JOURNAL OF TELECOMMUNICATIONS, VOLUME 5, ISSUE 1, OCTOBER 2010 1

Characteristics of FH Pattern Likelihood Ratio Decision Method against CW Jamming or/and Burst Noise Shin’ichi Tachikawa, and Kenji Kobayashi Abstract— This paper proposes an improved method of a lump likelihood ratio calculation in detection of frequency hopping (FH) pattern of multilevel FSK (MFSK). In a conventional lump likelihood ratio calculation, it is calculated by employing probability density function of AWGN and signal gain of each frequency slot. In this paper, a new calculation method employing a probability density function including CW jamming or/and burst noise is proposed. Theoretical analysis of the lump likelihood ratio and estimation methods of CW jamming and burst noise are derived. Then, by computer simulations, it is shown that BER of the proposed method is superior to that of the conventional method for several conditions. Index Terms—frequency hopping (FH), multilevel FSK (MFSK), lump likelihood ratio, CW jamming, burst noise

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1 INTRODUCTION

F

REQUENCY hopping (FH) communication systems have been popularly studied for applications of wireless LAN and power-line data transmission, because of its robustness against near-far problems and frequency diversity effects [1]. Using an inverse fast Fourier transform (IFFT) circuit by digital signal processor (DSP), hardware can be realized easily. When hopping rate (chip rate) is faster than bit rate, it is called “high rate FH system” which has always frequency diversity effect for each data. In this paper, we adopt the high rate FH system. In a conventional FH receiver, frequency slots of maximum value on frequency domain are selected for each chip, and FH pattern is detected by the figure of selected slots. When large fluctuation of signal level for each slot arises independently on the transmission line (e.g., multi-path fading channel and power line), the FH pattern detection has degraded seriously. If the signal gain (or loss) can be estimated, the performance is not improved because the degradation of signal to noise ratio remains However, we can estimate relatively the position of the desired signal tone on time domain even if the fluctuation of signal exists on frequency domain. More accurate estimation can be achieved on frequency domain using the information form the time domain. Further, the accuracy can be improved an iterative algorithm. This method is well known as an iterative likelihood ratio calculation, i.e., turbo decoding [2]. In the previous papers, an iterative likelihood ratio decision method was discussed [3]. To improve the iterative likelihood calculation, a lump likelihood ratio, in which the whole likelihood ratio is calculated from both time-axis and frequency-axis together, was proposed [4].

The lump method can be estimated more accurate and faster than the iterative method. These conventional likelihood calculation methods can be estimated accurately against large fluctuation of signal level for each slot. However, the effects are not discussed enough against CW jamming or/and burst noise. The modifications and improvements of the proposed system become necessary. In this paper, we focus on a probability density function (pdf) used in likelihood ratio calculation. First, in Sect. 2, system model (FH/MFSK system) and interferences (CW and burst noise) are explained. In Sect. 3, a conventional lump likelihood ratio decision method is explained. Next, a new calculation method that employs pdf including CW and burst noise parameters is proposed, and estimations methods of CW and burst noise parameters are shown. In Sect. 4, the effects of the proposed method are shown by computer simulations. Further, discussions for the condition including both CW jamming and burst noise, and the condition including CW with carrier offset are described. Finally, in Sect. 5, these results are concluded.

2 SYSTEM MODEL AND INTERFERENCE

2.1 FH/MFSK System Figure 1 shows system model of frequency hopping / multilevel frequency shift keying (FH/MFSK). Figure 2 show an example of FH/MFSK signal pattern matrix. In Fig. 1 (a), at transmitter, m bits binary data is converted to M-level (M=2m) signal as M-ary symbol by "2-2m converter" (Fig. 2 (a)), a transmitting pattern is generated by addition modulo M of the M-level signal and "address code" as hopping pattern, i.e., the hopping pattern is cyclically shifted by the M-level signal (Fig. 2 (b) and (c)). In Fig. 2, ———————————————— • S. Tachikawa is with the Nagaoka National College of Technology, Nagaoka, the number of information levels (i.e., the number of frequency slos) M is 4, the number of chips in one symbol Niigata, 940-2188, Japan. • K.Kobayashi was with the Nagaoka University of Technology, Nagaoka, duration L is 3, and a hopping pattern is (0, 1, 2). CorresNiigata, 940-2188, Japan.

