INTRODUCTION
Recently, IRUWB signal has gained a lot of attentions in both communication
and radar system due to its huge bandwidth, especially indoor localization system,
which fully utilizing the advantages of IR signal: the signal contains different
frequency components, which increase the probability that at least some of them
can go through or around the obstacle; a large absolute bandwidth offers high
resolution radars with improved ranging accuracy (Gezici
et al., 2005). According to the FCC’s regulation, the band between
3.1 and 10.6 GHz can achieve a time resolution of 0.133 n sec, which corresponds
to a spatial resolution of 4 cm. There are already some widely used localization
systems such as the Angle of Arrival (AOA), the Signal Strength (SS) and Time
of Arrival (TOA). In complicated indoor radio channel, it is difficult to accurately
measure AOA or SS so that most of the independent indoor positioning systems
mainly use TOA based techniques. In LineofSight (LOS) scenarios, a simple
triangulation scheme has been approved sufficient for precise localization.
There are three main sources of ranging errors in complicated indoor environment
(Heidari et al., 2007). The first source error
is multipath error due to a combination of bandwidth limitation and presence
of rich multipath. The absence of Direct Path (DP) due to blockage is also a
dominant error source and the third source of error is associated with propagation
delay and difference of the speed of the radio waves in media. Consequently,
the ranging measurements between receiver and transmitter are often positively
biased (Jourdan et al., 2008). In practice, for
a large demand in commercial, public safety and military applications, the need
for accurate and reliable localization in completely NLOS situation increases,
the IR propagation properties in specific environments become a serious challenge
to indoor localization system. Partial and complete LOS blockage deteriorates
the ranging accuracy due to refraction, which makes the real propagation distance
larger than the straight line between two nodes. Furthermore, the IR signal
has severe frequency dispersion undergoes per path waveform distortion when
transmitted though the obstacle (Molisch, 2005), which
lead to the pulse peak position biased in correlation receiver in localization
system.
Up to now, several works has been done on IRUWB waveform distortion problems.
Richard et al. (2003) considered that the IR
signals undergo waveform distortion. In terms of pulse shape and duration time
as propagating in multipath environments. (Qiu and Tai,
1999) and (Chenming and Qiu, 2007) addressed the
wide band signal waveform distortion due to frequency dependence in CDMA channel
modeling and later they extend these theories to the UWB system, the IR signal
diffraction distortion is taken into account using physicsbased methods, which
can cause template mismatch and results in a NSR loss. A physical model was
developed to investigate the positiondependent distortion of UWB pulse in LOS,
reflection and diffraction environments, the results indicate that both the
shadowed pulse and the scattered pulse are distorted (Ma
et al., 2006). The UWB pulse distortion due to the blockage of human
body is investigated in (Renzo et al., 2007).
And the propagation of IR signal through deterministic multipath channel with
different antennas are analyzed in terms of biterrorrate in correlation based
receiver (Qiang and Zhang, 2008). In (Yuan
and Win, 2008) the pulseoverlap coefficient is used to quantify the effect
of pulse distortion on ranging accuracy. Muqaibel et
al. (2005) measured the electromagnetic properties of construction materials
in the UWB frequency range and address the potential problems of UWB though
wall applications. However, all the above works had only considered the pulse
distortion in reflection and diffraction, which also haven’t taken into
account the media frequency dependence properties. As the dielectric constant
and conductivity of material vary with frequency, it’s difficult to derive
the timedomain expression of IR waveform distortion using Laplace transform
in the whole UWB bandwidth. Furthermore, as one of the most desirable feature
of IRUWB, transmission mechanism is also different compared with the traditional
narrow band system. In particular, NLOS propagation is unavoidable in indoor
localization system, so the analysis of IRUWB signal propagation and pulse
waveform distortion are necessary for developing ranging algorithm with improved
accuracy in NLOS environments.
In this study, without regarding the antenna effects, the localization system performance from the point of view of IRUWB electromagnetic wave propagating through obstacles are discussed based on the TOA algorithm and the NLOS ranging errors are derived in specific configuration. Combined with modified transmission theory, the frequency dispersion of materials in UWB bandwidth is taken into account by uniformly divided the pulse frequency band into several subbands. The influences of IR waveform distortions on localization accuracy are compared in specific environments.
