ieice communications express, vol.4, no.11, 317 320 ... · structure is the multiple assignment...

Optimal multiple assignmentscheme for strongly secureramp secret sharing schemeswith general accessstructures*

Ryutaroh Matsumotoa)

Dept. of Communications and Computer Engineering, Tokyo Institute of Technology,

Meguro-ku, Tokyo 152–8550, Japan

a) [email protected]

Abstract: Iwamoto et al. proposed the strong security definition for ramp

secret sharing schemes with general access structures, and also proposed an

integer optimization approach to construct a secret sharing with the smallest

share size and general access structure, based on a threshold secret sharing

scheme. This note proves that if the underlying threshold scheme is strongly

secure then the constructed multiple assignment scheme gives a strongly

secure secret sharing scheme.

Keywords: secret sharing, access structure, strong security

Classification: Fundamental Theories for Communications

References

[1] A. Shamir, “How to share a secret,” Commun. ACM, vol. 22, no. 11,pp. 612–613, Nov. 1979. DOI:10.1145/359168.359176

[2] D. R. Stinson, Cryptography Theory and Practice, 3rd ed., Chapman & Hall/CRC, 2006.

[3] G. R. Blakley and C. Meadows, “Security of ramp schemes,” Advances inCryptology–CRYPTO’84, Lecture Notes in Computer Science, vol. 196,pp. 242–269, Springer-Verlag, 1985. DOI:10.1007/3-540-39568-7_20

[4] H. Yamamoto, “Secret sharing system using (k, l, n) threshold scheme,”Electronics and Communications in Japan (Part I: Communications), vol. 69,no. 9, pp. 46–54, 1986 (the original Japanese version published in 1985).DOI:10.1002/ecja.4410690906

[5] W. Ogata, K. Kurosawa, and S. Tsujii, “Nonperfect secret sharing schemes,”Advances in Cryptology – AUSCRYPT ’92, Lecture Notes in ComputerScience, vol. 718, pp. 56–66, Springer-Verlag, 1993. DOI:10.1007/3-540-57220-1_52

[6] M. Iwamoto and H. Yamamoto, “Strongly secure ramp secret sharing schemesfor general access structures,” Inf. Process. Lett., vol. 97, no. 2, pp. 52–57,Jan. 2006. DOI:10.1016/j.ipl.2005.09.012

[7] M. Ito, A. Saito, and T. Nishizeki, “Multiple assignment scheme for sharingsecret,” J. Cryptol., vol. 6, no. 1, pp. 15–20, March 1993. DOI:10.1007/

+The same manuscript was submitted to an unrefereed domestic conference 38th Symposium on InformationTheory and its Applications (SITA2015) Kojima, Okayama, Japan, Nov. 24–27, 2015.

© IEICE 2015DOI: 10.1587/comex.4.317Received September 15, 2015Accepted October 6, 2015Published November 4, 2015

317

IEICE Communications Express, Vol.4, No.11, 317–320

http://dx.doi.org/10.1145/359168.359176

http://dx.doi.org/10.1145/359168.359176

http://dx.doi.org/10.1145/359168.359176

http://dx.doi.org/10.1007/3-540-39568-7_20

http://dx.doi.org/10.1007/3-540-39568-7_20

http://dx.doi.org/10.1007/3-540-39568-7_20

http://dx.doi.org/10.1002/ecja.4410690906



http://dx.doi.org/10.1007/3-540-57220-1_52

http://dx.doi.org/10.1007/3-540-57220-1_52

http://dx.doi.org/10.1007/3-540-57220-1_52

http://dx.doi.org/10.1007/3-540-57220-1_52

http://dx.doi.org/10.1016/j.ipl.2005.09.012






http://dx.doi.org/10.1007/BF02620229

http://dx.doi.org/10.1007/BF02620229

BF02620229[8] M. Iwamoto, H. Yamamoto, and H. Ogawa, “Optimal multiple assignments

based on integer programming in secret sharing schemes with general accessstructures,” IEICE Trans. Fundamentals, vol. E90-A, no. 1, pp. 101–111, Jan.2007. DOI:10.1093/ietfec/e90-a.1.101

[9] M. Nishiara and K. Takizawa, “Strongly secure secret sharing scheme withramp threshold based on Shamir’s polynomial interpolation scheme,” Trans.IEICE, vol. J92-A, no. 12, pp. 1009–1013, Dec. 2009. http://ci.nii.ac.jp/naid/110007483234/en

[10] R. J. McEliece and D. V. Sarwate, “On sharing secrets and Reed-Solomoncodes,” Commun. ACM, vol. 24, no. 9, pp. 583–584, Sept. 1981. DOI:10.1145/358746.358762

1 Introduction

Secret sharing (SS) [1] is a cryptographic scheme to encode a secret to multiple

shares being distributed to participants, so that only qualified sets of participants

can reconstruct the original secret from their shares. A set of participants is called

forbidden if the set has absolutely no information about the secret. A secret sharing

scheme is called perfect [2] if every set of participants is always qualified or

forbidden. If a set is neither qualified or forbidden in a secret sharing scheme, the

scheme is said to be ramp or non-perfect. A set is said to be intermediate if it is

neither qualified nor forbidden. A merit of the ramp schemes is to reduce share

size (the number of bits) while keeping the secret size [3, 4, 5]. A drawback of

ramp schemes is that part of the secret can be known to an intermediate set of

participants. To exclude such a possibility, Yamamoto and Iwamoto [4, 6] defined

the notion of strong security for the ramp schemes.

On the other hand, traditionally, the access structure called the threshold

structure has been the most focused one, where a set of participants is qualified

if and only if the number of participants is �t. A scheme with a threshold structure

is called a threshold scheme. A well-known method to realize an arbitrary access

structure is the multiple assignment scheme proposed by Shamir [1] and named by

Ito et al. [7]. It assigns multiple shares of a threshold scheme to single participant,

and a single share can be assigned to multiple participants.

Ito et al. [7] did not consider to minimize the share size. Later, Iwamoto et al.

[8] proposed an integer optimization approach to construct a secret sharing scheme

with the minimum share size based on a threshold scheme. Despite they proposed

the strong security criterion, they did not considered the strong security property of

their proposal [8]. This note shows that if the underlying threshold scheme is

strongly secure in the sense of [6] then the scheme constructed by [8] is also

strongly secure.

2 Notation and the main lemma

Let q be a prime power, and Fq the finite field with q elements. In this note we

assume that secret and all shares are vectors over Fq. We will define the access

structure when there are n participants and secret consists of L symbols in Fq. Let Vi


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http://dx.doi.org/10.1145/358746.358762

http://dx.doi.org/10.1145/358746.358762

http://dx.doi.org/10.1145/358746.358762

http://dx.doi.org/10.1145/358746.358762

be the random variable of the i-th share for i ¼ 1; . . . ; n, and S the random variable

of the secret. We assume the uniform probability distribution of S. The encoding

rule of a secret sharing scheme is a conditional joint probability distribution of

ðV1; . . . ; VnÞ given secret S. The encoding rule determines a joint probability

distribution of ðS; V1; . . . ; VnÞ. For a set T, 2T denotes its power set fT0 j T0 is a

subset of Tg, and we have j2T j ¼ 2jTj. For i ¼ 0; . . . ; L, we define Ai � 2f1;...;ng by

Ai ¼ fA � f1; . . . ; ng j IðS; ðVjÞj2AÞ ¼ ig;where Ið�; �Þ is the mutual information in logq. We assume

2f1;...;ng ¼[L

i¼0Ai:

The collection A0; . . . ;AL is called the access structure. Recall that secret S is a

random variable on FLq . Let Si be the i-th component of S. A given secret sharing

scheme is said to be strongly secure [6] when A 2 Ai, B � f1; . . . ; Lg and jBj ¼L � i implies IððSjÞj2B; ðVkÞk2AÞ ¼ 0.

The multiple assignment map was introduced in [1] and named in [7], which is

reviewed in the following. It constructs a secret sharing scheme with n participants

from that with m participants. Usually the underlying secret sharing scheme is a

threshold scheme. The original scheme and the constructed scheme have the same

secret denoted by a uniform random variable S on FLq . Let W1; . . . ; Wm be the shares

of the original scheme. A multiple assignment map is a map Φ from f1; . . . ; ng to

2f1;...;mg. In the new constructed secret sharing scheme, the i-th participant receives

fWj j j 2 �ðiÞg as his/her share, which is denoted by Vi. Denote the access

structure of the original scheme by Aold0 ; . . . ;Aold

L , and that of the new constructed

scheme by Anew0 ; . . . ;Anew

L .

