System based Code Evaluation Criteria for CDM Applications in Sensor
and Data Transmission Systems
Peter Stapf
1
, Marek G¨otten
1,2
a
, Andreas Ahrens
1 b
and Steffen Lochmann
1 c
1
Bereich Elektrotechnik und Informatik, Hochschule Wismar,
University of Technology Business and Design, Philipp-M¨uller-Straße 14, 23966 Wismar, Germany
2
Escuela T´ecnica Superior de Ingener´ıa y Sistemas de Telecomunicaci´on, Universidad Polit´ecnica de Madrid,
Technical University of Madrid, Crtra de Valenica, km 7, Madrid, Spain
Keywords:
Code-division Multiplex, Fibre Bragg Gratings, Optical Sensors, Binary Sequences.
Abstract:
To increase the multiplexing capability of code-division multiplexing (CDM) applied in optical sensor net-
works, a system based code evaluation is required. This contribution analyses evaluation criteria for sequences
applied in CDM systems. A comparison of an optical sensor application and a single user data transmission
system is presented. While a detection signal-to-noise ratio and the bit error rate are used to evaluate data
transmission systems, the proposed optical sensor application uses a modified signal-to-multiuser-interference
ratio (mSMUI). The main difference exists in the handling of interference. In contrary to data transmission,
the mSMUI requires a separation of positive and negative interferences. Both applications are simulated for
different binary sequences. While the Legendre sequence with a length of 503 chips achieves the over all best
results for the optical sensor application, the single user data transmission simulation shows no significant
sequence influence.
1 INTRODUCTION
Optical sensors, such as fibre-Bragg gratings (FBGs),
gained increased recognition due to their preferable
attributes (Jelbuldina et al., 2018), (Presti et al.,
2019). They are light, small, are immune to an elec-
tromagnetic environment and can be used together
with already known multiplexing techniques (Rajan,
2015). These can include wavelength-division multi-
plexing (WDM), code-division multiplexing (CDM),
time-division multiplexing (TDM), frequency shifted
interferometry (FSI) and optical frequency domain
refractometry (OFDR) (G¨otten et al., 2020), (Wang
et al., 2012), (Ou et al., 2017), (Kaplan et al., 2019).
Especially CDM increases the amount of FBGs that
can be evaluated in one sensor system to multiple
thousand sensors within a single fibre (G¨otten et al.,
2020). This allows detailed health monitoring cover-
ing a whole smart structure with dense spatial resolu-
tion (Braghin et al., 2013), (Nawrot et al., 2017).
With the introduction of code-division multiple
access (CDMA) in a third generation communica-
a
https://orcid.org/0000-0001-5032-5776
b
https://orcid.org/0000-0002-7664-9450
c
https://orcid.org/0000-0002-0938-2186
tion system the common correlation receiver and the
RAKE receiver are very popular receiver designs
(Lim et al., 2006). The correlation receiver optimizes
the signal-to-noise ratio (SNR), if only white noise
superimposes the signals at the receiver input. The
Rake receiver is a special receiver for radio channels
with multipath propagation and in systems with direct
sequence spreading. It consists of several correlators
according to the number of propagation paths (Price
and Green, 1958).
This work focusses on the evaluation of quality
criteria with regard to their applicability in system op-
timization. In data transmission the detection SNR, as
the argument of the complement error function, has
proven to be a suitable criterion when optimizing data
transmission systems. The transferability to sensor-
based systems has not yet been investigated. Section
2 explains the concept of CDM in optical sensor sys-
tems. A comparison of system based code evaluation
criteria is shown in Section 3. In Section 4 a simula-
tion of a CDM interrogated optical sensor system is
introduced. A single user data transmission simula-
tion is proposed and analysed in Section 5. Both sim-
ulations examine selected binary sequences, includ-
ing Gold-, Legendre-, M- and random sequences. A
78
Stapf, P., Götten, M., Ahrens, A. and Lochmann, S.
System based Code Evaluation Criteria for CDM Applications in Sensor and Data Transmission Systems.
DOI: 10.5220/0010247900780085
In Proceedings of the 10th International Conference on Sensor Networks (SENSORNETS 2021), pages 78-85
ISBN: 978-989-758-489-3
Copyright
c
2021 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
conclusion is given in Section 6.
2 SENSOR SYSTEM CONCEPT
A serial fibre optical sensor network can be interro-
gated as depicted in Figure 1. A broadband light
source provides light for the FBGs to reflect. A mod-
ulator applies a sequence consisting of ’1s’ and ’0s’.
