The Performance and Simulation of an OFDMA Pseudolite
Indoor Geolocation System
Ilir F. Progri, Member ION, William Ortiz, California State Polytechnic University, Pomona, CA; William R. Michalson,
Member ION, Worcester Polytechnic Institute, Worcester, MA, and Jinling Wang, University of New South Wales, Australia
BIOGRAPHY
ABSTRACT
Dr. Ilir F. Progri is currently an independent Consultant.
He was an Associate Professor with the Department of
Electrical and Computer Engineering at Cal Poly,
Pomona, California, where he taught undergraduate and
graduate courses and conducts research in the field of
navigation and wireless communications. Dr. Progri was
the
Program
Co-Chair
for
the
Wireless
Telecommunications Symposium 2006 and 2005
respectively. He was the faculty advisor of the ION-Cal
Poly Pomona student chapter of the ION-So Cal section
the 1st student ION chapter in LA area. He is a member
of ION, RIN, and AIG and a senior member of the IEEE,
Com Soc, and AESS. He received his Doctor of
Philosophy (Ph.D.) degree and Master’s of Science (MS)
degree in Electrical Engineering from Worcester
Polytechnic Institute (WPI), Worcester, Massachusetts in
May 2003 and in May 1997 respectively. He received his
Diploma of Engineer Degree in Electrical Engineering
from the Polytechnic University of Tirana (PUT), Albania
in July 1994.
Previously we have discussed the principle of operation,
the transmitter and receiver design of an Orthogonal
Frequency Division Multiplexing (OFDM) Frequency
Division Multiple Access (FDMA) (OFDMA) indoor
geolocation system. We have also presented the OFDMA
indoor geolocation system theoretical performance and
some preliminary simulation results.
William Ortiz is currently completing his MS degree at
Cal Poly Pomona.
Third, the receiver consists of four channels each one of
which is designated to each transmitter. On each receiving
channel the received signal is down-converted in the
baseband. Then the signal is demodulated and decoded.
As a result we can obtain an estimate of the distance
between the transmitter and the receiver. Four distance
estimates are used in Least Squares filter to provide an
estimate of the receiver location and time. It appears that
an OFDMA pseudolite indoor geolocaiton system may
provide sub-meter 3-D position error 99.9 % of the time
given that the pseudorange error is 10 cm or less.
Dr. William R. Michalson is a Professor in the ECE
Department at the Worcester Polytechnic Institute where
he performs research and teaches in the areas of
navigation, communications and computer system design.
He supervises the WPI Center for Advanced Integrated
Radio Navigation (CAIRN) and has been involved with
navigation projects for both civilian and military
applications with a special emphasis on navigation and
communication techniques in indoor, underground or
otherwise GPS-deprived situations.
Dr. Jinling Wang is a senior lecturer in the School of
Surveying & Spatial Information System at the University
of New South Wales. He is a member of the editorial
board for the international journal GPS SOLUTIONS, and
Chairman of the international study group on pseudolite
applications in positioning and navigation within the
International Association of Geodesy's Commission 4. He
was 2004 President of the International Association of
Chinese Professionals in Global Positioning Systems
(CPGPS), He holds a PhD in GPS/Geodesy from Curtin
University of Technology, Australia.
At the transmitter, the geolocation information consists of
the transmitter’s position and time. For each transmitter
this information is binary encoded data at a rate of 1 KHz.
The encoded geolocation signal is modulated on the
corresponding [2.0 2.3 2.6 2.9] GHz carrier signal via a
FDMA modulator to resist interference encountered in an
indoor environment. The OFDM signal is then used to
provide distance information. Four (4) transmitters are
simulated to enable a geolocation estimate on the
receiver.
Second, the channel consists of: (1) delay model and (2)
an additive white Gaussian noise.
Keywords: OFDMA, FDMA, OFDMA, pseudolite,
Rician, Rayleigh, Lognormal, indoor, geolocation
INTRODUCTION
Success of the Global Positioning System (GPS) has
made satellite navigation systems the most reliable means
for modern navigation. GPS, originally developed by the
US Department of Defense and managed by the US Air
Force, is currently the only fully functional satellite
navigation system in the world. Other systems, like the
Russian GLONASS – which currently has a limited
operation, the EU Galileo system and the Chinese Beidou,
are being developed as alternatives to GPS.
continuation of the work initially developed by Progri [1],
Cyganski, Orr, and Michalson [1-3], Progri, Michalson,
and Cyganski [4], Progri [5], and Michalson and Progri
[6]. Some initial simulation results are presented.
Orthogonal Frequency Division Multiplexing
Figure 1: Direct and Multipath and reflected GPS
signals—taken from [13].
