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Use of Super Resolution Algorithms for Indoor Positioning
Keeping Novel Designed WLAN Signal Structure
Tariq J.S. Khanzada,
∗University of Magdeburg,
Germany and
Mehran University of
Engineering and Technology,
Pakistan
Khanzada@ovgu.de
Ali R. Ali,
†University of Magdeburg,
Germany
ramadan@iesk.et.uni-
magdeburg.de
Sameh A. Napoleon,
‡Tanta University, Egypt.
s.napoleon@tu.edu.eg
Abbas S. Omar
§University of Magdeburg,
Germany.
a.omar@ieee.org
ABSTRACT
This paper presents the utilization of super resolution al-
gorithms for the indoor positioning applications in order to
estimate Time Difference of Arrival (TDOA) and distances
using Orthogonal Frequency Division Multiplexing (OFDM)
transceiver. Optimal reduction in Distance Measurement
Error (DME) is achieved. We have utilized OFDM/Single
Carrier-Decision Feedback Equalizer (OFDM/SC-DFE) sig-
nal structure presented in our previous works. The su-
per resolution algorithms Estimation of Signal Parameters
via Rotational Invariance Technique (ESPRIT), Root Mul-
tiple Signal Classification (Root-MUSIC) and Matrix Pencil
(MP) are compared for DME estimation. We have applied
Minimum Descriptive Length (MDL) criterion to these al-
gorithms, that provides optimized estimate of the length
∗Chair of Microwave & Communication Engineering, Fac-
ulty of Electrical Engineering & Information Technology
P.O. BOX 4120, D-39106, University of Magdeburg, Ger-
many and Department of Computer Systems and Software
Engineering, Mehran University of Engineering and Tech-
nology, Jamshoro, Pakistan.
†Chair of Microwave & Communication Engineering, Fac-
ulty of Electrical Engineering & Information Technology
P.O. BOX 4120, D-39106, University of Magdeburg, Ger-
many.
‡Department of Electronics and Electrical Communications
Faculty of Engineering, Tanta, Egypt
§Chair of Microwave & Communication Engineering, Fac-
ulty of Electrical Engineering & Information Technology
P.O. BOX 4120, D-39106, University of Magdeburg, Ger-
many
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IWDE 2010 Magdeburg, Germany
Copyright 2010 ACM 978-1-60558-992-3/10/06 ...$10.00.
of actual Channel Impulse Response (CIR) by eliminating
the noise component from the dispersive CIR. Our scheme
is based on two different antennas used to transmit the pre-
half-zero-carriers and post-half-zero-carriers OFDM symbols
respectively, mapped to multiple carriers using Wireless Lo-
cal Area Network (WLAN) system and received by the ob-
ject to be positioned.
Keywords
TDOA, OFDM, Matrix Pencil, WLAN, Super Resolution
Techniques.
1. INTRODUCTION
Time of Arrival (TOA) estimation is a typical issue in
multi-path wireless communication environments specially
in indoor positioning systems. In order to locate a particular
object in indoor positioning systems, accurate estimation of
TOA is required. Accurate estimation of the propagation
delay of the radio signal arriving from the Direct Line-of-
Sight (DLOS) propagation path is therefore necessary. The
DLOS cannot always be accurately detected [1] due to the
severe multi-path channel dispersion.
Multi-path highly faded channels disperse the actual Chan-
nel Impulse Response (CIR) by noise effects causing an in-
accurate estimate of the TOA. Super resolution algorithms
got noticeable attention in recent years for the time-domain
analysis [2] and the spectral estimation of multi-path time
dispersion parameters [3].
Algorithms like ESPRIT, Root-MUSIC and MP use the
eigenvalues (EV) of the decomposed noise and signal sub-
spaces. This opts to eliminate the effects of noise in the
received corrupted signal and to generate an accurate esti-
mate of the TOA for indoor portioning systems.
Recently a lot of research work has been carried out for
some of these algorithms. The performance of ESPRIT and
Root-MUSIC algorithms for TOA estimation has been stud-
ied through computer simulations based on measurements of
indoor radio propagation channels in [3] and [4]. The effects
of dielectric properties of the building materials on indoor
59
position estimates has been presented in [5]. Indoor posi-
tioning using multiple pseudolites signals, has been studied
in [6] to figure out an optimal geometric design for the indoor
positioning.
