Availability improvementschemes for multi-carrieroptical transmission systems
Hiroshi Yamamotoa), Kei Kitamura, Masahiro Yokota,Shohei Kamamura, Rie Hayashi, and Yoshihiko UematsuNTT Network Service Systems Laboratories, NTT Corporation,
3–9–11 Midori-cho, Musashino, Tokyo 180–8585, Japan
Abstract: In multi-carrier optical transmission systems, availability of a
transponder decreases in accordance with the increase in the number of
optical modules comprising the transponder. In this paper, we clarify promis-
ing schemes to improve availability by comprehensively comparing them.
We first clarify the condition under which availability problems become
apparent by analyzing the basic trend in availability. Then, we compare the
improvement in availability and difficulty in transmission system develop-
ment. As a result, we showed that the Pool scheme, where the small amount
of shared backup optical modules are implemented to avoid transponder
failure, is promising since it effectively increases availability with a small
amount of additional optical modules and has enough feasibility.
Keywords: multi-carrier optical transmission, availability improvement
Classification: Transmission Systems and Transmission Equipment for
Communications
References
[1] S. Chandrasekhar and X. Liu, “Terabit superchannels for high spectral efficiencytransmission,” Proc. 42nd European Conference and Exhibition on OpticalCommunication (ECOC), Torino, Italy, Tu.3.C.5, Sep. 2010. DOI:10.1109/ECOC.2010.5621580
[2] T. Tanaka, T. Inui, W. Imajuku, and A. Hirano, “Subcarrier restoration forsurvivable multi-flow transponders in elastic optical networks,” Proc. 21st Asia-Pacific Conference on Communication (APCC), Kyoto, Japan, pp. 14–16, Oct.2015. DOI:10.1109/APCC.2015.7412515
[3] A. Hirano, Y. Yamada, T. Tanaka, T. Oda, K. Shintaku, and T. Inui, “Costeffective and robust optical network by inversely aggregated networkingwith programmable protection architecture,” Electron. Lett., vol. 50, no. 20,pp. 1459–1461, Sep. 2014. DOI:10.1049/el.2014.2162
1 Introduction
Multi-carrier transmission technology, with which a large amount of client traffic is
transmitted using multiple channels called sub-carriers, is regarded as promising to
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accommodate continuously growing traffic demand [1]. In multi-carrier trans-
mission systems, a transponder is composed of a number of optical modules equal
to that of sub-carriers. Assuming that each optical module fails at a certain
probability, availability of a transponder decreases in accordance with the increase
in the number of optical modules comprising the transponder.
In this paper, we clarify promising schemes to improve availability of multi-
carrier transmission systems by comprehensively comparing them. We first clarify
the condition under which availability problems become apparent by analyzing the
basic trend in availability of multi-carrier transmission systems. Then, we compare
the improvement in availability and difficulty in transmission system development
based on two major schemes: (a) client traffic is continuously transmitted using
only non-failed sub-carriers (Polishing scheme) and (b) the small amount of shared
backup optical modules are implemented to avoid transponder failure (Pool
scheme). As a result, we showed that the Pool scheme is promising since it
effectively increases availability with a small amount of additional optical modules
and has enough feasibility.
2 Availability of multi-carrier optical transmission systems
In a multi-carrier transmission system, client traffic is transmitted at X � n Gbps
using n sub-carriers, each of which transmits the signal at X Gbps. The structures of
a multi-carrier transmission systems and transponders are illustrated in Fig. 1(a). A
transponder is composed of a framer and n optical modules. Client traffic is divided
into n signals by a framer on the sender side. Each divided signal is transmitted
through an optical module. Note that the standardization discussion of beyond
100G OTN (Optical Transport Network) in ITU-T has currently proceeded accord-
ing to the policy where partial failure in a transponder is treated as failure of the
entire transponder. Thus, in Normal scheme, communication between a pair of
transponders becomes completely unavailable if any of optical modules fails.
Assuming that each optical module fails at a certain probability, unavailability
of communication between a pair of transponders is formulated with the following
equation.
Pnormal ¼ 1 � ðð1 � �Þ2Þn � ð1 � �FÞ2;
� ¼ MTTR
MTBF þMTTR; �F ¼ MTTR
MTBFF þMTTR
ð1Þ
(a) Structure of multi-carrier optical transmission systems (b) Unavailability and number of sub-carriers
Fig. 1. Multi-carrier optical transmission systems (Normal)
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Here, α, �F , n, MTBF and MTBFF correspond to unavailability of an optical
module, that of a framer, the number of optical modules, mean time between failure
of an optical module, and that of a framer, respectively. MTTR corresponds to the
mean time to repairer of both of an optical module and a framer.
If two systems are operated under the redundant mode as shown in Fig. 1(a),
unavailability is the square of Pnormal in Eq. (1). The redundancy can be achieved
by OTN/ODU (Optical channel Data Unit) protection switching or IP rerouting.
Fig. 1(b) illustrates unavailability and number of sub-carriers. In the case of
two sub-carriers, the increase in unavailability does not cause a serious problem
since unavailability is only twice as large as that in a single carrier for non-
redundant. However, unavailability increases along with an increase in the number
of sub-carriers. For example, in the case of 5 sub-carriers, unavailability becomes 5
times as large as that for non-redundant and 25 times as large as that for redundant.
Thus, a countermeasure against increasing unavailability due to the number of
sub-carriers has become essential to keep unavailability as small as that of current
single carrier transmission system at least.
3 Schemes to improve availability of multi-carrier optical trans-
mission system
Assuming that optical modules, the number of which in a transponder is large, form
a bottleneck in availability of a multi-carrier transmission system, there are two
schemes for improving such availability: (a) client traffic is continuously trans-
mitted using only non-failed sub-carriers (Polishing scheme) and (b) the small
amount of shared backup optical modules are implemented to avoid transponder
failure (Pool scheme).
Fig. 2(a) illustrates the Polishing scheme. This scheme uses n optical modules
to transmit client traffic at X � n Gbps. When m (m < n) optical modules fail,
X � ðn � mÞ Gbps of client traffic is continuously transmitted using available optical
modules, while the rest is discarded.
In the Polishing scheme, unavailability, where more than X � m Gbps are
discarded, is the probability that more than m sub-carriers are unavailable. This
probability is formulated with the following equation.
(a) Polishing scheme (b) Pool scheme
Fig. 2. Schemes to improve availability of multi-carrier optical trans-mission system
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Ppolishingm
n
� �
¼Xni¼m
nCi � ð1 � ð1 � �Þ2Þi � ðð1 � �Þ2Þn�i � ð1 � �FÞ2 þ ð1 � ð1 � �FÞ2Þð2Þ
Fig. 2(b) illustrates the Pool scheme. This scheme uses additional �n shared
backup optical modules in addition to n working optical modules to transmit client
traffic at X � n Gbps. When the optical module i fails at one side of a pair of
transponders, all client traffic is transmitted continuously by assigning the signal
that is originally assigned to optical module i to one of the shared backup optical
modules in the transponder. Note that all client traffic is discarded if �n þ 1 optical
modules fail at either side of a pair of transponders. Several detailed schemes of the
Pool scheme have been proposed by Tanaka et al. [2] and Hirano et al. [3].
In the Pool scheme, unavailability is formulated with the following equation.
Ppool ¼ 1 �X�ni¼0
nþ�nCi � �i � ð1 � �Þnþ�n�i !2
� ð1 � �FÞ2 ð3Þ
4 Analysis on effectiveness and difficulty in transmission system
development
First, we evaluated availability. In the evaluation, n, �n, MTBF, and MTTR were
set to 5, 1, 20,000 hours, and 2 hours, respectively. We first focused on failure of
optical modules, and we set �F at 0. Fig. 3(a) shows the number of optical modules
and unavailability. The horizontal broken lines show unavailability for a single
carrier (n ¼ 1). In the case of non-redundant mode, unavailability for Normal
becomes higher than that for a single carrier. Fig. 3(b) shows the scale of failure,
which is defined by m=n as described in Eq. (2), and unavailability. With the
Polishing scheme, unavailability varies in accordance with the scale of failure. In
Fig. 3(a), the possible range of unavailability with the Polishing scheme is shown
with a red arrow. Unavailability for small failure (m=n ¼ 1=5), where one of optical
modules in a transponder fails, remains as high as that for Normal and becomes
higher than that for a single carrier, while unavailability for large failure decreases
greatly since multiple failure scarcely happens. For these reasons, improvement in
availability with the Polishing scheme is limited. In contrast, with the Pool scheme,
unavailability decreases drastically and remains significantly lower than that for a
single carrier, though the number of optical modules increases slightly due to
additional shared backup. Fig. 3(c) shows unavailability and the ratio of framer’s
MTBF to optical module’s MTBF. Regardless of the ratio of framer’s MTBF to
optical module’s MTBF, with the Pool scheme, unavailability decreases almost
constantly compared to other schemes. Due to the limitation of space, although
we showed results only for 5 sub-carriers, with the Pool scheme, unavailability
decreases, regardless of the number of sub-carriers. Note that the trend in avail-
ability in the case of redundant mode is the same as that in the case of non-
redundant mode.
We then discuss difficulty in transmission system development. In the recom-
mendation ITU-T G.709, a client signal is mapped into an ODU. This ODU signal
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is mapped into an OTU. Since an OTU can accommodate multiple ODU signals,
we consider two cases: (1) client traffic is transmitted at X � n Gbps using an ODU,
and an OTU accommodates the only one ODU signal (single ODU case), (2)
multiple groups of client traffic, each of which is transmitted at less than or equal to
X Gbps, are transmited using their dedicated ODUs, and an OTU accommodates
multipe ODU signals (multiple ODU case). For the Polishing scheme, in the single
ODU case, the establishment of operations, administration, and maintenance
(OAM) and alarm transfer methods for variable bandwidth links are required. In
addition, the management of traffic priority and the functionality to distribute traffic
based on the priority considering the structure of data packets accommodated in the
payload of the traffic are also required to select some client traffic to discard in the
case of failure. In the multiple ODU case, the management of the priority of ODU
signals and the functionality to re-assign ODU signals are still required to select
some ODU signals to discard in the case of failure, although the management of the
traffic priority considering the structure of data packets is no longer required.
In contrast, the Pool scheme requires only the implementation of the function-
ality to switch over from the failed optical module to the shared backup optical
module regardless of the above-mentioned cases.
As a result, the Pool scheme is promising to improve availability of multi-
carrier transmission systems since the scheme effectively increases availability with
a small amount of additional optical modules and has enough feasibility.
5 Conclusion
In multi-carrier transmission systems, availability of a transponder decreases in
accordance with the increase in the number of optical modules comprising the
(a) unavailability and number of optical modules (b) unavailability and failure scale (Polishing scheme)
(c) unavailability and ratio of framer's MTBF to optical module's MTBF (non-redundant)
Fig. 3. Numerical example
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transponder. In this paper, to clarify the promising schemes of improving avail-
ability, we comprehensively compared them based on the trend in availability and
difficulty in transmission system development. As a result, we showed that the Pool
scheme is promising since it increases availability more than that for a single carrier
with only one additional shared backup optical module in each transponder and has
enough feasibility.
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Experimental evaluation ofcommunication quality ofEthernet in relation toparameters of pulsedisturbances
Sayaka Matsushimaa), Tohlu Matsushimab),Takashi Hisakadoc), and Osami Wadad)
Graduate School of Engineering, Kyoto University,
Kyoto-daigaku-katsura, Nishikyo-ku, Kyoto 615–8510, Japan
Abstract: In this paper, in order to improve the reliability of Ethernet
communication, the effect of pulse disturbances on the communication
quality of 100BASE-TX was evaluated experimentally. A relationship be-
tween the threshold level of Ethernet and disturbances affecting communi-
cation quality was revealed when the amplitude and width of the pulse
disturbance were changed. A disturbance in which the pulse width was the
same as 1 bit time of the signal degraded the communication quality the
most. These findings should help in the effort to apply Ethernet to automo-
tive area network.
Keywords: Ethernet, 100BASE-TX, communication quality, pulse disturb-
ance
Classification: Energy in Electronics Communications
References
[1] ISO 11898-1:2015, “Road vehicles – Controller area network (CAN) – Part 1:Data link layer and physical signaling,” Dec. 2015.
