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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
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
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
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
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
[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
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.
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
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.
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.
[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
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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
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
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
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[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
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[6] G. Agrawal, “Theory of Raman amplifiers,” in Raman Amplification in Fiber
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
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
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.
�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.
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
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
�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
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
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
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.