Selected Papers

Location Determination Method for Wireless
Systems Based on Learning Vector Quantization
Tomoaki Ogawa†, Shuichi Yoshino, and Masashi Shimizu
Abstract
In future ubiquitous services, object location determination will be a key technology. We describe alocation determination method based on signal intensity using signals sent from base stations located at
known positions to a terminal located at an unknown position. Instead of using numerical coordinates todefine the object’s location, it determines the object’s location using a name that describes its locality.
This method is based on learning vector quantization (LVQ) algorithms. We tested it using a 802.11
wireless LAN (local area network) and RFID (radio frequency identification) tag systems. The results
show that it provides more accurate location data than the conventional least-squares method in areas far
from the base stations.

1. Introduction
The spread of cellular phones and personal mobile
terminals is creating an environment of ubiquitous
wireless networks. In the future ubiquitous services,
location determination will be a key technology. In
the ubiquitous era, wireless devices will be attachedto every object and all objects will be connected to the
network. It will be possible to determine an object’s
location from data from these wireless devices.
Therefore, applications using location determination
systems have begun to attract a great deal of interest[1] and the importance of being able to correctly
determine the location of an object or person has
grown. In most cases, numerical coordinates are used
to represent the location of objects or persons. In thispaper, we suppose that an object or a person with awireless interface represents an object, and that fixedbase stations (BSs) can communicate with that
object. Since the location determination techniques
are to be used for various purposes and under various
conditions, both outdoors and indoors, each technique must be well-matched to the system in which it
is to be used. These techniques use multiple distancemeasurements between the object and BS (for exam† NTT Network Innovation Laboratories
Yokosuka-shi, 239-0847 Japan
E-mail: ogawa.tomoaki@lab.ntt.co.jp

Vol. 1 No. 9 Dec. 2003

ple, a global positioning system (GPS) satellite or the
BS of a cellular system). The most popular techniquefor outdoor location determination uses GPS and iscommonly employed in car navigation systems [2].
This technique is based on the time of arrival (TOA)of a signal from the GPS satellite and calculates the
distance between the user terminal and the satellite tofind the coordinates of the user station. A networkassisted GPS technique has been proposed by SnapTrack, Inc. as a means of evaluating the accuracy ofGPS-based detection [3]. The user station of this system communicates with a stationary server on the
ground and revises the arrival time from the GPS. In
this manner, the user station can obtain more accurate
coordinates and the usage area can be expanded toinclude areas between tall buildings, or even indoors
if the user is next to a window. The Cricket Location
Support System is an indoor location system envisioned by MIT’s Project Oxygen [1]. This system
uses a combination of RF (radio frequency) and ultrasound technologies to provide a location-support service to users and applications using an RF signal
operating in the 418-MHz amplitude modulation
band. With each RF advertisement, the beacon transmits a concurrent ultrasonic pulse. Japanese PHS(1.9-GHz-band personal handy-phone system) carriers provide indoor location services to user stations
by using the received intensity of signals from BSs on
the premises [4]. Furthermore, techniques that have27Selected Papers

been tuned for high accuracy have been reported.
These include a positioning method that searches
within a limited area for a user station assumed to bemoving at walking speed [5] and one that calculates
the user position by using only high-confidence data
while ignoring low-confidence data from distant BSs[6]. TOA requires fast time resolution of less than ananosecond to calculate the distance with 1-m accuracy indoors. We focused on improving the accuracyof indoor location determination based on the intensity of a signal received by an object from a BS,
where the object cannot receive a GPS signal.
The conventional methods using signal intensity
calculate the numerical coordinates of the object
using an equation that predicts the distance based on
the intensity of the signal from the BS received by theobject. However, it is usually impossible to find theparameters of the equation for the correct propagation
environment because of the presence of objects thatshield or reflect radio waves.
In this paper, we propose a method that resolves
this problem by combining the following two
schemes. First, we propose a new paradigm for representing the location of an object. For this study, wemust first define the difference between ‘positioning’and ‘locating’. Our method is a ‘locating’ method andrepresents the location of the object by using thename or designation of the locality, and not by using
the coordinates of either the object or BS like conventional ‘positioning’ methods. Second, we developed a new locating method that uses a learning function in conjunction with data obtained in advance.
The conventional method that obtains data in advancewas presented in [9]. However, this method mustassign coordinate positions to all the obtained data.
Therefore, gathering data was troublesome. Our
method resolves this problem by combining the representation method using the location name with alocation determination method employing a fuzzylearning strategy. A field test showed that it can determine the location of the object more accurately thanconventional methods, such as the least-squares
method (LSM), which is a positioning algorithm.
2. Location representations
2.1 Location representation method based on
coordinates
We suppose that the object to be located is in abuilding and that the building has many BSs for wireless communications such as wireless LAN accesspoints, PHS BSs, or RFID (radio frequency identifi28