[2] IEEE LAN/MAN Standards Committee, IEEE Std 802.3bw-2015, “Amendment1: Physical layer specifications and management parameters for 100Mb/soperation over a single balanced twisted pair cable (100BASE-T1),” Oct. 2016.
[3] B. Körber, “EMC test specification for BroadR-reach transceivers ver. 2.0,”OPEN ALLIANCE, Dec. 2014.
[4] M. Mizoguchi, H. Mori, N. Maeda, H. Keino, T. Yasuda, and H. Goto,“Alternative technique to estimate the immunity performance for In-vehicleEthernet,” 7th Asia Pacific International Symposium on ElectromagneticCompatibility, pp. 703–705, Shenzhen, China, May 2016. DOI:10.1109/APEMC.2016.7522841
[5] K. Takaya, D. Tomita, K. Umeda, M. Ogawa, T. Matsushima, T. Hisakado, andO. Wada, “Packet error rate analysis considering collision probability between
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pulse disturbance and transmission packets,” IEICE Trans. Commun., vol. J100-B, no. 3, pp. 166–175, Mar. 2017 (in Japanese).
1 Introduction
Automotive Ethernet has been attracting great attention in recent years. This is
because Ethernet achieves faster communication than conventional means in
automotive area network, such as controller area network (CAN) [1]. In addition,
because Ethernet is already prevalent in local area network, it would be easy to
introduce it into the automotive area network. At present, BroadR-Reach is being
used as automotive Ethernet technology, and it has been standardized in 100BASE-
T1 [2].
Although high reliability and safety is needed in the automotive area network,
the communication quality of high-speed Ethernet does not yet satisfy these
requirements. Shielding the signal line is an effective method for improving the
required reliability and safety. However, when taking the weight and the cost of
a car into account, it is necessary to reduce the number of cables. Therefore,
automotive Ethernet needs to be able to meet the reliability and safety requirements
without shielding.
The purpose of this study is to clarify what is degrading communication quality
and to improve the reliability of Ethernet in automotive application. The first step in
this research focuses on the 100BASE-TX communication system, which is the
most commonly used in 100Mbps Ethernet technology.
In the conventional electromagnetic compatibility (EMC) test standard [3] and
the previous study [4] for automotive application of Ethernet, only the radio
frequency (RF) signal and the transient pulse are used as disturbances. However,
the typical waveform of interference in an automotive environment is damped
oscillation, which is usually generated by the switching operation of power
electronics devices. Therefore, continuous pulse disturbances are considered in
this paper.
2 Experimental injection of differential mode disturbances
In general, disturbances from power electronics devices are coupled with the pair of
cables as the common mode in the system. The common mode can convert to the
differential mode due to multiple imbalances in the system, and the differential
mode disturbs signal communication.
The purpose of this paper is to examine how differential mode disturbances
degrade the communication quality of Ethernet. Therefore, a differential mode
disturbance is directly injected into a UTP cable. Pulse amplitude Vp and pulse
width tp are changed as parameters of pulse disturbances. Packet error rate (PER),
which is measured with an Ethernet tester, is evaluated as the index value of the
communication quality.
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2.1 Injecting differential mode pulse disturbances
The epidermis of a UTP cable are peeled off, and a current probe (CT-6) is inserted
via a 300Ω resistor to inject disturbances. Fig. 1 shows a diagram and an
equivalent circuit for the section where the disturbance is applied. The distances
between the application point of the disturbance and the terminations are
l1 ¼ 150mm and l2 ¼ 750mm.
The resistor is inserted to prevent a short circuit between differential lines. The
differential impedance in the coupling circuit for applying the common mode
disturbance is 240Ω in the EMC test standards for automotive Ethernet [3], so the
resistance value is fixed at 300Ω (slightly larger than 240Ω). The resistance value
300Ω is slightly larger than 240Ω which is described in the EMC test specification
for automotive Ethernet [2].
Although the insertion impedance of the current probe is 1.1Ω at 10MHz and
1.3Ω at 100MHz, this impedance is ignored in the equivalent circuit shown in
Fig. 1(b). This is because the insertion impedance is considered to be sufficiently
smaller than the impedance of the resistance for the isolation of two wires.
(a) Injection of disturbance into Ethernet cable
(b) Equivalent circuit
(c) Overview of experimental system
Fig. 1. Injecting differential mode disturbances
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2.2 Effect of measurement system and pulse disturbance
Signal amplitude is attenuated because of the insertion of a 300Ω resistor between
differential lines. The attenuated signal’s amplitude can be calculated using the
transmission line theory. In Fig. 1(b), if the inserted resistor is assumed to be Zinp,
the characteristic impedance of the transmission line of the left or right side from
the connection portion of 300Ω and current probe is assumed to be Z1 or Z2, and
the parallel impedance of Zinp and Z2 is written as (Zinp == Z2), the voltage trans-
mission coefficient �t at the connection part is obtained as in the Eq. (1).
�t ¼ 1 þ ðZinp == Z2Þ � Z1ðZinp == Z2Þ þ Z1
ð1Þ
Since the differential line is terminated in the equivalent circuit, reflection at both
ends can be ignored. Therefore, �t is obtained as 67. Fig. 2(a) shows a comparison
between the actual measurement results with and without the insertion of the 300Ω
resistor. With the insertion of the resistor, the amplitude of the Ethernet signal is
0.89V. Therefore, the validity of �t ¼ 67obtained from Eq. (1) is deemed valid.
The injected pulse shown in Fig. 2(b) has a pulse amplitude of about 290mV,
a pulse width of 10 ns, rise and fall times of 2.5 ns and a frequency of 1MHz.
Fig. 2(c) shows typical signal waveforms with or without a disturbance pulse.
2.3 Measurement detail in Ethernet tester
The Ethernet Tester used to measure the PER has two ports, Port A and Port B. The
PER is obtained by comparing the signal generated from one port and the signal
received by the other port.
(a) Signal amplitude with 300 Ω resistor inserted
(b) Pulse disturbance (c) Signal waveform with pulse disturbance
Fig. 2. Effect of pulse disturbances on measurement system anddegradation of signal integrity
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In the experiments, the test signal is transmitted from Port A and received at
Port B. The length of the Ethernet frame is 100 bytes, the interframe gap is 12
bytes, and the test period is 30 seconds. Since the 1 bit time of the signal is 8 ns, a
total of 4:2 � 106 frames are transmitted in one test. Therefore, about 10�6 PER can
be evaluated in this test setup. In addition, the period of the pulse disturbance is
1000 ns (1MHz). Because one frame time is 6,400 ns, one Ethernet frame collides
the disturbance 6 times. The collision frequency is important for estimation of PER
[5].
2.4 Pulse amplitude and communication quality
Fig. 3(a) shows the relationship between PER and the pulse amplitude for pulse
widths of 5 ns and 10 ns. Each of them shows that the more the pulse amplitude
increases, the more the PER degrades. In addition, an error is more likely to occur
with a pulse width of 10 ns than at 5 ns.
The effect of inserting the 300Ω resistor results in signal voltage of −0.89V.Therefore, the pulse at which the amplitude exceeds 390mV is considered to
exceed the logical threshold value of the signal. In the experimental results,
although the minimum pulse amplitude causing packet error changes due to the
pulse width, the error is caused by a disturbance in which the amplitude almost
(a) Pulse amplitude and communication quality
(b) Pulse width and communication quality
Fig. 3. Pulse disturbance and communication quality
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exceeds the threshold value. In the next section, the PER characteristics against the
pulse width of the disturbance is examined.
2.5 Pulse width and communication quality
The relationship between PER and the pulse width of pulse amplitudes of 371mV,
406mV, and 446mV is shown in Fig. 3(b). In particular, in each experiment using
three disturbance voltages, the figure shows that the PER peaks when the pulse
width is about 10 ns. Since the 1 bit time of the signal of 100BASE-TX is 8 ns, the
communication quality is considered to be affected most when the pulse width of
the disturbance is about 1 bit time of the signal.
3 Conclusion
This investigation of the relationship between communication quality and distur-
bances revealed the relationship between the threshold level of the signal and the
disturbance voltage affecting communication quality. In particular, experiments
demonstrated that pulse disturbances with durations of about 1 bit time of the signal
affected communication quality the most.
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BER performance analysis ofmulti-dimensional modulationwith BICM-ID
Akira Nakaa)
The Department of Media and Telecommunications Engineering, Ibaraki University,
4–12–1 Naka-Narusawa, Hitachi-shi, Ibaraki 316–8511, Japan
Abstract: We numerically evaluate Bit Error Rate (BER) performance of
four- and eight-dimensional modulation formats with Bit-Interleaved Coded
Modulation Iterative Detection (BICM-ID) compared with Gray mapped
and natural binary mapped two-dimensional formats for high-speed optical
communication systems. The BICM-ID, which is composed of a demodu-
lator and a decoder, effectively improves power efficiency of the multi-
dimensional formats taking into account receiver sensitivity and transmission
capacity per symbol. Further, we quantitatively verify that the BER perform-
ances significantly depend on a priori/extrinsic mutual information ex-
change between a demodulator and a decoder, which is illustrated by
Extrinsic Information Transfer (EXIT) chart.
Keywords: multi-dimensional modulation, BICM-ID, EXIT chart
Classification: Fiber-Optic Transmission for Communications
References
[1] E. Agrell and M. Karlsson, “Power-efficient modulation formats in coherenttransmission systems,” J. Lightwave Technol., vol. 27, no. 22, pp. 5115–5126,2009. DOI:10.1109/JLT.2009.2029064
[2] D. S. Millar, T. Koike-Akino, R. Maher, D. Lavery, M. Paskov, K. Kojima,K. Parsons, B. C. Thomsen, S. J. Savory, and P. Bayvel, “Experimentaldemonstration of 24-dimensional extended golay coded modulation withLDPC,” Proc. OFC/NFOEC M3A.5, 2014. DOI:10.1364/OFC.2014.M3A.5
[3] X. Li and J. A. Ritcey, “Bit-interleaved coded modulation with iterativedecoding,” IEEE Commun. Lett., vol. 1, no. 6, pp. 169–171, 1997. DOI:10.1109/4234.649929
[4] H. Zhang, H. G. Batshon, C. R. Davidson, D. G. Foursa, and A. Pilipetskii,“Multi-dimensional coded modulation in long-haul fiber optic transmission,”J. Lightwave Technol., vol. 33, no. 13, pp. 2876–2883, 2015. DOI:10.1109/JLT.2015.2419821
[5] M. Nakamura, F. Hamaoka, A. Matsushita, K. Horikoshi, H. Yamazaki, M.Nagatani, A. Sano, A. Hirano, and Y. Miyamoto, “Coded eight-dimensionalQAM technique using iterative soft-output decoding and its demonstration inhigh baud-rate transmission,” J. Lightwave Technol., vol. 35, no. 8, pp. 1369–1375, 2017. DOI:10.1109/JLT.2017.2669919
[6] S. ten Brink, “Convergence behavior of iteratively decoded parallel concatenatedcodes,” IEEE Trans. Commun., vol. 49, no. 10, pp. 1727–1737, 2001. DOI:10.1109/26.957394
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[7] O. Alamri, B. Poupart, M. El-Hajjar, S.-X. Ng, and L. Hanzo, “Onmultidimensional BICM-ID constellation labelling,” IEEE International Confer-ence on Communications (ICC), pp. 1–5, 2010. DOI:10.1109/ICC.2010.5502739
[8] ETSI, Tech. Report 102 376, V1.1.1, 2005.[9] A. Naka and S. Yamada, “Characteristics of multi-dimensional modulation with
MIMO signal processing,” IEICE Commun. Exp., vol. 5, no. 12, pp. 461–466,2016. DOI:10.1587/comex.2016XBL0160
1 Introduction
Four-dimensional (4-D), eight-dimensional (8-D) and more dimensional formats
modulation format have recently attracted attention due to their better power
efficiency, namely, higher sensitivity considering the data rate, than the 2-D format
which has been used in commercial 100Gbps and beyond per wavelength high-
speed optical transmission systems. In such a multi-dimensional format, some
components of polarization modes, time-slot modes and/or frequency (wavelength)
modes in single-mode fiber as well as IQ modes are comprehensively treated as a
single symbol [1, 2].