Main Lemma: If the original secret sharing scheme generating W1; . . . ; Wm is

strongly secure then the constructed scheme is also strongly secure.

Proof: Let Vi be the i-th share of the new constructed scheme, and Anew �f1; . . . ; ng represent a set of shares Vi. Since Vi consists of W1; . . . ; Wm, the set

Aold ¼[

i2Anew

�ðiÞ

is the set of original shares corresponding to the set Anew of the new shares. For a

set B � f1; . . . ; Lg, we have the equality

IððViÞi2Anew ; ðSjÞj2BÞ ¼ IððWiÞi2Aold ; ðSjÞj2BÞ;which implies

Anew 2 Anewi , Aold 2 Aold

i : ð1ÞEquation (1) and the strong security of the original scheme generating W1; . . . ; Wm

imply the strong security of the new constructed scheme. ■

3 How to construct strongly secure optimal multiple assignment

scheme

Nishiara and Takizawa [9] proved that the McEliece-Sarwate ramp secret sharing

scheme [10] is strongly secure. The McEliece-Sarwate scheme satisfies the defi-


319


nition of ðt; L; mÞ-ramp secret sharing scheme required in [8 Section 5]. Therefore

one can apply Iwamoto et al.’s proposal [8] to the McEliece-Sarwate scheme.

Iwamoto et al.’s proposal [8] generates a multiple assignment scheme that is

optimal in the sense that it minimizes the share sizes. By the main lemma proved

in this note, one can see that the constructed ramp secret sharing scheme is strongly

secure.

Acknowledgment

The author would like to thank Prof. Mitsugu Iwamoto for helpful discussion. This

research is partly supported by the Japan Society for the Promotion of Science

Grant Nos. 23246071 and 26289116.


320


Receiver positioning usingreceived signal strength

Chuanxue Jin, Xiaoning Huanga), Zhi Chen, and Wanbin TangNational Communications Lab., University of Electronic Science and Technology

of China, Chengdu 611731, China


Abstract: In wireless positioning, estimating the location of a receiver is

extremely challenging since the receiver does not transmit signal and it is

invisible to sensors. To deal with the issue, we proposes a received signal

strength (RSS)-based method to position the receiver based on the signal

from the corresponding transmitter. Our results indicate that the proposed

method has about 20∼40 meters positioning error in average, which reaches

the same level of the positioning error as the conventional RSS-based Tx

positioning methods.

Keywords: estimation, receiver, RSS, wireless positioning

Classification: Sensing

References

[1] G. Mao and B. Fidan, Localization algorithms and strategies for wireless sensornetworks, 2009.

[2] X. Li, “RSS-based location estimation with unknown path loss model,” IEEETrans. Wireless Commun., vol. 5, no. 12, pp. 3626–3633, Dec. 2006. DOI:10.1109/TWC.2006.256985

[3] R. M. Vaghefi, M. R. Gholami, R. M. Buehrer, and E. G. Strom, “Cooperativereceived signal strength-based sensor localization with unknown transmitpowers,” IEEE Trans. Signal Process., vol. 61, no. 6, pp. 1389–1403, Mar.2013. DOI:10.1109/TSP.2012.2232664

[4] R. Zhang, “On active learning and supervised transmission of spectrum sharingbased cognitive radios by exploiting hidden primary radio feedback,” IEEETrans. Commun., vol. 58, no. 10, pp. 2960–2970, Oct. 2010. DOI:10.1109/TCOMM.2010.082710.090412

[5] E. Azzouz and A. Nandi, Automatic modulation recognition of communicationsignals, 2010.

[6] B. Ramkumar, “Automatic modulation classification for cognitive radios usingcyclic feature detection,” IEEE Circuits Syst. Mag., vol. 9, no. 2, pp. 27–45,Jun. 2009. DOI:10.1109/MCAS.2008.931739

[7] A. H. Sayed, A. Tarighat, and N. Khajehnouri, “Network-based wirelesspositioning: challenges faced in developing techniques for accurate wirelesslocation information,” IEEE Signal Process. Mag., vol. 22, no. 4, pp. 24–40,Jul. 2005. DOI:10.1109/MSP.2005.1458275

[8] 3GPP TR 25.814, “Physical layer aspects for evolved universal terrestrial radioaccess (UTRA),” 2006.

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http://dx.doi.org/10.1109/MCAS.2008.931739




http://dx.doi.org/10.1109/MSP.2005.1458275




1 Introduction

Positioning an unknown node has been extensively studied in the past decades [1],

which is the essential technique for location-aware applications. Fig. 1(a) provides

a conventional wireless positioning scenario: some fixed sensors with known

locations (called anchors) measure the transmitted signal from an unknown node

(called target), then they estimate the location of the target. In existing literatures,

positioning algorithms include received signal strength (RSS) [2, 3], time of arrival

(TOA), time difference of arrival (TDOA), angle of arrival (AOA), etc. However,

they all belong to transmitter positioning technique since they treat the unknown

transmitter as the target.

In contrast, few contributions discuss receiver positioning technique since the

receiver works in a passive way and it is invisible to sensors, i.e., the receiver does

not transmit signal during the reception1. Therefore, receiver positioning becomes

extremely challenging. This significantly impedes the development of the location-

aware applications.

In this paper, we proposes an RSS-based receiver positioning method under the

scenario2 that multiple transmitters communicate with a common receiver using

time division multiple access (TDMA) protocol. In the proposed method, we treat

the multiple transmitters as the anchors, and position the receiver by estimating the

transmitter-to-receiver (Tx-Rx) distances, i.e., Anchor-Rx distances. It is reason-

able to treat those transmitters as the anchors as the location of the transmitters can

be obtained using the conventional transmitter positioning methods [1]. Regarding

the Tx-Rx distance estimation, our method exploits the close-loop power control

Fig. 1. System model.

1Even though the receiver may feedback information to its transmitter, it goes through another frequency band infrequency division duplex (FDD) systems. Thus, the receiver is still invisible (or silent) to the sensors since thefeedback channel may not be known to the sensors.2Even though this letter considers the many-to-one scenario, the proposed method can also be used in the point-to-point scenario when the transmitter is moving. This is because during the geographic travel of the transmitter, thesensors can obtain multiple locations of the transmitter as well as the corresponding distances to the receiver.


322


(CLPC) between the transmitters and the receiver, which has been widely used in

modern wireless communication systems. Under CLPC, the power adjustment of

the transmitters actually carries the Tx-Rx distance information. Therefore, by

measuring the transmission power of the transmitters, the sensors are able to

estimate the Tx-Rx distances and then obtain the location of the corresponding

receiver.

2 System model

Fig. 1(b) provides the system model of this paper, where M transmitters (labeled as

Tx), a receiver (labeled as Rx), and N sensors are uniformly distributed on a disk

with the radius R. Here, we denote li as the distance between the i-th Tx (denoted as

Txi) and the receiver, and dij as the distance between the i-th Tx and the j-th sensor

(denoted as Sensorj). In particular, we assume that the Txi’s location and the

corresponding Txi-Sensorj distances dij are known to the sensors. Next, we provide

the signal models for the Tx-Rx and Tx-Sensor links, respectively.

• Tx-Rx Links: We denote gi and qiðkÞ as the path-loss and shadowing

coefficients between the Txi and the Rx, where the former is modeled as gi ¼ C=l�i(C is a constant and α is the path-loss coefficient) and the latter follows log-normal

distribution with the standard deviation of δ. Here, k (1 � k � K) is the index of

independent shadowing. In static scenarios, we have K ¼ 1 during the positioning.

In time-varying scenarios, the shadowing coefficient varies with time, and then the

Txi and the Rx experiences K > 1 independent shadowing coefficients during the

positioning.