PROBLEMS IN NLOS LOCALIZATION SYSTEM
The TOA position techniques rely on measurements of travel time τ of signals
between the transmitter node and the receiver node.

Fig. 1: 
Positioning
via TOA approach 
The well known triangulation approach is depicted in Fig. 1
(The dark nodes are the reference nodes). The distance between the nodes can
be calculated as: d = τ.c, where c is the velocity of light and this distance
determines the radius of a circle with the center at the receiver. In 2D situation,
at least three reference nodes are needed to determine the location of a given
node. Another important factor in TOA estimation algorithm is the synchronization
between nodes, in this study, we only concerned on the electromagnetic propagation
mechanism of IR signal in localization system, so we set all nodes time synchronization
at first. For a singlepath additive white Gaussian noise channel, the best
achievable accuracy of a distance estimate d derived from TOA estimation satisfied
the following inequality (Gezici et al., 2005):
where, c is the speed of light, NSR is the signaltonoise ratio and β is the effective (or root mean square) signal bandwidth. Therefore, the accuracy of a TOA approach can be improved by increasing NSR or effective bandwidth.
The basic theories described above assume the wave propagation velocity is
constant and there is no frequency dispersion when the signal interacted with
materials over the whole propagation process. However, IRUWB signal have very
large bandwidth, which makes the propagation mechanisms different with the traditional
narrow band signals, the frequency dependence of IR signal must take into account.
Especially in NLOS environment, the characteristics of materials and IR waveform
distortion influence the localization performance undoubtedly. The obstacle
produce an additional delay due to the change of the geometrical way of the
wave front caused by the refraction on the obstacle surfaces or inhomogeneities;
and the pulse waveform distorted due to the different propagation speed in the
slab. As shown in Fig. 1, the NLOS distance estimation may
extend to the red dashed circle, which increases the uncertainty of the node
position to the shadow region.
Conventionally, TOA estimation is performed via correlator or matched filter receiver. The position of the first peak is used as the input time of arrival in the localization algorithm. In completely NLOS environment, two major factors degrade the accuracy of the first peak arrival time are:
•  The
geometrical difference caused by refraction 
• 
The
peak position biased due to IR waveform distortion 
Assumed the dielectric interface was plane and homogeneous, see from Fig. 2, considered only one IR path transmitted through obstacle with thickness d, incidence angle θ, (x, y) and (x_{i}, y_{i}) are the coordinate of transmitter and receiver and their distance between the wall are d_{1} and d_{2}, respectively. The transmitter was fixed and the receiver can move along the dashed line which is parallel to the interface of obstacle and free space. In the absence of bandwidth and pulse distortion, the geometrical error can be calculated as follow:
The straight path between the transceivers is:
The actual transmitted distance between the transceivers is:
where,
is the relative dielectric constant of material. So, the geometrical error is
defined as Geo error and can be calculated as:
When considering the frequency dispersion, the IR signal undergo pulse distortion in transmission lead to the position of first peak biased, the peak position error defined as Peakerror can be expressed as:
where, is
the first peak arrival time in the period of actual received pulse, τ is
the ideal peak arrival time in the absence of pulse distortion and c is the
speed of light.

Fig. 2:  Geometric
error transmitted in slab 
The total distance error in completely NLOS environment is
Apparently, this will result a TOA estimation error and the transmitter may
bias to as
shown in Fig. 2. Theoretically, using the incidence angle,
the location of transceiver and thickness of obstacle, the geometrical error
can be easily calculated, however, the ranging error due to pulse distortion
in transmission is determined by its actual waveforms and this is the main point
of present study.
PROPAGATION THEORIES AND METHODS
Properties of materials: Generally, the effective permittivity of a
material can be described as: ,
where
and are
the real and imaginary part of dielectric constant, σ is conductivity and
is
often defined as the loss tangent. When the electromagnetic wave propagated
in loss media, the propagation constant k is a complex and a function of frequency,
furthermore, ε is also vary with frequency, which determined by the media’s
inherent characteristics. As the propagation of IRUWB signals is governed by
the properties of materials in the propagation medium, several studies had been
done to investigate the characteristics of materials on UWB bandwidth (Muqaibel
et al., 2005; Cuinas and Sanchez, 2002; Lao
et al., 2003). The dielectric constant and loss tangent of common
materials in indoor environment over UWB frequency range are compared in Fig.