Orthogonal frequency division occurs when the signal
seperation between two carrier frequencies is invariant to
the bit transmission rate [11]. The importance of
orthogonal frequency spacing (or separation) becomes
apparent when analyzing the performance of an FSK
system. For the purpose of demonstrating the effects of
orthogonal tone separation, a coherent detection matched
filter (or coherence detector) will be evaluated. The
correlation coefficient is given by [4]
(1)
ρ=
=
A2
∫
Tb
0
cos[2π ( f c − ∆f )] ⋅ cos[2π ( f c + ∆f )]dt
A 2Tb / 2
1 ⎡
Tb ⎣⎢
Tb
∫
0
cos 4πf c tdt +
Tb
∫
0
cos 4π∆ftdt ⎤
⎥⎦
Assuming f c >> ∆f , the first integral becomes negligible
and the correlation coefficient becomes
Figure 2: Raw GPS heading errors while driving a straight
street in a dense urban environment—taken from [13].
Still, amidst its success and global acceptance, satellite
navigation systems do not work well in heavily urbanized
metropolitan areas (e.g. New York City, San Francisco,
Sao Paolo, etc.) or inside canyons due to reflection
interferences or they do not work at all indoors. Figure 1,
obtained from the Trimble™ manual shows how
reflections affect GPS performance in a dense urban area.
The effects of reflections as such are evident in data
collected by Trimble™ when measuring a vehicle’s
heading error while driving on a straight street in a dense
urban environment, shown in Figure 2.
Satellite Navigation Systems are subject to even more
interference when working in indoor environments,
rendering these systems practically useless. Unlike an
outdoor geolocation system (i.e. GPS), an indoor
geolocation system would experience unique multi-path
fading and near-far effects; making its design and
development uniquely challenging.
Today, indoor
geolocation systems may be used in applications in fields
like RF planning and optimization, search and rescue, law
enforcement, military and exploration (i.e. inside
caverns). The principle of satellite navigation systems
can be adapted to indoor systems.
This paper describes the orthogonal frequency division
multiplexing (OFDM) / frequency division multiple
access (FDMA) indoor geolocation system and discusses
the proposed transmitter and receiver designs in
(2)
ρ=
sin 4π∆fTb
1 ⎡ Tb
cos 4π∆ftdt ⎤ =
∫
⎢
⎥
0
⎦
Tb ⎣
4π∆fTb
The goal is to have the smallest correlation coefficient ρ.
Using orthogonal tone spacing, that is ∆f = Rb / 2 ,
equation (2) reduces to ρ = 0 . This promises a unique
advantage of using orthogonal tones in digital
communications, which is the basis of this project.
OFDM Overview
Ultra Wide Band (UWB) systems employ narrow, pulsed
signals which eliminate multipath effects, thus making
UWB systems attractive for indoor applications [1-8].
Additionally, FDMA offers resistance to interference in
an indoor environment, making a combination of the two
attractive solutions for indoor applications.
The implementation of an OFDMA indoor geolocation
system offers two main advantages: (1) there is a large,
available spectrum - about 7.5 GHz, and (2) the FDMA
modulation scheme is well known to achieve the smallest
cross-channel interference [4].
OFDM signals can be used to measure the time of arrival
(TOA) among the pulses and determine the receiver’s
distance [4].
Correlated with location and time
information from the transmitters, the receiver location
can then be determined to within meter accuracy.
However, one of the main concerns of these systems is
synchronization.
PSEUDOLITE (OR TRANSMITTER)
sin( a − b)θ sin( a + b)θ
, evaluated over f
−
2( a − b )
2( a + b )
f +∆
(6)
Preliminary Analysis
The allocated spectrum profile of an OFDMA (or
spectralized UWB) indoor geolocation system is shown in
Figure 3 (left), the high-end UWB spectrum is divided
into 4 blocks of equal bandwidth, mapping each block to
a transmitter, thus the modulation scheme of the system is
on one hand FDMA. Each frequency block is composed
of N equally ∆-spaced tones (a tone is defined as a
narrowband signal whose bandwidth does not exceed 40
kHz [1]), thus the modulation scheme of the system is
OFDM on the other hand [4], making the system
OFDMA.