Let pi as the transmission power of the Txi, then the average SNR of the Rx

served by the Txi can be expressed as �iðkÞ ¼ pigiqiðkÞ, where the variance of the

noise at the Rx is normalized. When we consider the system with CLPC3, the Txiautomatically adjusts the transmission power to meet a certain target SNR at the Rx,

denoted as Γ4. Then, the transmission power of Txi can be obtained by

pi ¼ �

giqiðkÞ : ð1Þ

• Tx-Sensor Links: Similarly, we denote g0ij and q0ijðkÞ as the path-loss and

shadowing coefficients between the Txi and the Sensorj, which follow the same

model as in Tx-Rx links, then the average SNR at the Sensorj can be expressed as

� 0ijðkÞ ¼ pig0ijq

0ijðkÞ; ð2Þ

where the variance of the noise at the Sensorj is normalized. When adopting the

path-loss model g0ij ¼ C=d�ij and substituting (1) into (2), we can rewrite (2) as

� 0ijðkÞ ¼ �q0ijðkÞqiðkÞ

lidij

� ��

: ð3Þ

3Since this paper focuses on proposing the basic idea of Rx positioning, we consider the perfect CLPC [4], wherethe quantization error and time delay are not considered.4Even though Γ is the target SNR of the Rx, it can still be obtained by the Sensorj using blind signal processingtechnique, e.g., recognizing the modulation level of the Txi’s signal and obtaining the corresponding target SNR[5, 6].


323


3 RSS-based receiver positioning

3.1 Estimate the Tx-Rx distance

In this subsection, we first design a ML estimator to let each sensor obtain the Txi-

Rx distance. To facilitate the derivation, we rewrite (3) using dB unit and then

obtain the average SNR at the Sensorj as

� 0ij½dB�ðkÞ ¼ 10� log10lidij

� �þ q0ij½dB�ðkÞ � qi½dB�ðkÞ þ �½dB�: ð4Þ

Here, li is the unknown Tx-Rx distance to be estimated. q0ij½dB�ðkÞ and qi½dB�ðkÞare independent shadowing coefficients, which follow normal distribution in dB

unit, i.e., q0ij½dB�ðkÞ � Nð0; �2Þ and qi½dB�ðkÞ � Nð0; �2Þ. Then, we have q0ij½dB�ðkÞ �qi½dB�ðkÞ � Nð0; 2�2Þ.

If the sensor can obtain K average SNR with independent shadowing coef-

ficients, then we can obtain the K-dimension conditional probability density

function (PDF) as

f � 0ij½dB�ð1Þ; . . . ; � 0ij½dB�ðKÞjli

� � ¼ YKk¼1

e��0 ij½dB�ðkÞ�10� log10

�lidij

��½dB�

4�2ffiffiffiffiffiffi4�

p�

: ð5Þ

Using the standard maximum likelihood distance estimator, then the Sensorjcan obtain the Txi-Rx distance as

li ¼ dij � 101

10K�

PKk¼1

ð� 0ij½dB�ðkÞ��½dB�Þ: ð6Þ

Like other RSS-based distance estimators, the estimation in (6) is biased, i.e.,

Eflig ¼ E dij � 101

10K�

PKk¼1

ð� 0ij½dB�ðkÞ��½dB�Þ8<:

9=; ¼ li � e

�2

K�2 ; ð7Þ

where � ¼ 10K�= ln 10. By modifying the estimator, we can obtain the unbiased

estimation as follows

li ¼ dij � e��2

K�2 � 101

10K�

PKk¼1

ð� 0ij½dB�ðkÞ��½dB�Þ: ð8Þ

3.2 Positioning the receiver

Once we obtain the Tx-Rx distance, positioning the receiver becomes easy. Here,

we adopt the conventional linear method to estimate the Rx location [7]. Specif-

ically, we first derive the positioning method for one sensor, denoted as Sensorj,

and then obtain the Rx location using N sensors.

Let ðx0; y0Þ and ðxi; yiÞ as the locations of the Rx and Txi, respectively, where

i ¼ 1; 2; . . . ; M. We further let Di ¼ xi2 þ yi

2, then we have

HX ¼ b; ð9Þwhere

H ¼ðx2 � x1Þ ðy2 � y1Þ

..

. ...

ðxM � x1Þ ðyM � y1Þ

264

375; X ¼ x0

y0

� �; b ¼ 0:5

D2 � D1 � ðl22 � l21Þ...

DM � D1 � ðl2M � l21Þ

264

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DOI: 10.1587/comex.4.321Received June 12, 2015Accepted June 26, 2015Published November 11, 2015

324


Once solving the equation (9), we can obtain the location of the Rx as

X ¼ x0

y0

" #¼ ðHTHÞ�1HTb: ð10Þ

When we consider N sensors that can share their distance estimations, they can

obtain the average Tx-Rx distance by

�li ¼ 1

N

XNj

lðjÞi : ð11Þ

Substituting �li into (10), we can obtain the Rx’s location more accurately.

4 Simulation results

In this section, we demonstrate the performance of the proposed RSS-based

receiver positioning method. Here, M Txs, a Rx, and N sensors are uniformly

distributed on the disk with the radius R ¼ 100m. In the simulation, the system

bandwidth is B ¼ 10MHz, the power spectrum density of the noise is N0 ¼�174 dBm, and the target SNR of the Rx is � ¼ 10 dB. In wireless channels,

C ¼ �128:1 dB and � ¼ 3:76 are adopted according to [8]. Furthermore, 104

Monte Carlo trails are conducted for each simulation curve.

To evaluate the positioning performance, we define the root-mean-square error

(RMSE) as RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðx0 � x0Þ2 þ ðy0 � y0Þ2

p.

In Fig. 2, we consider the static scenario, where K ¼ 1. We assume that the

number of Txs M ¼ 10 in Fig. 2(a) and the number of sensors N ¼ 10 in Fig. 2(b).

From the two figure, we find that the number of Txs (M) dominates the RMSE as

the number of sensors (N) is larger than 5, i.e., N � 5. This is because we treat the

Tx as anchor and more anchors result in a better performance. In addition, we

compare the curves with different standard deviations of the shadowing. The

RMSE reduces as the standard deviation δ decreases from 6 to 2. This is because

the small δ introduces less uncertainty into the wireless channel.

Fig. 3 illustrates the RMSE of the proposed method versus the number of

independent shadowing coefficients (K), where M ¼ 10 Txs and N ¼ 10 sensors

are considered. Here, when K > 1, it is the time-varying scenario, which means that

Fig. 2. Impact of N and M on the RMSE of Rx positioning.


325


each node experiences K independent shadowing coefficients during the Rx

positioning. From the figure, the RMSE reduces as K increases from 1 to 20.

The reason is that the uncertainty of the shadowing can be reduced by considering

multiple independent shadowing coefficients. In particular, the proposed method

has about 20∼40m positioning error, where the Rx is uniformly located on a disk

with the radius 100m. This means that the proposed Rx positioning method

actually reaches the same level of the positioning error as the conventional RSS-

based Tx positioning methods. For example, the method in [2] has about 6m

positing error, where the Tx is uniformly located on a disk with the radius 20m.

5 Conclusions

In this paper, we proposed an RSS-based receiver positioning method to estimate

the location of an unknown receiver. Different from existing RSS-based position-

ing, our method treated the associated transmitters as the anchors, and conducted

the positioning by estimating the distances between the anchors and the receiver.

The simulation results showed the effectiveness of the proposed method.

With our method, the location-aware applications can be extended to many

scenarios. For example, a scenario where multiple wireless networks may share the

same frequency band, the proposed method enables one system to locate the other

base stations. This provides the crucial information for co-channel interference

management.

Acknowledgments

This paper is supported in part by the grant from Science and Technology on

Information Transmission and Dissemination in Communication Networks Labo-

ratory and by the National Natural Science Foundation of China (NS-FC) under

Grants 61271169.

Fig. 3. Impact of K on the RMSE of Rx positioning.


326


A simultaneous conjugate-matching algorithm forN-element array antennas

Kazuhiro Hondaa), Kazuki Kaga, Kun Li, and Koichi OgawaGraduate School of Engineering, Toyama University,

3190 Gofuku, Toyama-shi, Toyama 930–8555, Japan


Abstract: This paper presents an automatic impedance-matching algorithm

that can sequentially realize a simultaneous conjugate-matching state for all

the elements in an N-element array antenna. The analytical results show that

the converged solution obtained from the proposed algorithm agrees well

with the solution calculated by the analytical deterministic equation, con-

firming the validity of the proposed method. The method can be applied to

MIMO array antennas.