3. These materials can be approximately divided into three categories: (1)
glass: dielectric constant doesn’t change with frequency and loss tangent
near zero, can be considered as perfect dielectric, (2) dry wall, structure
wood, wooden door and plywood: their dielectric constant near 2.3 and only loss
tangent is frequency dependence, (3) partition and brick: both dielectric constant
and loss tangent change with frequency. Clearly, the electrical parameters vary
with frequency in a random way. So, the analysis of IR propagation is no longer
the same as the traditional narrow band system.

Fig. 3: 
Electrical
parameters of materials 
Propagation of IRUWB signal: Due to the complexity of material’s
properties with frequency, the frequency domain method was used to analysis
the propagation of IR signal. Suppose the plane wave incidence in the direction
of ,
the electric field in the media is
where, E_{i} (ω) is the Fourier transform of incidence IR signal
,
is the refraction coefficient at the interface, for a linear polarization wave
T = 1+R, R is the Fresnel reflection coefficient. At the interface of loss media,
the refractive angle θ satisfied the generalized refraction theory β_{o}
sin θ = β sin θ_{t} that is
As the waveform and transmission loss are very important to localization system,
when the thickness of the obstacle is not too large compared to IR pulse wavelength,
traditional Fresnel reflection coefficient need to be corrected in both amplitude
and phase. The actual propagation characteristics in obstacle can be approximated
by a multiray model (Qiu, 2004). The reflection coefficient
and propagation loss in (7) should be replaced by the modified transmission
coefficient as follow:
where, k_{0} and k are propagation constant in free space and obstacle respectively, l is the path length inside the slab show in Fig. 2, s is path length difference of two departing consecutive reflections and α is attenuation constant.
Considering the frequency dispersion, the transmission coefficient in the whole UWB bandwidth is the combination of each subband, this process can be expressed as:
where, T_{i}(ω) and w_{i} (ω) is the frequency transmission coefficient and the window function at theth subband, respectively and M is the total number of subbands.
PULSE DISTORTIONS IN TRANSMISSION
The second derivative of Gaussian pulse is used as IRUWB waveform in the simulation, the original pulse can be expressed as:
where, A is the pulse amplitude, T_{c} is the time shift and τ is the characteristic time of the pulse. Here these parameters are set as A = 1V, τ = 0.134 n sec and T_{c} = 0.
In completely NLOS indoor environment, the IR waveform distortions caused by
signal propagation in different obstacles are investigated here. The obstacles
are assumed to be isotropic and homogeneous. Classical electromagnetic theory
indicated that there is no waveform distortion and loss in perfect dielectric
medium, such as glass. The IR pulse waveform distortions transmitted through
several materials are shown in Fig. 4 with different incidence
angle and slab thickness. The IR waveforms through dry wall, structure wood
and wooden are distorted slightly and retain general shape characteristics of
the original Gaussian pulse. This can be explained by the fact that the electrical
parameters of those materials are almost constant in the whole UWB bandwidth.
Another phenomenon is the right trough of the pulse attenuated faster than the
peak and left trough of the pulse, according to transient electromagnetic theory,
the pulse’s higher frequencies arrive at later times, as we see the right
trough of the pulse in time domain is correspond to the higher frequencies.

Fig. 4: 
IR
transmitted waveforms through obstacles. (a) θ = 0, d = 0.1∼0.4
m and (b) d = 0.1 m θ = π/12∼5 π/12 
In contrast, the pulse waveforms were noticeable changed in amplitude and
phase when transmitted through partition, brick and plywood. The received waveform
can’t keep its original shape: the pulse waveform is no longer symmetric
and has much wider tail than the transmitted pulse. And the position of the
first peak is no longer in the central of the pulse duration time apparently
compared with the second derivative of Gaussian pulse.
Further compared these results, there are several +similar trends when IR penetrated
through obstacles: the waveform distortion is inherently determined by the bandwidth
of IR signal, the electrical properties of media which interact with the transmitted
pulse and the geometric configuration of obstacle. In indoor environment, the
change of incidence angle doesn’t distort the pulse waveform apparently;
however, the waveform distortions become obviously as the thickness of obstacle
increases, also with deeper propagation loss.