cation) tag receivers. We also assume that the object
can link to a BS.
In most location representation methods, numericalcoordinates are used to represent the location of theobject. The coordinates are usually two-dimensional(horizontal plane), but may sometimes be threedimensional (including height). In practice, the position of the object is calculated using a positioning
algorithm and visually represented on a digital map.
In response to requests from applications, the results
are matched against a database that stores the names
and coordinates of landmarks. When the object is auser’s terminal, this database information is then conveniently provided to the terminal, for example,“there is an entrance nearby”. Thus, it requires two
steps for the user to receive the information he or sheneeds: one process for calculating the coordinates
and another for matching the location to a name in the
database.
For services utilizing the location determination
capability, the location name (e.g., the building’s
room number) is more useful to the user than theexact numerical coordinates. Moreover, even if theexact coordinates are obtained, this information is
worthless if a mistake is made in converting them andyou end up with the wrong room number.
2.2 Proposed representation method using
locality nameWe propose a new method for representing an
object’s location, which uses the designation of thelocalized area (locality name). It treats the signal
intensities from the BSs to the object as inputs andtreats the locality name as the output. It applies thelearning algorithm described in Section 3.2 to training data gathered in advance by, for example, walking
around in the entire target area with a measuring terminal to obtain the signal intensities. The signal
intensities are allocated as input. At the same time,
the locality name is entered with a keyboard and allocated as output. Then the learning algorithm learns all
the obtained input/output pairs in the entire target
area directly. In the operation of the location determination system, the input data (signal intensities) are
obtained and the filter generated by learning calculates the locality name. This representation method
has two merits. One is that it does not need to convert
the coordinates into a locality name, so it takes only
one step to obtain the location. The other is that
nobody needs to know the coordinates of the BSs.
Namely the person who installs them does not need to
input accurate coordinates for them. This method is
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Selected Papers

suitable for navigation systems using small user terminals that have no screen and that provide only
audio navigation instructions, because it outputs only
location names.
3. Location determination algorithms
Here, we describe the conventional positioning
algorithm and the proposed algorithm, assuming thatthese algorithms are used in a system comprising
wireless BSs and user stations. We suppose that a BS
broadcasts a signal such as a beacon periodically anda user station can measure the intensities of signals
received from the BSs.
3.1 Conventional position determination
algorithm using LSM
LSM is often used for position determination using
the intensities of signals received from multiple wireless BSs. In this method, the distance from each BS to
the user station is estimated by assuming that theattenuation of signal intensity is inversely proportional to the distance. Assuming that the user station is ina typical office space and uses a 2.4-GHz wirelessinterface, the function used to calculate the received
intensity is expressed by Eq. (1) in logarithmic form
(see ITU-R Recommendation P-1238-1 [7]), where
the propagation constant is 3.0.
Lk = 40.9 + 30 · log(dk),(1)

where Lk is the propagation loss, dk is the propagation
distance, and 40.9 is the coefficient.
Position determination works on the principle oftriangulation. The position of the user station can becalculated using three or more distances on a twodimensional plane. First, dk is acquired using Eq. (1)and the known positions of the BSs (xk, yk). Then,
LSM is applied. This is a practical method for deriving the optimum parameters; the minimum value ofthe square error is found by changing the parameters.
In position determination, the position (X, Y) of theuser station is given by the minimum value of Eq. (2).
n

F( X , Y ) = ∑ ( ( X − x k )2 + (Y − yk )2 − dk )2

(2)

k =1

The LSM method and similar methods that determine
the user position by using distances calculated fromreceived intensities have two problems.
1. They require information concerning the propagation environment in the target areas, but thecorrect propagation environment is usually
impossible to ascertain from one parameter,
because there are usually objects that shield or
reflect radio waves in the area, especially indoors(Fig. 1).
2. The error in the distance estimated using Eq. (1)is large in areas far from the BSs, because thedistance attenuation expressed in logarithmic
form is small in such an area.
Base station

Base station

Obstacle

Intensity

Intensity

ObjectDistance
Ideal propagation(line of sight)

Distance
Obstacle in line of sight(poor propagation environment)

Fig. 1. Relationship between signal intensity and distance from base station in an office.