On the other hand, coded modulation has been proposed for wireless commu-
nication to realize improved performance closer to Shannon limit, where the
modulation and coding are combined in a single entity. Bit-Interleaved Coded
Modulation Iterative Detection (BICM-ID), which is one of the coded modulations,
offers remarkable improvements of BER performance by iteratively exchanging
bitwise soft information between a demodulator and a decoder [3]. A few optical
transmission experiments have been recently reported using multi-dimensional
modulation with the BICM-ID [4, 5].
In this paper, BER performances of 4-D and 8-D modulation formats based on
Quadrature Phase Shift Keying (QPSK) are analyzed in comparison with those of
two different 2-D QPSK formats with numerical simulation. The obtained results
quantitatively indicate that the BER performances of 4-D and 8-D QPSKs degraded
by unavoidable non-Gray mapping are partially recovered by BICM-ID, and 4-D
and 8-D QPSKs comprehensively retain their advantage in terms of power
efficiency as compared with the 2-D QPSKs. Further, the Extrinsic Information
Transfer (EXIT) charts analyses, which characterize the flow of information
between a demodulator and a decoder [6], are shown to be consistent with the
BER performance, so that BICM-ID should be carefully designed to derive good
performances of multi-dimensional modulations by means of the EXIT chart. To
be noted, multi-dimensional formats in [7], which consist only of combining n
consecutive 2-dimensional M-ary symbols are quite different the ones treated in
this letter which consist of subsets of the format in [7] to enlarge minimum Euclid
distance.
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2 Calculation model
2.1 System configuration
Fig. 1 shows the block diagram of BICM-ID system [3], which is set to exchange
bitwise soft information of log likelihood ratio (LLR) up to 10 round trips between
a demodulator and a decoder via interleaver and de-interleaver (outer iteration) in
this paper. Encoder and Decoder use Low-Density Parity-check Code (LDPC) code
defined by Digital Video Broadcasting–Satellite–Second Generation (DVB-S2) [8]
with codeword length of 64,800. Two LDPC code rates of 5/6 and of 3/5 are
applied to our calculation. Each LDPC code is assumed to have 20 Inner iteration.
The length of interleaver is 64,800 highly enough to ensure the LLR values to be
uncorrelated.
At the optical modulator, firstly one bit and four redundancy bits are respec-
tively generated by following calculations, where ðb1 b2 b3Þ and ðb1 b2 b3 b5Þ arerespectively LDPC encoded bits to be transmitted by 4-D and 8-D QPSKs;
4-D QPSK: b4 ¼ b1 � b2 � b3 ð1Þ
8-D QPSK:
b4 ¼ b1 � b2 � b3
b6 ¼ b1 � b2 � b5b7 ¼ b2 � b4 � b5
b8 ¼ b5 � b6 � b7
8>>><>>>:
ð2Þ
Then, two and four sets of ð2bi � 1; 2biþ1 � 1Þ are respectively mapped to corre-
sponding number of QPSK consternations to generate 4-D QPSK and 8-D QPSK,
where i is an odd number. Each set of ð2bi � 1; 2biþ1 � 1Þ represents I and Q
components of QPSK in mutually orthogonal modes of polarization, time-slot
modes and/or frequency (wavelength) modes in single-mode fiber. For instance,
four-dimensional polarization switched QPSK (4-D PS-QPSK) is formed by
ð2b1 � 1; 2b2 � 1Þ in X polarization mode and ð2b3 � 1; 2b4 � 1Þ in Y mode [9].
Optical Signal-to-Noise Ratio (OSNR) sensitivities of 4-D and 8-D QPSKs by
the above procedures respectively become 3 dB and 6 dB better than that of 2-D
QPSK in Symbol Error Rate (SER) performance due to enlarged Euclid distances
between symbols. However, these sensitivity improvements in SER are not directly
converted to the improvement in Bit Error Rate (BER), since Gray mappings
cannot be realized in these multi-dimensional formats [1, 9]. Although the symbol
pairs furthest away from each other is set to be inverted binary codes to minimize
bit error in the above procedures, one symbol error of 4-D QPSK and 8-D QPSK
respectively become 1.5 bit errors and 2 bit errors on average, according to the
relations between the numbers of transmitting bits and adjacent symbols. Due to
Fig. 1. Block diagram of BICM-ID system using optical modulationand LDPC code.
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these bit error increases, OSNR sensitivity improvements of 4-D and 8-D QPSKs in
BER performances respectively become much less than 3 dB and 6 dB in high BER
regions, while the respective sensitivities asymptotically approach 3 dB and 6 dB in
small BER regions.
2-D QPSK formats are also generated from the optical modulator in two
mapping methods for comparison; namely Gray mapping and non-Gray natural
binary mapping. Adjacent symbols on the 2-D plane each differ by one bit in the
former, while one of two adjacent symbols differ by two bit in the latter. Similar to
4-D and 8-D QPSKs, each symbol error of natural binary mapped 2-D QPSK
becomes 1.5 bit errors on average due to non-Gray mapping, whereas each symbol
error of Gray mapped 2-D QPSK remains at 1 bit error.
When outer 7% hard decision forward error correction (HD-FEC) is assumed,
where its BER threshold is 4:5 � 10�3 [5], overhead ratios out of the transmitting
bits become 22.5% and 44.2% in cases of LDPC code rates of 5/6 and 3/5,
respectively. To compare the performances of two LDPCs, 32Gbaud and 45Gbaud
are respectively assumed for the two LDPCs in order to transmit the same net rate
of 50Gbps at 2-D QPSK, 75Gbps at 4-D QPSK (37.5Gbps per 2-D) and 100Gbps
at 8-D QPSK (25Gbps per 2-D). To be noted, transmission speeds per one
dimension are respectively reduced by 1.25 dB in 4-D QPSK and by 3 dB in 8-D
QPSK compared to 2-D QPSKs. In addition, optical noise is added after the
modulator, the amount of which determines OSNR conditions.
3 Calculation result
3.1 BER performance
Fig. 2 show the calculated BER performances as a function of OSNR with the four
modulation formats. Upper and lower figures are respectively obtained with LDPC
code rate of 5/6 and 3/5.
White marks with solid lines in the upper figure show that BERs of Gray-
mapped 2-D QPSK. These results illustrate that this format has a single BER cliff
irrespective to the number of outer iteration, achieving BER of 4:5 � 10�3 at OSNRof around 9.1 dB corresponding to BER without LDPC of around 3:6 � 10�2. Onthe other hands, natural binary mapped 2-D QPSK has several BER cliffs indicated
by blue marks with dotted lines, which illustrates that BER performances are 0.5 dB
improved by the iterations in OSNR sensitivity. The OSNR at BER of 4:5 � 10�3 ofthis formats finally turns into only 0.3 dB difference from that of Gray-mapped 2-D
QPSK. This result clearly shows that BICM-ID almost recovers the amount of BER
deterioration caused by non-Gray mapping.
Orange marks with broken lines in the upper figures show that BERs of 4-D
QPSKs. OSNR sensitivity differences from Gray-mapped 2-D QPSK on the
condition of no LDPC are around 2.0 dB at BER of 4:5 � 10�3 and around
1.4 dB at BER of 3:6 � 10�2. The decrease of the OSNR sensitivity is due to
unavoidable non-Gray mapping in 4-D. This OSNR sensitivity difference of 1.4 dB
almost turns into the difference between Gray-mapped 2-D QPSK and 4-D with
non-iterative BICM, or with only once use of LDPC decoder. Further, BICM-ID
improves the OSNR sensitivity up to 1.9 dB in total. Eventually, the power
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efficiency of 4-D QPSK is 0.65 dB superior to that of Gray-mapped 2-D QPSK,
subtracting 1.25 dB of less transmission speed per one dimension.
Similar to the results of 4-D QPSK, BER improvement by BICM-ID is also
observed in 8-D QPSK indicated by magenta marks with dash-dotted lines. BICM-
ID improves the sensitivity up to 4.0 dB compared to Gray-mapped 2-D QPSK.
Eventually, the power efficiency of 8-D QPSK is 1.0 dB superior to that of Gray-
mapped 2-D QPSK, taking account into transmission speed per one dimension.
These obtained results show 4-D and 8-D QPSK formats retain their advantage in
terms of power efficiency as compared with the 2-D QPSKs thanks to BICM-ID.
In contrast, Fig. 2(b) shows that BER improvements due to BICM-ID are much
smaller at the code rate of 3/5 compared to those at the rate of 5/6 for all non-
Grayed mapped formats, though absolute OSNR sensitivities are improved due to
the larger overhead of LDPC. OSNR sensitivity differences respectively turn into
1.4 dB and 3.1 dB between 4-D QPSK/8-D QPSK and Gray-mapped 2-D QPSK.
These results are respectively converted into only 0.15 dB and 0.1 dB better power
efficiency of 4-D and 8-D QPSK. Therefore, it is necessary to carefully design
BICM-ID in order to derive good BER performance improvement.
3.2 EXIT chart
Figs. 3(a) and (b) show EXIT charts which constitute powerful tools used for
designing BICM-ID, which predict the convergence behavior by examining the
(a)
(b)
Fig. 2. BER performance as a function of OSNR.(a) LDPC code rate of 5/6. (b) LDPC code rate of 3/5.Calculation conditions of modulation formats and numbers ofouter iteration are indicated in the margin on the right side ofthe figures.
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evolution of the input/output or a priori/extrinsic mutual information (MI) ex-
change between a demodulator and a decoder in consecutive iterations [6].
As examples, the trajectories of mutual information exchange between natural
binary mapped 2-D QPSK demodulator and the decoder are respectively shown by
the dotted step type lines in each figure, which respectively move between the
broken line and the dotted line with square marks without any intersections. The
vertical components of the step type lines represent the demodulator processing,
and the horizontal components represent the decoder processing. Each of the
trajectories respectively has reached the right edge of the graph, where extrinsic
MI value of decoder is 1.0, showing that perfect transmissions were respectively
achieved without error with a few iterations corresponding to the number of steps.
In addition to natural binary mapped 2-D QPSK, 4-D QPSK and 8D-QPSK are
also able to have trajectories leading to extrinsic MI value of 1.0 in both figures.
These three curves have slopes closer to the one of the decoder curve in the left
figure than the right figure, so that BICM-ID works more effectively under LDPC
code rate of 5/6. On the other hand, each solid line with white marks, representing
Gray mapped 2-D QPSK, have no slope in each figure. This shows that no iteration
improvement is expected with BICM-ID, because the trajectory would not have
plural steps. Under the lower OSNR conditions, all four curves of demodulators in
each figure would move downward and cross the decoder curve, so that no error
free transmission is performed any more. These features appearing on the EXIT
charts are consistent with the results of BER shown in Figs. 2(a) and (b).
4 Conclusion
BICM-ID with LDPC code rate of 5/6 was shown by numerical calculations to
improve BER performances of 4-D and 8-D QPSK, so that the power efficiencies of
them respectively get 0.65 dB and 1.0 dB superior to that of Gray-mapped 2-D
QPSK, despite the degradation of non-Gray mappings. And the obtained BER
performances was shown to be consistent with the result of the EXIT chart.
Acknowledgments
This work was supported by JSPS KAKENHI Grant Number 16K06333.
(a) (b)
Fig. 3. EXIT charts. (a) LDPC code rate of 5/6.(b) LDPC code rate of 3/5. The horizontal axis of each figurerepresents input MI of each demodulator and output MI ofdecoder. The vertical axis is vice versa, that is, it representsoutput MI of each demodulator and input MI of decoder.
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Carpet cloaking consisting ofreflectarray with omega-shaped elements
Yuki Fujimotoa), Hiroyuki Deguchi, and Mikio TsujiFaculty of Science and Engineering, Doshisha University,
Miyakodani, Tatara, Kyotanebe, Kyoto 610–0321, Japan
Abstract: This paper presents omega-shaped resonant elements construct-
ing a reflectarray for a carpet cloak. The dimension of a unit cell in the x
and the y directions are dx = dy = 10.0 [mm] and the thickness of dielectric
substrate with permittivity ¥r = 1.67 is h = 5.0 [mm]. We use 12 kinds of
elements at the design frequency 10GHz. To verify usefulness of the
proposed elements, a carpet cloak constructed by them is designed and
fabricated for experimental consideration. The scatterer has a triangular
shape, and the horizontal width and the height are 240 [mm] and 35
[mm], respectively. The effectiveness is verified thorough evaluation of the
calculated and the measured radiation patterns.