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ponding to the transmitting pattern, the tones are formed by "Frequency synthesizer or IFFT". In Fig. 1 (b), at receiver, a received pattern is detected by using M phased lock loops (PLLs) or IFFT (Fig. 2 (d)), the received pattern is subtracted "address code" by modulo M (Fig. 2 (e)), and the received level is decided by the frequency slot number for the maximum summation values in row.

Binary data

mod 2m 2-2m converter

Frequency synthesizer or IFFT

+ + Address code

4.4.

2.3 Burst Noise Burst noise is an impulsive noise that occur unpredictable time and continues short time duration, and has large energy in various environments. Probability density function (pdf) of burst noise follows several models [5][6]. In this paper, we use additive Gaussian noise as a convenience burst noise model. In FH system, burst noise interfere some neighboring chips. Here, a time-interleaver is adopted, and non neighboring burst noise is assumed, so that we evaluate in condition which includes only a burst noise chip in a FH pattern

3

LUMP LIKELIHOOD RATIO DECISION

(a) Tramsmitter model of MFSK

mod 2m Wave detector

f-slot detecsion

2-2m converter

+ -

3.1 Conventional Method A lump likelihood ratio decision method is a hopping pattern decision method using a whole likelihood ratio, which is calculated from both time-axis and frequencyaxis together to M kinds of transmitting patterns. Then, a received pattern matrix is decided as the most similar transmitting pattern as shown Figure 3. A lump likelihood ratio ω(m) is given as [4],

Binary data

Address code

(b) Receiver model of MFSK

Λ (m ) = ln

Fig.1 System model of MFSK.

Pr (R, Dm ) M −1

∑ Pr (R, D )

(2)

i

i = 0 ,i ≠ m

where Pr(R,Dm) and Pr(R,Dn) is a probability of transmitting pattern matrix Dm and Dn when the received pattern matrix is R. An example of the transmitting pattern matrix for FH/MFSK, which has the number of information levels M=4, the number of chips in one symbol duration L=3 and a hopping pattern h = (0, 1, 2), is shown as

: Desired tone

Frequency slots

: Interference

Time chips (a) Data level pattern

(b) Hopping pattern

(c) Tx pattern

(d) Rx pattern

(e) Demodulated

Fig.2 An example of FH/MFSK modulation patterns M=2m=4, L=3, hopping pattern (0, 1, 2).

D2

2.2 CW Jamming Continuous wave (CW) is sine-wave that has a constant angular-frequency ω and an amplitude Acw, the CW can be expressed as Acwcos(ωt+ φ), where φ is a phase of the wave. In FH system, when the CW frequency is given by fcw=fi+a/Tc, the coherent detector output on slot fi can be written as 2 TC

D0

pattern

0  0 =  0  1

0

0  1 =  0  0 

1

0 1 0

0 0 0

0

,

0  0 D1 =  1  0

0   0  0  , 1 

1  0 D3 =  0  0

0

0   1  0   0 

CW

Λ (0 ) = ln

nT C

0

0 0 1

,

0   0  1   0 

.

(3)

Pr {R , D 0 } Pr {R , D 1 }+ Pr {R , D 2 }+ Pr {R , D 3 }

= λ 00 + λ10 + λ 02 + ln

cos (2π f CW t + ϕ ) cos (2π f i t )dt

sin (π a )  A cos (π a (2 n + 1) + ϕ ) a ≠ 0 =  CW π a  ACW cos ϕ a=0

0

1   0  0   0 

A lump likelihood ratio ω(0) of transmitting pattern D0 is calculated as follows,

(n +1 )TC

∫A

1

1  exp (λ10 + λ11 + λ12 )   2 2 2   + exp (λ 0 + λ1 + λ 2 )  3 3 3   + exp (λ 0 + λ1 + λ 2 )

(4)

This expression modifies general expression as (1)

where n is the chip number and the double frequency component is ignored. If fcw is equal to fi, a=0. In this paper, first, a=0 is assumed for convenience. Discussion about a>0 (it's named "offset carrier CW") is described in

Λ (m) = ∑ j =0 λmj + ln

1

L −1

∑

(

exp ∑ j=0 λij i =0,i ≠ m M −1

L−1

)

(5)

