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Optik 125 (2014) 2582–2586

Contents lists available at ScienceDirect

Optik

jo ur nal homepage: www.elsev ier .de / i j leo

comparative study between LMS and PSO algorithms on the opticalhannel estimation for radio over fiber systems

yhan Yazgan ∗, I. Hakki Cavdarepartment of Electrical Electronics Engineering, Karadeniz Technical University, 61080 Trabzon, Turkey

r t i c l e i n f o

rticle history:eceived 30 May 2013

a b s t r a c t

In this paper the particle swarm optimization (PSO) and least mean square (LMS) algorithms are compar-atively studied to estimate the optical communication channel parameters for radio over fiber systems.

ccepted 1 November 2013

eywords:adio over fiber systemsptical channel estimationarticle swarm optimizationeast means square

It is observed that especially in low noise one tap optical channels, the convergence of LMS algorithm isapproximately same with PSO algorithm. On the other hand, as a communication medium, selecting highnoisy fiber optical channels or free space optical channels; PSO reaches better mean square error values.The computational complexity which is one of the most important features for optimization algorithmshas also been taken into account.

© 2013 Elsevier GmbH. All rights reserved.

. Introduction

In order to achieve a high quality data transmission betweenransmitter and receiver, some implementations at the receiveride must be carried out. First of all, the effect of the commu-ication channel should be determined. Then, the equalizationrocess is pursued and the negative effect of communication chan-el is eliminated. Therefore, to reach the transmitted informationith high accuracy, channel estimation becomes a vital part of

ommunication systems and this topic attracts great attention byelecommunication researchers and engineers [1]. As the opti-al communication is the backbone of the whole communicationetwork, the optical channel estimation becomes an importantrocess especially for radio over fiber (RoF) systems. Since theirpplications are constrained by their high cost in optical domain,lthough the physical communication channel is an optical fiber,ome processes such as channel estimation and equalization maye implemented in electrical domain such as maximum likelihoodequence detection (MLSD) [1]. In this technique, the knowledge ofhe statistics of the received samples is required [2]. Another tech-ique is to utilize the high order modulation techniques in whichulticarrier signals are used to estimate the effect of the communi-

ation channel [3,4]. On the other hand, adaptive algorithms which

ave been extensively studied especially in the signal processingeld may be good candidate for channel estimation [5]. One ofhe most investigated adaptive techniques is the least mean square

∗ Corresponding author.E-mail address: ayhanyazgan@ktu.edu.tr (A. Yazgan).

030-4026/$ – see front matter © 2013 Elsevier GmbH. All rights reserved.ttp://dx.doi.org/10.1016/j.ijleo.2013.11.015

(LMS) algorithm which is used for different disciplines of scienceas an effective adaptive algorithm such as channel tracking imple-mentations in telecommunication. However it is quite sensitive tothe adjustment of the step-size parameter which is the tradeoffbetween the speed of convergence and the misadjustment [6]. Inthis paper, the particle swarm optimization (PSO) algorithm is pro-posed to estimate the coefficients of the optical channel filter forRoF systems. It is assumed that the channel is single mode opticalfiber. The simulation parameters are commercially available suchas 17 ps/(nm km) for dispersion parameter and 0.2 dB/km for atten-uation coefficient. In the results section, a comparison between LMSand PSO algorithms on the ability of fast convergence for differentnoise conditions and the computational complexity is presented. Soas to see the effect of particle number on the optical channel esti-mation, different particle numbers of the PSO algorithm are alsocomputed and presented in the results section.

The paper is organized as follows. Section 2 outlines the opticalchannel model. Section 3 describes the adaptive algorithms. Section4 presents and discusses the results comparatively. Consequently,Section 5 discusses the results and the future work, and Section 6concludes the paper.

2. Optical channel model

The channel profile is selected as one tap and given in Fig. 1.

The complex channel coefficient is selected as 0.6–0.9i. It shouldbe explained here that there is not any criterion for this selection.Therefore, it is determined randomly with the acceptable ampli-tude and phase variations.

A. Yazgan, I.H. Cavdar / Optik

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given in Figs. 4–7. Selecting 20 particles, the error value is obtainedas 0.0005292 after 21 iterations. But for the same iteration number,using PSO with 5 particles, this error value is observed as 0.003927.From the Figs. 2–3, it is also clear that the more particles are used

Fig. 1. Optical channel model.

