Global Positioning System Reference
In-Depth Information
5.2 Second derivative correlator
A new technique to mitigate multipath by means of correlator reference waveform was
proposed in Weill (1997). This technique, referred to as Second Derivative correlator, generates
a signal correlation function which has a much narrower width than a standard correlation
function, and is therefore capable of mitigating multipath errors over a much wider range
of secondary path delays. The narrowing of the correlation function is accomplished by
using a specially designed code reference waveform (i.e. the negative of the second order
derivative of correlation function) instead of the ideal code waveform used in almost all
existing receivers. However, this new technique reduces the multipath errors at the expense of
a moderate decrease in the effective Signal-to-Noise Ratio (SNR) due to the effect of narrowing
the correlation function. A similar strategy, named as Slope Differential (SD), is based on the
second order derivative of the correlation function Lee et al. (2006). It is shown in Lee et al.
(2006) that this technique has better multipath performance than nEML and Strobe Correlator.
However, the performance measure was solely based on the theoretical MEE curves, thus its
potential benefit in more realistic multipath environment is still an open issue.
5.3 Peak tracking
Peak Tracking (PT) based techniques, namely PT based on 2
nd
order Differentiation (PT(Diff2))
and PT based on Teager Kaiser (PT(TK)), were proposed in Bhuiyan et al. (2008). Both the
techniques utilize the adaptive thresholds computed from the estimated noise variance of the
channel in order to decide on the correct code delay. The adaptive thresholds are computed
according to the equations given in Bhuiyan et al. (2008). After that, the advanced techniques
generate the competitive peaks which are above the computed adaptive thresholds. The
generation of competitive peaks for PT(Diff2) technique is shown in Fig. 6 in two path
Nakagami-m fading channel. For each of the competitive peak, a decision variable is formed
based on the peak power, the peak position and the delay difference of the peak from the
previous delay estimate. Finally, the PT techniques select the peak which has the maximum
weight as being the best LOS candidate. It was shown in Bhuiyan et al. (2008) that PT(Diff2)
has superior multipath mitigation performance over PT(TK) in two to five path Nakagami-
m
fading channel.
5.4 Teager Kaiser operator
The Teager Kaiser based delay estimation technique is based on the principle of extracting the
signal energy of various channel paths via a nonlinear TK operator Hamila (2002), Hamila
et al. (2003). The output
Ψ
TK
(
x
(
n
))
of TK operator applied to a discrete signal
x
(
n
)
, can be
defined as Hamila et al. (2003):
x
∗
(
(
(
)) =
(
−
)
−
)
Ψ
TK
x
n
x
n
1
n
1
(3)
1
2
[
x
∗
(
x
∗
(
−
x
(
n
−
2
)
n
)+
x
(
n
)
n
−
2
)]
If a non-coherent correlation function is used as an input to the nonlinear TK operator, it can
then signal the presence of a multipath component more clearly than looking directly at the
correlation function. At least three correlation values (in-prompt, early and very early) are
required to compute TK operation. But usually, TK based delay estimation utilizes a higher
number of correlators (for example, 193 correlators were used in the simulations reported in
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