Keywords: simultaneous conjugate-matching, sequential algorithm,

MIMO array antenna

Classification: Antennas and Propagation

References

[1] K. Ogawa, T. Hayashi, and A. Yamamoto, “An analysis of frequencycharacteristics of a parallel dipole MIMO antenna considering the effects ofimpedance matching circuit,” IEICE Trans. Commun., vol. J92-B, no. 9,pp. 1416–1430, Sep. 2009.

[2] B. K. Lau, J. B. Andersen, G. Kristensson, and A. F. Molisch, “Impact ofmatching network on bandwidth of compact antenna arrays,” IEEE Trans.Antennas Propag., vol. 54, no. 11, pp. 3225–3238, Nov. 2006. DOI:10.1109/TAP.2006.883984

[3] K. Kagoshima, S. Takeda, A. Kagaya, and K. Ito, “Design and analysis ofdecoupling and matching feeding networks for array antennas,” IEICE Trans.Commun., vol. J97-B, no. 9, pp. 699–713, Sep. 2014.

[4] K. Kagoshima, T. Tanaka, S. Obote, and Y. Ichikawa, “Determination methodfor matched load impedance of a receiving array antenna,” IEICE Trans.Commun., vol. J90-B, no. 5, pp. 543–546, May 2007.

[5] J. W. Wallace and M. A. Jensen, “Termination-dependent diversity performanceof coupled antennas: network theory analysis,” IEEE Trans. Antennas Propag.,vol. 52, no. 1, pp. 98–105, Jan. 2004. DOI:10.1109/TAP.2003.822444

[6] K. Kaga, K. Li, K. Honda, and K. Ogawa, “A sequential automatic impedance-matching algorithm to achieve simultaneous complex-conjugate condition inmulti-element antennas,” IEEE International Workshop on Electromagnetics,Sapporo, Japan, PO1.12, pp. 24–25, Aug. 2014. DOI:10.1109/iWEM.2014.6963617

[7] K. Ogawa, T. Matsuyoshi, and K. Monma, “An analysis of the performance ofa handset diversity antenna influenced by head, hand and shoulder effects at© IEICE 2015

DOI: 10.1587/comex.4.327Received September 4, 2015Accepted October 15, 2015Published November 16, 2015

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900MHz: part I— effective gain characteristics,” IEEE Trans. VehicularTechnol., vol. 50, no. 3, pp. 830–844, May 2001. DOI:10.1109/25.933316

1 Introduction

In mobile terminals, degradation of throughput occurs because of the bio-electro-

magnetic effects generated between the users and the terminal. In [1], it is reported

that the multiple-input multiple-output (MIMO) antenna applied to the conjugate-

matching, denoted as CM in [1], has a higher channel capacity compared with the

self-matching condition, denoted as Z11 in [1], when the bandwidth is less than

�1% with an antenna separation of 0:05� (see Figs. 16 and 17 in [1]). In the LTE

systems, the frequency bandwidth is 20MHz, which is 1% for the center frequency

of 2GHz. Therefore, the conjugate-matching is advantageous to the LTE MIMO

systems to increase the channel capacity.

In [2], it is reported that the matching efficiency of the multiport conjugate

match is higher than that of the input impedance match (see Fig. 10 in [2]), in

which the input impedance match is equivalent to the conjugate-matching intro-

duced in [1]. Therefore, the matching efficiency of the conjugate-matching will be

lower than that of the multiport conjugate match. However, the multiport conjugate

match needs to be applied to both transmitting and receiving sides simultaneously.

Thus, we use the conjugate-matching because it can be achieved only at receiving

side.

The methods described in [2, 3, 4, 5] must determine the analytical solution for

non-linear equation to achieve the conjugate-matching. However, it is difficult for a

MIMO mobile terminal to achieve the conjugate-matching using the analytical

method because self and mutual impedances are needed to analyze the non-linear

equation. Moreover, self and mutual impedances may be affected significantly

when the terminal is used in the vicinity of the human body or the metal object.

Therefore, a sequential method for achieving the conjugate-matching is required.

In this paper, we propose an optimum algorithm that can sequentially realize

simultaneous conjugate-matching state for all the elements in an N-element array

antenna [6]. The validity of the proposed method was verified, which indicates that

our algorithm can be applied to MIMO array antennas.

2 Automatic matching algorithm

Fig. 1 shows the structure of an N-element array antenna including an impedance

matching circuit (MC). In Fig. 1, ZLk and Zink (k ¼ 1 � N) indicate the complex

impedance at the load side and at the antenna side, respectively.

The purpose of the proposed method is to achieve a conjugate match ZLk ¼Zink

� in each element, where the asterisk (�) denotes the complex conjugate. The

following procedure demonstrates the proposed algorithm when N ¼ 2:

1. Determine Zin1 (ZL2 ¼ 50Ω as an initial value).

2. Make ZL1 ¼ Zin1� by adjusting MC1.

3. Determine Zin2.© IEICE 2015DOI: 10.1587/comex.4.327Received September 4, 2015Accepted October 15, 2015Published November 16, 2015

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http://dx.doi.org/10.1109/25.933316

4. Make ZL2 ¼ Zin2� by adjusting MC2.

5. Back to the step 1 to determine Zin1.

Step 1 to Step 5 is repeated until jZLk � Zink�j < " (ε: Residual target).

Although the procedure mentioned above is exemplified for N ¼ 2, the proposed

method can be applied to any number of elements. For example, when N ¼ 3, the

algorithm can be used by adding the following two steps between Step 4 and

Step 5: Determine Zin3, Make ZL3 ¼ Zin3� by adjusting MC3.

Using the abovementioned algorithm, simultaneous conjugate-matching state

for all the elements in an N-element array antenna is possible, irrespective of the

structure of the array antenna.

3 Realization of the proposed algorithm

In order to realize the proposed algorithm, the circuit configuration mounted on a

terminal needs to be clarified. Fig. 2 shows the configuration of matching circuit for

one element. The matching circuit (MC1) of the antenna #1 is shown in detail, and

that of the other antennas is not shown for simplicity. The matching circuit shown

in Fig. 2 is a typical example because the circuit configuration may change

depending on the type of antenna. To achieve the conjugate-matching, the complex

impedances ZLk and Zink (k ¼ 1 � N), as shown in Fig. 1, are needed. In Fig. 2, the

complex impedances can be obtained by extracting signals from the three ports (A1,

B1 and C1) using two directional couplers and a switch SW1.

The voltage reflection coefficient �in1 with respect to the reference-plane (a)

between MC1 and antenna #1 shown in Fig. 2, is calculated from Eq. (1),

�in1 ¼ V1Ar

V1Atð1Þ

where the voltage V1At is a transmission voltage that is applied to MC1 from the

source Vg1A, and it is measured at port C1 when SW1 selects SA. The voltage V1Ar is

a reflection voltage flowing from the antenna #1 to MC1, and it is measured at port

Fig. 1. Proposed method of a sequential automatic impedance-match-ing.


329


A1 when SW1 selects SA. Then the complex impedance Zin1 can be calculated using

Eq. (2),

Zin1 ¼ Z01 þ �in1

1 � �in1ð2Þ

where Z0 ¼ 50Ω.

On the other hand, the voltage reflection coefficient �L10 with respect to the

reference-plane (a)B shown in Fig. 2, is calculated from Eq. (3),

�L10 ¼ V1Br

V1Btð3Þ

where the voltage V1Bt is a transmission voltage that is applied to MC1 from the

source Vg1B, and it is measured at port A1 when SW1 selects SB and Vg1A ¼ 0. The

voltage V1Br is a reflection voltage flowing from MC1 to the source Vg1B, and it is

measured at port B1 when SW1 selects SB and Vg1A ¼ 0. To achieve the conjugate-

matching, the voltage reflection coefficient �L1 with respect to the reference-plane

(a) in Fig. 2 should be evaluated, which can be calculated using �L10 from Eq. (3),

as shown in the following equation,

�L1 ¼ �L10e�j2�c ð4Þ

where �c is the phase shift value of the directional coupler between the reference-

plane (a) and (a)B in Fig. 2, where the insertion loss of the directional coupler is

assumed to be negligibly small. Then the complex impedance ZL1 can be calculated

using Eq. (5).