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3.2 Proposed location determination method
using a learning function
In this paper, for indoor location determination, we
propose a fuzzy strategy using a learning function asa solution to the above problems. First, the whole area
is divided into several small zones or localized areas(e.g., Room A and Room B), which are used to indicate the location of the user.
(1) Acquiring input and output data
The proposed method uses the following data sets
as training data.
a) Input: Intensities of signals received from BSs ata particular position.
b) Output: Designation of the localized area for aparticular set of input data.
The input/output pairs are obtained as training data
for the entire target area. The proposed method learns
these pairs and makes a rule for deciding the output
for new input data. The rule gives the designation of
the localized area as output data. Figure 2 shows anexample of obtaining data sets for learning in the four
localized areas (Rooms A–D), including three BSs.
The data for N measuring points are obtained, and aroom designation is assigned to each point’s data as
output.
(2) Learning process using LVQ algorithm
The proposed method uses the LVQ algorithm tolearn the above training data sets. LVQ is a supervised learning algorithm for neural networks and it isused commonly in the field of image analysis. In thisRoom Aalgorithm, a set of input elements is considered to bea vector. When S BSs and N measuring points areused, N input vectors are plotted in the feature space,
and the value of each vector element is used as an axisof S-dimensional feature space. Reference vectors areplotted in the feature space for quantizing all measuring points. Figure 3 shows an example of plotting the
input vectors and the reference vectors in a 3-dimensional feature space. Each reference vector represents
a room in the feature space, and the locations of thereference vectors are moved within the feature spaceaccording to the learning rule. This rule compares the
input vectors with reference vectors and moves thereference vectors to more suitable positions to represent the rooms. Figure 4 shows an example of the reference vector activity using this learning rule. It canbe proved that LVQ can establish optimal borders forlogically discriminating each localized area (rooms inthis case), where these lines are called Bayes discrimination [8]. The flow diagram in Fig. 5 describes
the LVQ learning process in the proposed method.
After the process of learning, the generated rule isused to determine the location. When the user station
receives new signals from BSs, the received signal
intensities are used to construct the input vector in thefeature space. This new input vector searches for thereference vector that minimizes the square norm
between the input vector and the reference vector.
Then, the output of the reference vector, which is the
locality name (e.g., room name), is linked to the new
BS1

A1
BS2
A2

Room CAN
AN-1

Room B
Room D
BS3

A1
A2......

Input: intensity from BS
BS1
BS2
BS3
50
84
10
46
92
14
......
......
......

AN-1
AN

85
88

Measuring
point

40
38

54
48

Output:room designation
Room A
Room A......
Room CRoom C

Fig. 2. Example of obtaining data sets for learning.

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BS3 intensity

Room A

Room B

Wn1

Room DBS2 intensity

BS

1 in

ten

Input
Vector: V

Reference
Vector: W

Room A .....

sity

Room B .....

Wn2

Room C .....

Room CRoom D .....

BS3 intensity

Fig. 3. Example of plotting input vectors and reference vectors in 3-dimensional feature space.

Vm1
Wn1(i+1)

Wn1(i)

Input
Vector: V

Reference
Vector: W

Room A .....
BS2 intensity

y

nsit

Vm2

te
1 in

BS

Room B .....
Room C .....
Room D .....

Wn2(i)
Wn2(i+1)

Fig. 4. Example of reference vector activity using the proposed learning rule.

set of received intensities.
In the conventional non-linear optimizing method,
it is necessary to measure numerical coordinates of
positions throughout the entire area using a pulse
counter or optical camera in advance. In contrast, inthe proposed method, the BS coordinates do not need
to be recorded (Fig. 6). Furthermore, information
about the propagation environment is automaticallyprojected in the information of the reference vectors.
Vol. 1 No. 9 Dec. 2003

This algorithm can also be used for other architectures. For example, in an active RFID tag system, theuser (or object) has a tag that broadcasts its ID code,and receivers that can measure the intensity from thetag are established as base points. The server collects
the data and calculates the location of the tag. Experimental results using active RFID tags are given in
[10].

