Noise suppressions in synchronized chaos lidars · 2017. 10. 11. · Noise suppressions in synchronized chaos lidars Wen-Ting Wu, Yi-Huan Liao, and Fan-Yi Lin∗ Institute of Photonics

Noise suppressions in synchronizedchaos lidars

Wen-Ting Wu, Yi-Huan Liao, and Fan-Yi Lin∗

Institute of Photonics Technologies, Department of Electrical Engineering,National Tsing Hua University, Hsinchu 30013, Taiwan

∗[email protected]

Abstract: The noise suppressions in the chaos lidar (CLIDAR) and thesynchronized chaos lidar (S-CLIDAR) systems with the optoelectronicfeedback (OEF) and optical feedback (OF) schemes are studied numerically.Compared with the CLIDAR system, the S-CLIDAR system with the OEFscheme has better correlation coefficients in the large noise regime forSNR < 15 dB. For the S-CLIDAR system with the OF scheme, betterdetections are also achieved in wide ranges depending on the levels of thephase noise presented in the channel. To have the best synchronization anddetection quality, the optimized conditions for the coupling and feedbackstrengths in the S-CLIDAR system are also discussed.

© 2010 Optical Society of America

OCIS codes: (010.3640) Lidar; (140.1540) chaos; (140.5960) semiconductor lasers.

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#136528 - $15.00 USD Received 13 Oct 2010; revised 24 Nov 2010; accepted 26 Nov 2010; published 30 Nov 2010(C) 2010 OSA 6 December 2010 / Vol. 18, No. 25 / OPTICS EXPRESS 26155

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1. Introduction

Chaos lidar (CLIDAR) utilizing laser chaos was proposed and studied [1] due to its advantagesof high resolution and long unambiguous range in ranging. The unique characteristics of CLI-DAR were mostly benefited by the broadband chaotic waveforms used, which can be generatedwith nonlinear laser dynamics in an optical feedback (OF) [2] [3], an optoelectronic feedback(OEF) [4] [5] [6], or an optical injection (OI) [7] [8] [9] scheme. Similar to other conventionalmodulated continuous-wave lidars [10] [11] [12], target detections in the CLIDAR system arerealized by correlating the signal waveform backscattered from the target with a delayed replicafrom the transmitter laser. Although the proof-of-concept experiments have been demonstratedpreviously [1] where the range resolutions and peak-to-sidelobe levels have been investigated,the effect of channel noise on the detection performance has not yet been discussed.

To understand the behavior of the CLIDAR system in a real environment with atmospheredisturbance, perturbations of additive white Gaussian noise and random phase noise on theamplitude and phase, respectively, of the signal waveforms are considered in this study. Tomitigate the degradation in detection due to the undesired noise and to take a step further to fullyexploit the advantages of laser chaos, a modified synchronized-CLIDAR (S-CLIDAR) systemusing a receiver laser to synchronize with the transmitter laser are proposed and studied. Insteadof detecting the noise-contaminated signal with a photodetector directly, the signal waveform iscoupled into a receiver laser and drives it into synchronization [13] where the receiver laser canreproduce the original chaotic waveform from the transmitter laser without being distorted bythe channel noise. In this paper, the detection performances of the CLIDAR and the S-CLIDARsystems under the OEF and the OF schemes are compared and investigated numerically. Withthe CLIDAR system as the benchmark, noise suppressions of the S-CLIDAR systems underdifferent levels of noise are studied. The optimized conditions to have the highest possiblecorrelation coefficients are also discussed and given.

2. Model

Figures 1(a)-(d) show the schematic setups of the original CLIDAR and the newly proposedS-CLIDAR systems with the OEF and the OF schemes. The yellow and blue dots denote thetransmitter and receiver outputs. For the CLIDAR systems as shown in Figs. 1(a) and (b), therange delays of the targets are determined directly from the correlations of the receiver outputs(the backscattered signals detected by the photodetectors) (blue dots) and the transmitter out-puts (the reference signals from the transmitter lasers (Tx) (yellow dots). On the other hand,for the S-CLIDAR systems as shown in Figs. 1(c) and (d), the backscattered signals are insteadcoupled into the receiver lasers (Rx), electrically for the OEF and optically for the OI schemes,to drive the Rx to synchronize with the Tx. The receiver outputs (the synchronized waveforms)(blue dots) are then used to correlate with the transmitter output (yellow dots). Note that, the Rxhas its own feedback loop governed by the feedback strength ηR and the delay time τR, whereηR = 0 represents cases when the Rx is in an open-loop configuration and ηR �= 0 representsthe cases when the Rx is in a close-loop configuration.