ZL1 ¼ Z01 þ �L1

1 � �L1ð5Þ

Using the circuit configuration shown in Fig. 2, the proposed algorithm can be

realized. The experimental verification will be addressed in future studies.

4 Analytical verification of the proposed method

An investigation was carried out using the method of moments with half-wave-

length dipole antennas at 900MHz. Fig. 3(a) shows the configuration of the array

when N ¼ 2, 3, and 4 in a square arrangement. The element spacing d was set to

Fig. 2. Configuration of a matching circuit.


330


2 cm (0:06�). The residual target ε was set to 0.1. Fig. 3(b) shows the relationship

between the iteration number and Zin1. Zin1 is the impedance looking into the

antenna side from the reference-plane (a) shown in Fig. 2. In Fig. 3(b), the blue,

red, and green lines show the relationship when N ¼ 2, 3, and 4. The combination

of the array elements used in different arrays is represented by boxes of the same

color in Figs. 3(a), 3(b) and 3(c); the array for N ¼ 2 is constructed with the

elements #1 and #2, and the array for N ¼ 3 is constructed with the elements #1,

#2, and #3. The solid and dashed curves in Fig. 3(b) represent the real and

imaginary part of the impedance, respectively.

The star symbols in Fig. 3(b) indicate the analytical solutions calculated from

the matched-load-determination equation when N ¼ 2 and 3 [4, 7]. Since the

determination equations are non-linear when N > 3 [4], we carried out numerical

analysis (Trust Region Method) using MATLAB to obtain the solution when

N ¼ 3. Extensive investigation is needed to obtain the solution when N > 4. This

will be addressed in our future studies.

In Fig. 3(b), the convergence is achieved for both the real and imaginary part of

the input impedance when iteration number is more than 10, irrespective of the

element number N. We also see that the convergence values agree well with the

analytical solutions, denoted by the star symbols. This assures that the proposed

method can be used for a multiple-element array antenna.

Fig. 3(c) shows the relationship between the VSWR of element #1 and the

iteration number. The VSWR was calculated by the following formulae:

� ¼ Zin1ðiÞ � ZL1ði � 1Þ�Zin1ðiÞ þ ZL1ði � 1Þ ð6Þ

(d) VSWR vs. residual target εε

(a) Configuration of the array (b) Zin1 vs. iteration number

(c) VSWR vs. iteration number

Fig. 3. Analytical results when N ¼ 2, 3, and 4.


331


VSWR ¼ 1 þ j�j1 � j�j ð7Þ

As shown in Fig. 3(c), when the number of elements increases, the convergence

condition varies. However, it can be seen that the VSWR converges to unity

irrespective of the number of elements when iteration number is more than 10.

Fig. 3(d) shows the relationship between the VSWR and the residual target ε.

If the VSWR needs to be limited to VSWR ¼ 1:2, ε should be less than 4 in the case

of N ¼ 2 whereas ε should be less than 3 in the case of N ¼ 3 and 4. Therefore,

considering the desired VSWR of different applications, ε must be adjusted to the

optimum value.

5 Conclusion

In this paper, we have proposed an automatic impedance-matching algorithm that

can sequentially realize simultaneous conjugate-matching state for all the elements

in an N-element array antenna. The analytical results show that the VSWR

converges to unity irrespective of the number of elements, demonstrating that the

antenna performance is improved by applying the proposed method to MIMO array

antennas. Future studies include experimental verifications of the proposed method.


332


An adaptive coarse timesynchronization methodfor factory automationin wireless control networkbased on OFDM systems overfading channels

Wenjian Wanga), Chang-Jun Ahn, Tatsuya Omori,and Ken-ya HashimotoGraduate School of Engineering, Chiba University,

1–33 Yayoi, Inage, Chiba 263–8522, Japan


Abstract: An accurate estimation of symbol timing is significant for

orthogonal frequency division multiplexing (OFDM) since the symbol tim-

ing inaccuracy will lead to phase offset (FO), inter-symbol interference (ISI)

and inter-channel interference (ICI). In this letter, a metric function has been

designed by taking advantage of the correlation properties of OFDM signals.

Computer simulation results show that the scheme is superior because it gets

a larger probability that fall into the ISI and ICI free region and has lower

computational complexity compared with the conventional methods over

frequency-selective channels, which can be used for factory automation (FA)

in wireless control network (WCN).

Keywords: frequency-selective channels, factory automation, symbol tim-

ing offset

Classification: Transmission Systems and Transmission Equipment for

Communications

References

[1] H. Minn, V. K. Bhargava, and K. B. Letaief, “A robust timing and frequencysynchronization for OFDM systems,” IEEE Trans. Wireless Commun., vol. 2,no. 4, pp. 822–839, July 2003. DOI:10.1109/TWC.2003.814346

[2] B. Park, H. Cheon, C. Kang, and D. Hong, “A novel timing estimation methodfor OFDM systems,” IEEE Commun. Lett., vol. 7, no. 5, pp. 239–241, May2003. DOI:10.1109/LCOMM.2003.812181

[3] H. Huh, “ML frame synchronization for OFDM systems using a known pilotand cyclic prefixes,” IEICE Trans. Commun., vol. E95-B, no. 7, July 2012.DOI:10.1587/transcom.E95.B.2296

[4] J. J. van de Beek, M. Sandell, and P. O. Borjesson, “ML estimation of time andfrequency offset in OFDM systems,” IEEE Trans. Signal Process., vol. 45,no. 7, pp. 1800–1805, July 1997. DOI:10.1109/78.599949

[5] M. Speth, F. Classen, and H. Meyr, “Frame synchronization of OFDM systems

© IEICE 2015DOI: 10.1587/comex.4.333Received October 19, 2015Accepted October 26, 2015Published November 20, 2015

333






http://dx.doi.org/10.1109/LCOMM.2003.812181




http://dx.doi.org/10.1587/transcom.E95.B.2296





http://dx.doi.org/10.1109/78.599949

http://dx.doi.org/10.1109/78.599949

http://dx.doi.org/10.1109/78.599949

in frequency selective fading channels,” Proc. IEEE VTC’97, pp. 1807–1811,May 1997. DOI:10.1109/VETEC.1997.605870

[6] T. Keller and L. Hanzo, “Orthogonal frequency division multiplex synchroniza-tion techniques for wireless local area networks,” Proc. IEEE PIMRC’96,pp. 963–967, Oct. 1996. DOI:10.1109/PIMRC.1996.568424

[7] D. Lee and K. Cheun, “Coarse symbol synchronization algorithms for OFDMsystems in multipath channels,” IEEE Commun. Lett., vol. 6, pp. 446–448, Oct.2002. DOI:10.1109/LCOMM.2002.804247

[8] S. Ma, X. Pan, G. Yang, and T. Ng, “Blind symbol synchronization based oncyclic prefix for OFDM systems,” IEEE Trans. Vehicular Technol., vol. 58,no. 4, pp. 1746–1751, May 2009. DOI:10.1109/TVT.2008.2004031

[9] W. Chin, “ML estimation of timing and frequency offsets using distinctivecorrelation characteristics of OFDM signals over dispersive fading channels,”IEEE Trans. Vehicular Technol., vol. 60, no. 2, pp. 444–456, Feb. 2011.DOI:10.1109/TVT.2010.2102058

1 Introduction

Orthogonal Frequency Division Multiplexing (OFDM) has been applied in many

areas including digital audio broadcasting (DAB), WLAN and Ultra-wideband

(UWB). Unlike single-carrier systems, OFDM systems demand high synchroniza-

tion performance and synchronization inaccuracy will bring about some serious

problems like sampling clock offset (SCO), symbol timing offset (STO), and carrier

frequency offset (CFO).

