot for the proposed AOA model vs RT data
Figure 4. CDF Plot for the proposed AOA model vs RT data
Copyright © 2010 SciRes JGIS
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
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