The ’1s’ and ’0s’ represent light turned on and off.
After the reflection at the FBGs, the light is split into
two paths, where each reflected sequence is again
modulated. The first (direct) path uses the same se-
quence, while the second (inverted) path modulates
the inverted sequence. The modulators are driven
with a specific time delay, which defines the interro-
gated FBG. A spectrometer collects the light after
the corresponding modulation step. The inverted path
spectrum is than subtracted from the direct path spec-
trum which corresponds to sequence inversed key-
ing (SIK). This results in a difference spectrum. The
corresponding peak wavelength of the chosen FBG
can be detected and evaluated. The set up can be fur-
ther expanded by using WDM. With the inclusion of
multiple different Bragg wavelengths, the number of
sensors can be increased even further (G¨otten et al.,
2020).
While CDM and WDM can be used in optical
sensor networks, they originate from data transmis-
sion applications, such as cellular and global position-
ing system (GPS) systems (Lim et al., 2006). WDM
is the optical equivalent to frequency-division mul-
tiplex (FDM) in data transmission systems. CDM
spreads a single transmitted symbol, applying a code
sequence. On the receiver side correlation is used to
regain the transmitted symbol out of a signal distorted
by multiaccess-interference (MAI). With this proce-
dure multiple data transmissions can take place over
a single channel (Price and Green, 1958).
Light Source
Modulator
λ
0
λ
0
Modulator Modulator
Spectrometer Spectrometer
Differential Spectrum
Code
∆t
INV
Figure 1: Setup of CDM Interrogation System (G¨otten
et al., 2020).
0
10
20
-30 -20 -10 0 10 20 30
Ψ
M
(τ)
τ
(a) M-Sequence
0
10
20
-30 -20 -10 0 10 20 30
Ψ
L
(τ)
τ
(b) Legendre Sequence
0
10
20
-30 -20 -10 0 10 20 30
Ψ
G
(τ)
τ
(c) Gold Sequence
0
10
20
-30 -20 -10 0 10 20 30
Ψ
R
(τ)
τ
(d) Random Sequence
Figure 2: Cyclical autocorrelation function (ACF) obtained
applying SIK of different sequence types with a length of
31 chips.
One of the important aspects for CDM is the se-
lected sequence. Since the cross-correlation func-
tion (CCF) between sequences, for example for a set
of Gold-sequences, is minimal, data can be received
asynchronously (Gold, 1967). For the optical sensor
application a single code is used to take advantage
of the different optical path lengths for different FBG
sensors. Together with an advantageous autocorrela-
tion function (ACF) of an applied sequence, this can
be used to read out a specific sensor. Due to the differ-
ent arrival times of the reflected sequences, the time
delay for the second set of modulators is crucial. The
reflected sequence of the interrogated FBG needs to
be synchronous to the modulators, which corresponds
to the ACF peak. Hence, all interfering sensors are at-
tenuated with the value of the side lobes.
Thus, the side lobes of the ACFs of each sensor
for the optical sensor application, as well as the side
lobes of the ACFsof each data transmission have to be
investigated, as they can influence the measurement.
System based Code Evaluation Criteria for CDM Applications in Sensor and Data Transmission Systems
79
Therefore, different sequences shown in Figure (fig-
ure 2) are evaluated.
Since binary Legendre and M-sequences provide
side lobes of -1 in their cyclical bipolar-bipolar ACF,
they are chosen for these particular CDM applica-
tions (Boehmer, 1967). By nature, incoherent light
can only be turned on and off. The unipolar ver-
sion of these sequences needs to be used. Apply-
ing SIK, their cyclical unipolar-bipolar ACF is cal-
culated, which leads to side lobes with the value zero,
as depicted in Figures 2a and 2b. Gold sequences find
usage in CDM systems because of their good cross
correlation behaviour within a set of Gold sequences.
Their cyclical unipolar-bipolar ACF is shown in Fig-
ure 2c. Additionally, random sequences with their in-
herent good orthogonality are investigated, as well.
They rely on a statistical process, that has best cor-
relation behaviour only to its identical sequence, as
seen in Figure 2d. Gold and random sequences do not
provide side lobes with all zero values.