Considering an orthogonal frequency division multiplexingOFDM) modulation as a digital communication technique, theasic equations of the optical channel model, are given in (1)–(5),here cmn and c′

mn are transmitted and received data, respectively.n is the transfer function of nth subcarrier, ϕm is the phase drift ofhe mth transmitted symbol to be estimated, and nmn is the opti-al noise for the related subcarrier. The transfer function or theroup velocity delay (GVD) of the optical channel consists of a lin-ar variable related to the time delay of the first signal �0, opticalber chromatic dispersion parameter Dt in the unit of ps/nm forach km and a dc variable ϕ0. ϕD(n) is the dispersion affected phaseomponent of nth subcarrier (fn) because of the fiber chromatic dis-ersion, fLD1 is the laser frequency at the transmitter, and c is thepeed of light in the fiber core [7]. If the amplitude of the reflectionss higher than the expected, then the multipath effect needs to beonsidered for the channel. But for a single mode optical fiber cable,his multipath effect can be neglected by considering the dispersionffect.

′mn = cmn.hn. exp(jϕm) + nmn (1)

n =∣∣hn

∣∣ exp(j(ϕ0 + 2˘�0fn + ϕD(n))) (2)

2 = �LD12

2�cDt (3)

D(n) = 12

ˇ2ω2nL (4)

D(n) = c.�

f 2LD1

Dtf2n L (5)

. Adaptive algorithms for channel estimations

.1. LMS algorithm

LMS algorithm can be defined using three equations given in6)–(8). Here, c(k) is the input signal vector, y(k) is the estimated

hannel output, w(k) is the adaptive filter coefficient vector, c′(k)s the channel output, e(k) is the estimation error and � is the stepize which must be selected precisely to reach the best convergencealue.

(k) = w(k)T c(k) (6)

(k) = c′(k) − y(k) (7)

(k + 1) = w(k) + �e(k)c(k)∗ (8)

125 (2014) 2582–2586 2583

3.2. PSO algorithm

PSO is a stochastic optimization method discovered by Kennedyand Eberhart in 1995. This robust algorithm was inspired by socialbehavior of bird flocking or fish schooling. Less parameter neces-sity and fast convergence property are some of the most importantadvantages of PSO algorithm [8–10]. PSO is composed of particleswhich individually try to solve the problem by updating their ownlocation and velocity vectors. The particle velocity and position arecalculated in (9)–(12) respectively, where v is the velocity vector,x is the position vector, i is the particle index and k is the itera-tion number. The number of particles is selected as 5, 20, and 30for the simulations. However, it can be increased according to thecomplexity of the problem.

vi(k + 1) = vi(k) + f1(k) + f2(k) (9)

f1(k) = c1rand1(k)(pbesti(k) − xi(k)) (10)

f2(k) = c2rand2(k)(gbest(k) − xi(k)) (11)

The number of iterations may be either predefined or adap-tively changed according to the defined cost function’s convergencevalue. rand1 and rand2 are uniformly distributed random numbersand give the free moving ability to the particle in the problem space.In this powerful algorithm, pbest and gbest are the best position val-ues for the particle and swarm respectively. c1 and c2 are learningfactors selected between 0 and 4 to define movement policy of aparticle. These factors stand for to figure out whether the motionof the particle is determined by its own experience or the swarm’sexperience. If the stopping criterion is satisfied, gbest becomes thesolution of the problem. For this simulation, gbest is a complexnumber which restores the optical channel coefficient.

xi(k + 1) = xi(k) + vi(k + 1) (12)

4. Results

According to the results, the mean square error (MSE = E{e(k)2})defined as the expectation of the square of the difference betweenthe estimated channel output and the exact channel output,decreases as clearly seen in Figs. 2 and 3, where the particle con-vergence is proportional to the number of iterations.

In order to see the number of particle effect on the convergencespeed and accuracy, the particle number is increased from 5 to 20 as

Fig. 2. Mean square error variation using PSO algorithm with 5 particles.

2584 A. Yazgan, I.H. Cavdar / Optik 125 (2014) 2582–2586

Fig. 3. Mean square error variation using PSO algorithm with 20 particles.

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Fig. 6. PSO with 20 particles after 2 iterations.

Fig. 7. PSO with 20 particles after 10 iterations.

Fig. 4. PSO with 5 particles after 2 iterations.

or optimization, the less iteration is needed to reach the same MSEalue. According to the algorithm nature, the particle velocity andosition is updated as described before. After this procedure thelobal best value is stored at the end of the each iteration to obtainhe expected optical channel coefficient 0.6–0.9i.