Assuming that disturbance noise is an Gaussian model, Pr (Rkj | d kj = 1) λmj = ln (6) Pr (Rkj | d kj = 0)

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(12)

 (R − ρ )2  1 exp − kj 2 k  2σ 2π σ   = ln 2   R 1 exp − kj 2   2σ  2π σ  

=

1 2 2Rkj ρk − ρk 2σ 2

(

(7)

)

(8)

)

3

1

Pr (Rk j | d k j = 1)

(13)

Pr (Rk j | d k j = 0)

2     R − ρ 1 + Vcw      kj k  −  exp ρ 2 2 2π (σ awgn + σ burst )   2(σ 2 + σ 2 k )   awgn burst   = ln 2      R − ρ  0 + Vcw   1   kj k   exp  − ρ 2 2 )   2(σ 2  + σ 2 k )  2π (σ awgn + σ burst awgn burst  

1

where (9) k = m + h j mod M dkj is an element value of transmitting pattern matrix, Rkj is an element value of received pattern matrix, ωk is signal gain of k-th slot, hj is a j-th value of hopping pattern and ω2 is variance of AWGN.

(

λnj = ln

=

 1 Vcw   2 2 2 ) 2 Rk j ρ k − ρ k 1 + 2 ρ k  . 2(σ awgn + σ burst

9

0

3

-3 -1

However, it is necessary to estimate Vcw and ω2burst from a received pattern matrix.

1

Pr(r|d=0)

Pr(r|d=1)

p. d. f

Rx pattern

variance σ 2awgn

r

ρ 0 (a) Conventional Pr(r|d=0)

Tx pattern at data level ‘2’

Pr(r|d=1)

variance

p. d. f

Tx pattern at data level ‘1’

(15)

7

-4 12 -2

Tx pattern at data level ‘0’

(14)

Tx pattern at data level ‘3’

σ 2awgn + σ 2burst

Fig.3 Lump likelihood ratio decision method. VCW

ρ + VCW

r

(b) Proposed

3.2 Proposed Method A pdf of conventional lump likelihood ratio calculation is Gaussian distribution with which variance and signal gain of frequency slot, that is  (r − ρd )2  1 exp−  2σ 2  2π σ 

(10)

as illustrated in Figure 4 (a). The pdf agrees with a fading environment, so that the conventional lump likelihood ratio decision method can estimate hopping pattern accurately in a fading environment, but cannot estimate enough in a CW or/and burst noise environment. Therefore, if a new pdf with influence of CW or/and burst noise is derived, the problem can be solved. We propose a new pdf modified from eq. (10) as follows, 2    Vcw    r d − + ρ   1    exp − ρ   2 2 )   2(σ 2 + σ 2 )  + σ burst 2π (σ awgn awgn burst  

)

3.3 Estimation method of CW jamming Two Estimation methods of CW: averaged power (AP) method and voltage distribution (VD) method are introduced using training frame which is some received frames. (1) Averaged power method Averaged power (AP) method is estimation method of CW using averaged power of each slot at training frame. Average power of received training frame is 2 (16) PRXi = PTXi + σ awgn + Pcw where PRXi is averaged power of received training frame on i-th slot, PTXi is averaged power of transmitting training

(11)

where ω2awgn is AWGN variance, ω2burst is burst-noise variance and Vcw is CW voltage. The new pdf is shifted by Vcw, and the new variance is changed to be large than AWGN one as illustrated in Figure 4 (b). Thus, ω(m) is calculated as L −1 1 Λ (m ) = ∑ j =0 λmj + ln M −1 L −1 exp ∑i=0,i≠m ∑ j=0 λij

(

Fig.4 Probability density function of likelihood ratio decision.

frame on i-th slot, so that Pcw is calculated and the slot of CW frequency is decided by threshold α2 as follow 2 (17) PRXi − PTXi − σ awgn > α 2 . Vcw is calculated as follow in case of eq. (17), (18) Vcwi = ± PRXi − PTXi − σ 2awgn . Otherwise, Vcw = 0.

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(2) Voltage distribution method Voltage distribution method is an estimation method of CW using different distribution between interfered slot and non-interfered slot by CW. The (M-1)/M of received values follow median 0 of normal distribution on interfered slot by CW, while the 1/M of received values follow median Vcw of normal distribution on non-interfered slot, so that the interfered slot can be decided by appropriate parameters a and b. (19) Pr(Ri > ± aσ ) > b .