In this project, we employed sinusoidal signals with the
same initial phase to represent the tone signals. Thus,
their representation is given by
(3)
A sin(2π ( f + a∆f ) + θ ) ,
for (a = 0, 1, 2 ,3 …)
Two signals are considered orthogonal if their inner
product, denoted by x1 (t ), x 2 (t ) , is zero. The inner
product is defined by
(4)
∫
b
x1 (t ), x 2 (t ) = x1 (t ) x 2 * (t )dt
a
If x1 (t ) and x 2 (t ) are said to be sinusoidal as described
by (3), and considering only the real elements of x1 (t )
and x 2 (t ) for simplicity, the inner product x1 (t ), x 2 (t )
for the signals used in the system can be expressed as
(5)
b
x1 (t ), x 2 (t ) = ∫ sin aθ ⋅ sin bθ ⋅ dθ , for a = f and
a
b= f +∆ =a+∆
Evaluating the integral yields
OFDMA Signal Structure
and
Noting that a − b = − ∆ , the expression further simplifies
to
sin − ∆θ sin( 2a + ∆)θ
−
2( 2 a + ∆ )
− 2∆
sin − ∆θ sin 2aθ ⋅ cos ∆θ + cos 2aθ ⋅ sin ∆θ
=
−
4a + 2∆
− 2∆
(7)
Since a >> ∆ , we could say cos 2aθ ⋅ sin ∆θ is rather
small, and the expression could be further simplified to
sin − ∆θ sin 2aθ ⋅ cos ∆θ
−
− 2∆
4a + 2 ∆
4a sin − ∆θ + 2∆ sin − ∆θ + 2∆ sin 2aθ ⋅ cos ∆θ
=
− 8a∆ + 4∆2
(8)
It can be seen from the expression the numerator
minimizes and the denominator maximizes as a >> ∆ .
Thus, the whole expression minimizes (or approaches
zero) as a >> ∆ , meeting the inner product requirement
for orthogonality – this is true for any two consecutive
tones spaced by ∆f . This means that as long a >> ∆ ,
the spaced tones will retain their orthogonality. In this
project values of a = 100 MHz and ∆f = 1MHz were
used.
For the purpose of this project an OFDMA pseudolite
indoor geolocation system consists of four transmitters
and one receiver. The high-end UWB spectrum is divided
into four blocks of equal bandwidth of 10 MHz. Each
frequency block is mapped to each transmitter; composed
of ten equidistant and consecutive tones, thus the channel
(or transmission) bandwidth for each transmitter is at least
20 MHz.
OFDM Signal Block Diagram
FDMA Modulation
1 TX 2nd TX 3rd TX 4th TX
st
1
Out1
2
2.3
2.6
2.9
f (GHz)
OFDM Modulation
∆
f1
f2
f3
100 101 102
Sine Wave 0
fN f (MHz)
Sine Wave 5
Sine Wave 1
Sine Wave 6
Sine Wave 2
Sine Wave 7
Sine Wave 3
Sine Wave 8
Sine Wave 4
Sine Wave 9
109
Figure 3: OFDMA signal structure(left) and Simulink block diagram of an OFDM pseudolite (or transmitter) signal (right).
OFDMA Transmitter Block Diagram
Carrier
Wave1
B-FFT
1
Out1
Modulation1
Zero-Order
Hold Rx1
Demod Filtered
Tx 1
Tone Signals 1
1
B-FFT
B-FFT
Tones 1
Scope
OFDMA Receiver CH1 Block Diagram
Zero-Order
Hold Tx1
Spectrum
Scope Tx1
Zero-Order
Hold Tx1
Modulated
FDATool
In 1
2
Spectrum
Scope Tx1
Modulated
Demodulation1
Carrier
Wave1
Rx Gain1
Spectrum
Scope Rx1
Demod Filtered
1
Rx 1
Digital
Filter Design
Figure 4: Simulink block diagram of an OFDMA pseudolite (or transmitter) (left) and receiver (right).
The design of all of the transmitters is exactly the same
for this type of wireless system. What makes each
transmitter different is that the carrier frequency signal
utilized to modulate the signal is unique for transmitter.
The Simulink block diagram of an OFDM transmitter is
shown in Figure 4 (left).
Signal design
The transmitted signal is a superposition of ten tones
(sinusoids) spaced at 1 MHz interval. This kind of signal
structure is often referred to as OFDM owing to the exact
orthogonality of its components over a fundamental
period [4]. The tones are generated using the same clock,
thus they have the same initial phase. The tones are then
combined into an analog combiner, and the combined
OFDM signal is used to modulate the carrier frequency
before is transmitted. Figure 3 (left) shows the OFDMA
signal structure in the frequency domain.
the system is 109 MHz + 2.9 GHz = 3.009 GHz , by
Nyquist’s theorem, the minimum sampling frequency
required is 2 × 3.009GHz = 6.018GHz . For this project,
the sample frequency was set at 10 GHz (or 1 × 10 −10
sample time.)