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All input vectors are plotted in S-dimensional feature space.
N: Number of input vectors.
Vn: The n-th input vector.
S: Dimension of feature space = number of base stations.
Fig. 3 is example of 3-dimensional space in Fig. 1.
Define the number of reference vectors
M: Number of reference vectors.
N >> M > number of rooms.
Wm: The m-th reference vector.
Define the initial input/output of the reference vectors,
and plot them in the feature space
Input/output of reference vector is defined randomly.
Inputs are intensity values from base stations,and the output is the room designation.
Figure 3 is an example of plotting reference vectors.
Define the iteration steps of the algorithm
I: Defined iteration steps.
i: The i-th iteration step.
Iterate following the flow from 0 to I

Iterate following the flow from 1 to N

Search for reference vector Wm that minimizes the square norm
between Wm to Vn in the feature space.

Is output of Wm equal to output of Vn ?
No
Yes

Wm(i+1) = Wm(i) - a1(Wn(i) - Vm)

Wm(i+1) = Wm(i) + a2(Wn(i) - Vm)

Moving close to Vm

Moving away from Vm

a1, a2: Coefficients for convergence. Decrease according to number of iterations.

Determine new Wm(i+1).
In Fig. 4, Vm1 finds Wn1. The output of Wn1 is the same as that of Vm1, so Wn1 is
moved to Vm1. In contrast, the output of Wn2 found by Vm2 is not the same as theoutput of Vm2. Therefore, Wn2 moves away from Vm2.

End of learning process

Fig. 5. Flow of learning process by LVQ.

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X = 20, y = 7
Input

MeasureArea A

Area A
MeasureMeasureMeasureX = 10, y = 5
Input

MeasureMeasureX = 15, y = 10
Input

MeasureArea B

Area B
MeasureMeasureMeasureMeasureMeasureMeasureConventional method

Proposed methodMust input data from all measuring points.

In one area, only need to input the area name once.

Fig. 6. Difference between conventional and proposed methods of gathering data.

4. Experiment
4.1 Obtaining input (signal
intensity) and output(location name) data
We obtained experimental data inan actual office, and compared thelocations calculated using the proposed method against thoseobtained using the conventional
LSM method. Table 1 shows theconditions for obtaining the data,
and Fig. 7 shows the layout of theoffice.
A frequency hopping wireless
LAN conforming to IEEE 802.11
was used as the wireless interface.
Signals with the station ID werebroadcast from each BS, and thereceived signal intensities wereobtained at all measuring points. A
time period averaged over 0.5 to 20
s was used for the intensities. The
room was divided into five zones(areas A to E in Fig. 7). We obtained1000 data sets per measuring pointfrom 300 measurement points. The
data were obtained over several days
because there were fluctuations inthe signal intensity.

Table 1. Experimental conditions.
Room conditions

25.2 × 13.5 m

Number of base stations

5

Signal from base station

Broadcast signal including ID of base station

Signal interval

200 ms (average)

Wireless interface

IEEE 802.11 frequency hopping wireless LAN

Number of localized areas

5

Number of measuring points

300

Measuring point interval

1m

Averaging time for measuring data

0.5 s to 20 s

Test data

1000 per measuring point
25.2 mBS1

Partition board

13.5 m

4.2 Learning process specifications
Table 2 gives the specifications of the learning
process of the proposed method. The training data forVol. 1 No. 9 Dec. 2003

BS3

A

BS2
B

D

E

C
BS4

BS5

: Base station

Fig. 7. Layout of office used in the experiment.

learning contained not only the intensities, but also
the actual localized areas. We obtained 10 training
data sets at 300 measuring points for a total of 3000
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Table 2. Specifications of proposed learning process.

Reference vectors
Iteration steps

1

3000

0.9

40

0.8

100,000

0.7

points. The number of reference vectors was 40, andthe reference vectors scattered in the feature space
filled in 3000 input vectors of the training data. The
learning involved 100,000 iteration steps.

