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coherent detectors, the correlation operation and
template generation must be performed at very
high speed, which implies a tradeoff between
power consumption and template generation
accuracy. However, for low-power operation, a
simple template is desired (Ryckaert, Verhelst
et al. 2007). UWB coherent detectors that use
windowed sinusoids have been proposed in the
literature as an alternative solution for low-power
template generation in the analog domain, since
windowed sinusoids can approximate the optimal
templates and are easily generated in the analog
domain (Sangyoub 2002). However, this solu-
tion suffers from the sensitivity of the correlator
output SNR to timing errors. Receiver structures
with suboptimal sinusoidal templates are more
sensitive to timing errors as compared to optimal
receivers (Sangyoub 2002). Complex sinusoids
were proposed to compensate for the SNR deg-
radation in the presence of timing errors, but
this structure requires nearly double the power
required for the corresponding structure with
real sinusoids (Huang, Yin et al. 2004; Ryckaert,
Verhelst et al. 2007).
approach for accurate indoor positioning is the
TOA estimation of the first detected path. In such
systems, the detection of the first arriving path in
non-line-of-sight (NLOS) multipath environments
is challenging, where the first arriving path, if ex-
ists, is not the strongest path (Di-Benedetto and
and Giancola 2004; Di Renzo, Buehrer et al. 2007).
Error bounds are essential for providing a
performance limit of any estimator in terms of
the mean square error (MSE). The Cramer-Rao
lower bound (CRLB) defines the lower bound on
the ranging accuracy in terms of the signal band-
width (Dardari, Chong et al. 2006). The error of
the range estimation
ε
d
is defined as (Irahhauten,
Bellusci et al. 2006):
ˆ
ε
ˆ
=
−
d d
(1)
d
where |.|is the absolute value,
d
is the distance,
and
d
is the distance estimate. From the estimation
theory, the MSE
σ
2
of any unbiased estimate
τ
of
τ
is bounded by the CRLB as follows (Darda-
ri, Chong et al. 2006):
UWB TOA Estimators and
Theoretical Lower Bounds
{
}
≥
RLB
2
(
)
ˆ
σ
2
= E
τ
−
τ
C
(2)
ˆ
Ranging refers to the process of estimating the
distance of a target node from a reference node.
Common ranging techniques include received-
signal-strength-indicator (RSSI) and time-of ar-
rival (TOA) measurements. In particular, while
various approaches can be used for ranging, the
most promising approach for UWB signaling is
the time-based approach, whose accuracy can
be improved by increasing either the SNR at the
receiver or the effective signal bandwidth of the
transmitted signal. Since UWB signals have very
large bandwidths, this property allows for ex-
tremely accurate location estimates (Di-Benedetto
and and Giancola 2004; Arslan, Chen et al. 2006;
Di Renzo, Buehrer et al. 2007). The most accu-
rate and frequently used distance measurement
ˆ
=
− and E{.} denotes the statisti-
cal expectation (Dardari, Chong et al. 2006). The
CRLB of the ranging error estimate
σ
d
(cm) can
be calculated from the relation:
where,
ε
τ
τ
σ
=
c
σ
τ
(3)
ˆ
ˆ
d
where,
c
=3.10
8
m/sec is the speed of light (Chung
and and Ha 2003). When no-multipath is present,
the CRLB is calculated as (Dardari, Chong et al.
2006):
N
E
/ 2
=
1
C
RLB
=
0
(4)
2
2
β
2
β
SNR
p
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