RECEIVER
As depicted later by the simulation results, a minimum
number of four transmitters is required to achieve a submeter 3-D position error; therefore, the receiver should
include at least four channels; however, having more
channels is desirable but not required. The received
signal is demodulated via the respective carriers:
Channel 1 – [2.0] GHz; Channel 2 – [2.3] GHz;
Channel 3 – [2.6] GHz; Channel 4 – [2.9] GHz.
The spectrum for the tones was selected to be from 100110 MHz for the sake of simplicity. The tone frequencies
were allocated as follow:
After demodulation, each OFDM signal is extracted by a
simple infinite impulse response (IIR) digital filter and
gain. The OFDM signal is then ready for further
processing. Figure 4 (right) shows a Simulink block
diagram of a receiver channel model.
OFDM signal – [100, 101, 102, 103, 104, 105, 106, 107,
108, 109] MHz
SIMULATION
Since no filters were implemented in the transmitter, and
wanting to avoid interference by overlapping modulated
signals, the carrier frequencies were allocated to allow for
300 MHz separation as follow:
Transmitter 1 – [2.0] GHz; Transmitter 2 – [2.3] GHz;
Transmitter 3 – [2.6] GHz; Transmitter 4 – [2.9] GHz.
Figure 4 (left) shows the Simulink block diagram of an
OFDMA transmitter. Given that the highest frequency for
4 Transmitter 2-D scenario
The locations for the four transmitters were determined by
placing them equally spaced from each other in a circle
with radius 200 m as shown in Figure 5 consistent with
our previous theoretical scenarios discussed extensively in
[1, 4, 5]. (Part of the reason for selecting this radius was
because the simulation would not allow for detection of a
signal with delay smaller than 0.1 µs, which equates to 30
m or larger 1.333 µs which equates to than 400 m.)
2-D scenario of an OFDMA pseudolite indoor geolocation system
150
TR2
TR1
100
50
Starting point
y (m)
Direction of movement
0
True receiver location
Estimated receiver location
-50
-100
TR4
-150
-150
Good signal area that enables resolving
the distance with no ambiguity
4 transmitter OFDMA
pseudolite indoor geolocatio
system can acheive meter
accuracy 99.9 % of the time
-100
-50
0
50
TR3
100
150
x (m)
Figure 5: A 4 transmitter 2D scenario of an OFDMA pseudolite indoor geolocation system.
The true receiver trajectory consists of 8 segments. Each
segment contains 1000 points. Hence we have a total of
8000 points in the total simulation time. Assuming a 1 s
time delay between two consecutive points we obtain a
8000 s simulation time which is equal to 2 h 3 min and 20
s. This simulation time is reasonable for the majority of
firefighter, emergency, or rescue mission in a particular
area.
2.
Very good synchronization to less than 1 µs. This
might still be an issue for the current hardware and
the current approach used for synchronization;
however, we have to strive to improve
synchronization to less than 1 µs. Synchronization
this tight might be achievable for outdoor transmitters
that are using GPS as a time reference, but is
probably not achievable without GPS visibility.
So the firefighter (or rescue personnel) would start in the
center and then move to the left for 1000 s and then move
up for 1000 s and so forth as shown in the Figure 5 and
ultimately come back in the same position as he/she
started.
3.
Very stable clocks at least in short term. The total
simulation time is 8000 sec or less than 2 h and 14
min which is reasonable time to complete a
firefighter or emergency or rescue mission.
4.
Kalman filter or better navigation filter. The current
simulation uses a simple least squares filter. We are
assuming that we should be able to do 50 iterations
for every single point because standard GPS receivers
are able to provide raw pseudoranges once every 50th
of a second.
5.
We are not however discussing here the
computational issues in the DSP or FPGA or ASIC.
While we cannot mention every single detail about the
simulation it is important to mention the most important
ones as follows:
1.
Pseudorange error to about 1-m 1 sigma value (or 67
% of the time). We are not sure how possible would
that be with real hardware given that the multipath is
very severe in indoor environments. However, we
have to consider the fact that the largest possible
range would be less than 400 m. So under this
condition we should be able to achieve this
requirement.
Nevertheless, if all these conditions are met than a 4
transmitter OFDMA pseudolite indoor geolocation system
can achieve 2-D meter position error 99.9 % of the time.
8 Transmitter 2-D scenario
8 Transmitter 3-D scenario
The locations for the eight transmitters were determined
by placing them equally spaced from each other in a circle
with radius of 200 m as shown in Figure 6 consistent with
our previous theoretical scenarios discussed extensively in
[1, 4, 5]. (Part of the reason for selecting this radius was
because the simulation would not allow for detection of a
signal with delay smaller than 0.1 µs, which equates to 30
m or larger 1.333 µs which equates to than 400 m.)