Symbol synchronization is generally divided into two major categories, pre-

amble-aided and non-preamble-aided. For preamble-aided approaches, a single

training symbol with identically repetitive structure of different periodic length in

the time domain can be used in [1]. To effectively solve the problem that the

declining curve is not steep enough, training symbols with circular conjugate

symmetry format are employed, it makes the correct timing position close to the

pulse form which can be correctly captured by the synchronizer [2]. Another type

of technique is to exploit a synchronization word and CP simultaneously [3], it

provides better performance in the condition that the influence of the multipath is

not serious. Using the symbol training sequence can obtain accurate delay estima-

tion, but the introduction of extra redundancy will significantly reduce the band-

width utilization efficiency. In order to make full use of spectrum resources,

recently, blind synchronization algorithms have been widely studied. The repre-

sentative algorithms are maximum likelihood (ML) [4], minimum mean square

error (MMSE) [5] and the maximum correlation (MC) [6]. The estimator counter-

acting multipath fading has been developed in [7]. The disadvantage of this

approach is that the exact channel length is needed. In [8, 9], some schemes were

presented that needless to know the channel state information (CSI) which can

accurately obtain the original start position of the FFTwindow, but the computation

complexity is increased significantly.

To mitigate above-mentioned problems, in this letter, a novel timing estimator

based on the redundancy of CP is proposed for high-speed OFDM systems over

multipath fading channels. Numerical results show that the proposed approach


334


http://dx.doi.org/10.1109/VETEC.1997.605870




http://dx.doi.org/10.1109/PIMRC.1996.568424








http://dx.doi.org/10.1109/TVT.2008.2004031








achieves better performance and manifests its robustness to multi-path fading

channels.

2 System model and correlation properties

Consider the correlation properties of the received OFDM signals yðnÞ and

yðn þ NÞ. Here, the intervals are divided into three parts namely A1 ¼ f�; � þ1; . . . ; � þ L � 2g, A2 ¼ f� þ L � 1; � þ L; . . . ; � þ Ncp � 1g and A3 ¼ f� þ Ncp;

� þ Ncp þ 1; . . . ; � þ Ncp þ L � 2g. The correlation between yðnÞ and yðn þ NÞthus satisfies

EfyðnÞy�ðn þ NÞg

¼ e�j2�"XL�1l¼0

jhðlÞ2jEfxðn � l � �Þx�ðn þ N � l � �Þg

¼

Q1ðnÞe�j2�"; for n 2 A1

�m2e�j2�"; for n 2 A2

Q2ðnÞe�j2�"; for n 2 A3

0; otherwise

8>>>><>>>>:

ð1Þ

where

Q1ðnÞ ¼Xn��l¼0

jhðlÞj2�x2 < �m2; ð2Þ

�m2 ¼ EfjyðnÞj2g � �n

2 ¼XL�1l¼0

jhðlÞj2�x2; ð3Þ

Q2ðnÞ ¼XL�1

l¼n��Ncpþ1jhðlÞj2�x2 < �m

2: ð4Þ

where XðkÞ denotes the datas transmitted in the OFDM symbol over the kth

subcarrier. After inverse fast fourier transform (IFFT) of N samples size, the signal

turns out to be xðnÞ. hðlÞ is the channel impulse response with the lagged channel

response of L � 1 samples. The symbol timing offset η and the normalized carrier

frequency offset ¥ (ratio of the CFO to subcarrier spacing �f, shown as � ¼foffset=�f) are modeled as a delayed signal in the receiver and a phase offset in

time domain respectively. The complex white Gaussian noise in yðnÞ is defined

as !ðnÞ with zero mean and the variance of �2n. Note that since CP is to extend

the OFDM symbol length by copying the last Ncp samples into its front, for

n; n þ n1 2 f0; 1; . . . ; Ncp � 1g, the correlation relationship between xðnÞ and

xðn þ n1Þ can be shown as

E½xðnÞx�ðn þ n1Þ� ¼�x

2; n1 ¼ 0 or N

0; otherwise

(ð5Þ

where �x2 ¼ E½jxðnÞj2�. As shown above, the correlation characteristics are decided

by the channel condition. When the signal yðnÞ is located in A2 region, known as

ISI-free region, the correlation value will reach the peak simply because it contains

the information of all the channel taps. Otherwise, it will be reduced correspond-

ingly on account of ISI under frequency-selective fading channels.


335


3 Proposed synchronization algorithm

Fig. 1 shows the block diagram of the discrete-time baseband high-speed OFDM

and the proposed scheme.

A metric function is proposed by means of utilizing sampling datas that is not

influenced by ISI. Since the exact channel length is not clearly known, in order to

avoid the influence of multipath fading, we use the block length b (b < Ncp) instead

of using all the samples in the CP. We perform the correlation calculation between

two data blocks at a span of N samples. The block length b must be set

appropriately so that the probability that the overall block falls into ISI-free region

is high. The purpose of designing the metric function is to find a point in the

interval A2 on the premise that we do not know the exact channel length L. The

metric function can be expressed as

�ðnÞ ¼Xb�1k¼0

Efyðn þ kÞy�ðn þ N þ kÞg��

��

2

Xb�1k¼0

½Efjyðn þ kÞj2g þ Efjyðn þ N þ kÞj2g�

n 2 f0; 1; . . . ; N þ Ncp � 1g; ð6Þwhere

� ¼ fE½jyðnÞj2� � E½j!ðnÞj2�g=E½jyðnÞj2�¼ �m

2=ð�m2 þ �n2Þ ¼ SNR=ðSNR þ 1Þ: ð7Þ

From the discussion above, the function in (6) becomes

�ðnÞ ¼Xb�1k¼0

Efyðn þ kÞy�ðn þ N þ kÞg��

�� b�m2: ð8Þ

we make an analysis as follows:

Case i: for n þ b � 1 < � þ L � 1,

�ðnÞ < b�m2 � b�m

2 ¼ 0: ð9ÞCase ii: for ðn � � þ L � 2Þ \ ðn þ b � 1 � � þ L � 1Þ, here we assume the length

of the block that falls within the interval A1 is b1, it yields

�ðnÞ ¼ b1Q1ðnÞ þ ðb � b1Þ�m2 � b�m2

< b�m2 � b�m

2 ¼ 0: ð10Þ

Fig. 1. Block diagram of high-speed OFDM for WCN.


336


Case iii: for ðn � � þ L � 1Þ \ ðn þ b � 1 < � þ NcpÞ,�ðnÞ ¼ b�m

2 � b�m2 ¼ 0: ð11Þ

Case iv: for ðn þ b � 1 � � þ NcpÞ \ ðn � � þ Ncp � 1Þ, here we assume the length

of the block that falls within the interval A2 is b2, �ðnÞ is obtained as

�ðnÞ ¼ b2�m2 þ ðb � b2ÞQ2ðnÞ � b�m

2

< b�m2 � b�m

2 ¼ 0: ð12ÞCase v: for n > � þ Ncp � 1,

�ðnÞ < b � 0 ¼ 0; ð13Þnmax ¼ argmax

nf�ðnÞg: ð14Þ

In regard to deciding b, Fig. 2(a) shows the lock-in probability outside the

interval A2 as a function of block length in FSF channel at the SNR of 22 dB. To

verify whether the value of b ¼ 4 can be commonly used, we consider the other two

cases when the system parameters such as the Ncp and L are changed to show its

generality. In high speed WCN, the duration of transmission time for one OFDM

symbol (N þ Ncp ¼ 160) is set to 10 µs with Ncp is about 2 µs in our system. In

general, short-range communication of WCN for FA has a small delay spread. To

show the feasibility of the model, we choose the maximum delay about 0.5 µs,

which is enough to satisfy conditions of real environment. Based on this point, we

select L to be 5 and 10 with the minimum and maximum respectively to determine

the block length. The simulation results show that with the increase in block length,

the probability will rise correspondingly except for the first point. Hence, the block

length is set to be 4 samples (b ¼ 4) to achieve the best performance. Furthermore,

the lock-in probability in A2 is also improved with the increase of CP length at a

given channel length, however it is reduced with the increase of channel length at a

given CP length.

Known from above, due to the influence of the multipath, new timing metric

will have a period of platform with the length of p at the rear-end of cyclic prefix.

