ieice communications express, vol.6, no.12, 633

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

a) [email protected]

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

© IEICE 2017DOI: 10.1587/comex.2017XBL0120Received August 3, 2017Accepted August 31, 2017Publicized September 13, 2017Copyedited December 1, 2017

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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


635


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.


638


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


b) [email protected]

c) [email protected]

d) [email protected]

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

© IEICE 2017DOI: 10.1587/comex.2017XBL0116Received July 21, 2017Accepted August 31, 2017Publicized September 19, 2017Copyedited December 1, 2017

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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


641


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.


644


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

© IEICE 2017DOI: 10.1587/comex.2017XBL0123Received August 8, 2017Accepted September 6, 2017Publicized September 20, 2017Copyedited December 1, 2017

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http://dx.doi.org/10.1109/26.957394

http://dx.doi.org/10.1109/26.957394

http://dx.doi.org/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

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.


647


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.


649


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.


650


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

© IEICE 2017DOI: 10.1587/comex.2017XBL0132Received August 28, 2017Accepted September 7, 2017Publicized October 4, 2017Copyedited December 1, 2017

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http://dx.doi.org/10.1126/science.1125907



http://dx.doi.org/10.1109/TMTT.2015.2487275





http://dx.doi.org/10.2528/PIER15032005

http://dx.doi.org/10.2528/PIER15032005

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.


654


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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http://dx.doi.org/10.1109/TWC.2006.1576525




http://dx.doi.org/10.1109/LCOMM.2012.050412.120482





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


656


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


657


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

658


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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http://dx.doi.org/10.1117/12.633153

http://dx.doi.org/10.1117/12.633153

http://dx.doi.org/10.1117/12.633153

http://dx.doi.org/10.1093/ietcom/e89-b.3.715





http://dx.doi.org/10.1364/OE.20.010100

http://dx.doi.org/10.1364/OE.20.010100

http://dx.doi.org/10.1364/OE.20.010100

http://dx.doi.org/10.1364/OE.20.010100

http://dx.doi.org/10.1364/OE.20.010100

http://dx.doi.org/10.1109/PHOSST.2016.7548735




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


662


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.


663


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.


664


�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.


665


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.


666


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


667


http://dx.doi.org/10.1002/(SICI)1099-1247(199707/08)15:4<155::AID-SAT577>3.0.CO;2-U








http://dx.doi.org/10.1109/ICOSP.2010.5656806




http://dx.doi.org/10.1109/7.826312

http://dx.doi.org/10.1109/7.826312

http://dx.doi.org/10.1109/7.826312

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.


668


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


669


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:


670


�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


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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].


672


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

673


http://dx.doi.org/10.1109/ICSGTEIS.2016.7885765




http://dx.doi.org/10.1007/BF01475864

http://dx.doi.org/10.1007/BF01475864

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.


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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.


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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.


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ieice communications express, vol.6, no.12, 633

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