The locations for the eight transmitters were determined
by placing them equally spaced from each other in a circle
with radius of 250 m as shown in Figure 7 consistent with
our previous theoretical scenarios discussed extensively in
[1, 4, 5]. The 3-D scenario consists of a multistory (11
floors) building with 5 m adjacent floor separation. This is
a typical scenario of a big shopping mall, airport, business
center etc. Without going through the fine details we have
depicted a trajectory of a person starting in the 1st floor
and going up to the 5th floor and then down to the 1st floor
and anywhere in between. As indicated in Figure 7 the
person (who has the receiver) is always within the good
signal area (which is the surface of a spherical sphere with
radius 144 m and hence the receiver is able to measure the
pseudorange without ambiguity to 10 cm or less.
An 8 transmitter 2-D OFDMA pseudolite indoor
geolocation system can achieve meter position error 99.9
% of the time provided that the pseudorange error is 1 m
or less. The only reason for using 8 instead of 4 is for
redundancy and to get some idea about the position error.
Now we see the rational why we chose the scenario for
analyzing the theoretical performance of the signal
structure of an MC-CDMA indoor geolocation system [1,
5] or OFDM/FDMA indoor geolocation system [4] with
the transmitters equally spaced in the circle and the
receiver in the center because if the system is able to
provide the desired performance in the center than it also
able to provide the same performance anywhere within
the good signal area.
An 8 transmitter 3-D OFDMA pseudolite indoor
geolocation system can achieve meter accuracy position
error 99.9 % of the time provided that the pseudorange
error is 10 cm or less and that all the remaining
requirements mentioned in the 4 transmitter 2-D scenario
subsection.
2-D scenario of an OFDMA pseudolite indoor geolocation system
250
True receiver location
Estimated receiver location
TR3
200
TR2
150
Direction of movement
TR4
100
Starting point
y (m)
50
TR1
0
-50
-100
-150
the distance with no ambiguity
TR8
TR6
-200
-250
-250
TR5
8 transmitter OFDMA
pseudolite indoor geolocatio
system can acheive submeter
accuracy 99.9 % of the time
Good signal area that enables resolving
TR7
-200
-150
-100
-50
0
50
100
x (m)
Figure 6: An 8 transmitter 2D scenario of an OFDMA pseudolite indoor geolocation system.
150
200
250
3-D scenario of an OFDMA pseudolite indoor geolocation system
TR3
TR2
11th floor
60
TR4
TR1
50
40
z (m)
True receiver location
Estimated receiver location
TR5
6th floor
30
TR8
TR6
TR7
20
10
8 transmitter 3-D OFDMA
0
pseudolite
indoor geolocatio
system can acheive submeter
-10
accuracy
99.9 % of the time
200
1st floor
Direction of movement
Good signal area that enables resolving
the distance with no ambiguity
Starting point
100
0
-100
y (m)
-200
-200
-150
-100
-50
0
50
100
150
200
x (m)
Figure 7: An 8 transmitter 3-D scenario of an OFDMA pseudolite indoor geolocation system.
Transmission Channel
The transmission channel consists of (1) a delay model,
and (2) additive white Gaussian noise.
The distance to each transmitter is determined by the
delay of the received signal. In reality, the delay is
determined by the delta between the TOA and the time
reference on the signal. For the purpose of this project,
we introduced a delay on the signal and measured it using
a “delay detection” model. The delays were predetermined based on the already-established distances to
each transmitter.
The respective delays for each
transmitter are:
⎛ 120m ⎞
−8
⎜
⎟ = 40 × 10 s = 0.4µs
8
⎝ 3 × 10 m / s ⎠
Transmitter 4:
⎛ 180m ⎞
−9
⎜
⎟ = 60 × 10 s = 0.6µs
8
⎝ 3 × 10 m / s ⎠
Transmitter 2:
The transmitters' signals are eventually combined and
transmitted over a lossy channel.
In reality, the
transmission channel must be modeled with (1) delay
model, (2) free-space path loss, (2) Rician, Rayleigh, and
Lognormal fading channels, (3) receiver thermal noise,
(4) phase frequency offset and (5) additive white
Gaussian noise. For the purpose of this simulation (in
part also due to the difficulties of matching complex and
real signal in the simulation), only delay and additive
white Gaussian noise models were used. A Signal-toNoise ratio (SNR) of 10 dB was applied to the AWGN
channel.
60m
⎛
⎞
−8
⎜
⎟ = 20 × 10 s = 0.2µs
8
⎝ 3 × 10 m / s ⎠
Figure 8 illustrated the complete Simulink block diagram
of a 4 transmitter OFDMA pseudolite indoor geolocation
system.