In this paper we have utilized OFDM/SC-DFE signal struc-
ture presented in our previous works [7] and [8] to exam-
ine the performance of earlier stated super resolution algo-
rithms. Furthermore we have applied Minimum Descriptive
Length (MDL) criteria that provides optimized estimate of
the length of actual CIR by eliminating the noise compo-
nent from the dispersive CIR. In sequel, we present a short
introduction to the algorithms used, along with the analy-
sis of the actual estimates obtained using these algorithms.
Our scheme is based on two different antennas used to trans-
mit the OFDM symbols mapped to multiple carriers using
WLAN system. Two multi-path faded signals, corrupted
by Additive White Gaussian Noise (AWGN) are received
through OFDM receiver and both signals are added. Super
resolution algorithms like ESPRIT, Root-MUSIC and MP
are used to estimate the TDOA and consequently the ac-
tual distance between the transmitter and the receiver ob-
ject. DME are compared for the conventional and super
resolution techniques. Analysis of DME estimation is pre-
sented for the effects of change of the bandwidth and for the
multiple number of carriers on that.
The rest of the paper is organized as following, section 2
introduces the block structure for OFDM symbols transmit-
ted and the system setup for the current analysis, section
3 describes the MP algorithm and MDL criterion used for
the estimation of time of arrival and the distance. Section 4
presents the simulation results and analysis discussion and
section 5 concludes the discussion.
2. SYSTEM DESCRIPTION
This section describes the system setup used for our anal-
ysis. Figure 1 shows the block diagram of the TDOA estima-
tion system. For simplicity we have skipped the details of
OFDM/SC-DFE transceiver, however detailed description
can be found in our previous works [7] and [8]. Two differ-
ent QAM modulated symbol blocks are generated. In the
first block, the first half of carriers from the total number
of Nare retained while the rest half carriers are replaced
by zero padded termed as pre-half-zero-carriers. In the sec-
ond block reverse way is adopted i.e. post-half-zero-carriers
as shown in Figure 1. Both blocks are separately transmit-
ted through two different antennas using OFDM/SC-DFE
transceiver. At the receiver both signal blocks are added.
The Channel Transfer Function (CTF) and the CIR are
calculated using known transmitted signals from both an-
tenna 1 and 2. Conventional algorithms like IFFT and
correlation, super resolution algorithms like ESPRIT, Root-
MUSIC and MP, are applied to estimate the TDOA of the
received signal. Section 3 describes these algorithms in some
more details. Super resolution algorithms use the EV de-
composition of the correlation matrix of CTF, for which the
number of active sources are to be estimated, which is done
through MDL criteria.
TDOA is calculated by considering the time delay of the
first arrived signal using all previously specified super reso-
lution algorithms separately. These TDOAs are then used
to estimate the distance between the transmitter and the
receiver and hence to estimate the DME in case of each
algorithm. The ultimate goal of the super resolution algo-
rithms is to minimize DME which is high enough for the
conventional algorithms.
The next section describes the mathematical model for
the MP algorithm. Due to the limited scope of this paper,
we skip the details of the conventional and other super res-
olution algorithms which can be found in [9] [10] and [11].
2x1 Antenna WLAN System for Distance
Estimation using Super Resolution Algorithms
OFDM / SCT
Transsciever
N
o of Carriers
Symbol 1
Symbol 2
Generated Carriers
Inserted Zeros
Tx 1
Tx 2
Multi
Path
Channel
AWGN
N
o of Carriers
Rx1 + Rx2
CIR
Estimation
Super
Resolution
Algorithm
For TDOA
Estimation
Figure 1: TDOA Estimation System Block Diagram
with Transmitted Signal structure
3. MATRIX PENCIL ALGORITHM
Matrix Pencil (MP) is an efficient kind of super resolution
algorithm. It uses a generalized pencil function which ob-
tains the exponents of a sum of complex exponentials. The
signal components can be distinguished exactly by mapping
the noise components to the null space. It is an accurate al-
gorithm for calculating time domain parameters of the net-
work analyzer. The parametric model for the discrete com-
plex frequency domain channel response can be written as
Hn=H(fn) = PL−1
l=0 hle−j2πfnτl, n = 0,1,...,N−1 where
Lis the number of multi-path components, Nis the num-
ber of measurement points and fnis the frequency. Time
domain sampled values can be written as Hn=PL−1
l=0 ˆ
hlzn
l
where ˆ
hl=hle−j2πfoτl,zl=e−j2π∆fτl, ∆fis the frequency
spacing between the adjacent channel samples and f0is the
starting measurement frequency.