The nonlinear dynamics of the Tx and Rx for the CLIDAR and the S-CLIDAR systems can


Cτ

Cτ

Tx

Rx

Target

B

Rx

Tx

Rx

Tx

M

Rτ

Target

M

M

ROEF,η

PD

PD A

PD

BS

Tx

Rx

Tx

M

Target

PD

M

Rx

Tx

Rx

Target

M

M

Tτ

Cτ

COEF,η

Tτ

T,OFη

Rτ

ROF,η

COF,η

COF,η

( )a

( )c

( )b

( )d

CL

ID

AR

S-C

LID

AR

OEF OF

TOEF,η

Tτ

TOEF,η

B

Tx

MPD

BS

MA

Tx

PD

BS

MA

Cτ

COEF,η

PD

BS

BSPD

BSTx

M

M

Tτ

T,OFη

BSPD

BS

PD

Fig. 1. (Color online) Schematic setups of the CLIDAR and the S-CLIDAR systems withthe OEF and the OF schemes. Tx and Rx are the transmitter and the receiver lasers. ηT andηR are the feedback strengths of the Tx and Rx and ηC is the coupling strength from thechannel to the Rx, respectively. τT and τR are the feedback delay times of the Tx and Rxand τC is the target range delay in the channel, respectively.

be modelled by the following coupled rate equations:

daT

dt=

12

[γcγn

γsJTnT − γp(2aT +a2

T)

](1+aT)

+ηOF,T(1+aT(t − τT))cos(φT(t − τT)−φT(t)+ωTτT) (1)

dφT

dt=−b

2

[γcγn

γsJTnT − γp(2aT +a2

T)

]

+ηOF,T(1+aT(t − τT))

1+aTsin(φT(t − τT)−φT(t)+ωTτT) (2)

dnT

dt=−γsnT − γn(1+aT)

2nT − γsJT(2aT +a2T)+

γsγp

γcJT(2aT +a2

T)(1+aT)2

+ηOEF,Tγs(JT +1)(1+2aT(t − τT))+aT(t − τT)2 (3)


daR

dt=

12

[γcγn

γsJRnR − γp(2aR +a2

R)

](1+aR)

+ηOF,R(1+aR(t − τR))cos(φR(t − τR)−φR(t)+ωRτR)

+ηOF,C(1+aC(t − τC))cos(φC(t − τC)−φR(t)+ωTτC −Δωt) (4)

dφR

dt=−b

2

[γcγn

γsJRnR − γp(2aR +a2

R)

]

+ηOF,R(1+aR(t − τR))

1+aRsin(φR(t − τR)−φR(t)+ωRτR)

+ηOF,C(1+aC(t − τC))

1+aRsin(φC(t − τC)−φR(t)+ωTτC −Δωt) (5)

dnR

dt=−γsnR − γn(1+aR)

2nR − γsJR(2aR +a2R)+

γsγp

γcJR(2aR +a2

R)(1+aR)2

+ηOEF,Rγs(JR +1)(1+2aR(t − τR))+aR(t − τR)2

+ηOEF,Cγs(JR +1)(1+2aC(t − τC))+aC(t − τC)2, (6)

where a is the normalized optical field, φ is the optical phase, n is the normalized carrier density,J is the normalized dimensionless injection current parameter, γc is the cavity decay rate, γn

is the differential carrier relaxation rate, γp is the nonlinear carrier relaxation rate, γs is thespontaneous carrier relaxation rate, b is the linewidth enhancement factor, η is the couplingrate, τ is the delay time, and Δω is the angular frequency detuning between the Tx and Rx. Thesubscripts T, R, and C denote the Tx, Rx, and channel, respectively. The laser parameters usedhere are b= 4, γn = 0.667×109s−1, γp = 1.2×109s−1, γs = 1.458×109s−1, γc = 2.4×1011s−1,Δω = 0, and J = 0.333 [14].

To simulate the disturbance in the transmission channel and study the degradation in detec-tion affected by the noise, amplitude and phase noises are added to the backscattered signalsbefore receiving by the photodetector in the CLIDAR and by the Rx in the S-CLIDAR systems,respectively. Modelled by an additive white Gaussian noise RN1 with zero mean and varianceof σ2

RN1 and a random phase noise RN2 evenly distributed in the range between [−π,π], theamplitude and phase noise are added to the respective amplitude aC(t) and the phase φC(t) ofthe received signals,

aC(t) = aT(t)+RN1(t) (7)

φC(t) = φT(t)+mRN2(t), 0 ≤ m ≤ 1 (8)

The relative strength of the amplitude noise is defined by the signal-to-noise ratio (SNR)

SNR = 10logPs

σ2RN1

, (9)

where Ps is the average power of the transmitted signal. The influence of the phase noise iscontrolled by m, where m = 0 is the case when no phase noise is considered.