Transmitter 1:
30m
⎞
⎛
−8
⎟ = 10 × 10 s = 0.1µs
⎜
8
⎝ 3 × 10 m / s ⎠
Transmitter 3:
OFDMA Pseudolite Indoor Geolocation System Block Diagram
Tx 1
Tx 2
Scope
Transport
Delay 1
Rx 1
In1
In 1
Out1
Rx 2
Transmitter1
Receiver Ch 1
Delay Detection
Distance Estimation 1
36.33
Distance to Tx1 (m)
B-FFT
Tx 2
Transmitter2
Transport
Delay 2
Zero-Order
Hold Tx
Spectrum
Scope Tx
In 2
Rx 2
Receiver Ch 2
In1
Out1
Delay Detection
Distance Estimation 2
66.33
Distance to Tx2 (m)
AWGN
AWGN
Channel
Tx 3
Transmitter3
Transport
Delay 3
In 3
Rx 3
Receiver Ch 3
In1
Out1
Delay Detection
Distance Estimation 3
126.3
Distance to Tx3 (m)
B-FFT
Zero-Order
Hold CH
Spectrum
Scope CH
Tx 4
Transmitter4
Transport
Delay 4
In 4
Rx 4
Receiver Ch 4
Figure 8: Complete Simulink block diagram of a 4 pseudolite OFDMA indoor geolocation system.
In1
Out1
Delay Detection
Distance Estimation 4
186.5
Distance to Tx4 (m)
using a Binary Phase Shift Keying (BPSK) modulator.
The modulated BPSK data is combined with the OFDM
signal and decoded at the receiver. At the receiver, the
signal is again demodulated using BPSK. The output of
the BPSK demodulator is a binary stream, which must be
converted to parallel (by 8 bits). A buffer model was used
to buffer the binary stream by 8 bits, which are then
decoded onto integers to recover the data transmitted.
During the simulation it became increasingly difficult to
add the data signals to the OFDM, thus they were
simulated separately. Figure 9, Figure 10, and Figure 11
show the data transmission model, and its modules.
Data Transmission
Figure 9, Figure 10, and Figure 11 display the data
transmission which consists of the information being
transmitted such as transmitters’ location and time to
which is combined with the TOA measurements (or
pseudorange) enable the receiver to compute its 3-D
position and local time in any geolocation system. For
the purpose of this simulation, the transmitters’ location
and reference time is encoded before transmitting them
over the OFDM signal. A binary encoder was used to
convert the data onto binary. An 8-bit encoder was
selected to have a resolution of 0.25 in the data entry
(with the intention of having a 0.25 meters resolution in
distance to transmitters). However, if higher position
resolution is required then a 12-bit or 14-bit encoder
should be used instead.
Delay Detection
Once the OFDM signal is extracted, it is used to
determine the TOA between a (pseudolite) or transmitter
and the receiver also known as pseudorange. In order to
detect the delay, the signal must be compared to its
original. At the receiver, a replica of the original OFDM
signal is locally generated with no delay.
The binary data is then converted to serial using a unbuffer model, to create a binary stream with a 1 kHz
frequency. The binary stream can then be modulated
Data Transmission Block Diagram
8
9
Out1
In1
BPSK Tx
Out1
10
12.5
BPSK Rx
X, Y, Z, Time
B-FFT
Zero-Order
Hold
Spectrum
Scope
Figure 9: Data transmission model.
0
BPSK Data Transmission Block Diagram
0
1
0
32
0
36
0
40
0
50
0
Integers Encoded
0
Bits
[8; 9; 10; 12.5]
X, Y, Z, Time
Convert
010...
Uniform
Encoder
Data Type Conversion
Figure 10: BPSK data transmitter module.
Integer to Bit
Converter
Integer to Bit
Converter
BPSK
1
Out1
Unbuffer
BPSK
Modulator
Baseband
BPSK Data Reception Block Diagram
1
Bit to Integer
Converter
BPSK
In1
BPSK
Demodulator
Baseband
Bit to Integer
Converter
Buffer
int8
1
010...
Out1
Data Type Conversion1
Uniform
Decoder
Figure 11: BPSK data receiver module.
Delay Detection and Distance Estimation Block Diagram
Out1
Tone Signals 1
1
sRef Find
sDel Delay
In1
delay
Find Delay 1
u*(1e-10)
Fcn1
u*(3e8)
Fcn1b
1
Out1
1.117e-007
Time Delay 1
Figure 12: Delay detection and distance estimation model.
Comparing the extracted OFDM signal to its locally
generated signal at the receiver provides the delay in the
signal via a simple cross-correlation technique as depicted
in [1, 4]. For the purpose of this simulation, a “find
delay” module was used. Figure 12 shows a delay
detection and distance estimation model.