3 CODE EVALUATION CRITERIA
As the concept of CDM originates in data transmis-
sion applications, the applicable evaluation criteria
can be considered. The first criterion, the detection
SNR ρ denotes the squared half worst case vertical
eye opening after the correlation U
A
divided by the
noise power P
N
applied to the channel
ρ =
U
2
A
P
N
=
(U
S
U
Int
)
2
P
N
, (1)
where U
Int
represents the sum of all interferences. For
an additive white gaussian noise (AWGN) channel,
U
A
is equal to the signal amplitude U
S
. Assuming
a time-dispersive channel, intersymbol-interference
(ISI) diminish the half vertical eye opening. Consid-
ering multiple users in a CDM system, MAI, which
is included in U
Int
, is subtracted, too. In Figure 3 the
relation between combined interferences U
Int
, ρ and
0 0.2 0.4 0.6 0.8 1
0
5
10
0
0.2
0.4
0.6
U
Int
/U
S
Detection SNR
Bit Error Rate
Figure 3: Relation between combined interferences U
Int
,
detection SNR ρ and bit error rate (BER) P
E
, assuming
P
N
= 0.1V
2
and U
S
= 1V.
bit error rate (BER) P
E
is displayed. An optimum
of ρ = 10 and P
E
= 7.8e
4
is depicted for no inter-
ferences. If U
Int
matches U
S
, ρ reaches zero, conse-
quently P
E
is at it’s maximum 0.5.
The bit error rate (BER) P
E
, which is the second
criterion, states the number of falsely transmitted bits,
that equal the symbols, the bit errors, divided by the
number of all transmitted bits. It is one of the basic
criteria to evaluate data transmission systems. For a
two level transmission system it can also be estimated
by applying the complementary error function (erfc)
to the previously defined detection SNR ρ
P
E
=
1
2
erfc
r
ρ
2
. (2)
Hence, the detection SNR and the BER are suitable
criteria for a CDM transmission system.
A corresponding criterion can be considered for
the sensor application, derived from ρ. It is based
on the spectral behaviour of a sensor system and de-
picted in Figure 4. Referring to the high amount of
FBGs in an optical sensor network mentioned in Sec-
tion 1, it is inevitable that multiple sensors operate at
the same wavelength, which are distributed in differ-
ent sections. CDM distinguishes between these sec-
tions. The interrogated sensor is referred to as sig-
nal, while the rest is considered as positive or nega-
tive multiuser-interference (MUI), depending on the
applied code. To evaluate the measurand, the wave-
length shift of a sensor is analysed. Consequently,
the peak wavelength of a sensor can shift according
to the applied strain or temperature. This applies to
each single sensor in each section k in the network, so
that the interfering sensors can be spectrally shifted,
too. Out of all combinations, the worst-case is consid-
ered for the criterion. When all positive interference
MUI
+
k
is spectrally shifted and all negative interfer-
ence MUI
k
overlaps with the signal from the interro-
gated sensor s
k
, the signal peak is diminished and in
competition with the positive interference. The ratio
between the remaining signal peak and the positive
λ λ
P
o
P
o
MUI
+
k
MUI
+
k
MUI
k
MUI
k
Signal
s
k
Signal
s
k
Figure 4: Graphic representation of mSMUI, where P
o
is
the spectral optical power density depending on the wave-
length λ.
SENSORNETS 2021 - 10th International Conference on Sensor Networks
80
interference is defined as a modified signal-to-MUI
ratio mSMUI
k
for section k. The spectral noise den-
sity N
0
can be added to the ratio as well, so that the
equation results in
mSMUI
k
=
s
k
MUI
k
MUI
+
k
+ N
0
. (3)
Comparing the detection SNR with the mSMUI it can
be seen, that the signal U
S
for data transmission and
s
k
for the sensor application are diminished by U
Int
or MUI respectively. Due to the possibility of spec-
tral shifting and the need for a worst case considera-
tion, the MUI in the sensor network has to be split into
positive and negative parts. In data transmission sys-
tems this separation is not required, as interferences
affect the detection SNR only at the point of deci-
sion at the receiver side. Therefore, interferences can
be constructive or destructive for the half vertical eye
opening.