Success rate

Training data sets

0.6
0.5
0.4
0.3
Proposed method
Conventional (LSM)

0.2
0.1

4.3 Conditions for the conventional method
The conditions of the LSM method were as follows.
The propagation constant of Eq. (1) was 1.5. Thiscoefficient was defined using the received intensity
measured in advance in the experimental room. We
searched for F(X, Y) in Eq. (2) at intervals of 0.5 m
throughout the experimental room. For comparison
with the proposed method, the coordinate positions of
the LSM results were changed to the designations of
the localized areas.
5. Experimental results

0
0

5

10

15

20

Averaging time (s)Fig. 8. Success rate versus averaging time of received
intensity.

the conventional method was only approximately
60%.
The distributions of the success rate for the experimental room are shown for the conventional and proposed methods in Figs. 9 and 10, respectively. The
areas where the success rate was lower than 70% areshown in red. In Areas A, B, C, and E, the successrates of both methods were almost equal. On the other
hand, in Area D, there was a large difference between
them. In the whole of Area D, the success rate of the

We compared the results for the proposed methodwith those for the conventional method using the success rate to determine whether or not the methods
could correctly indicate the correct localized area.
The answers provided by the
LSM method were convertedAfrom coordinates into localiBty names (areas A to E in
Fig. 7) and judged.
Figure 8 shows the success rate versus the averagDE
ing time of the receivedC
intensities for a wireless: Success rate 0% - 70%
LAN. For both methods, as: Success rate 70% - 100%time elapsed, the success rate
Fig. 9. Distribution of success rate using conventional method in experimental room.
increased until the averaging
time was longer than 5 s.
This indicates that it takes 5 sA
to obtain the correct answer
Bwith either method. The success rate of the proposed
method was higher than thatDE
for the conventional method
for all averaging times. The
C
upper limit of the success: Success rate 0% - 70%
rate for the proposed method: Success rate 70% - 100%
was approximately 70%,
Fig. 10. Distribution of success rate using proposed method in experimental room.
whereas the upper limit of34

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Success rate

proposed method was higher than 70%, whereas that
intensity with distance when using the RFID tags wasof the conventional method was lower than 70%. This
greater than that using the 802.11 wireless LAN, andis because, in areas that contain BSs, the dispersions
there was little signal reflection from RFID tags nearof the received intensity are small and the intensity
attenuation with distance is large, so the propagation1
environment can be easily estimated. Thus, the con0.9
ventional method can easily detect a user station near
0.8
a BS. However, in areas that do not include a BS and
0.7
in ones that are far from a BS, such as Area D, Eq. (1)0.6
in the conventional method does not accurately
Proposed method
0.5model the actual propagation behavior, so the successConventional (LSM)
0.4rate is lower. Our method can usually detect the user
0.3
correctly in Area D, because it characterizes Area D
using the reference vectors as “an area without a BS”
0.2
in the feature space. Figure 11 shows the success rate
0.1
versus the averaging time of the received intensities
0
0
5
10
15
20
in Area D. We can see that the upper limits are 75%
for the proposed method and 25% for the conventionAveraging time (s)al method.
Fig. 11. Success rate versus averaging time of received
We obtained similar results using active RFID tags.
intensities in Area D.
Figures 12 and 13 show the
distribution of the successrate for the conventional
and proposed methods
using RFID tags. The
A
Bexperimental conditions
were as follows: a 12 × 9 m2
room was logically divided
into four zones, five tag: Dividing line
receivers were attached toCD
the ceiling, and the broad: Receiver
casting interval for tags was: Success rate 70% - 100%
2 s. The results show that: Success rate 0% - 70%
the success rate of the proposed method was approxiFig. 12. Distribution of success rate using conventional method with RFID tags.
mately 90% and that of theconventional method wasapproximately 40%. The
conventional method used a
propagation constant in
Areas C and D, but the conA
B
stant was not suitable for
Area A or B, so the successrate was low in these areas.
On the other hand, the suc: Dividing line
cess rate of the proposedCD
method was high for all: Receiverareas, because the reference: Success rate 70% - 100%
vectors expressed the char: Success rate 0% - 70%
acteristics of the propagation environment. The
Fig. 13. Distribution of success rate using proposed method with RFID tags.
attenuation of the signal
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the walls. Therefore, the success rate of the proposed
method using RFID tags was higher than that using
the 802.11 wireless LAN.
6. Conclusion
We described a location determination method
based on Learning Vector Quantization using the signal intensities from base stations. The method
employs a unique concept combining the following
two schemes: 1) a location representation method
using the locality name and 2) a learning function
based on Learning Vector Quantization algorithms.
An experiment conducted in an office showed thesuperior success rate of this method, 70% for a wireless LAN and 90% for wireless active tags, comparedwith 60% and 40%, respectively, for the conventional method. This new location determination method
located the target object more accurately than theconventional method throughout the office. It was
especially better in areas that had no base station.
This method is effective for indoor human navigation
or object detection systems. In the future, we plan to
improve the method of obtaining data and investigate
user-friendly location determination systems.
References[1]