The detected delay (in samples) is then converted into
time, and eventually into distance with the following
function models:
Function 1a: (input * ×sample _ time ) = time _ delay
* (input = sample delay)
Function 1b: (input * * × light _ speed ) = dist.
** (input = time delay)
Results
As previously mentioned, the distance estimation and data
transmission models were simulated separately.
Due to the resource-demanding model (again, the sample
frequency was set at 10 GHz or 1 × 10 −10 sample time) the
simulation time for the distance estimation model was
limited to 10 µs ( 1 × 10 −5 s ); the results were obtained in
just 5.86 µs. Starting with the orthogonal tones, Figure 13
shows the output of the tones model for transmitter 1 in
time and frequency domain, where it can be seen the
tones’ amplitudes are compounded with a frequency of 1
MHz (or every 0.1× 10 −5 s .) In the FFT, although only
one frequency appears to be shown, there are actually ten
(10) frequencies corresponding to the ten orthogonal
tones.
The modulated OFMDA signal in the frequency domain
is shown in Figure 14 (left). As depicted in the figure the
entire OFDM signal is shifted by the amount of the carrier
frequency to the right and left.
The combined OFDMA signal from all four transmitters
(not taking into consideration multipath) is shown in
Figure 15 (left).
After applying a delay to each OFDMA signal, Figure 17
shows the OFDMA signal before and after delay and
before and after filtering. A similar plot can be generated
for the other OFDMA signals. However we used this plot
to analyze the additional errors caused by the receiver in
the delay detection and distance estimation.
Figure 13: OFDMA signal in time (left) and frequency (right) domain.
Figure 14: OFDMA signal from the 1st transmitter (left) and 1st receiver’s channel at 10 dB SNR (right) in the frequency
domain.
Figure 15: Combined noiseless OFDMA signal (left) and noisy OFDMA signal at 10 dB SNR (right) in the frequency
domain.
Figure 16: Combined noisy OFDMA signal (left) and 1st receiver’s channel (right) at −30 dB SNR in the frequency domain.
Figure 17: OFDMA signal from the 1st transmitter and 1st receiver channel: (from the top) the 1st subplot corresponds to the
OFDM signal; the 2nd OFDMA signal; the 3rd subplot corresponds to the noiseless delayed OFDMA signal; the 4th subplot
noisy delayed OFDMA signal; and the 5th subplot corresponds to the extracted OFDM signal at 10 dB SNR.
After transmission over the lossy channel, Figure 15
(right) shows the OFDMA signals at 10 dB SNR as
detected at the receiver after being transmitted over the
transmission cannel models. In the figure, it can be seen
how the noise floor is raised by the addition of noise in
the AWGN channel.
The OFDMA signal is then detected and demodulated at
each of the receiver’s channel. Figure 14 (right) shows
the FFT output of the 1st receiver channel at 10 dB SNR.
The combined noisy OFDMA signal at −30 dB SNR is
shown in Figure 16 (left) and the 1st receiver channel at 10
dB SNR is shown in Figure 16 (right).
Once demodulated, the OFDM signal is compared to its
original to detect its delay. Figure 8 shows the results of
the delay detection model for all channels.
shows the results of the data transmission model and the
successful data recovery.
CONCLUSIONS
We have proposed a 3-D OFDMA pseudolite based
indoor geolocation system as a possible candidate for
indoor geolocation. Such a system is suitable for areas
with radius up to 250 m and our direct approach is good
for SNR −30 dB or higher.
However, for such a system to have any real, practical 3D applications a certain number of requirements must be
met:
It can be seen the delay detection model introduces an
error.
For channel 1 the error is of
0.1987 × 10 −6 − 0.167 × 10 −6 = 0.0317 × 10 −6 s .
After
careful analysis, it is determined the delay estimation
error is due to imperfections in demodulating and filtering
the OFDMA signal at the receiver. Taking the output
from the transmitter directly into the delay detection
model showed the delay error was zero. The delay is then
used to estimate the transmitter’s distance. From the
Figure 8 it can be seen that the delay estimation errors at
10 dB SNR translated onto distance measurement errors
are as follow:
Ch 1: (36.33 − 30) = 6.33m ; Ch 2: (66.33 − 60) = 6.33m ;
Ch 3: (126.3 − 120) = 6.3m ; Ch:4: (186.5 − 180) = 6.5m .
As indicated from Figure 17 about 6.5 m error comes
from the filter delay there fore the actual error in the
distance measurement is less than or equal to 20 cm.
However, at −30 dB SNR the distance measurement
errors are as follows:
Ch 1: (36.27 − 30) = 6.27m ; Ch 2: (66.33 − 60) = 6.33m ;
Ch 3: (126.3 − 120) = 6.3m ; Ch:4: (186.7 − 180) = 6.7 m .