4 SENSOR SYSTEM
SIMULATION
Based on the previously, in Section 2, explained
CDM-WDM system, a simulation is programmed. It
is used to provide information about the usability of
applied sequences. The simulation is situated on the
chip-level, meaning the single logical ’1’s and ’0’s
of the binary sequence. This automatically includes
a rectangular chip shaping that is applied in the
mentioned interrogation system. The optical correla-
tion of this system comprises a multiplication step,
realized by an optical modulator and a summation
step, realized by a spectrometer. This setup needs to
be transferred into a mathematical description. The
size of the sum, how many chips are summed up, is
defined by the integration time of the spectrometer
and the duration of each chip. At the beginning of
the integration time, the first modulator starts and
the light needs to travel through the whole sensor
network before it arrives at the second modulator.
Depending on the optical path length, the reflected
sequence arrives with a different time delay. Besides
this sequence, the modulator is synchronized to,
interfering reflections arrive sooner and later. There-
fore, the modulator is driven with a sequence starting
with the beginning of the integration time. To create
the appropriate time delay, the sequence is rotated,
so that the last chips of the sequence are at the very
beginning. To fill the integration time, the sequence is
repeated several times and at the end both modulators
stop with the actual last chip of the sequence. The
integration time is set so that no sequence is truncated
at the end. Instead, the modulators are driven with
logical ’0’s, to fill the remaining integration time.
The simulation uses a matrix calculation to obtain the
autocorrelation results for each section of the system,
assuming the minimum distance of sensors operating
at the same wavelength equal to the chip duration.
The investigated sequence c
c
c consists of a certain
number of chips c
n
where n = 0,1,.. .,N 1 and
N denotes the length of the sequence. The arriving
sequences with different time delays at the second
modulator are represented in the matrix S
S
S
(K×I)
where
K stands for the number of sections and I for the
integration time in chips. The integration time I
needs to be equal to or greater than the length of the
sequence N.
S
S
S =
c
0
... c
N1
0 ... 0
0 ... c
N2
c
N1
... 0
.
.
.
.
.
.
0 ... 0 c
0
... c
N1
(4)
The delay is implemented on the chip level by adding
zeros in front of the first sequence. For each section
an additional zero indicates an additional time delay
matching the distance of sensors at the same wave-
length. The sequence itself is repeated to fill the in-
tegration time I. No sequence is truncated. Instead,
zeros fill the remaining columns of the matrix. Thus,
all sequences from different sections, meaning with
different time delays, are represented in the matrix S
S
S.
The behavior of the second modulator is defined in
matrix R
R
R
(K×I)
. Instead of the leading zeros for the
time delay, the matrix is filled with rotated parts of
the sequence. Therefore the last chips of a sequence
appear in front of the first chip.
R
R
R =
c
0
... c
N1
0 ... 0
c
N1
... c
N2
c
N1
... 0
.
.
.
.
.
.
c
1
... c
0
c
1
... c
N1
(5)
This matrix realizes each synchronization point, thus
each possible time delay for the simulated network.
The integration time here is filled with zeros at the
end, as well. Each element in one line of the matrix S
S
S
needs to be multiplied with the correspondingelement
of each line of the matrix R
R
R. All these elements need
to be summed up to fulfill the correlation of both se-
quences. This happens line-wise and can be realized
by a matrix multiplication
A
A
A = S
S
S· R
R
R
T
. (6)
The matrix A
A
A
(K×K)
contains all correlation func-
tions for each section in its lines. All side lobes can
be assigned to the corresponding section and the ACF
System based Code Evaluation Criteria for CDM Applications in Sensor and Data Transmission Systems
81
L31
M31
M63
L67
L127
M127
L251
M255
L503
M511
0
10
20
30
40
50
60
Sequences
mSMUI (in dB)
30 sections
50 sections
62 sections
126 sections
250 sections
254 sections
502 sections
510 sections
Figure 5: Simulated mSMUI as a function of selected code sequences and network size (with reference to Table 1).
peaks can be found along the main diagonal. Hence,
the vector s
s
s contains all ACF peaks
s
s
s = (a
0,0
,a
1,1
,.. .,a
K1,K1
), (7)
whereas the matrix M
M
M
(K×K)
M
M
M = A
A
A diag(s
s
s) (8)
contains all interference between each section.
