Crossover-Cat Swarm Optimization

Transcription

1 Australian Journal of Basic an Applie Sciences, 0(5) Special 06, Pages: -6 AUSTRALIAN JOURNAL OF BASIC AND APPLIED SCIENCES ISSN: EISSN: Journal home page: RBFNN Equalizer using Crossover-Cat Swarm Optimization Rabi K. Mohapatra, Archana Sarangi, 3 Tumbanath Samantara, 4 Siba P. Panigrahi an 5 Santanu K. Nayak KIT, Berhampur, Oisha,Inia SOA University, Bhubaneswar, Oisha, Inia 3 OEC, Bhubaneswar, Oisha, Inia 4 NIT, Arunachal Praesh, Inia 5 Berhampur University, Oisha, Inia Aress For Corresponence: Siba P. Panigrahi, NIT, Arunachal Praesh, Inia. siba_panigrahy5@reiffmail.com A R T I C L E I N F O Article history: Receive January 06 Accepte February 06 Available online March 06 Keywors: Raial Basis Function Neural Network;Channel Equalization;Particle swarm optimization;cat swarm optimization; Crossover cat swarm optimization. A B S T R A C T Raial Basis function Neural Networks (RBFNN) is one of most popular equalizers to mitigate the channel istortions. Most challenging problem associate with esign of RBFNN Equalizer is the traitional hit an trial metho. The problem is formulate as an optimization problem an solve using a hybriize version of Cat Swarm Optimization (CSO) terme as Crossover Cat Swarm Optimization (Cross-CSO). Here, the exploration an exploitation of the existing CSO is increase by aing the concept of crossover in genetic algorithm to CSO. The new Cross-CSwith the stanar particle swarm optimization (PSO) an original CSO to prove its algorithm is compare effectiveness with some stanar benchmark functions. The simulation results prove the superior performance of the propose Cross-CSO as compare to the traitional algorithms. INTRODUCTION Present ay research on filter esign an channel equalization focuses aroun use of swarm an evolutionary algorithms. However, use of artificial neural network (ANN) is common an popular in a wie range of engineering problems incluing the problem channel equalization. A etaile review on channel equalization using Multi-layer Perceptron (MLP), functional-link artificial NN (FLANN) an neuro-fuzzy systems is provie in (Burse et al,, 00, Subramanian et al., 04). Recent literature on channel equalization shows a pointer for use of neural networks (Ruan an Zhang, 04, Cui et al., 04). But, ANNs have inherent limitations of large complexity an also fall to local optima. However, RBFNN contains only one hien layer fins global minima (Gan et al., 0). RBFNN is less complex an provies better performance then ANN base equalizers. Recent research on channel equalization (Civicioglu et al., 005, Kaur, 03, Schilling et al., 00, Yavuz an Yilirim, 008} also proves popularity of RBFNN. Design of RBFNN still remains as a challenge. Maor issues with RBFNN esign are etermination of the number of Raial Basis functions (RBFs), number of cluster centres etc. This trial-an-error process of esigning these terms is also time-consuming. The key parameters like weights, centers, an spreas an their esign remains as a challenge in RBFNN esign. To avoi this time consuming process an also to improve local optimal problems, Barreto et.al (00) use Genetic Algorithm (GA) an Feng (006) use Particle Swarm Optimization (PSO). These are use to ecie these key an bias parameters. Minimization of the Mean Square Error (MSE) between the esire an actual outputs is actual criteria in the esigns formulate in (Barreto et al., 00. Feng, 006) Search space in PSO is limite an hence to local minima (Bergh an Engelbrecht, 00). In Open Access Journal Publishe BY AENSI Publication 06 AENSI Publisher All rights reserve This work is license uner the Creative Commons Attribution International License (CC BY). /4.0/ To Cite This Article: Rabi K. Mohapatra, Archana Sarangi, Tumbanath Samantara, Siba P. Panigrahi an Santanu K. Nayak., RBFNN Equalizer using Crossover-Cat Swarm Optimization. Aust. J. Basic & Appl. Sci., 0(5): -6, 06