Vcw is calculated as follow in case of eq. (19), Vcwi = ± PRXi − PTXi − σ 2awgn .

(20)

Otherwise, Vcw = 0. (3) Estimation parameters Parameters of estimation methods are decided by computer simulations. Table 1 shows the specification of simulation. At first, it is decided that the number of training frame is 10 because estimation error of Vcw is enough stable in 10 frames in Eb/No=6.8dB. Next, we decide "α=0.45" and "a=1.5, b=0.417" as optimum values for AP and VD methods, respectively. Table 1 Specification of simulation in CW jamming. System model Number of slots Number of chips Hopping sequence Transmission line Carrier detection CW

MFSK/FH-SS 16 3 (0, 1, 2) AWGN+CW Coherent cos φ φ is randam number from 0 to 2π on 1 slot

3.4 Estimation method of burst noise Two Estimation methods of burst noise; practical variance (PV) method and voltage distribution (VD) method are introduced. (1) Practical variance method Practical variance (PV) method is estimation method of burst noise using received practical variance σ 2p of each chip at training frame. If practical variance σ 2p becomes αburst times larger than σ 2awgn , i.e., σ 2p > αburst σ 2awgn , it is de-

cided burst noise is present. Burst noise variance is calculated as follows, 2 (21) σ burst ≈ σ 2p − σ 2awgn 2 Otherwise, σ burst = 0.

(2) Voltage distribution method Voltage distribution (VD) method is estimation method of burst noise using different distribution between interfered chip and non-interfered chip by burst noise. The variance in interfered chip is much larger than that of non-interfered chip, so that the interfered chip is decided by appropriate parameters a and b. (22) Pr(Ri > ± aσ ) > b , and burst noise variance is calculated as follows,

2 σ burst ≈ σ 2p − σ 2awgn .

Otherwise,

2 σ burst

(23)

= 0.

(3) Estimation parameters Table 2 shows the specification of simulation. we decide "α=4.0" and "a=2.0, b=0.287" as optimum values in Eb/No=6.8dB for PV and VD methods, respectively. Table 2 Specification of simulation in burst noise. System model Number of slots Number of chips Hopping sequence Transmission line Carrier detection Burst noise

MFSK/FH-SS 16 3 (0, 1, 2) AWGN+CW Coherent Gussian noise 10 times varinace of AWGN one on 1 chip/frame

4 SIMULATIONS AND DISCUSSIONS 4.1 CW jamming Figure 5 (a) and (b) show performance of bit error rate (BER) in CW jamming environment. In the Fig. 5, "Soft" curve is the conventional soft decision, "Con. LLR" curve is the conventional lump likelihood ratio decision, "Pro. LLR (estimation AP)", "Pro. LLR (estimation VD)" and "Pro. LLR (correct values)" curves are the proposed lump likelihood ratio decisions employed AP, VD estimation methods, and correct parameters of CW, respectively. In Fig. 5(a), BER of the proposed method (correct values) is superior to that of a conventional method, and it is nearly equal to that of the proposed methods (estimation AP and VD). It means that the estimation method is properly worked. In Fig. 5 (b), the larger the power of CW jamming, the more BER degradation of the conventional method is increased. While, when the power of CW jamming is large more and more, BERs of the proposed methods (correct values, estimation AP and VD) do not increase and become almost constant.

JOURNAL OF TELECOMMUNICATIONS, VOLUME 5, ISSUE 1, OCTOBER 2010 5

Soft Con. LLR Pro. LLR (estimation AP ) Pro. LLR (estimation VD) Pro. LLR (correct values)

1.E+00

1.E+00

Bit error rate

1.E-01

1.E-01 Bit error rate

1.E-02 1.E-03 1.E-04 1.E-05

1.E-02 1.E-03 1.E-04

0

1

2

3

4 5 6 Eb/No [dB] (a) BER vs. Eb/No

7

8

9

10 1.E-05 0

1.E+00 1.E-01

1

2

3

4 5 6 Eb/No [dB] (a) BER vs. Eb/No

7

8

9

10

1.E+00

1.E-02

1.E-01 Bit error rate

Bit error rate

Soft Con. LLR Pro. LLR (estimation PV) Pro. LLR (estimation VD) Pro. LLR (correct values)

1.E-03 1.E-04

1.E-02

1.E-03 1.E-05 -10

-5

0

5

10

Power of CW jamming [dB] (b) BER vs. power of CW jamming

Fig. 5 BER performance in CW jamming environment.