The interference of section j on section k is indi-
cated by the matrix element m
k, j
. Consequently, all
elements on the main diagonal are zero, since there
cannot be an interference of a section on itself. The
interference can be positive or negative, so that the
separate sums of all positive and of all negative inter-
ference for each section k are calculated by
MUI
+
k
=
j
m
k, j
j {0, 1,.. .,K 1|m
k, j
> 0}, (9)
MUI
k
=
j
|m
k, j
|
j {0, 1,.. .,K 1|m
k, j
< 0}. (10)
The corresponding signal s
k
of the section k is an
element in vector s
s
s. Thus, signal, positive interfer-
ence and negative interference are calculated and can
be used for determining the criteria mSMUI
k
to evalu-
ate the sequence c
c
c. This mSMUI
k
is section and inte-
gration time dependent. The integration time defines
the number of repetitions of the sequence c
c
c and the
amount of zeros in the last columns of matrix S
S
S and
matrix R
R
R. Non-cyclical ACFs contain boundary ef-
fects at the beginning and at the end of the sequence.
In contrary, the cyclical ACF attained with SIK for M-
sequences and Legendre sequences contains zeros for
all side lobes. Meaning, for every additional repeti-
tion of the sequence, the signal s
k
increases while the
interference stays the same. Therefore, the worst-case
criterion mSMUI
k
can be improved by additional rep-
etitions. In the testbed they are limited by the integra-
tion time of the spectrometer. Hence, the simulation
can calculate the criterion for a few repetitions of the
sequence c
c
c and the results can be scaled to the corre-
sponding integration time. The scaling only applies
when a full repetition is added. Therefore, the simu-
lation calculates all mSMUI
(I)
k
for each section k and
for each integration time I until another repetition fits
inside without truncating the sequence. Out of these
results the worst mSMUI
(I)
k
is considered for the eval-
uation of the sequence c
c
c.
The simulation parameters are depicted in Table 1.
The chip duration T
c
equals 5 ns which corresponds to
a distance of 1 m between two sensors operating at the
same wavelength (G¨otten et al., 2020). The integra-
tion time is set from 13000 chips to 13000+ N chips,
where N indicates the length of the sequence. Thus,
all boundary effects resulting in interference are con-
sidered for the mSMUI. The actual integration time
can be calculated by multiplying the amount of chips
Table 1: Simulation parameters.
Parameter Value
Chip duration T
c
5ns
Scaling factor ×100
Integration time 13000 ... 13000+ N chips
Resulting I-time 6.5 ms ... 6.5ms+ N · T
c
Number of sections 30 . .. 510 sections
SENSORNETS 2021 - 10th International Conference on Sensor Networks
82
+
Symbol Chip Symbol
Symbol
Stream
CDM
Spreader
Channel
Chip
Equalizer
CDM
Receiver
Noise
Figure 6: Simulation of data transmission using a single user CDM system.
with T
c
that results in 6.5 µs for 13000 chips. Mea-
surements with the interrogator testbed show integra-
tion times of 6.5 ms. Therefore, a scaling factor
of ×100 is chosen to correspond to actual measure-
ments. The number of sections varies from 31 to 510.
It is chosen to exhaust the maximum coverage of the
investigated sequences which is one section less than
the length N. 50 serial WDM sections have already
been interrogated in the testbed. The analyzed se-
quences range from suitable Legendre sequences with
the lengths from 31 to 503 chips (L31 L503) and
M-sequences ranging from 31 to 511 chips (M31
M511). In the case of M-sequences, all possible se-
quences with different generator polynomials are an-
alyzed. Gold and random sequences are not depicted
since they provide side lobes in their cyclical ACF
that lead to a very low mSMUI.
Figure. 5 depicts the simulation results. The criterion
is represented in the dB-scale, since possible nega-
tive ratios (when s
k
< MUI
k
) can be excluded and set
to 0 dB. The dependency of the maximum coverage
on the sequence length can be seen by the amount of
sections each sequence can handle. The scenario for
30 sections leads to results for all tested sequences.
50 sections are not supported by sequence lengths of
31 chips. The more sections, the longer the sequence
has to be. The number of repetitions of a sequence
does not influence the mSMUI. Sequence L31 pro-
vides an mSMUI of 53.45dB for 30 sections. Se-
quences M255 and L503 reach similar values, while
the rest is lower. Whereas the Legendre sequence L31
in the 30 sections scenario provides better results than
the M-sequence M31, no general rule for Legendre
and M-sequences can be found. For complete cover-
age and equal lengths, the Legendre sequence L31 is
superior to M31 and L127 is equal to M127. L503
seems to be an all-rounder for all simulated scenar-
ios. It has no major drawback for a small amount of
sections and is superior for all numbers of sections
until complete coverage of 502 sections. The inter-
rogation of such a network length suffers from other
influences that cannot be improved by the sequence
itself (G¨otten et al., 2020).