Keywords: mircrostrip, reflectarray, infinite periodic array, carpet cloak
Classification: Antennas and Propagation
References
[1] J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,”Science, vol. 312, no. 5781, pp. 1780–1782, 2006. DOI:10.1126/science.1125907
[2] T. Nagayama and A. Sanada, “Planar distributed full-tensor anisotropicmetamaterials for transformation electromagnetics,” IEEE Trans. Microw.Theory Techn., vol. 63, no. 12, pp. 3851–3861, Dec. 2015. DOI:10.1109/TMTT.2015.2487275
[3] L. Y. Hsu, T. Lepetit, and B. Kante, “Extremely thin dielectric metasurface forcarpet cloaking,” Prog. Electromagnetics Res., vol. 152, pp. 33–40, 2015.DOI:10.2528/PIER15032005
[4] A. Wada, Y. Fujimoto, H. Deguchi, and M. Tsuji, “Investigation on carpetcloaking and illusion using metasurface,” Proc. Int. Symp. Antennas andPropagation (ISAP), vol. 1, pp. 186–187, 2016.
1 Introduction
Carpet cloaking is a technology which can make an object on a ground plane
electromagnetically invisible. In 2006, Pendry [1] proposed an approach to design
the invisible cloak by using the technique called transformation optics [2]. Such a
technique can realize invisibility by the cloak consisting of medium with proper
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permittivity and permeability. However, it is difficult to fabricate it because the
constitutive parameter becomes usually high anisotropic. More recently, a cloaking
technology using a reflectarray constructed by resonant elements has been proposed
to overcome this disadvantage of transformation optics [3, 4]. By controlling the
wave propagation through reflecting elements, it is possible to restore the reflection
phase front distorted by a scatterer. In this paper, we propose a carpet cloak using
the reflectarray with Ω-shaped elements. A cloaking device using the reflecting
elements has very thin thickness, so they are especially suitable for cloaking.
Usefulness of the design method and the proposed elements are confirmed by
evaluating radiation properties of the designed carpet cloak numerically and
experimentally.
2 Design method
We design a Ω-type resonant element made of strip conductors at the frequency
10GHz, as indicated in Fig. 1. This element is easy to increase the strip length in a
limited area of the unit cell and has a lot of parameters, so that the ideal reflection-
phase property is relatively obtainable. The parameter values shown in Fig. 1(a)
and (b) are given as follows;
a ¼ 0:5; b ¼ 0:3; c ¼ 0:3; k ¼ 0:25; l ¼ 10:0; h ¼ 5
d; e; m ¼ variable value ½mm�
A carpet cloak which arranges periodically optimized reflecting elements provides
an additional phase to the wavefront to compensate the phase distorted by a
scatterer on the ground plane so that the reflected wave behaves as if there is no
scatterer. We consider here conducting bump with the width w ¼ 240mm and the
hegiht h ¼ 35mm shown in Fig. 2. To reshape the reflection phase front equal to
that from the ground plane, the reflection phase of the reflecting element required at
an arbitrary point on the bump φ is given by
’ðxÞ ¼ �2k0yðxÞ þ ’0 ð1Þwhere k0 is the wavenumber in the free space, yðxÞ is the height from the ground
plane, and ’0 is the reflection phase of the ground plane. When the reflection phase
(a) Front view. (b) Side view.
Fig. 1. Structural drawing of the proposed Ω-shaped reflectingelement.
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determined by (1) is realized on the reflectarray, we can cloak the bump on the
ground plane. Fig. 2 shows the designed structure of the carpet cloak, shapes of
reflecting elements, and the reflection phase properties. It is clear that the reflecting
elements have ideal properties at the design frequency 10GHz. Therefore, arrang-
ing the elements on the bump as shown in Fig. 2, it is expected that they work as
a carpet cloak well.
3 Radiation patterns
To confirm usefulness of the proposed elements, we fabricated reflectarrays work-
ing as the carpet cloak, shown in Fig. 3(a). Fig. 3(b) shows the calculated and the
measured far field radiation patterns for the ground plane, the bump, and the carpet
cloak at 10GHz. The calculated results demonstrate that the proposed carpet cloak
substantially suppresses the scattering from the bump. In addition, the measured
radiation patterns agree well with the calculated radiation patterns, so effectiveness
of the carpet cloak is verified experimentally.
Fig. 2. Designed carpet cloak and reflection characteristics.
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4 Conclusions
We have presented reflecting elements for a carpet cloak and have confirmed that
these elements provide the amount of reflection phase range more than 360° and
have the ideal properties to work as a carpet cloak. A carpet cloak designed by the
proposed elements has been evaluated from radiation patterns through numerical
and experimental considerations. As a result, the measured radiation patterns agree
well with the calculated ones, and effectiveness of the proposed carpet cloak is
verified.
Acknowledgments
This work was supported in part by a Grant-in-aid for Scientific Research (C)
(15K06090) from Japan Society for Promotion of Science.
(a) Fabricated carpet cloak.
(b) Radiation patterns.
Fig. 3. Fabricated carpet cloak and radiation patterns.
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PAPR reduction for OFDMsystems using pilot derivedphase factors
Muhammad Sakir Hossain1a) and Tetsuya Shimamura21 Graduate School of Science and Engineering, Saitama University,
Shimo-okubo, Sakura-ku, Saitama 338–8570, Japan2 Information Technology Center, Saitama University,
Shimo-okubo, Sakura-ku, Saitama 338–8570, Japan
Abstract: In this letter, we propose a novel peak-to-average power ratio
(PAPR) reduction scheme based on orthogonal pilot sequence (OPS) for
orthogonal frequency division multiplexing (OFDM) systems. We change
the pilot symbols’ phases iteratively according to a set of orthogonal
sequences, and use the phases of the pilot subcarriers as the phase factors
for data subcarrier groups. The proposed scheme can achieve up to three
times more PAPR reduction compared to the conventional schemes without
sacrificing side information (SI)-free transmission.
Keywords: OFDM, PAPR, energy efficiency, pilot, spectral efficiency
Classification: Wireless Communication Technologies
References
[1] Y. Rahmatallah and S. Mohan, “Peak-to-average power ratio reduction inOFDM systems: A survey and taxonomy,” IEEE Commun. Surveys Tuts.,vol. 15, no. 4, pp. 1567–1592, 2013. DOI:10.1109/SURV.2013.021313.00164
[2] M. J. Fernandez-Getino Garcia, O. Edfors, and J. M. Paez-Borrallo, “Peak powerreduction for OFDM systems with orthogonal pilot sequences,” IEEE Trans.Wireless Commun., vol. 5, no. 1, pp. 47–51, 2006. DOI:10.1109/TWC.2006.1576525
[3] W.-W. Hu, C.-P. Li, and J.-C. Chen, “Peak power reduction for pilot-aidedOFDM systems with semi-blind detection,” IEEE Commun. Lett., vol. 16, no. 7,pp. 1056–1059, 2012. DOI:10.1109/LCOMM.2012.050412.120482
1 Introduction
Orthogonal frequency division multiplexing (OFDM) is seen as a potential candi-
date waveform of the fifth-generation networks. The major drawback of OFDM is
its high peak-to-average power ratio (PAPR) which degrades bit error rate (BER),
out-of-band radiation, and energy efficiency.
There has been a plethora of solutions suggested to solve this problem. A
survey of the suggested solutions can be found in [1]. Out of these endeavors, most© IEICE 2017DOI: 10.1587/comex.2017XBL0134Received August 29, 2017Accepted September 20, 2017Publicized October 4, 2017Copyedited December 1, 2017
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of the existing schemes are spectrum inefficient because they require to send side
information (SI). To overcome this shortcoming, a promising PAPR reduction
scheme using orthogonal pilot sequence (OPS) is proposed in [2], where the pilot
symbols’ phases are generated according to the Walsh-Hadamard (W-H) sequence.
The phases are changed iteratively to find the lowest-PAPR providing phase set. An
efficient blind phase detection algorithm is proposed which exploits the orthogon-
ality of the pilot symbols’ phases, hence it requires no SI transmission. This
scheme, however, attains low PAPR reduction due to the limited number of OPSs
available in the search space. Since the W-H matrix is a square matrix, the number
of available OPSs in the search space is equal to the number of pilot subcarriers.
Thus, to achieve more PAPR reduction, it requires to use more pilot subcarriers,
which results in the reduction of the subcarriers used for data transmission, causing
in turn spectrum inefficiency. To obtain more PAPR reduction, the W-H sequence is
replaced by a sub-sampled Zadoff-Chu sequence (SZCS) in [3]. This technique
allows using a large number of sequences in the search space, hence achieves more
PAPR reduction. However, it needs to send SI. Furthermore, the computational
overhead of the SZCS scheme is far greater than that of the OPS scheme. Thus, a
rigorous investigation is required to find a scheme which will improve the PAPR
reduction capability of the OPS scheme without sacrificing the no-SI transmission
feature.
2 Proposed scheme
In this letter, we propose a new PAPR reduction scheme, called pilot derived phase
factor (PDPF) scheme, which achieves more PAPR reduction compared to the OPS
and SZCS schemes. It has two forms: modified OPS (MOPS) scheme which is
based on the original OPS scheme [2] and modified SZCS (MSZCS) which uses
SZCS sequence as the orthogonal sequence. While the MOPS does not need SI, the
MSZCS requires. We will refer to the PDPF when something is applicable to both
MOPS and MSZCS; otherwise, each will be referred separately.
The block diagram of the PDPF scheme is shown in Fig. 1. In the PDPF
scheme, the available subcarriers are divided into two groups: data subcarriers and
pilot subcarriers. Suppose that Nd and Np denote the number of data and pilot
subcarriers, respectively. Hence, the total number of subcarriers is N ¼ Nd þ Np.
The input binary data sequence is firstly converted to a vector of complex numbers,
B ¼ ½b1 b2 b3 . . . bNd�T , where T denotes matrix transpose operation, according to
a mapping technique. The mapped data symbols are partitioned into Np disjoint
groups. Suppose that the set G ¼ fg1; g2; g3; . . . ; gNpg consists of all data groups,
where gk ¼ ½gk½1� gk½2� . . . gk½N��T denotes the kth group. The content of the kth
group is given by
gk½l� ¼b� for ðk � 1ÞR þ k � l < ðk � 1ÞR þ � þ k � 1
and ðk � 1ÞR þ � þ k � 1 < l � kR þ k
0 otherwise,
8><>: ð1Þ
where R ¼ Nd
Np, l and k are integers for 0 < l � N and 1 � k � Np, respectively, and
γ is the index of the first zero element of g1. Actually, γ is equal to the lowest value
of l for which g1½l� ¼ 0, indicating the location of the first pilot symbol. The
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parameter ρ is an integer defining the index of a particular element of B, b�, copied
to gk. The relationship between ρ, l and k is defined as
� ¼l � k þ 1 for ðk � 1ÞR þ k � l < ðk � 1ÞR þ � þ k � 1
l � k and ðk � 1ÞR þ � þ k � 1 < l � kR þ k.
�ð2Þ
In MOPS scheme, each group, gk, is then multiplied by the phase factor, qij;k,
where qij;k is the kth element of the jth W-H sequence of the ith group of sequences.
In the first turn, the kth group is multiplied by the kth element of the first W-H
sequence. After the multiplication, the ½ðk � 1ÞR þ � þ k � 1�th symbol of the kth
group is replaced by the kth pilot symbol of the first W-H sequence to form the kth
sub-block. The resulting Np sub-blocks are added together to form a block, S ij,
where i is an integer ranging from 1 to I and I equals to 1 and Np for MOPS and
MSZCS, respectively, and j ¼ 1 for the first W-H sequence. The newly formed
block S ij is then converted to a time-domain (TD) signal by inverse fast Fourier
transform (IFFT). Then PAPR of this TD signal is computed and stored along with
the signal. Afterwards, a new W-H sequence is generated (the increment of j in
Fig. 1 indicates the new sequence generation). Each of the previously formed
groups is multiplied by the respective element of this newly generated W-H
sequence, and all the subsequent operations are carried out as before. This loop
continues until the target PAPR is achieved or the allowable maximum number of
sequence Np is reached. Out of the Np TD signals, the signal having the lowest
PAPR is selected and transmitted. Pertinently, the system PAPR determination
block of Fig. 1 has no function for the MOPS scheme. It is only used by the
MSZCS scheme. The W-H sequence which provides the transmitted signal is
detected at the receiver using the algorithm proposed in [2].