To quantify the performance of target detection in different schemes, the correlation coeffi-cients under different noise levels are calculated as

ρ(Δτ) =〈[ST (t)−〈ST (t)〉] [SR(t +Δτ)−〈SR(t)〉]〉〈|ST (t)−〈ST (t)〉|2〉

12 〈|SR(t)−〈SR(t)〉|2〉

12

, (10)


where ST(t) and SR(t) are the intensity outputs of the transmitter (yellow dot) and the receiver(blue dot), 〈·〉 denotes the time average, and Δτ is the relative time difference between the trans-mitter and the receiver, respectively. The correlation coefficient is bounded with −1 ≤ ρ ≤ 1,where a larger value of |ρ | indicates better quality of detection.

3. Results and discussions

CLIDAR

Tx Rx

(a)

(b)

(c)

(d)

(e)

(f)

S-CLIDAR

Fig. 2. (a) Time series and (b) autocorrelation of the transmitted waveform from the Txof the OEF scheme with a delay time τT = 9.5 and a feedback strength ηOEF,T = 0.123.(c)-(f) The detected waveforms in the receivers and their corresponding correlations to thetransmitted waveform for the CLIDAR and the S-CLIDAR systems, respectively.

Figures 2(a) and (b) show the time series and autocorrelation of the transmitted waveform fromthe Tx of the OEF scheme with a delay time τT = 9.5 ns and a feedback strength ηOEF,T = 0.123,respectively. For the S-CLIDAR system with the OEF scheme, since the backscattered light isconverted to the electric signal before coupling to the Rx, little effect of the phase noise fromthe channel is found. Under the influence of the amplitude noise with SNR = 0 dB, the detectedwaveforms in the receivers and their corresponding correlations to the transmitted waveform forthe CLIDAR and the S-CLIDAR systems are shown in Figs. 2(c)-(f), respectively. As can beseen, compared with the received waveform in the CLIDAR system that is noisy and severelydistorted from the transmitted waveform, the waveform reproduced by the Rx through syn-chronization in the S-CLIDAR system has little distortion. Correlation coefficients of 0.73 and0.97 are obtained for the CLIDAR and the S-CLIDAR systems at a delay of 15.5 ns, which isthe range delay of the target in the transmission channel τC = 15.5 ns under the generalizedsynchronized condition. Note that, to have the best synchronization for the highest possiblecorrelation coefficient, the coupling strength ηOEF,C and the feedback strength ηOEF,R of theS-CLIDAR system have to be optimized with different levels of noise presented in the chan-nel. Through simulations, for SNR = 0 dB, optimized coupling strength and feedback strengthof ηOEF,C = 1.3 and ηOEF,R = 0 are found showing that the S-CLIDAR system has a bettersynchronization performance under a generalized synchronization condition with an open-loop


configuration. Detailed investigations on the optimized coupling strengths under different SNRsfor the S-CLIDAR systems with the OEF and the OE schemes will be discussed and given inFig. 6.

S-CLIDAR (m = 0.5)

Tx

Rx

S-CLIDAR (m = 0) S-CLIDAR m = (0.75)

(a) (b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

CLIDAR

Fig. 3. (a) Time series and (b) autocorrelation of the transmitted waveform from the Txof the OF scheme with a delay time τT = 9.5 ns and a feedback strength ηOEF,T = 0.2.(c)-(j) The detected waveforms in the receivers and their corresponding correlations to thetransmitted waveform for the CLIDAR and the S-CLIDAR systems with the phase noiselevels of m = 0, 0.5, and 0.75, respectively.

Figures 3(a) and (b) show the time series and autocorrelation of the transmitted waveformfrom the Tx of the OF scheme with a delay time τT = 9.5 ns and a feedback strength ηOF,T = 0.2,respectively. Unlike in the OEF scheme, the phase noise is found to affect the synchronizationsignificantly in the Rx for the S-CLIDAR system with the OF scheme. With SNR = 0 dB,Figs. 3(c)-(j) show the time series of the detected waveforms and their corresponding correla-tions to the transmitted waveform for the CLIDAR and the S-CLIDAR systems with the phasenoise levels of m = 0, 0.5, and 0.75, respectively. As can be seen, although not being affectedby the phase noise, the detected waveform of the CLIDAR system as shown in Fig. 3(c) is dis-torted severely from the transmitted waveform solely because of the influence of the amplitudenoise where a correlation coefficient of only 0.36 is found. On the contrary, the S-CLIDAR sys-tem shows good ability in filtering both the amplitude and the phase noises, where correlationcoefficients of 0.88, 0.82, and 0.53 are achieved for phase noise levels of m = 0, 0.5, and 0.75,respectively.