IMPACT OF PULSE DISTORTION ON NLOS ERROR
The pulse distortion through obstacles lead to the time of arrival of IR signal
biased to some degrees in the correlation receiver and finally result in a NLOS
error in TOA based ranging system. As shown in Fig. 2, suppose
the coordinate of transmitter is (0, 0) and d_{1}, d and d_{2}
are known, the geometric coordinate of receiver node is
and the linear distance between the transceiver can be calculated using Eq.
2. The transmitted distance estimated by the pulse peak position in correlation
receiver is calculated through frequency domain method mentioned in previous
parts.
The NLOS ranging errors due to the blockage of brick with different conditions
are compared in Fig. 5. Set the distance of d_{1}
and d_{2} equal to 1m, when θ increases from 0 to 5π/12, the
thickness of slab d is set as 10 cm and when the thickness of slab increases
from 5 to 40 cm, the IR signal is normal incidence. Notice that when the slab
thickness is fixed and the incidence angle is relative small, for θ<π/6,
the Geo_error and Peak_error are keep in the same degree, but it is clear that
the Geo_error is extremely larger than Peak_error, which is the main NLOS error
in this situation. As the IR signal is perpendicular incident on the interface
of obstacles, the Geo_error is identically equal to zero. The NLOS error is
totally decided by the Peak_error. From Eq. 5 in part II,
the propagation time in loss media with thickness d and no waveform distortion
is
is the actual IR peak arrival time. The value of Peak_error is negative means
IR peak is arrived in advance and in contrast positive value means the peak
is delayed in some degrees. In Fig. 5, it’s clearly that
the absolute value of Peak_error increases with slab thickness approximately
in a linear manner which is different compared with the incidence angle. Moreover,
the pulse width of IR signal used in this paper is about 6cm, but the peak biased
caused by waveform distortion almost reaches the pulse width in specific situation.
The Total_error is the sum of Peak_error and Geo_error in both conditions,
the Total_error becomes considerably larger with incidence angle and slab thickness
increase. So under completely NLOS environment, due to the variation of electrical
characteristics of materials, the IR waveforms were distorted undoubtedly. In
order to achieve higher localization accuracy, the incidence angle needs to
be as small as possible and the straight line between transmitter and receiver
should perpendicular to the interface of free space and obstacle to obtain better
penetration gain.

Fig. 5: 
NLOS
ranging errors 
Above all, it is obviously that the media characteristics, NLOS geometrical
configuration and IR signal propagation property are important factors which
affect the accuracy of indoor localization system. Although, 802.11.4a channel
model has already addressed the pulse distortion problem in a statistical manner,
its impact on system performance in complicated indoor environment is not very
clearly. Since different materials cause complicated waveform distortions, IR
pulse distortion described in statistical way need further corrected, especially
in specific environment.
CONCLUSION
In this study, we have investigated the IRUWB pulse distortions in several
specific indoor environments and its influences on the TOA based localization
accuracy through the aspect of electromagnetic theory. In completely NLOS environment,
due to the extremely large bandwidth, the IR signals undergo waveform distortion
with amplitude decreased and phase shifted when transmitted through obstacles.
In time based localization system, this distortion result in pulse peak position
biased and ranging estimation error in correlation receiver. For larger incidence
angle and obstacle thickness, the localization error is bigger, under the conditions
set in this paper, this ranging error most approximates to the pulse width.
In order to achieve high accuracy localization in completely NLOS situation,
the position of transceiver need to be adjusted to make the straight line of
the two nodes perpendicular to the surface of obstacle and further more a relative
small incidence angle is even better. However, the indoor environment is always
complicated and unpredictable, it’s necessary to investigate IR signal
propagation properties in specific environment with different structures and
search for NLOS error mitigate algorithm to improve the localization accuracy
is still an important task need to be done.
ACKNOWLEDGMENTS
This study was supported by the National Nature Science Foundation of China under Grant No. 60702034. The author would like to thank Mr. T.T. Zhang and Ms. T. Lu for their assistance in this study.