Furthermore, after the platform there is a falling edge, as a result, channel length

0 5 10 15 20 25 30

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

SNR (dB)

The

pro

babi

lity

of in

corr

ect

posi

tion

ing

in A

2 by

met

ric

func

tion

proposed metric function (Ncp = 32, L = 10)proposed metric function (Ncp = 64, L = 10)proposed metric function (Ncp = 32, L = 5)

2 4 6 8 10 12 14 16 18 200.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Block lengthT

he p

roba

bilit

y of

inco

rrec

t po

siti

onin

g in

A2

by m

etri

c fu

ncti

on

proposed metric function (Ncp = 32, L = 10)proposed metric function (Ncp = 64, L = 10)proposed metric function (Ncp = 32, L = 5)

(a) (b)

Fig. 2. The probability of incorrect positioning in ISI-free region A2 bymetric function versus block length and SNR in frequency-selective fading channels. (N ¼ 128, SNR ¼ 22 dB) in (a) and(N ¼ 128, b ¼ 4) in (b).


337


can be roughly estimated, L ¼ Ncp � b � p þ 2. In fact the detailed procedures for

deciding p can be figured out by finding the first dip where �ðnÞ is below the given

threshold which is zero theoretically. After that, we search to obtain the value nmaxin (14) that correspond to the maximum point in the platform. Fig. 2(b) show the

estimation accuracy achieved by the metric function with different GI length and

channel length. Obviously, with the increase of SNR, the lock-in probability in A2

is improved.

4 Simulation results

4.1 BER performance by proposed estimator

We consider an OFDM system with 128 subcarriers and CP length of 32. The

transmission bit rate is 16 � 106 bits/s and the modulation mode is QPSK.

Frequency selective fading channels with 10 Rayleigh-fading taps (L ¼ 10) were

considered here. The path separation is Tpath ¼ 62:5 nsec and its power presents

exponential decay with the form of 100�ððtap�1Þ=10Þ. Channel responses were

produced by taking advance of complex Gaussion random variable which satisfies

that the power summation of every normalized path amplitude is equal toPl jhðlÞj2 ¼ 1.

Fig. 3 shows the BER performance of proposed symbol synchronization

method compared with the existing methods. Note that in order to see the effect

of STO, the signal after taking FFT has not been compensated in any form. The

BER performances of MMSE, MC and ML methods are severely degraded because

they have unnecessary summation lengths under the condition of no exact channel

length, which results in high error rate. The 2-D search method in [8] achieves

relatively high BER at the cost of a high computational complexity. The proposed

method has gained better effect than the others, which simplifies the subsequent

error compensation.

4.2 Computational complexity

The computational complexity is calculated in terms of complex multiplications. In

our system, the mathematical OFDM symbol numbers are assumed to be S. That

0 5 10 15 20 25 3010

−3

10−2

10−1

100

SNR (dB)

BE

R

MMSEproposed for initial timingMCMLOFDM with exact timing 2−D search method

Fig. 3. The BER performance subject to STO with equalization forinitial time synchronization in frequency-selective fadingchannels. (L ¼ 10, b ¼ 4).


338


means S consecutive high-speed OFDM symbols are sent and should be timing

synchronized at a time. The computational complexity that required in MC,

MMSE, ML algorithm are SNcpðN þ NcpÞ, 3SNcpðN þ NcpÞ, 3SNcpðN þ NcpÞ re-

spectively. The 2-D search algorithm in [8] can achieve high STO estimation

accuracy, however, the complexity is 3SNcpðNcp þ 1ÞðN þ NcpÞ=2 which is far

larger than the others. Under the given system parameters, we perform the metric

function with varying b to decide the appropriate block length in the first OFDM

symbol and use the decided b in the remaining OFDM symbols. As a result,

the proposed algorithm has the complexity of 3ðN þ NcpÞð2 þ 20Þ � 19=2 þðS � 1Þ½3bðN þ NcpÞ�. The selected block length satisfies b ¼ 4, moreover, N ¼128, Ncp ¼ 32, and L ¼ 10 are considered respectively. Since a large amount of

high-speed OFDM symbols are sent successively in the actual uplink WCN

systems and each symbol needs to be synchronized. An actual situation is discussed

here, in fact, when S > 31, we have the following property of complexity relations:

proposed ¼ 98400 þ 1920S < MC ¼ 5120S

< ML ¼ MMSE ¼ 15360S < ½8� ¼ 253440S ð15ÞAs shown above, the proposed algorithm has lower computational complexity for

practical application.

5 Conclusion

A fast time synchronizer has been proposed for high-rate wireless control network.

We do not use preamble ahead for the reason that the reduction of preamble is

highly beneficial since the transmission time of preamble is longer than that of the

payload. By utilizing a metric function to find a sampling point in ISI-free region,

the proposed algorithm achieves better BER performance subject to STO for initial

time synchronization under frequency-selective fading channels, moreover, it has

lower computational complexity compared with the existing method when consid-

ering the actual situation, which can fully meet the real-time requirement in WCN

systems for FA.

Acknowledgement

This work was partially supported by the grant of scientific research No. 26420339

from JSPS.


339


Secure parent node selectionscheme in route constructionto exclude attacking nodesfrom RPL network

Iuchi Kenji, Takumi Matsunagaa), Kentaroh Toyoda,and Iwao SasaseDept. of Information and Computer Science, Keio University,

3–14–1 Hiyoshi, Kohoku, Yokohama 223–8522, Japan


Abstract: We propose a secure parent node selection scheme in the IPv6

Routing Protocol for Low-power and Lossy networks (RPL) so that each

child node can select a legitimate node as its parent. In the proposed scheme,

each node chooses a parent after excluding too good candidate if multiple

parent candidates exist. Our scheme utilizes the fact that an attacking node

claims falsely a lower rank than that of legitimate nodes. Simulation results

show that the proposed scheme reduces the total number of child nodes

attached to attacking nodes.

Keywords: IoT, RPL, security, sensor network

Classification: Network

References

[1] K. Ashton, “That ‘Internet of Things’ Thing,” RFID Journal, 2009. http://www.rfidjournal.com/articles/view?4986

[2] T. Winter, P. Thubert, A. Brandt, J. Hui, R. Kelsey, P. Levis, K. Pister, R.Struik, J. Vasseur, and R. Alexander, “RPL: IPv6 routing protocol for low-power and lossy networks,” RFC 6550, 2012. http://tools.ietf.org/html/rfc6550

[3] A. Le, J. Loo, A. Lasebae, A. Vinel, Y. Chen, and M. Chai, “The impact ofrank attack on network topology of routing protocol for low-power and lossynetworks,” IEEE Sensors J., vol. 13, no. 10, pp. 3685–3692, 2013. DOI:10.1109/JSEN.2013.2266399

[4] A. Dvir, T. Holczer, and L. Buttyan, “VeRA— version number and rankauthentication in RPL,” Proc. IEEE Conference on Mobile Adhoc and SensorSystems (MASS), pp. 709–714, Oct. 2011. DOI:10.1109/MASS.2011.76

[5] S. Raza, L. Wallgren, and T. Voigt, “SVELTE: real-time intrusion detection inthe Internet of things,” Ad Hoc Netw., vol. 11, no. 8, pp. 2661–2674, 2013.DOI:10.1016/j.adhoc.2013.04.014

[6] H. Perrey, M. Landsmann, O. Ugus, T. C. Schmidt, and M. Wählisch, “TRAIL:topology authentication in RPL,” arXiv:1312.0984, 2013. http://arxiv.org/abs/1312.0984

[7] C. Karlof and D. Wagner, “Secure routing in wireless sensor networks: attacksand countermeasures,” Ad Hoc Netw., vol. 1, no. 2, pp. 293–315, 2003. DOI:10.1016/S1570-8705(03)00008-8

[8] A. Dunkels, B. Gronvall, and T. Voigt, “Contiki— a lightweight and flexible

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[10] P. Thubert, “Objective function zero for the routing protocol for low-power andlossy networks (RPL),” RFC 6552, 2012. http://tools.ietf.org/html/rfc6552

1 Introduction

In the Internet of Things (IoT), resource-constrained sensing devices are connected

to the Internet via IPv6 network so as to monitor and control everything, e.g.,

energy consumption of appliances or everlasting structure monitoring [1]. The IPv6

Routing Protocol for Low-Power and Lossy Networks (RPL) is selected as a

standard routing protocol to realize the IoT [2]. In RPL, nodes create a loop-free

tree-based topology to send collected data to the sink. In order to construct the

tree topology network, each node has a rank which is a cumulative value, e.g., the

number of hops from the sink, and selects the least rank neighbor node as its parent

node.