The MOPS is designed to improve PAPR without sending any SI. However, we
can further improve the PAPR using MSZCS in which the no-SI requirement is
compromised. We generate a number of groups of orthogonal sequences using
Zadoff-Chu sequence, and each group consists of Np sequences with each sequence
consisting of Np elements. For I groups, a Zadoff-chu sequence of IN2p elements are
generated, which is followed by a sub-sampling which in turn is followed by an
interleaving. The process of the whole sequence generation is given by
Fig. 1. Block diagram of the PDPF transmitter
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Z½v� ¼ e
ffiffiffi�1p�v2
IN2p ; ð3Þ
where v is an integer ranging from 0 to IN2p. Then, the sub-sampling is carried out.
The uth element of the jth sequence in the ith group is produced using the following
interleaving rule [3]:
Y ij;u ¼ Z½ði � 1ÞNp þ j þ uINp�: ð4Þ
All sequences in a particular group, generated following Eq. (4), are orthogonal to
each other [3].
For a particular group i, the MSZCS scheme works similarly to the MOPS
scheme: for each sequence of the group, it produces a TD signal along with its
PAPR; thereby, each group provides Np TD signals with Np PAPRs. Of them, the
signal having the lowest PAPR is stored, and the next group of SZCS sequences is
tried, which is shown in Fig. 1 by the increment of i. Thus, this procedure gives I
TD signals with PAPR, one from each group. Of them, the lowest-PAPR providing
signal is transmitted, and the index of the group which contributes the transmitted
signal is transmitted as SI. It requires to send log2ðIÞ bits as SI. Since the SI is
usually not included in the OFDM block and is transmitted separately, its trans-
mission does not affect the PAPR of an OFDM signal. Knowing the lowest-PAPR
providing group index, i, the receiver uses the OPS detection algorithm [2] to find
the ith group’s jth sequence which provided the lowest PAPR signal.
3 Performance evaluation
We evaluate the proposed system’s performance in terms of PAPR, BER, and
computational complexity. The simulation parameters are as follows: 64 subcar-
riers, 4 or 8 pilot subcarriers, 4-times oversampling, 3 � 105 OFDM symbols, and
quadrature phase shift keying (QPSK) modulation.
Fig. 2(a) shows the comparative PAPRs of MOPS scheme using complemen-
tary cumulative distribution function (CCDF). It is evident that MOPS can achieve
more PAPR reduction compared to both OPS and SZCS. At a CCDF level of 10�4
with Np ¼ 4, it achieves three times and 40% more PAPR reduction compared to
the OPS and SZCS, respectively, from the original OFDM. It also reveals that the
use of more pilot subcarriers results in more PAPR reduction. PAPR of the MOPS
scheme with Np ¼ 4 is less than that of the OPS and SZCS with Np ¼ 8. Since
using more subcarriers as pilot reduces data subcarriers, MOPS achieves better
spectrum efficiency compared to both schemes. Pertinently, the SZCS achieves
PAPR reduction compromising the no-SI transmission while MOPS does not
compromise it. The PAPR reduction performance of the MSZCS scheme is
investigated in Fig. 2(b) for I ¼ 32. The MSZCS outperforms the SZCS. For
Np ¼ 4, it improves PAPR by 45% compared to the SZCS. When the number of
pilot subcarriers increases, it still outperforms the SZCS by 0.51 dB. One interesting
point is that the PAPR achieved by the SZCS for Np ¼ 8 can be obtained by the
MSZCS using only four pilot subcarriers. Thus, for a given PAPR performance, the
MSZCS is more spectrum efficient. In terms of BER, the PDPF has almost the same
performance as the OPS and SZCS schemes as is revealed from Fig. 2(c). Thus, we© IEICE 2017DOI: 10.1587/comex.2017XBL0134Received August 29, 2017Accepted September 20, 2017Publicized October 4, 2017Copyedited December 1, 2017
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can say that the PDPF improves PAPR significantly without markedly affecting
other performance factors.
In computational complexity comparison, the computations that are common in
all schemes are not considered. Table I gives the computational complexity
comparison, where P ¼ Nlog2ðN Þ þ 4N � 1 and Q ¼ N2log2ðN Þ þ 4N þ 1. MOPS
scheme is found slightly more complex than the OPS scheme in case of multi-
plications. For N ¼ 64, Np ¼ 4, and I ¼ 16 in case of the SZCS scheme, the MOPS
scheme requires 94% and 97% less addition and multiplication operations, respec-
tively, compared to the SZCS scheme. The MSZCS scheme has slightly more
computational complexity compared to the SZCS scheme.
4 Conclusion
In this letter, we proposed a new PAPR reduction scheme for OFDM systems by
using the phases of pilot subcarriers as phase factors. Through simulations, the
Fig. 2. Performance of PDPF based OFDM systems
Table I. Computational complexity comparison
Scheme Additions Multiplications Complex exponential
OPS NpP NpQ �SZCS NpIP NpIðQ þ 3NpÞ N2
pI
MOPS NpP NpðQ þ 2NdÞ �MSZCS NpIP NpIðQ þ 3Np þ 2NdÞ N2
pI
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PDPF scheme was found to be the most PAPR reducing technique. The proposed
MOPS scheme reduced more PAPR than the traditional schemes. The MSZCS
scheme outperformed traditional as well as MOPS in terms of PAPR, with reduced
spectrum efficiency compared to MOPS.
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Highly sensitive Raman gaincoefficient measurement bydetecting spontaneousRaman scattering power fordistributed Ramanamplification systems
Hiroji Masudaa) and Kokoro KitamuraInterdisciplinary Graduate School of Science and Engineering, Shimane University,
1060 Nishikawatsu, Matsue, Shimane 690–8504, Japan
Abstract: We propose a highly sensitive method that can safely measure
the Raman gain coefficient spectrum by detecting the spontaneous Raman
scattering emitted from the transmission fiber pumped by a single-polar-
ization laser-diode light source in distributed Raman amplification systems.
With the proposed method, we have successfully obtained an accurate
Raman gain coefficient spectrum with a significantly low pump power of
∼0.35mW at a small Raman gain of 0.01 dB.
Keywords: distributed Raman amplification, gain coefficient
Classification: Fiber-Optic Transmission for Communications
References
[1] J. Bromage, “Raman amplification for fiber communications systems,” J.Lightw. Technol., vol. 22, no. 1, pp. 79–93, Jan. 2004. DOI:10.1109/JLT.2003.822828
[2] H. Masuda, “Advanced transmission systems using distributed Ramanamplification technologies,” Proc. SPIE, vol. 6012, pp. 601204-1–601204-13,2005. DOI:10.1117/12.633153
[3] H. Masuda, M. Tomizawa, Y. Miyamoto, and K. Hagimoto, “High-performancedistributed Raman amplification systems with limited pump power,” IEICETrans. Commun., vol. E89-B, no. 3, pp. 715–723, 2006. DOI:10.1093/ietcom/e89-b.3.715
[4] H. Takara, H. Ono, Y. Abe, H. Masuda, K. Takenaga, S. Matsuo, H. Kubota, K.Shibahara, T. Kobayashi, and Y. Miaymoto, “1000-km 7-core fiber transmissionof 10 × 96-Gb/s PDM-16QAM using Raman amplification with 6.5W perfiber,” Opt. Express, vol. 20, no. 9, pp. 10100–10105, Apr. 2012. DOI:10.1364/OE.20.010100
[5] H. Masuda and K. Kitamura, “Distributed optical amplification technologies formulticore fiber transmission,” 2016 IEEE Photonics Society Summer TopicalMeeting on SDM for Optical Comm., Newport Beach, USA, pp. 76–77, ME4.2,Jul. 2016. DOI:10.1109/PHOSST.2016.7548735
[6] G. Agrawal, “Theory of Raman amplifiers,” in Raman Amplification in Fiber
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Optical Communication Systems, ed. C. Headley and G. Agrawal, pp. 33–102,Elsevier Academic Press, USA, 2005.
1 Introduction
Distributed Raman amplification (DRA) has been intensely studied as a powerful
technique that can significantly improve the optical signal-to-noise ratios of
optically amplified wavelength-division-multiplexed (WDM) transmission systems
[1, 2, 3]. In recent years, DRA technology has been also applied to some multicore-
fiber transmission systems [4, 5]. In a terrestrial Raman amplified WDM trans-
mission system, which has an optical fiber transmission line installed in the field,
the spectrum of the Raman gain coefficient (g) must be measured in an accurate
and safe manner in order to confirm the feasibility of the system [2, 3]. In the
conventional measurement methods, polarization-multiplexed laser-diode (LD)
pump light sources (LSs) with optical powers greater than ∼100mW were used
to obtain accurate values of g [1, 2, 3]. In this paper, we propose a novel method
that can accurately and safely measure g of a field transmission line using a single-
polarization LD pump with a significantly low and eye-safe power of ∼0.35mW at
a Raman gain as small as 0.01 dB. In the proposed method, we have accurately
obtained g by detecting the spontaneous Raman scattering (SpRS) power emitted
from the transmission fiber.
2 Experimental configuration
The experimental configuration is shown in Fig. 1. Two spools of 20-km single-
mode fiber (G.652.D, SMF-1 and -2) with a total length of 40 km (SMFDUT) were
pumped by a pump LS. The pump LS was a single-polarization LD module for
our proposed method (called “SpRS method” in this paper) or was a polarization-
multiplexed module with two LDs for the conventional pump on–off method
[1, 2, 3]. Each LD had an external cavity configuration with a fiber Bragg grating
(FBG) reflector; thus, the LD is called an “FBG LD.” The wavelength of the pump
LS wavelength was 1455 nm. The distributed Raman gain (G) in units of dB is
defined as the difference in the signal output powers with and without Raman
pumping, Ps;with and Ps;without, respectively, in units of dBm, i.e., G ¼ Ps;with �Ps;without. The signal light was emitted from a tunable light source (TLS). The output
signal power and SpRS power were measured by an optical spectrum analyzer
(OSA, Anritsu MS9740A). A polarization scrambler (PS) was placed after the TLS
to accurately measure the signal light power launched into the OSA by averaging
the states of the signal polarization. The pump light emitted from the pump LS was
coupled to SMFDUT via a wavelength-selective coupler placed after the pump LS
(WSC-b). Then, the pump light emitted from SMFDUT was launched into an optical
power meter (PM) via another wavelength-selective coupler placed after SMFDUT(WSC-f ). The PM was used to monitor the pump power launched into SMFDUT(Ppin). A variable optical attenuator (VOA) was placed after the pump LS to adjust
Ppin. Three optical isolators (ISOs) were placed in the experimental setup in order to
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suppress the excess noise caused by some residual reflections. In the proposed
SpRS method, G is numerically calculated using the measured power of the
spontaneous Raman scattering emitted from SMFDUT (Pn). The values of G
measured by the SpRS method and conventional method are denoted as GSpRS
and Gon-off , respectively.
3 Experimental results
G is expressed as follows when the depletion in the pump power is negligible:
G ¼ ð10= ln 10ÞgLeff Ppin; ð1Þwhere Leff is the effective length [1, 2, 3, 6]. G has a spectral peak at a signal
wavelength (λ) of 1554.0 nm, which was measured using the conventional pump
on–off method so that Gon-off ¼ 3:92 dB at Ppin ¼ 121mW. We further measured
the spectra of GSpRS at several predetermined target values of G (Gtarget) at � ¼1554:0 nm. Gtarget was set to 2, 1, 0.5, 0.2, 0.1, 0.05, 0.02, 0.01, 0.005, 0.002, and
0.001 dB. The target value of Ppin at each value of Gtarget was determined by Eq. (1)
using the set of measured values of Gon-off of 3.92 dB and Ppin of 121mW.
