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Optimization of Adaptive Up-and-Down Method for Equivalent Time
Signal Conversion
K. Kruminsh and V. Plocinsh
Institute of Electronics and Computer Science, Dzerbenes Str. 14, Riga, Latvia
Keywords: Equivalent Time Conversion, UWB Radar, Adaptive Methods, Up-and-Down Method.
Abstract: This study relates to comparator type equivalent time signal conversion. The influence of parameters of
combined adaptive up-and-down method on accuracy of signal conversion is studied. Optimal values of
parameters are obtained, using which the minimal amount of the samples is ensured. As an input signal, a
model of UWB radar signal (sine monocycle) is used. Method is intended for application in UWB radar
receivers. The design guidelines for application of the method in UWB radar receivers are outlined.
1 INTRODUCTION
Two types of equivalent time converters are known,
namely, gate type converters (Kahrs, M., 2003) and
comparator type converters (Херманис, Э. Х.,
Карклиньш, В. Г., 1977), (Bergman, D. I., 2006.),
(Askerzade, I. N., 2006). This article refers to the
comparator type equivalent time converters. In such
converters, the measurement of the instantaneous
value of the signal is achieved through comparisons
with a known threshold. The threshold is changed
according to chosen procedure until the signal is
measured with sufficient precision. One of the most
efficient comparator type methods is the combined
adaptive up-and-down method, named as
α - k -up-
and-down method (Krumin’sh, K. and Plotsin’sh,
V., 2013). The aim of this study is to optimize the
parameters
, nn /
1
and v of this method. The
study uses an example of designing UWB radar
receiver.
The simplest of comparator type signal
conversion method is up-and-down method
(Krūmiņš, K. and Kārkliņš, V., 2005). According to
this method, the measurement of the signal proceeds
as follows. In a specified phase
i
t=t signal
i
U
1,
is
compared with the noisy threshold
e of comparator.
Therefore, we can assume that the signal
i
U
1,
is
masked with an additive noise
(variance
2
1
=DX and mean value 0=EX ):
X+U=u
i,i 11,
.
(1)
The threshold is adjusted according to expression:
ji,iji,+ji,
eUsigns+e=e
1,1
,
(2)
where
is the step of the method.
After a sufficiently large number
n of
comparisons, the last value of threshold is used as a
measurement result:
ni,i
e=u
2,
.
(3)
Afterwards the phase is shifted to the next point,
and the value of signal in that phase is measured.
The initial value of threshold in next phase point
remains the last threshold in previous phase point:
ni,,i
ee
11
.
(4)
According to the combined method the
measurement of instantaneous value of signal
proceeds as follows. Total number
n of
comparisons is divided in two parts
n=n+n
21
. In
the first part the threshold is changed according to
up-and-down procedure (2) with step
0
s=s . After
1
n comparisons the number
+
n
1
of threshold
exceedances is counted. Afterward the value of step
i
s=s is calculated according to expression
v+
n
n
ks=s
r
+
i
1
1
1
0
,
(5)
597
Kruminsh K. and Plocinsh V..
Optimization of Adaptive Up-and-Down Method for Equivalent Time Signal Conversion.
DOI: 10.5220/0005010205970603
In Proceedings of the 11th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2014), pages 597-603
ISBN: 978-989-758-039-0
Copyright
c
2014 SCITEPRESS (Science and Technology Publications, Lda.)