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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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personal or classroom use is granted without fee provided that copies are

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permission and/or a fee.

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. SIMULATIONRESULTSANALYSISAND

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.

7. REFERENCES

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