The differential equation for the SpRS power Pn propagating in the axial z
direction in SMFDUT in the case of the SpRS method is given by
dPnðzÞdz
¼ ��nPnðzÞ þ g�ðzÞP�pðzÞPnðzÞ þ 2gP�
pðzÞðNk þ 1Þh�n��n; ð2Þ
where �n is the loss coefficient of the SpRS light; h is Planck’s constant; �p and �n
are the frequencies of the pump light and SpRS light, respectively; ��n is the
bandwidth of the SpRS light; Nk is the phonon occupation number: Nk ¼1=fexp½hð�p � �nÞ=kBT� � 1g; kB is Boltzmann’s constant; T is the absolute tem-
perature; g is the Raman gain coefficient averaged over two polarization states;
g�ðzÞ is the local Raman gain coefficient for single-polarization pumping; and
Pp�ðzÞ is the local power of the pump light with a single polarization state. g�ðzÞ
takes values between go and gp, which are the Raman gain coefficients for the
orthogonal and parallel polarization configurations, respectively [6]. g is equal to
the average of go and gp. We employed the following approximation for g�ðzÞ. It isconsidered that the pump light and SpRS light have fairly randomized polarization
states in SMFDUT. Moreover, the second term on the right-hand side of Eq. (2) has
a small contribution to the calculation when G is small, as in the case of this
experiment: g�ðzÞ ¼ g.
The SpRS power at the output of SMFDUT (Pn;out) was measured by the OSA.
We define Pn;out to be the power at the point (SMFout) just inside the fusion splicing
Fig. 1. Experimental configuration.
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point between SMFDUT and WSC-b (point A in Fig. 1). G and g were obtained by
numerically solving Eq. (2) with the measured powers of Pn;out. The temperature
near SMFDUT was ∼25 °C (T ¼ �298K).
Let the optical power Pn;out at a wavelength of λ be Pn;outð�Þ. The measured
optical spectra of Pn;outð�Þ in dBm at the several values of Gtarget from 2 to 0.001 dB
are shown in Fig. 2(a). The wavelength resolution, the video bandwidth, and the
number of sampling points per nanometer were 0.927 nm, 10Hz, and 10, respec-
tively. The ripples in Pn;outð�Þ in the low-power region of Fig. 2(a) were caused by
the system noise of the OSA, i.e., the noise generated when no light was launched
into the OSA. The depth of each spectral ripple increased as Pn;outð�Þ decreased.The Raman gain spectra obtained by the SpRS method (GSpRSð�Þ) that were
obtained from the measured Pn;outð�Þ spectra are shown in Fig. 2(b) at the same
values of Gtarget from 2 to 0.001 dB. The ripples in GSpRSð�Þ in the low-gain region
are straightforwardly attributed to the ripples in Pn;outð�Þ (Fig. 2(a)).Fig. 3 shows characteristics of G and g. We obtained the spectral peak gain
(GSpRS;peak) as the average value from 1553.5 to 1554.5 nm. Let the relative gain
accuracy at � ¼ 1554:0 nm at each target gain Gtarget in percent be �Grel ¼ððGSpRS;peak=GtargetÞ � 1Þ � 100. Moreover, let the maximum and minimum gains
in the wavelength range from 1553.5 to 1554.5 nm be Gmax and Gmin, respectively.
Let the relative spectral gain variation at � ¼ 1554:0 nm at each target gain Gtarget in
percent be �Gspec ¼ ðGmax � GminÞ=GSpRS;peak � 100. �Grel and �Gspec are plotted
as a function of Gtarget in Fig. 3(a). As shown in the figure, the absolute value of
�Grel increased as Gtarget decreased. Moreover, �Gspec increased as Gtarget decreas-
ed. This is because the depths of the ripples in the Pn;outð�Þ spectra (Fig. 2(a))
increased as Gtarget decreased. The absolute values of both �Grel and �Gspec
increased as Gtarget decreased and were as small as less than 5% in the Gtarget
range from 2 to 0.001 dB. Moreover, the relative accuracy of and the spectral
variation in g (�grel and �gspec) at � ¼ 1554:0 nm in percent are equal to those of G,
Fig. 2. Spectral characteristics of (a) the spontaneous Raman scatteringpower and (b) the Raman gain measured using the SpRSmethod for target gain values from 2 to 0.001 dB.
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�Grel and �Gspec, as shown in Fig. 3(a), because of the relation between G and g
in Eq. (1).
GSpRS and Gon-off as a function of the measured pump power (Ppin0) are shown
in Fig. 3(b) for Gtarget from 2 to 0.001 dB. Ppin0 was measured at the optical-
connector splicing point between the VOA and WSC-b (point B in Fig. 1). Gon-off
was measured for Gtarget from 2 to 0.5 dB, whereas GSpRS was measured for Gtarget
from 2 to 0.001 dB. The Raman gains calculated using Eq. (1) (Gc) are also shown
in Fig. 3(b). As shown in Fig. 3(b), the three gains, Gon-off , GSpRS , and Gc, show
good coincidence.
The spectra of g were calculated by Eq. (1) using the measured Raman gains
GSpRS shown in Fig. 2(b) and Ppin and are shown in Fig. 3(c) for typical values of
Gtarget of 0.1, 0.01, 0.005, 0.002, and 0.001 dB. The spectral peak value of g at
each value of Gtarget (gðGtargetÞ) was normalized by that of g(0.1 dB) and added to
the shifts of 0.4, 0.3, 0.2, 0.1, and 0 (without a shift) for Gtarget ¼ 0:1, 0.01, 0.005,
0.002, and 0.001 dB, respectively. The spectral peak value of g(0.1 dB) was
0.44 km−1·W−1. The values of Ppin0 from the pump LS launched into WSC-b were
3.5, 0.35, and 0.035mW at Gtarget ¼ 0:1, 0.01, and 0.001 dB, respectively. There-
fore, we can obtain the g spectra at significantly lower pump powers using the
proposed SpRS method compared with the conventional method, which requires
pump powers greater than ∼100mW. When GSpRS ranged from 0.1 to 0.001 dB
(from 2.3% to 0.023% on a linear scale), GSpRS was so small that the amplification
of the SpRS light was negligible. As for the typical performance of the proposed
SpRS method, we obtained an accurate g spectrum at a small value of Ppin0 of
Fig. 3. Raman gain (G) and gain coefficient (g) characteristics: (a)relative differences of G and g, (b) G as a function of the pumppower, and (c) normalized spectra of g.
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0.35mW with GSpRS ¼ 0:01 dB, which is more than ∼100 times smaller than that
needed for the conventional method (more than ∼100mW), with �gspec ¼ 0:7%
and �grel ¼ 2:9% (Fig. 3(a)).
4 Conclusion
We have proposed a novel method that can accurately and safely measure the
Raman gain coefficient spectrum by detecting the spontaneous Raman scattering
power emitted from a transmission fiber. With the proposed method, we have
successfully obtained an accurate Raman gain coefficient spectrum using a single-
polarization LD pump LS with a significantly low and eye-safe power of
∼0.35mW at a Raman gain as low as 0.01 dB.
Acknowledgments
The authors thank Mr. Atsushi Moritaka for his technical assistance during the
experiment. This work was supported in part by JSPS KAKENHI, Grant Number
JP16K06355.
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Error analysis of ephemeriscalibration for dual-satelliteTDOA/FDOA geolocation
Takeshi Amishimaa) and Nobuhiro SuzukiInformation Technology R&D Center, Mitsubishi Electric Corporation,
5–1–1 Ofuna, Kamakura, Kanagawa 247–8501, Japan
Abstract: In this paper, we provide a theoretical error analysis of a satellite
ephemeris calibration for the dual-satellite TDOA/FDOA geolocation meth-
od. First, the error covariance matrix for the ephemeris calibration is derived.
Then, the result is incorporated into the error covariance matrix for geo-
location. The derived equation is numerically evaluated to provide an
intensive error analysis in time and spatial coordinates. Further, Monte Carlo
simulation results are provided, and it is shown that the theoretical results
coincide with the Monte Carlo simulation results.
Keywords: ephemeris, geolocation, TDOA/FDOA
Classification: Sensing
References
[1] D. P. Haworth, N. G. Smith, R. Bardelli, and T. Clement, “Interferencelocalization for eutelsat satellites -the first European transmitter locationsystem,” Int. J. of Sat. Comm., vol. 15, pp. 155–183, 1997. DOI:10.1002/(SICI)1099-1247(199707/08)15:4<155::AID-SAT577>3.0.CO;2-U
[2] H. Yan, J. K. Cao, and L. Chen, “Study on location accuracy of dual-satellite,”ICSP, pp. 107–110, 2010. DOI:10.1109/ICOSP.2010.5656806
[3] T. Pattison and S. I. Chou, “Sensitivity analysis of dual-satellite geolocation,”IEEE Trans. Aerosp. Electron. Syst., vol. 36, no. 1, pp. 56–71, 2000. DOI:10.1109/7.826312
[4] T. Amishima, et al., “Satellite orbit determination by time and frequencydifferences of arrival of multiple reference stations,” IEICE Society Conf.,B-2-7, 2006.
[5] T. Amishima, et al., Japanese Patent Application, No. 2006-241903.[6] A. Gelb, ed., “Applied Optimal Estimation,” the M.I.T. Press, Cambridge, 1974.[7] F. R. Hoots and R. L. Roehrich, “Spacetrack Report No. 3: Models for
Propagation of NORAD Element Sets,” 1988/12.
1 Introduction
In satellite communications, uplink interference from unknown emitters has be-
come one of the major issues. In [1], the authors have proposed a method based on
the dual-satellite TDOA/FDOA localization technique to locate unknown emitters
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on the earth surface. The proposed method utilizes a priori knowledge on satellite
orbital information. In [2, 3], the authors have pointed out that accurate satellite
ephemeris information is essential for the localization accuracy. To improve
accuracy, an ephemeris calibration method is proposed in [4, 5]. As shown in
Fig. 1, the authors utilize multiple known emitters and estimate the ephemerides
of two satellites simultaneously. However, although this method seems promising,
the authors have not provided any theoretical error bound for the calibration
accuracy. Therefore, it requires a trial-and-error analysis to evaluate the resulting
geolocation accuracy when the calibrated information is used. Error analysis in time
and spatial coordinates has been of special interest to estimate the system design. In
this paper, we provide an intensive theoretical error analysis. First, we derive the
ephemeris calibration error covariance matrix. Second, we incorporate it into the
geolocation error covariance matrix. By evaluating the proposed equations, we
show the calibration performance both in time and spatial coordinates.
2 Ephemeris calibration error covariance matrix for TDOA/FDOA-
based geolocation
2.1 Satellite ephemeris calibration
The position and velocity vectors of the two satellites at time tk are defined as
�k ¼ ½pTs1;k vTs1;k pTs2;k vTs2;k�T . Given the multiple known emitters, the so-called
references, the TDOA/FDOA measurement model is described as follows:
�ð�kÞ ¼1
cfkpr;k � ps1;kk � kpr;k � ps2;kk � kpr0 � ps1;kk þ kpr0 � ps2;kkg; ð1Þ
fð�kÞ ¼1
�
vTs1;kðpr;k � ps1;kÞkpr;k � ps1;kk
� pTs2ðpr;k � ps2;kÞkpr;k � ps2;kk
� vTs1;kðpr0 � ps1;kÞkpr0 � ps1;kk
þ vTs2;kðpr0 � ps2;kÞkpr0 � ps2;kk
� �: ð2Þ
Here, pr;k is a known reference position at time tk, c is the speed of light, and λ is
the wavelength. Note that Eqs. (1) and (2) have the form of a differential. The
reference position pr0 will be used for geolocation as well as to cancel ephemeris
errors and unknown time and frequency shifts at the satellites [1]. Further, we
define the ephemeris vectors of the two satellites by � ¼ ½�T s1 �T s2�T and �si ¼½Mo;si esi Asi !o;si �o;si io;si�T , where Mo;si, esi, Asi, !o;si, �o;si, and io;si are
true anomaly, eccentricity, semi-major axis, argument of perigee, right ascension of
Fig. 1. Ephemeris calibration.
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the ascending node, and inclination, respectively [7]. Since �k is a function of � and
tk, we can express �ð�kÞ and fð�kÞ as �kð�Þ and fkð�Þ. Then, using the definitions
above, we solve the following optimization problem [4, 5]:
�̂ ¼ argmin�
XKk¼1
ð�obs;k � �kð�ÞÞTV�1ð�obs;k � �kð�ÞÞ; ð3Þ
�obs;k ¼�obs;k
fobs;k
" #; �kð�Þ ¼
�kð�Þfkð�Þ
" #; V ¼
�2� 0
0 �2f
" #; ð4Þ
where �obs;k is the vector of the TDOA and FDOA observation values �obs;k and
fobs;k at time tk, �kð�Þ is the corresponding observation model, V is the error
covariance matrix whose diagonal elements are the variances �2� and �2
f of the
TDOA and FDOA measurement errors, respectively.