To apply MP algorithm for the measured frequency re-
sponse, the following vector is constructed [12]
Di= [Hi, Hi+1,...,Hi+N−P−1]T(1)
where Nis the number of measurement points and Pis the
pencil parameter chosen between N/3 to 2N/3 to get good
performance. The value of Pshould be greater than that
of L, which is the number of paths. The next step is to
construct ˇ
Y1,ˇ
Y2and ˇ
Yusing the following equations
ˇ
Y1= [D0, D1,...,DP−1] (2)
ˇ
Y2= [D1, D2,...,DP] (3)
then the following MP is considered
ˇ
Y2−Λˇ
Y1= 0 (4)
where Λ is defined as Λ = diag(λ0, λ1,...,λN) and it con-
tains the EVs of the received vector.
ˇ
Y=V∆U~(5)
60
where
ˇ
Y= [D0, D1,...,DP] (6)
and Vand Uare the unitary matrices and ∆ is a diagonal
matrix containing EVs of ˇ
Y. The parameter Lis chosen
such that the singular values beyond Lare set to zero.
The time delays are estimated from Λlas following
ˇτl=ln(Λ)
−j2π∆f
(7)
The amplitudes of hlof the multi-path components can be
calculated by solving the system HX =ˆ
husing linear least
squares as
ˆ
h= ([X]~[X])−1[X]~H(8)
where
X= [X(τ0), X(τ1),...,X(τL−1)] (9)
X(τk) = [1, e−j2πfsτk,...,e−j2π(N−1)fsτk]T(10)
and
ˆ
h= [ ˆ
h0,ˆ
h1,..., ˆ
hL−1]T(11)
3.1 Minimum Descriptive Length (MDL) Cri-
terion
MDL is a criterion to calculate the minimum effective
length of the channel. There is no need to find the auto-
correlation matrix or its EVs in MDL, which significantly
reduces the computational complexity. MDL [13] is defined
as
MDL(k) = L(θ) + f(k, Np) (12)
where f(k, N p) and L(θ) are the penalty function and the
log-Likelihood function, given by (13) and (14), respectively.
f(k, N ) = 1
2k(2N−k) log(MB) (13)
L(θ) = −Nlog(det(RHH )) −tr(RHH )−1RH H (14)
In (14) tr represents the trace of the matrix.
The CIR length Lis taken to be the value of k∈0,1,...,N −1
for which MDL(k) is minimum. We have applied the con-
ventional algorithms and compared the super resolution al-
gorithms for estimating the distance directly from the CIR.
The number of effective paths is estimated from the EVs of
the correlation matrix according to a predefined threshold,
which is in fact related to the noise variance. For distance
estimation, we are interested in the first tap only. Regard-
ing the accuracy of the super resolution algorithms, we have
applied a known virtual channel (with some paths) to the
transmitted signal by simple delay shifting and summation.
The algorithms give very accurate distance estimation. An-
other issue is estimating the number of paths that may cause
variations in the estimation, as we have encountered for dif-
ferent situations. We have applied the MDL criteria, dis-
cussed in section 3.1, to resolve this problem.
4. SIMULATION RESULTS ANALYSIS AND
DISCUSSION
This section provides simulation results and their analysis.
Simple experiments for estimating DME, and analyzing the
effects of change of the bandwidth and as well as of the
number of carriers on DME are performed using the super
resolution algorithms.
A typical number of experiments are performed through
our system described in section 2. Figure 2 shows the mean,
median and standard deviation values of the distance esti-
mations for the conventional and the super resolution algo-
rithm. Having a reasonable number of experiments, it is
concluded for the further analysis that the optimal estima-
tion results are achieved by ESPRIT and MP algorithms. As
1 2 3 4 5
0
5
10
15
20
25
30
35
1−IFFT 2−Corr 3−ESPRIT 4−RootMUSIC 5−MatrixPencil
Distance Measured (m)
Comparision of Estimated and Original Distances
Original Distance
Medean
Mean
STD
Figure 2: Mean, Median and Standard Deviation of
the experiments
specified in section 2, the time resolution effects the DME.