Figure 4 shows the correlation coefficients of the CLIDAR and the S-CLIDAR systems withthe OEF and the OF schemes for different levels of noise. As shown in Fig. 4(a), both theCLIDAR and the S-CLIDAR systems with the OEF scheme show excellent performance withcorrelation coefficients close to unity for SNR > 15 dB. As for −17 dB < SNR < 15 dB, the S-CLIDAR shows better performance benefitted from the noise filtering through synchronization.After the amplitude noise increases to a level of SNR <−17 dB, the synchronization condition


(a) (b)

Fig. 4. (Color online) Correlation coefficients of the CLIDAR and the S-CLIDAR systemswith (a) the OEF and (b) the OF schemes for different levels of noise.

is broken and both the CLIDAR and the S-CLIDAR systems cannot determined the range delayfrom the correlation coefficients.

For the OF scheme as shown in Fig. 4(b), the correlation coefficients of the CLIDAR and theS-CLDAR systems maintain at constant levels for SNR > 15 dB. While the S-CLIDAR systemhas the same correlation coefficient of a value close to unity as in the CLIDAR system for m= 0,the performance degrades as the level of phase noise increases. For −17 dB < SNR < 15 dB,the correlation coefficient of the CLIDAR system drops quickly even when only affecting bythe amplitude noise. Meanwhile, the correlation coefficients of the S-CLIDAR system stay athigher levels benefitted by the synchronization process.

<

>

Fig. 5. (Color online) The differences of the correlation coefficients Δρ between the S-CLIDAR and the CLIDAR systems for different levels of noise

Using the CLIDAR system as the benchmark, the capabilities of the S-CLIDAR system innoise suppression with the OEF and the OF schemes under different noise levels are calculatedand shown in Fig. 5. Figure 5 shows the differences of the correlation coefficients between theS-CLIDAR and the CLIDAR systems

Δρ = ρS-CLIDAR − ρCLIDAR. (11)

As can be seen, a range of suppression of about 32 dB (−17 dB < SNR < 15 dB) is found forthe OEF scheme where the S-CLIDAR system outperforms the CLIDAR system. Compared


with the OEF scheme that is inherently not influenced by the phase noise, the OF schemeshows better performance when the phase noise is not presented (m = 0). While the range ofsuppression gradually decreases as the level of the phase noise increases, suppression rangesof 29.1 and 22.4 dB are still obtained for m = 0.5 and 0.75 in a low SNR regime similar topractical scenarios [15] [16].

(a) (b)

Fig. 6. (Color online) The optimized coupling strengths of ηOEF,C and ηOF,C for the S-CLIDAR system with (a) the OEF and (b) the OF schemes under different levels of noise

In this study, the coupling and the feedback strengths of the Rx in the S-CLIDAR system areoptimized for the highest possible correlation coefficients. With all levels of noise, an open-loopconfiguration and a generalized synchronization condition are found to have the best perfor-mance in general. Figures 6(a) and (b) show the optimized ηOEF,C and ηOF,C for different noiselevels, respectively. For the OEF scheme in a low noise regime with SNR > 15 dB, a largerηOEF,C is desired for better synchronization. As the level of noise increases to SNR < 15 dB,the optimized coupling strength decreases as the noise level increases. In this regime, a strongcoupling couples too much noise into the Rx and causes the degradation in synchronization.For the OF scheme, a larger ηOF,C is also desired in the low noise regime when the phase noiseis not presented (m = 0). When the phase noise is notable (m = 0.5 and 0.75) or when theamplitude noise increases (lower SNR), lower the coupling strengths are required for optimalsynchronization and target detections.

4. Conclusions

In conclusion, the noise suppressions of the CLIDAR and the S-CLIDAR systems with the OEFand the OF schemes are numerically studied and compared. With the capability of noise filteringthrough synchronization, the S-CLIDAR system with the OEF scheme shows better detectionperformance for SNR < 15 dB. The S-CLIDAR system with the OF scheme also shows betterdetections in the low SNR regime, where the range outperforming the CLIDAR system grad-ually decreases when the phase noise in the channel increases. The conditions for the highestpossible correlation coefficients are also given, where an open-loop configuration under a gen-eralized synchronization condition along with an optimized coupling strength depending on thenoise level are desired. Experimental characterizations on the noise suppressions and detectionperformance of the S-CLIDAR system will be carried out and reported separately.

Acknowledgments

This work is supported by the National Science Council of Taiwan under contract NSC-97-2112-M-007-017-MY3.


Documents

Noise suppressions in synchronized chaos lidars · 2017. 10. 11. · Noise suppressions in synchronized chaos lidars Wen-Ting Wu, Yi-Huan Liao, and Fan-Yi Lin∗ Institute of Photonics