1.E-04 0

5

10

15

20

Power of burst noise [dB] (b) BER vs. power of burst noise

Fig. 6 Performance of bit error rate in burst noise environment.

4.2 Burst noise Figure 6 (a) and (b) show performance of bit error rate (BER) in burst noise environments. In the Fig. 6, "Pro. LLR (estimation PV)" is the proposed lump likelihood ratio decisions are employed PV estimation method. In Fig. 6(a), BER of the proposed method (correct values) is superior to that of a conventional method, and it is nearly equal to that of the proposed methods (estimation PV and VD). It means that the estimation methods are properly worked. In Fig. 6 (b), the larger the power of burst noise, the more BER degradation of the conventional method is increased. While, when the power of burst noise is large more and more, BERs of the proposed methods (correct values, estimation PV and VD) do not increase and become almost constant.

4.3 CW jamming and burst noise Figure 7 (a) and (b) show performance of bit error rate (BER) in CW and burst noise environments. In the Fig. 7 (a), "CW : AP" and "CW : VD" are employed the estimation method of AP and VD against CW, and "burst : PV" and "burst : VD" are employed the estimation method of PV and VD against burst noise, respectively. In Fig. 7 (a), BER of the proposed method (correct values) is superior to that of a conventional method, however, as for the estimation methods, BER of employed them are inferior to that of proposed method (correct values), because the estimation of CW and burst noise is interfered by burst noise and CW, each other. Figure 7 (b) shows BER performance employed the estimation method without values of interfered slots or chips as follows. (1) Interfered chips by burst noise are estimated by PV or VD method on training frame. (2) CW voltages and interfered slots by CW are estimated by AP or VD method without values of the interfered chips by burst noise on training frame. (3) Burst noise variances are estimated by PV or VD me-

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thod without values of the interfered slots by CW on training frame. In Fig. 7 (b), BER of proposed methods employed the estimation methods are much superior to that of conventional methods when Eb/No is less than 9 or 10 [dB]. It means that the estimation methods are properly worked. However, when Eb/No becomes more than 9 or 10 [dB], BER of proposed methods employed PV of the burst are degraded. As a reason, the power of CW increases together when Eb/No increases, so that the error of noise variance measurement increases and the PV method of burst noise works degraded. Soft Con. lump LLR Pro. LLR (CW: AP burst: PV) Pro. LLR (CW: AP burst: VD) Pro. LLR (CW: VD burst: PV) Pro. LLR (CW: VD burst: VD) Pro. LLR (correct values)

worked, because offset carrier CW interferes some chips and Vcw is fluctuated as eq. (1). Figure 8 (b) shows BER performance employed lump likelihood ratio decision method without the values of mainly interfered slots by CW as follows. (1) Interfered slots by CW are estimated by PV or VD method. (2) Lump likelihood ratio decision is carried out as values of the interfered slots are all 0. In Fig. 8 (b), BER of proposed methods employed the lump likelihood ratio decision are much superior to that of conventional methods. It means that the estimation methods are properly worked. However, the estimation method is not still enough, it is necessary to correspond to the fluctuation of Vcw.

1.E+00 1.E+00

1.E-01

1.E-01

1.E-02 Bit error rate

Bit error rate

Soft Con. LLR Pro. LLR (estimation AP ) Pro. LLR (estimation VD) Pro. LLR (correct parameters)

1.E-03 1.E-04

1.E-02 1.E-03 1.E-04

1.E-05 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Eb/No [dB] (a) Simple combination each estimation

1.E-05 0

1

2

3

4 5 6 Eb/No [dB]

7

8

9

8

9

10

1.E+00 1.E-01

1.E+00

1.E-02

1.E-01

1.E-03 1.E-04 1.E-05 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Eb/No [dB] (b) Method subtracting other disturbance each estimation

Fig. 7 BER performance in CW jamming and burst noise environment.