The estimation can be improved by increasing the band-
width of the system, in other words, by decreasing the time
resolution. This can be analyzed by studying the results in
figure 3 obtained by our simulations. The figure is divided
in four different portions. The top portion shows the DME
comparisons of the super resolution algorithms for higher
(Ghz) bandwidth systems, the rest of the bottom three por-
tions show the similar results for the lower bandwidth sys-
tems subsequently. It can be clearly verified that the higher
bandwidth systems (Ghz) reduce the DME in centimeters
(cm) range from the tens of meters (m) of that for the lower
bandwidth systems (khz). Again it is worth to notify that
the MP algorithm got most accurate estimates than ESPRIT
and Root-MUSIC in all the time resolutions. Analysis re-
sults for the effects of increasing the number of carriers on
the OFDM/SC-DFE system is shown in Figure 4. It can be
notified that the MP algorithm estimates the DME in the
range of 0.8 m to 0.3 m for 32 to 64 carriers, while the other
two counterparts get more reduced DME. However when the
number of carriers are increased to the higher order, the re-
duction in DME is more achievable by the MP algorithm,
which approaches to zero when we increase the number of
carriers beyond 1024. All the above results are obtained at
the laboratory level in order to confirm the reliability of the
WLAN positioning system. The DME analysis helps im-
proving the quality of transmitted signal. The laboratory
level tests of the presented algorithm are performed as the
integrated task under the partial project 2 of Virtual &
Augmented Reality for Security and Reliability of
61
0.5 1 5 6
0
0.005
0.01
0.015
Ghz system
DME at different time resolution for the system
10 50 100
0
0.5
1
Mhz system
200 300 400
0
2.5
5
Mhz system
500 1000 1500 1800
0
10
20
Time Resolution (nSec)
Mhy/ khz system
ESPRIT
ROOTMUSIC
MATRIX PENCIL
2, 1 Mhz & 666 Mhz
5, 3.3 & 2.5 Mhz
100, 20 & 10 Mhz
2, 1 Ghz & 200 Mhz
DME (m)
Figure 3: DME comparisons for different bandwidth
of the systems
32 256 512 1024 2048
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1No of Carriers Vs DME
No of Carriers
DME (m)
ESPRIT
ROOT MUSIC
MATRIX PENCIL
32 64 128 256 512300 350 400 450 512
0
0.2
0.4
0.6
0.8 Scaled View
Figure 4: Effects of increasing number of carriers on
DME
Embedded Systems (ViERforES) 1project [14].
5. CONCLUSION
We have simulated the super resolution algorithms along
with the conventional ones for comparison. In order to es-
timate the distance and TDOA for the indoor positioning
applications we have used OFDM/SC-DFE transceiver. Op-
timal reduction in DME is achieved. Three super resolution
algorithms i.e. ESPRIT, Root-MUSIC and MP are com-
pared for DME estimations. MDL criteria is applied for
these algorithms to optimize the performance. An analysis
of the DME is presented for variable time resolutions vari-
able bandwidth and multiple number of carriers. DME re-
duction approaching to zero is achieved by the MP algorithm
1ViERforES is currently on going research project with the
collaboration of Fraunhofer Institut for Experimental Soft-
ware Engineering (IESE), Kaiserslautern, Fraunhofer Insti-
tut for Fabric and Automation (IFF) Magdeburg, Society
for the Promotion of Applied Research Munich, Otto-von-
Guericke-University, Magdeburg and Technical University
Kaiserslautern, Germany.
using our scheme. The conventional algorithms fails to esti-
mate the distance beyond 50 nsec and above this level DME
increases drastically, which is unacceptable for indoor posi-
tioning applications. However super resolution algorithms
also got increment in DME with increasing time resolutions,
but it is in the range of tens of meters, even in very high
time resolution systems.
The MP algorithm estimates the DME in range of 0.8
m to 0.3 m for 32 to 64 number of carriers, while the other
two counterparts get more reduced DME. However when the
number of carriers are increased to higher order the reduc-
tion in DME is more improved by MP, which approaches to
zero.
6. ACKNOWLEDGMENT
This research is funded by the German Ministry of Educa-
tion and Science (BMBF) within the ViERforES project (no.
01IM08003C). It is partially funded by the Mehran UET
Pakistan through Higher Education Commission (HEC) Pak-
istan.
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