In the second part of the study, LMS and PSO algorithms are com-aratively studied on the ability of convergence speed in differentoise conditions. Results in Figs. 8 and 9, show the MSE variationccording to the signal to noise ratio (SNR) and iteration number.

onsidering 30 iterations with 30 dB SNR, while PSO algorithm with

particles converges to 0.599–0.899i, the LMS algorithm convergeso 0.598–0.901i complex channel coefficient. Since the physicalhannel is a single mode fiber optical cable, the multipath effect

Fig. 5. PSO with 5 particles after 10 iterations.

Fig. 8. Mean square error variation using PSO with 5 particles.

Fig. 9. LMS mean square error variation.

A. Yazgan, I.H. Cavdar / Optik 125 (2014) 2582–2586 2585

Fig. 10. PSO convergence with 5 particles.

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Fig. 11. LMS convergence.

s not dominant and can be neglected. For this reason especially inow noisy one tap channels the convergence of LMS algorithm ispproximately same with PSO algorithm. On the other hand PSOeaches better MSE values in high noisy channels.

The convergence variation is also simulated for both algorithmss given in Figs. 10 and 11. It is clear that LMS always changes itsrevious value for each iteration. However PSO only change thebest value if the new value is better than the previous one. Onhe other hand, the fast convergence property of the PSO can ben advantage for both high and low noisy channels. The reasonf obtaining almost the same performance in low noisy channelsan be explained by the nature of the optical channel profile. If theomplexity of the physical communication channel is increased,he effectiveness of the PSO algorithm can be seen more clearly.

Since the complexity of an optimization algorithm determinests applicability for a hardware implementation, the computationalomplexity becomes an important parameter that should be takennto consideration. Having two different updating equations whichre velocity and position, a PSO algorithm complexity is larger thanMS algorithm as given in Table 1, where M is the filter size and P

s the particle number.

able 1omputational complexity.

Complexity LMS PSO

Addition 2M P (5M)Multiplication 2M + 1 P (4M + 2)

Fig. 12. PSO with 30 particles and LMS convergence.

5. Discussion

In order to see the effectiveness of the PSO algorithm, and makea better comparison with LMS, the number of channels is increasedto 100 for both algorithms. All channels are randomly selected andthe averaged results are given in Fig. 12. Here, we also increase theiteration number from 30 to 150. It should be noted that the numberof particles is an important parameter for convergence propertyand it is also increased to 30. According to the result given in Fig. 12,especially in high noisy channels with low iteration number, thePSO algorithm has better convergence values comparing to LMSalgorithm. For this reason as a future work a multimode fiber orwireless optical channels can be modeled to see the effectivenessof the PSO algorithm more clearly. In this case, the multipath effecthas to be taken into account while modeling the correspondingoptical channel mathematically.

6. Conclusions

The effect of the swarm intelligence on the optical channelestimation was investigated. Comparing to the LMS algorithm itis observed that the swarm intelligence is stronger and a bettercandidate especially for channel tracking applications. The com-putational complexity of the both algorithms was investigated.Even PSO includes more complexity compared to LMS; it has agreat advantage to be suitable for parallel computing such as anfield-programmable gate array (FPGA) implementations. Since thechannel is a single mode fiber optical cable, the multipath effect isnot dominant and can be neglected. For this reason, especially inlow noisy one tap channels the convergence of LMS algorithm isapproximately same with PSO algorithm. On the other hand, PSOreaches better MSE values in high noisy fiber optical or opticalwireless channels.

References

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MLSD in optical communication systems, IEEE Photonics Technology Letters18 (19) (2006) 1984–1986.

[3] W. Shieh, C. Athaudage, Coherent optical orthogonal frequency division multi-plexing, IEE Electronics Letters 42 (2006) 5–589.

[4] A. Yazgan, I.H. Cavdar, The tradeoff between bit error rate and optical link dis-tance using laser phase noise fixing process in coherent optical OFDM systems,Wireless Personal Communications 68 (2013) 907–919.

[5] B. Widrow, S.D. Stearns, Adaptive Signal Processing, Prentice Hall, Englewood

Cliffs, NJ, 1985.

[6] A. Ozen, A novel variable step size adjustment method based on channel out-put autocorrelation for the LMS training algorithm, International Journal ofCommunication Systems 24 (2011) 938–949.

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[7] A. Yazgan, The tradeoff between BER and link distance for a constant signal tonoise ratio in coherent optical OFDM systems, in: TSP 2011, Budapest, Hungary,2011, pp. 126–130.

[8] J. Kennedy, R. Eberhart, Particle swarm optimization, in: IEEE InternationalConference on Neural Networks Proceedings, 1995, pp. 1942–1948.

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