2.2 Deriving the ephemeris calibration error covariance matrix
By following the method in [6] and after solving the optimization problem in
Eq. (3), the ephemeris error covariance matrix P� can be expressed by the
following equation:
P� ¼ Efð� � �̂Þð� � �̂ÞTg ¼XKk¼1
GTk ð�ÞV�1Gkð�Þ
" #�1; Gkð�Þ ¼
r��kð�ÞTr�fkð�ÞT
" #; ð5Þ
where Ef:g is the expectation operator and b: is the estimated value. The detailed
expression of Gkð�Þ is omitted due to space limitation and can be found in [5]. The
error covariance matrix P�k of the position-velocity vector �k can be defined as
follows:
P�k ¼ Efð�k � �kð�̂ÞÞð�k � �kð�̂ÞÞTg ¼ G�!�kP�GT�!�k
; ð6ÞG�!�k ¼ r�xs1;kð�Þ � � � r� _zs1;kð�Þ r�xs2;kð�Þ � � � r� _zs2;kð�Þ
� �: ð7Þ
A detailed expression of Eq. (7) is described in [5]. Using Eqs. (6) and (7), the
error equations ERRsi;pos;k and ERRsi;vel;k for positions and velocities of the two
satellites i at time tk are obtained as follows:
ERRsi;pos;k ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXn¼6ði�1Þþ1;...;6ði�1Þþ3
P�kðn; nÞs
; ERRsi;vel;k ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXn¼6ði�1Þþ4;...;6i
P�kðn; nÞs
: ð8Þ
2.3 Incorporating ephemeris calibration error covariance matrix into
geolocation error covariance matrix
In the following, we omit the time index k because the geolocation requires only a
single set of TDOA and FDOA and no multiple sets as we have seen for the
ephemeris calibration. The position vector of the unknown emitter location pint is
estimated using the position and velocity vectors psi and vsi of the two adjacent
satellites and by simultaneously solving the following equations with the constraint
that the unknown emitter is located on the earth surface:
�ðpint; �Þ ¼1
cfkpint � ps1k � kpint � ps2k � kpr0 � ps1k þ kpr0 � ps2kg; ð9Þ
fðpint; �Þ ¼1
�
vTs1ðpint � ps1Þkpint � ps1k
� vTs2ðpint � ps2Þkpint � ps2k
� vTs1ðpr0 � ps1Þkpr0 � ps1k
þ vTs2ðpr0 � ps2;kÞkpr0 � ps2k
� �: ð10Þ
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Note that (9) and (10) are both functions of pint and � since the sensitivity function
is derived from both parameters. Further, we define the error deviation of the
satellite positions and velocities by ��. Denote the sensitivity function from �� to
the deviations in τ and f, by �� and �f. Further, we denote the gradient of � by r�.
The first-order expansion is obtained by the following equations:
��ðpint; �Þ ¼ ½r��Uðpint; �ÞT � r��Uðpr; �ÞT ��� ≐ F1ðpint; �Þ��; ð11Þ�fðpint; �Þ ¼ ½r�fUðpint; �ÞT �r�fUðpr; �ÞT��� ≐ F2ðpint; �Þ��; ð12Þ
r��Uðp; �Þ ¼
�1
c
p � ps1kp � ps1k03�1
1
c
p � ps2kp � ps2k03�1
266666664
377777775; ð13Þ
r�fUðp; �Þ ¼
1
�� vs1kp � ps1k
þ vTs1ðp � ps1Þkp � ps1k3
ðp � ps1Þ� �
1
�
p � ps1kp � ps1k
�1
�� vs2kp � ps2k
þ vTs2ðp � ps2Þkp � ps2k3
ðp � ps2Þ� �
�1
�
p � ps2kp � ps2k
26666666666664
37777777777775: ð14Þ
Random errors due to thermal noise are denoted by n� and nf, and their variance are
�2n� ¼ Efn2�g and �2nf ¼ Efn2fg, respectively. The error vector �vðpint; �Þ is definedas:
�vðpint; �Þ ≐��ðpint; �Þ þ n�
�fðpint; �Þ þ nf
" #: ð15Þ
Subsequently, its covariance matrix Rvðpint; �Þ isRvðpint; �Þ ¼ Ef�vðpint; �Þ�vTðpint; �Þg
¼F1ðpint; �ÞP�F
T1 ðpint; �Þ þ �2
v� F1ðpint; �ÞP�FT2 ðpint; �Þ
F2ðpint; �ÞP�FT1 ðpint; �Þ F2ðpint; �ÞP�F
T2 ðpint; �Þ þ �2
vf
" #:
ð16Þ
The sensitivity of �vðpint; �Þ is determined by the deviation �pint. The gradient with
respect to pint is denoted by rpint . The first-order expansion is then given as follows:
�vðpint; �Þ ¼ rpint�ðpint; �Þ rpintfðpint; �Þ� �T
�pint ≐ GT ðpint; �Þ�pint; ð17Þ
rpint�ðpint; �Þ ¼1
c
pint � ps1kpint � ps1k
� pint � ps2kpint � ps2k
� �; ð18Þ
rpintfðpint; �Þ ¼1
�
vs1kpint � ps1k � vs1
T ðpint � ps1Þkpint � ps1k3
ðpint � ps1Þ� �
� 1
�
vs2kpint � ps2k
� vs2Tðpint � ps2Þ
kpint � ps2k3ðpint � ps2Þ
� �:
ð19Þ
The coordinate transformation from the two-dimensional earth surface coordinates
xsurf � ysurf to earth-centered earth-fixed coordinates [7] is defined by BðpintÞ.Then, Eq. (17) can be expressed as follows:
© IEICE 2017DOI: 10.1587/comex.2017XBL0133Received August 29, 2017Accepted September 20, 2017Publicized October 6, 2017Copyedited December 1, 2017
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�vðpint; �Þ ¼ GT ðpint; �ÞBðpintÞ�xint;surf ; ð20Þwhere �xint;surf is a deviation in position on the earth surface. With Pint;surf ¼Ef�xint;surf �xint;surf Tg, Eq. (16), and Eq. (21), the geolocation error covariance
matrix Pint;surf becomes:
Pint;surf ¼ ððGTðpint; �ÞBðpintÞÞTR�1v ðpint; �ÞðGT ðpint; �ÞBðpintÞÞÞ�1: ð21Þ
The error equation for geolocation is obtained as follows:
ERRint;surf ≐ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPint;surf ð1; 1Þ þ Pint;surf ð2; 2Þ
p: ð22Þ
As shown in Eq. (16), the ephemeris error covariance matrix is incorporated in the
error equation for geolocation.
3 Errors analysis of ephemeris calibration and geolocation
3.1 Simulation setting
In this section, we numerically evaluate theoretical error bounds in time and spatial
coordinates. We assume two geostationary satellites located at 158E and 162E,
respectively. The orbital elements are obtained via NORAD resources [7]. The
TDOA and FDOA accuracy is 1 µs and 1mHz, respectively. The reference
locations are Tokyo, Kobe, Sapporo, and Fukuoka whose uplink frequencies are
14GHz. Tokyo is set as pr0. The measurement interval and the measurement time
length are 10min and 24 h, respectively. The calibrated orbital elements are used
for computing the orbit for geolocation at a specified time. For error analysis in
time coordinates, we fix the location of the unknown emitter at Niigata, and the
geolocation is conducted every 20min. Both theoretical and Monte Carlo simu-
lations of 1000 trials are evaluated. For error analysis in spatial coordinates, we fix
the orbital time at 12 h and evaluate the theoretical error for the region around Japan
and its surrounding seas.
3.2 Simulation results
Figs. 2(a)–(c) show the calibration and geolocation errors versus time. (a) and (b)
show the #1 and #2 satellites’ position and velocity errors, and (c) the geolocation
error. In (d) and (f ), the theoretical geolocation error map is shown. (d) shows the
error map without calibration and (e) with calibration. In (f ), the difference between
with and without calibration is shown.
From (a) and (b), we first note that the theoretical and Monte Carlo results are
in good agreement. Therefore, the derived equation can be applied to evaluate
calibration and geolocation performances. From (c), we notice periodic peaks every
12 h. This is because the TDOA and FDOA lines align parallel to each other during
this points in time. The resulting locations cause a large error along the two lines.
Similar results are discussed in [1].
Comparing (d) and (e), we confirm that by using the calibration results, the
error has been reduced at all mentioned locations on earth. Further, the closer the
reference station, the more the geolocation error is reduced. This is due to the
satellite ephemeris-error-canceling effect by using known reference emitters. Re-
garding (f ), it is worthwhile to mention that the farther the region from the
reference position, the larger the difference in geolocation error. This implies that
© IEICE 2017DOI: 10.1587/comex.2017XBL0133Received August 29, 2017Accepted September 20, 2017Publicized October 6, 2017Copyedited December 1, 2017
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IEICE Communications Express, Vol.6, No.12, 667–672
in regions with a marginal canceling effect, the ephemeris error causes a large
geolocation error. Therefore, calibration is crucial in these regions.
4 Conclusion
In this paper, we have provided a mathematical foundation to predetermine the
performance of the dual-satellite geolocation system. First, we have derived the
ephemeris calibration error covariance matrix and incorporated it into the geo-
location error covariance matrix. Based on the theoretical result, we showed the
ephemeris calibration performance both in time and spatial coordinates. The results
coincide with the Monte Carlo simulation results.
(a) (b)
(c) (d)
(e) (f)
Fig. 2. Calibration error vs. time for (a) Satellite #1, (b) Satellite #2,(c) Geolocation error, (d) Geolocation error map withoutephemeris calibration [km], (e) Geolocation error map withephemeris calibration [km], (f ) Difference between with andwithout ephemeris calibration [km].
© IEICE 2017DOI: 10.1587/comex.2017XBL0133Received August 29, 2017Accepted September 20, 2017Publicized October 6, 2017Copyedited December 1, 2017
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Fundamental study on almostperiodic frequencyarrangements for super-multi-access radiocommunication systems
Isao Nakazawaa) and Ken UmenoGraduate School of Informatics, Kyoto University,
Sakyo-ku, Kyoto 606–8501, Japan
Abstract: In this paper, we investigate the almost periodic frequency
arrangement (APFA) asynchronous system for super-multi-access radio
systems, and APFA configuration procedure on a frequency domain multi-
plex scheme by using almost periodic function (APF). We report on the
relationship between the total number of prime numbers, the number of
sub-carriers, and the normalized frequency standard deviation for a system
with up to one million users. By using computer simulations, we show the
multi-carrier modulation and asynchronous demodulation based on APFA,
in which ICI interference by nonlinear elements is improved compared with
the orthogonal frequency-division multiplexing (OFDM).
Keywords: chaotic spreading sequence, almost periodic function, almost
periodic frequency arrangement, super-multi-access radio communication
system
Classification: Wireless Communication Technologies
References
[1] K. Umeno, “Spread spectrum communications based on almost periodicfunctions: Almost periodic code approach versus chaotic code approach forcommunications,” IEICE Tech. Report, NLP2014-62, pp. 87–90, Oct. 2014.
[2] T. Naohara and K. Umeno, “Performance analysis of super dense multiple access(SDMA) communications systems using almost periodic function codes,” IEICETech. Report, NLP2014-101, pp. 11–16, Dec. 2014.
[3] I. Nakazawa, K. Umeno, “Almost periodicity frequency arrangement andapplication to satellite communication system,” IEICE Tech. Report, vol. 115,no. 178, CCS2015-33, pp. 23–26, Aug. 2015.