Hence the actual error in the distance measurement is less
than or equal to 23 cm. For SNR lower than −30 dB the
pseudorange measurement error seem to increase rapidly.
On the data transmission model, the model is started with
data entry. Entries for the transmitter’s location (x, y, z)
are entered, and time reference. In the simulation, the
following values were used: x = 8, y = 9, z = 10, time =
12.5.
The data is then encoded and converted into binary (8
bits.) The binary data are parallel 8 bits, which must be
converted into a serial stream by means of an unbuffer
model before modulating into BPSK. Figure 9 shows the
BPSK transmitter’s results.
After the process is reverted at the BPSK receiver, the
data is then recovered after transmission. Figure 10
1.
pseudorange error less than or equal to 10 cm
2.
very good synchronization to less than or equal
to 1 µs. Synchronization this tight might be
achievable for outdoor transmitters that are using
GPS as a time reference, but is probably not
achievable without GPS visibility.
3.
very stable pseudolite clocks in short term
4.
good navigation filer (Kalman based)
5.
high processing power in the DSP, FPGA or
ASIC.
The most important requirement to meet is the
pseudorange error to less than or equal to 10 cm for any
indoor environment. We believe that the state of the art
signal structure and hardware design and implementation
is not capable to provide pseudorange errors equal to 10
cm or less; however, that should be the direction of the
research.
We need to add more realism to our channel model in
Simulink such as (1) free-space path loss, (2) Rician,
Rayleigh, and Lognormal fading channels, (3) receiver
thermal noise, (4) phase frequency offsets.
We need to combine our data transmission with the
geolocation signals.
We need to add a better navigation filter and for low
SNRs and multipath we have to consider more
sophisticated filters such as maximum likelihood or
Bayesian filter with Mote Carlo Markov Chain
integration, which remain to be studied in the future.
Ultimately we need to add more realism to our system
based on a real hardware and software implementation of
the system.
REFERENCES
1.
Progri, I.F. “An assessment of indoor geolocation
systems,” Ph.D. dissertation, Worcester Polytechnic
Institute, Worcester, MA, May 2003.
2.
D. Cyganski, J.A. Orr, W.R. Michalson, “A multicarrier technique of precise geolocation for
indoor/multipath environments,” Proceedings of ION
GPS/GNSS, 2003, Portland, OR, Sept. 9-12, 2003.
3.
D. Cyganski, J.A. Orr, W.R. Michalson,
“Performance of a precision indoor positioning
system using a multi-carrier approach,” Proceedings
of ION NTM 2004, San Diego, CA, January 26-28,
2004.
4.
Progri, I.F., W.R. Michalson, and D. Cyganski, “An
OFDM/FDMA
indoor
geolocation
system,”
NAVIGATION J. Inst. Nav., vol. 51, nr. 2, pp. 133142, summer 2004.
5.
Progri, I.F. “A MC-CDMA indoor geolocation
system,” in Proc. PIMRC 2005, Berlin, Germany, pp.
2535-2542, 9-14 Sep. 2005.
6.
Michalson, W.R. and I.F. Progri, “Reconfigurable
geolocation system,” US Patent 7,079,025, July 18,
2006.
7.
Parikh, H., W. Michalson, and J. Duckworth,
“Performance evaluation of the RF receiver for
precision positioning system,” in Proc. ION GNSS
17th International Technical Meeting of Satellite
Division, pp. 1908-1917, Sep. 2004.
8.
J.W. Coyne, R.J. Duckworth, W.R. Michalson, H.K.
Parikh, “2-D radio navigation system using MCUWB,” personal communications, 2006.
9.
Sun, Y. “Bandwidth-efficient wireless OFDM,” IEEE
Journal S. Areas in Commun, vol. 19, nr. 11, pp.
2267-2278, Nov. 2001.
10. Gerakoulis, D., and P. Salmi, “An interference
suppressing
OFDM
system
for
wireless
communications,” ICC 2002, vol. 1, pp. 480-484,
2002.
11. Kaiser, S. “OFDM code-division multiplexing in
fading channels,” IEEE Trans. on Commun., vol. 50,
nr. 8, pp. 1266- 1273, Aug. 2002.
12. Lin, D.-B., P.-H. Chiang, and H.-J. Li, “Performance
analysis of two-branch transmit diversity block-coded
OFDM systems in time-varying multipath rayleighfading channels,” IEEE Trans. on Veh. Tech, vol. 54,
nr. 1, pp. 136-148, Jan. 2005.
13. GPS / Dead Reckoning Application Note Trimble
Placer GPS 455/DR, Trimble.