5 DATA TRANSMISSION
SYSTEM SIMULATION
The simulation of data transmission describes a sin-
gle user CDM system, since ISI is the equivalent to
the MUI in the sensor system and therefore, a bet-
ter comparability is achieved. Included are a binary
generator, a CDM spreader and receiver, a pair of
root-raised cosine filters, a chip level equalizer and a
frequency selective channel with noise influence. An
overview is provided in Figure 6. The binary gener-
ator provides a bipolar 1’, ’-1 symbol stream. The
CDMA spreader increases the required bandwidth, by
spreading each transmitted data symbol with a spe-
cific sequence. The CDM receiver works by corre-
lating the received signal with the original sequence.
Channel coefficients and noise can be individually de-
fined. The equalizer works on chip level (Darwood
et al., 2001), (Elders-Boll, 2001). After the CDM re-
ceiver, evaluation mechanisms are used to assess the
received signal. These mechanisms include a decider,
which converts the received signal back into symbols,
and a comparison of received and transmitted symbol
stream.
The channel impulse response g
c
(t) is given with
g
c
(t) =g
0
· δ(t)
+g
1
· δ(t T
S
)
+g
2
· δ(t 1.5T
S
). (11)
The channel coefficients are selected with g
0
=
0.8578, g
1
= 0.4289 and g
2
= 0.2831, so that the
channel impulse response is power neutral.
The comparedcodes include M-sequences, Legendre-
sequences, Gold-sequences and random sequences
with the length of 31 and 127 chips. Furthermore,
an example of M-sequences with a length of 15 and
63 chips are tested. The noise is given through the
energy per bit to noise power spectral density ratio
10 · lg(
E
S
/N
0
) with 10 dB. As this simulation is de-
scribing a single user system, the MAI, mentioned in
Section 3, is set to zero. Every simulation was done
with and without the application of a chip level equal-
izer.
System based Code Evaluation Criteria for CDM Applications in Sensor and Data Transmission Systems
83
M15
L31
M31
G31
R31
M63
L127
M127
G127
R127
10
-2
10
-1
Sequences
Bit Error Rate
without equalizer, est.
without equalizer, sim.
with equalizer, est.
with equalizer, sim.
Figure 7: Simulated BER as a function of selected code sequences with an SNR 10· log
10
(
E
S
/N
0
) of 10 dB.
The results are shown in Figure 7. For the simula-
tions without equalizer it is shown, that the calculated
values are about half of the simulated values. This
is explained by taking into account, that the calcula-
tion assumes the worst case half vertical eye opening,
while the simulation includes all possible half vertical
eye openings. This difference changes, for the simu-
lations with equalizer, as it sets all half vertical eye
openings near to the value of 1V. It can be seen, that
over all sequences the BER P
E
for the respective set
ups and calculations is similar.
The channel coefficient g
2
is multiplied by the cor-
responding side lobe of the ACF, which affects the
half vertical eye opening. This explains the differ-
ences in results for estimated values for G127 and
R127 without equalizer. Simulated results are subject
to statistical processes, such as symbol stream gener-
ation and noise application. With the inclusion of the
equalizer into the estimation, the values are the same
for all sequences up to the length 63. The half verti-
cal eye opening for these sequences is set to 1 V. As
the half vertical eye opening drops slightly for the se-
quences with a length of 127, down to 0.98V for M-,
Legendre- and Gold sequences and 0.985V for the
random sequence, P
E
is slightly worse for the same
amount of equalizer coefficients.
6 CONCLUSION
In this work three system based code evaluation crite-
ria are introduced. The main difference between data
transmission and sensor applications is the handling
of interferences. For data transmission applications,
the worst half vertical eye opening caused by all in-
terferences is considered to estimate the criteria. The
worst case criteria for the sensor application is not a
superposition of all influences, but a separate eval-
uation of positive and negative MUI. Different se-
quences result in different mSMUI and the sequence
length defines the maximum number of sections, that
can be interrogated. While the ACF obtained by SIK
of Legendre- and M-sequences provides zero values
for all side lobes, Gold- and random sequences show
non-zero values and are therefore not applicable. The
Legendre sequence with a length of 503 chips shows
an overall best result. In contrary, in the proposed sin-
gle user CDM system the spreading sequence shows
no major influence.
ACKNOWLEDGEMENTS
This work has been funded by the German Ministry
of Education and Research (No. 13FH030PX8).
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