[4] I. Nakazawa and K. Umeno, “Performance evaluation of wideband radiocommunication systems using almost periodic frequency arrangement,” Proc. ofICSGTEIS 2016, Bali, Oct. 2016. DOI:10.1109/ICSGTEIS.2016.7885765
[5] H. Weyl, “Uber die Gleichverteilung von Zahlen mod. Eins,” Math. Ann.,vol. 77, pp. 313–352, Sept. 1916. DOI:10.1007/BF01475864
© IEICE 2017DOI: 10.1587/comex.2017XBL0135Received September 4, 2017Accepted September 21, 2017Publicized October 12, 2017Copyedited December 1, 2017
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1 Introduction
To face an age of the Internet of things (IoT) and machine to machine (M2M)
communication, the transition to multi-layered, heterogeneous, and seamless net-
works will form a foundation for future of the communication systems.
Recently, chaotic spreading codes generated by almost periodic functions
(APFs) were reported to be advantageous for super-multi-access communication
systems [1, 2]. Simulations were performed for applications to satellite communi-
cations and it was shown that the almost periodic frequency arrangement (APFA)
has different characteristics compared to periodic signals. More recently, we
reported on the applicability of the APFA method for radio communication systems
[3, 4].
In this paper, we explain the fundamentals, method of modulation and demod-
ulation, and features of APFA generated by the Weyl function [5]. Since APFA is
specified based on the reference frequency allocation, it is also possible for an
arrangement to have an orthogonal frequency-division multiplexing (OFDM) fre-
quency allocation or an arbitrary frequency allocation. The normalized frequency
standard deviation (�M) of the frequency difference between the reference and the
APF frequency is used to represent their degree of similarity. Moreover, by using
simulations we show that inter-carrier interference (ICI) is significantly reduced by
more than 3 dB of suppression as compared to that in the OFDM scheme.
2 Application of the APF to the frequency band
APFs were first introduced in the study of spread spectrum communications in
2014 [1], where the functions for generating spreading sequence were studied
originally in 1924, by H. Bohr as an extension of conventional periodic functions as
represented below.
jfðx þ �Þ � fðxÞj � "; ð1Þwhere fðxÞ is a complex function, x is a real parameter, and τ is a distance from x
on fðxÞ that belongs to ε as a positive number. In the case of " ¼ 0, Eq. (1)
corresponds to the condition for periodic functions. The minimum value of the
period τ is called the fundamental period. Features of spread spectrum communi-
cation based on APF function and the performance of super multiple access
communication system using APF codes were presented previously [1, 2].
Therefore, we attempt to generalize the Weyl sequence to show a uniform
distribution that is the same as that of the Weyl function shown in this paper.
The Weyl sequence using an irrational number generated from the power root
of a prime number is expressed by the following equation.
xlðk; pÞ ¼ ffiffiffipk
p � l ðmod 1Þ ðl ¼ 1; 2; � � � ; LÞ; ð2Þwhere k is a natural number of root, p is an arbitrary prime number, and l is a
natural number. The amplitude distribution of xlðk; pÞ is uniformly distributed over
½0; 1Þ, where the parenthesis ð Þ is an open interval and the bracket ½ � is a closedinterval. We have chosen prime numbers as an index to maintain independence
amongst the power root sequence of natural numbers. By extending (2), a uniform
distribution with a real number r instead of a natural number l can be expressed by
the formula.
© IEICE 2017DOI: 10.1587/comex.2017XBL0135Received September 4, 2017Accepted September 21, 2017Publicized October 12, 2017Copyedited December 1, 2017
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xkðr; pÞ ¼ ffiffiffipk
p � r ðmod 1Þ: ð3ÞThe number �ðN Þ of prime numbers less than or equal to a natural number N is
expressed by the well-known prime number theorem as follows.
�ðN Þ � N= lnðN Þ; ð4Þwhere lnðN Þ is the Napierian logarithm. Here, defined as PN :¼ �ðN Þ, hereafter it isexpressed in PN . While Eq. (4) is not a particularly good approximation, however it
is sufficient for simulations of performance evaluation of the APFA in terms of the
number of prime numbers.
The probability of prime gaps �p between two successive prime numbers is
shown in Fig. 1(a), where the PN ¼ 5 � 108. In the figure, the vertical axis
represents the probability Prð�pÞ on a logarithmic scale and the data are dispersed
with respect to linear regression line. The center line of the data is a straight red line
obtained by the linear regression, as follows.
Prð�pÞ ¼ 10�0:003��p�0:75; ð�p ¼ 1; 2; 4; 6 � � �Þ ð5ÞThen, the standard deviation �p of prime gaps �p is 6.58 from Fig. 1(a).
The distribution of the Weyl APF sequence generated from the prime number
sequence is important in determining the APFA.
In this paper, we define APF frequency (APFF) using (3) as below.
fkðpÞ ¼ ffiffiffipk
p ðmod 1Þ: ð6ÞThe APFF fkðpÞ is almost discrete, and uniformly distributed over the normalize
frequency band ð0; 1Þ in (6). Fig. 1(b) shows the probability mass function (PMF)
of adjacent APFF intervals corresponding to scatter diagrams of adjacent APFF
with k ¼ 2. Here, the logarithmic scales are used for both the vertical and horizontal
axes and the number of prime numbers is PN , where PN ¼ 5 � 106. Figs. 1(c) and
1(d) show that the PMF of adjacent APFF intervals with k ¼ 3 and 5, respectively.
(d) PMF of APFF intervals(c) PMF of APFF intervals
(b) PMF of APFF intervals(a) PMF of prime gaps (Δp)
Fig. 1. Probability of prime gaps and PMF of APFF intervals.
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3 APFA configuration procedure
The APFA suggested here is generated with reference to a target frequency which
can be arranged at arbitrary intervals of a normalized frequency range (FR) being
greater than 0, and less than 1, and by selecting the sub-carrier frequency fm close
to the k-th root of the target number of prime numbers.
The closeness of the selected almost periodic frequency to the normalized
frequency, can be evaluated by the frequency standard deviation (�M) of difference
from the target frequency arrangement (TFA).
The procedure for determining the M and �M of APFA is as follows.
Step 1. Determine the number of sub-carriers M
The communication capacity of the system is determined by the trans-
mission rate and the number of sub-carriers M.
Step 2. Determine the �M of difference from the TFA.
The closeness of the selected almost periodic frequency to the TFA
means that the peak-to-average power ratio (PAPR) is near to the PAPR
of OFDM as �M decreases as mentioned [4].
Therefore, the �M of APFA are determined from the PAPR design target.
Step 3. The natural numbers N and k for obtaining the k-th root are determined
from M, the PN and the �M selected at step 1 and step 2.
The Fig. 2(a) shows an example of the TFA of OFDM.
Here, M is the number of sub-carriers, fm is the m-th sub-carrier and �f is
1=M.
The m-th sub-carrier frequency of the TFA of OFDM is given by the following
expression.
fm ¼ 1
Mm � 1
2M; ð1 � m � M Þ: ð7Þ
Using the target frequency fm, the deviation of each APFA frequency �fkðm; PNÞis shown in (8).
APFFkðm; PNÞ is defined by minp2PN
jfkðpÞ � fmj, where p has been taken from all
the prime numbers less or equal to PN .
�fkðm; PNÞ ¼ fm � APFFkðm; PNÞ: ð8ÞTherefore, the APFA frequency standard deviation �Mðk; PNÞ can be calculated
by the following equation.
�Mðk; PNÞ ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPMm¼1
f�fkðm; PNÞg2
M
vuuut: ð9Þ
Figs. 2(b) and 2(c) show the relation between PN , number of channels M and
the standard deviation �Mðk; PNÞ obtained by using the APFA scheme. From these
data, we obtained a common approximation of APFA frequency standard deviation
�M ðk; PNÞ that holds regardless of k from data according to the following
expression as shown in (10).
�Mðk; PNÞ ¼ 10�0:9719�log10ðPN�64=MÞþ1:635;M < 1;000;000; ð10ÞFrom Fig. 2(b), Fig. 2(c) or (10), the PN can be determined from the desired
�MðkÞ and M. Here, up to one million sub-carriers M can be applied as shown in
Fig. 2(b) and Fig. 2(c).
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4 APFA characteristics
Multi-carrier communication systems arranged at frequencies represented by the
OFDM method are known to have an inter-carrier interference (ICI) caused by the
deterioration of sub-carrier orthogonality that can result from hardware imperfec-
tion. We evaluated the ICI of the OFDM and APFA system using computer
simulations. Fig. 3(a) shows the constellations of the transmission signal of a
sub-carrier frequency configuration. Here, �T is the standard deviation of trans-
mission signal TXðtÞ in (11). Here, Coded is a modulation code and �d is a phase
shift for user d due to asynchronism of the APFAs.
TXðtÞ ¼XMd¼1
Codedej2�APFFkðd;PN Þtþj�d : ð11Þ
For the demodulation, we use the same APFF as the transmission system and detect
the code of the modulation from the complex cross correlation ρ with the receiving
signal RxðtÞ and reference signal SmðtÞ.
�ðRx; S�mÞ ¼
1
Tm
R Tm0ðRxðtÞ; S�mðtÞÞdt
1
Tm�
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR Tm0ðRxðtÞ; R�
x ðtÞÞdtq
�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR Tm0ðSmðtÞ; S�mðtÞÞdt
q : ð12Þ
Here,
RxðtÞ ¼XMm¼1
Iej2�ffiffiffiffipm
kp
t;
SmðtÞ ¼ ej2��APFFkðm;PNÞ�t;Tm ¼ dM � APFFkðm; PNÞe=APFFkðm;PNÞ;d e means ceiling function;� means complex conjugate:
In multi-carrier communication schemes such as OFDM, a very large peak of
signals is inevitably generated by the combination of codes to be transmitted. The
sub-carrier is degraded by ICI due to saturation of the transmitting amplifiers. The
transmission signal TX 0ðtÞ at output of the transmitter is then given by (13), where s
is ratio of the saturation level and �T of transmission signal TXðtÞ.
(a) Target of frame structure (0-1)
(b) APFA frequency standard deviation (c) APFA frequency standard deviation
Fig. 2. Relation between PN, M, and �MðkÞ.
© IEICE 2017DOI: 10.1587/comex.2017XBL0135Received September 4, 2017Accepted September 21, 2017Publicized October 12, 2017Copyedited December 1, 2017
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jTX 0ðtÞj ¼ jTXðtÞj ; jTXðtÞj <¼ s�T
s�T ; jTXðtÞj > s�T
�: ð13Þ
The ICI-ratio of the intermodulation products of the OFDM and APFA method is
expressed as shown in (14). Here, iOm and jOm are the n-th real part and imaginary
part of sub-carrier vector by saturation amplifier in the OFDM, iAm and jAm are in
the APFA by saturation amplifier, and IOm, JOm, IAm, or JAm are the m-th real or
imaginary part without saturation amplifier respectively.
ICI-ratio ¼ 10 � log
PMm¼1
½ðiOm � IOmÞ2 þ ðjOm � JOmÞ2�PMm¼1
½ðiAm � IAmÞ2 þ ðjAm � JAmÞ2�
0BBB@
1CCCA ½dB�: ð14Þ
We evaluated the ICI-ratio (in dB) of the OFDM and APFA systems using
computer simulations. Fig. 3(b) shows ICI-ratio of the OFDM to the APFA due
to saturation of levels s ¼ 1:1, 1.3, and 1.5 for the cases of 64 to 131,072 sub-
carriers. The ICI of APFA system shows more than 3 dB improvement, which is
much better than that of the OFDM system with 64 to 131,072 sub-carriers. This
shows that APFA asynchronous systems are generally more robust than synchro-
nous OFDM systems coming from asynchronous characteristic.
5 Conclusion
We investigate the APFA asynchronous system for super-multi-access radio com-
munication. We applied an APFA configuration procedure to a frequency domain
multiplex scheme by using APFs. We determined the relationship between �ðN Þ,number of sub-carriers M, and the normalized frequency standard deviation
�Mðk; �ðN ÞÞ for a system of up to one million users. By using computer simulations
we showed that ICI of APFA method is fairly reduced with more than 3 dB
suppression as compared to that in the standard OFDM method.
(b) ICI-ratio (in dB) of the OFDM and APFA systems using computer simulations
(a) Constellations of transmission signal of sub-carrier frequency configuration.
Fig. 3. Standard deviation of ICI due to saturation level with 64 to131,072 sub-carriers.
© IEICE 2017DOI: 10.1587/comex.2017XBL0135Received September 4, 2017Accepted September 21, 2017Publicized October 12, 2017Copyedited December 1, 2017
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