However, attacking nodes that may drop, collapse, or tamper collected packets

can claim a forged rank that is lower than the true one to collect more packets from

child nodes in RPL [3]. Although many attacking nodes detection schemes [4, 5, 6]

have been proposed, each has shortcomings. The scheme in [4] has a problem that

computation complexity is heavy for resource limited nodes, e.g., sensor nodes.

The schemes in [5, 6] have a problem that the sink or each parent node detects

attacking nodes after route construction so that child nodes might send data to

an attacking node. Therefore, it is necessary that more child node can select a

legitimate node as its parent in route construction.

In this paper, we propose a secure parent node selection scheme in RPL so that

more child nodes can select a legitimate node as its parent. If multiple parent

candidates exist, each node selects a parent after excluding a too good candidate.

Therefore, more nodes might avoid selecting an attacking node as its parent node

and sending packets to the attacking node.

We show that the proposed scheme reduces the total number of child nodes

attached to attacking nodes than that in the conventional RPL scheme. We also

show that the attacking nodes have no merits to claim lower ranks than true ones so

as to collect more packets.

2 Attacker model

The goal of attacking nodes is to collect as many packets as possible from their

child nodes in order to drop, collapse, and tamper packets [7]. Hence they claim a

fake rank so that more child nodes select them as parents. Scenario 1 assumes that

attacking nodes pretend to be the sink, i.e., they broadcast the same ranks as sink.© IEICE 2015DOI: 10.1587/comex.4.340Received October 13, 2015Accepted November 5, 2015Published November 30, 2015

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http://dx.doi.org/10.1109/LCN.2004.38











Scenario 2 assumes sophisticated attacking nodes that pretend to be the legitimate

node, i.e., they broadcast ranks as (true rank � 1) not to be detected as attacking

nodes easily. Scenario 3 assumes that attacking nodes behave as the legitimate

node, i.e., without faking their ranks.

3 Proposed scheme

Here we propose a secure parent node selection scheme in RPL network so that

more child nodes can select a legitimate node as its parent. At the route construction

phase, each node selects a parent after excluding a too good candidate by utilizing

the threshold. Each node can judge whether a rank value broadcast by its neighbor

nodes is too low since it can obtain a maximum and average rank of its neighbor

nodes. This notion comes from the fact that attacking nodes intend to falsely claim

a lower rank than legitimate nodes. After that, each node selects its parent node

except for nodes whose rank is judged to be too low. Therefore, each node avoids

not only selecting an attacking node as its parent node but also sending packets to

the attacking node. The proposed scheme has a merit that attacking nodes cannot

collect more packets if they falsely broadcast lower rank. The attacking nodes we

assume have no merits to claim lower rank than true one so as to collect more

packets.

3.1 Algorithm

In the route construction phase, each node i calculates its own threshold thresholdiwith the maximum and average rank of its neighbor nodes. thresholdi is calculated

as follows

thresholdi ¼ Rave � Rmax � K ð1Þwhere, Rave and Rmax are the average and the maximum rank values among node i’s

neighbors, and K (0 < K < 1) is a constant parameter, respectively. If its neighbor

node’s rank is lower than thresholdi, it judges the neighbor node as an attacking

Fig. 1. An example of the route construction phase.


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node and excludes it from parent candidates. Then, it selects a node that is the

lowest rank in its neighbor nodes except for the attacking node.

We show an example of route construction phase in Fig. 1. Node 1 calculates

thresholdi with its neighbor ranks. In this case, Rave ¼ ð1 þ 3 þ 3 þ 4 þ 4Þ=5 ¼ 3

and Rmax ¼ 4. If K ¼ 0:25, thresholdi ¼ 3 � 4 � 0:25 ¼ 2. Node 1 excludes a node

whose rank is lower than thresholdi from its parent candidates since 1 (¼ attacking

node’s falsely claimed rank) < 2 (¼ thresholdi). Therefore, in the proposed

scheme, node 1 avoids selecting an attacking node as its parent.

3.2 Threshold

We discuss why we set thresholdi as Eq. (1). If thresholdi is too large, more nodes

avoid selecting not only attacking nodes but also better legitimate nodes as its

parent. As a consequence, detour may occur and the number of hops from each

node to the sink may increase. If thresholdi is too small, more nodes may select an

attacking node as its parent so that the probability of avoiding attacking nodes from

a parent is decreased. As a result, we calculate thresholdi with Rave as a reference

value. thresholdi needs to be less than Rave since the least rank in legitimate

neighbor nodes is usually lower than Rave. Thus, we decrease thresholdi with Rmax

and the parameter K. We can maintain small thresholdi by calculating it with Rmax

even if an attacking node claims much higher rank so that thresholdi becomes

higher than legitimate nodes. Moreover, thresholdi needs to be easily calculated

for resource constraint devices. Therefore, we only use simple arithmetic to

calculate thresholdi. In this paper, we heuristically determine the parameter K to

take into account both the number of hops and the probability of avoiding an

attacking node.

4 Evaluation

4.1 Simulation model

We evaluate the number of child nodes that select an attacking node as their parents

by Contiki’s network simulator Cooja [8, 9]. We compare the proposed scheme

with the conventional RPL scheme since, as described in Section III in [5, 6], each

node selects its parent node by the same method as the conventional RPL scheme.

We simulate three scenarios as described in attacker model. We show the

simulation model in Table I. The threshold K is based on empirical evaluation. The

sink is fixed at a corner in the simulation area, while legitimate and attacking nodes

are randomly deployed.

4.2 Simulation results and discussion

Fig. 2(a) shows the total number of child nodes attached to attacking nodes, which

we denote as Nattacked , versus the number of attacking nodes. Fig. 2(b) shows

Nattacked versus the number of hops from the sink to an attacking node. From

Fig. 2(a) and 2(b), the proposed scheme achieves the lower Nattacked than RPL in

both scenario 1 and scenario 2. In RPL, Nattacked is larger than those in our scheme

since each node selects a node that has the lowest rank as its parent. On the other

hand, in our scheme, Nattacked gets less since each node excludes attacking nodes© IEICE 2015DOI: 10.1587/comex.4.340Received October 13, 2015Accepted November 5, 2015Published November 30, 2015

343


from its parent candidates. We then compare the effect of our scheme against

various scenarios. As we can see from Fig. 2(a) and 2(b), our scheme achieves that

scenario 3 is the largest Nattacked of the three scenarios. In scenario 1 and scenario

2, ranks of attacking node are lower than those of legitimate ones. On the other

hand, in scenario 3, a rank of attacking nodes is same as that of legitimate ones.

Here, we assume other attacking nodes that claim higher rank than true rank so that

thresholdi becomes higher than legitimate nodes. If an attacking node claims a

rank as (true rank + 1), Rave is increased by 1=n (< 1), where n is the number of

neighbor nodes. As a result, the attack can hardly exclude legitimate node from

parent candidate. Moreover, the attacking node’s rank is higher so that it is difficult

to selected as a parent. Therefore, the scenario 3, i.e., when an attacking node

claims its true rank, is the best strategy for attacking nodes regardless of the number

Fig. 2. Nattacked versus the number of attacking nodes and the numberof hops from sink to an attacking node.

Table I. Simulation model

Name Value

Simulator Cooja

Simulation area 200m � 200m

Number of all nodes 32

Number of sink 1

Number of attackers 1–3

Transmission range 50m

Interference range 100m

MAC protocol IEEE 802.15.4

Objective function Objective Function 0 [10]

Threshold K ¼ 0:25


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of attacking nodes and the number of hops from the sink to an attacking node. From

these results, the attacking nodes we assume have no merits to claim falsely lower

ranks than true ones when our parent selection scheme is applied.

5 Conclusion

In this paper, we have proposed a secure parent selection scheme so that more child

nodes can select a legitimate node as its parent. In the proposed scheme, each node

tries to select a legitimate node by excluding too good candidates with a threshold.

We show that the proposed scheme reduces the total number of child nodes

attached to attacking nodes in comparison with the conventional RPL scheme

and that the attacking node we assume have no merits to falsely claim lower ranks

than true ones by computer simulation.

Acknowledgments

This work is partly supported by the Grant in Aid for Scientific Research

(No. 26420369) from Ministry of Education, Sport, Science and Technology,

Japan.


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