J. Hightower and G. Borriello, “A Survey and Taxonomy of Location
Systems for Ubiquitous Computing,” Technical Report UW-CSE 0108-03, pp. 57-66, IEEE, Aug. 2001.
[2] E. D. Kaplan, “Understanding GPS Principles and Applications,”
ARETECH HOUSE, 1996.
[3] SnapTrack, Inc., “An Introduction to SnapTrack Server-Aided GPS
Technology,” http://www.snaptrack.com/, 1999.
[4] H. Koshima and J. Hoshen, “Personal Locator Services Emerge,”
IEEE Spectrum, 37(2), pp. 41-48, Feb. 2000.
[5] A. Shibuya, M. Nakatsugawa, and S. Kubota, “High Accuracy Detection Method on the Positioning Information System, P-POINTS,”
Proc. of the Coms. Soc. Conf., IEICE, Chiba, Japan, A-17-4, Sep.
1999 (in Japanese).
[6] A. Shibuya, D. Uchida, M. Nakatsugawa, E. Kudoh, and S. Kubota,“Far-marker Exclusion Algorithm for the Local Information and Positioning System,” Proc. of the Coms. Soc. Conf., IEICE, Nagoya,Japan, B-5-54, 2000 (in Japanese).
[7] Rec. ITU-R P.1238-1, “Propagation data and prediction methods forthe planning of indoor radio communication systems and radio local
area networks in the frequency range 900 MHz to 100 GHz,” 19971999.
[8] T. Kohonen, G. Barna, and R. Chrisley, “Statistical pattern recognition with neural networks: benchmarking studies,” Proc. ICNN,Tokyo, Japan, Vol. I, pp. 62-68, Aug. 1988.
[9] P. Bahl and V. N. Padmanabhan, “RADAR: An In-Building RFBased User Location and Tracking System,” Proceedings of IEEE
Infocom 2000, Tel-Aviv, Israel, Mar. 2000.
[10] T. Ogawa, S. Yoshino, and M. Shimizu, “Estimation of the Location
Detection Method Adopting Learning Algorithms,” Proc. of theComs. Soc. Conf., IEICE, Niigata, Japan, SB-4-7, Sep. 2003 (inJapanese).

36

Tomoaki Ogawa
Engineer, Wireless Systems Innovation Laboratory, NTT Network Innovation Laboratories.
He received the B.A. degree in environmental
information and Master degree in media andGovernance from Keio University, Kanagawa in
1996 and 1998, respectively. After working at
NTT Wireless Systems Laboratories from 1998
to 1999, he joined NTT Network Innovation
Laboratories where he has been working on wireless ad-hoc networking and local positioning
systems. He is a member of the Institute of Electronics, Information and Communication Engineers (IEICE).

Shuichi Yoshino
Senior Research Engineer, Wireless Systems
Innovation Laboratory, NTT Network Innovation Laboratories.
He received the B.E. and M.E. degrees inmechanical engineering from Kanazawa University, Ishikawa, in 1990 and 1992, respectively.
He joined NTT Laboratories in 1992 and worked
on satellite Internet system development. He iscurrently engaged in R&D on wireless networking technology for ubiquitous services.

Masashi Shimizu
Senior Research Engineer, Supervisor, Wireless Systems Innovation Laboratory, NTT Network Innovation Laboratories.
He received the B.E. and M.E. degrees inmechanical engineering from Keio University,
Yokohama, in 1986 and 1988, respectively. In
1988, he joined NTT Wireless Systems Laboratories, Yokosuka, Japan. Since then, he has been
engaged in research on the pointing control for
deployable space antennas and surface error
compensation through feed distributions control.
His recent interest focuses on active RFID and its
applications. He is a member of IEICE.

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