4.4 Offset carrier CW Figure 8 (a) and (b) show performances of bit error rate (BER) in offset carrier CW jamming environments. In the Fig. 8 (a), BER of the proposed method (correct values) is superior to that of conventional methods, however, BER curves of proposed methods estimation are inferior to that of conventional method and they are not properly

Bit error rate

Bit error rate

(a) Conventional CW estimation method

1.E-02 1.E-03 1.E-04 1.E-05 0

1

2

3

4 5 6 Eb/No [dB]

7

10

(b) Eliminating slot of CW estimating

Fig. 8 BER performance in CW jamming environment non-carrier frequency.

5 CONCLUSIONS In this paper, we have proposed a new lump likelihood ratio calculation method of FH pattern against CW jamming and burst noise. The likelihood ratio has been mod-

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ified by CW jamming or/and burst noise. The estimation methods for parameters of these jamming and noise have been described. By computer simulations, the improvements of the proposed methods have been shown in comparisons with the conventional method for several conditions. For further studies, it will be necessary that fluctuating CW voltage is estimated in offset CW jamming environment.

REFERENCES [1]

[2] [3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

G. Marubayashi, M. Nakagawa and R. Kohno, “Spread Spectrum Communications and its Applications,” The Institute of Electronics, Information and Communication Engineers (IEICE), Corona-sha, 1998. (Book style) H. Ogiwara, “Introduction of Turbo Codes,” Triceps, 1999. (Book style) H. Yoshihara and S. Tachikawa, “On a Detection Method of FH Pattern with Likelihood Ratio Decision,” Technical Report of the Institute of Electronics, Information and Communication Engineers (IEICE), SST2002-247 pp.141-145, March 2002. (Technical report) M. Sakai, S. Tachikawa and M. Hamamura, “On a FH Pattern Lump Likelihood Ratio Decision Method,” Technical Report of the Institute of Electronics, Information and Communication Engineers (IEICE), WBS2004-49 pp.23-28, Dec. 2004. (Technical report) D. Middleton, “Statistical-Physical Models of Electromagnetic Interference, ” IEEE Trans. Electromagnetic Compatibility, vol. EMC-19, no.3, pp.106-126, Aug. 1977. (IEEE Transactions ) H. Takeuchi and G. Marubayashi, “Measurements of noise in residential power line,” The Institute of Electronics, Information and Communication Engineers (IEICE), Spring National Convention, B-268, Mar. 1989. (Technical report) D. J. Goodman, P. S. Henry and V. K. Prabhu, “FrequencyHopped Multilevel FSK for Mobile Radio,” Bell System Tech. J., Vol. 59, No. 7, pp.1257-1275, Sep. 1980. (Journal or magazine citation) F. Nishijo, H. Mori, S. Tachikawa and G Marubayashi, “On a MMFSK System for High Frequency Power-Line Communications in a Burst Noise Environment,” Shin-Etsu Sec. Conv. Rec. of the Institute of Electronics, Information and Communication Engineers (IEICE), pp.1-2, Oct. 2003. (Technical report) K. Kobayashi and S. Tachikawa, “On a FH Pattern Lump Likelihood Ratio Decision Method against CW jamming or Burst noise,” Technical Report of the Institute of Electronics, Information and Communication Engineers (IEICE), WBS2005-54 pp.43-48, Dec. 2005. (Technical report) K. Kobayashi and S. Tachikawa, “FH Pattern Likelihood Ratio Decision Method against CW Jamming or/and Burst Noise,” 2006 IEEE ninth International Symposium on Spread Spectrum Thechniques and Applications (ISSSTA), pp. 21-25, Aug. 2006. (Conference proceedings)

Shin'ichi Tachikawa was born in Niigata, Japan. He received the B.S., M.S. and Dr. Degrees in electrical engineering from Nagaoka University of Technology, Nagaoka, Japan, in 1980, 1982 and 1991, respectively. He was engaged at Nagaoka University of Technology from 1982 to 2009. Since 2009, he has been a member of Engineering at Nagaoka National College of Technology, where he is now a Professor. His current research interests lie in the areas of spread spectrum communication system, ultra wideband systems, coding theory and signal processing. Dr. Tachikawa is a member of IEICE (The Institute of Electronics, Information and Communication Engineers) of JAPAN. Kenji Kobayashi was born in Chiba, Japan. He received the B.S. and M.S. Degrees in electrical engineering from Nagaoka University

of Technology, Nagaoka, Japan, in 2005 and 2007, respectively. His current research interests lie in areas of communication systems.