2 Rabi K. Mohapatra et al, 06 Australian Journal of Basic an Applie Sciences, 0(5) Special 06, Pages: -6 this paper we make use of The CSO (Chu S.C., an Tsai, P.W. 007) an Cross-CSO (Sarangi et al., 06) for training of RBFNN base equalizer. The Cat Swarm Optimization (CSO) algorithm eals with the cat behavior an accomplishe in two submoels.here, population size for cats can be etermine by the user. For each of the iterations.in a M- imensional space, each cat efines its position, velocity in each irection. A fitness value enotes the efficiency of the cat an a flag ientifies the present moe of the cat, seeking or tracing moe. The best position of the best cat provies the final solution. CSO keeps the best solution until it reaches the en of the iteration. In this paper, a new hybri algorithm is propose by introucing the concept of crossover of genetic algorithm to the traitional CSO algorithm to increase the exploration an exploitation of the existing search space in a better way. The Problem: A igital communication system consiere in this paper is illustrate through figure. If, x( k) transmitte ata at time instant, the channel can be moelle as a FIR filter with output, y ( k) instant where, y N i i= 0 ( k ) = h x( k i) is the, at the same time () Fig. : Base-ban moel of igital communication system. Here, ( i = 0,, N ) h i L enotes the tap weights for the channel an N enotes its length. Thechannel introuces non-linear istortion which is presente by a separate block NL. The mostly use nonlinear function: y ( k ) = F( y ( )) ( ) ( ) 3 k = y k + by k () Here, b is a constant. Therefore, the channel output becomes: N N ( ) ( ) ( ) 3 y k = hi x k i + b hi x k i i= 0 i= 0 (3) The channel output is once again affecte by noise, η ( k). The noise assume here as aitive zero mean σ. The corresponing output signal that reaches the receiver, r ( k) is: white gaussianwith variance, r ( k ) r( k) + η( k) (4) This is the input signal for the equalizer. The ob of the equalizer is to recover the original sequence (while consiering transmission elay, δ ) by nullifying the effects of istortion an noise. x ( k δ ). This signal is terme as an given by: s k = x k (5) ( ) ( δ ) The equalization process is treate as a classification problem [-4], where the equalizer task is to partition the input equalizer space x( k ) = [ x( k), x( k ), L x( k N + ) ] T into two separate regions. Bay s theoryprovies an expression for an optimum solution to a nonlinear classification problem by a ecision function:

3 3 Rabi K. Mohapatra et al, 06 Australian Journal of Basic an Applie Sciences, 0(5) Special 06, Pages: -6 ( k ) N x c ( ( )) f bay x k = β exp = σ (6) For binary transmitte symbols: ( + ) + for c C β = ( ) for c C (7) ( + ) ( ) Here, C / C is the set of channel states, c is binary symbol, x ( k δ ) = +/. In figure, the block Equalizer enotes RBFNN. GA is use to fin number of layers an number of neurons in each layer (except input layer) for this RBFNN an shown by the block OA.Number of neurons In input layer is same as number of taps in the channel, N. The equalizer output: f RBF Here, W k ϕ z ( s( k )) = = = W T ( k) ϕ( k) ( k) s t w exp α ( ) = [ w ( k ) w ( k) w ( )] T,, L z k ( k) = [ φ ( k) φ ( k), Lφ ( k) ] T, ( k ) z s t φ = exp for =,, Lz α Here, t anα respectively enotes the centers an the spreas of the neurons hien layers an enotes the connecting weights. The equation (8) that is an implementation of the Bay s ecision function of equation (6) consiers t same as the channel states, c with the aequately regulate connecting weights. s Therefore, the ecision function for the RBFNN equalizer is: + f ANN ( x( k) ) 0 k δ = elsewhere ( ) The ifference between the RBFNN equalizer output ( xˆ ( k δ )) an esire output ( x ( k δ ) error, e ( k ) Bit Error Rate (BER), E[ e( k )] Here, E is the expectation operator. (8) w (9) ) is the, an use for upating the equalizer weights. Two popular inexes for performance are, MSE an. Cat Swarm Optimization: Cat Swarm Optimization is a population base algorithm evelope by Chu an Tsai (007}. The CSO algorithm moels the nature of cats into two moes: Seeking moe an Tracing moe. Cats in CSO play the same role as the particles in PSO. Each of the cat are represente by their position an velocity in D-imensions. Efficiency of the cats evaluate by their fitness he moe of the cat (seeking or tracing) is ientifie by their flag. The best position of the best cat provies the optimize final solution. Algorithm terminates at arrival of global best solution or preset value of maximum number of iterations. For etails on the moes of cats one can refer to. The algorithm steps reprouce below for ease of reaing. Generate L number of cats an ranomly initialize the position an velocity of these cats thus creating L D matrices in the process where D is the imension corresponing to the weights of IIR filter. Evaluate the fitness of each cat an store best position as P gm, where m=,,.d. Sprinkle the cats into the search space an pickup the number of cats which woul unergo tracing moe with the help of mixture ratio(mr) an cats unergoing seeking moe are ivie by seeking memory pool(smp) Change the position of the cats accoring to their flags if cat is in seeking moe, then seeking process is applie otherwise it goes for tracing moe. The fitness of the cats are evaluate again an best among them has position P lm where m =, D. Compare P g an P l to get the better position an upate accoringly. If the termination conition is satisfie then stop to get best solution otherwise repeat stops.

4 4 Rabi K. Mohapatra et al, 06 Australian Journal of Basic an Applie Sciences, 0(5) Special 06, Pages: -6 Crossover Cat Swarm Optimization: In orer to achieve better exploration of the search space with higher accuracy, Cross over CSO (CCSO) algorithm was propose by Sarangi et al (06).First the fitness of cat calculate an is store in best position. Accoring to mixture ratio an SMP we calculate the number of cats which woul go to tracing moe an seeking moe.the fitness of cat which are present in seeking moe is evaluate in aaptive way so that we store the best position. The cats present in tracing moe are separate into parent an parent. By using crossover mechanism of GA new offspring are generate. The offspring an the parent are mixe.then fitness of all the cats are evaluate an best position is store. By comparing the previous position with new position we upate the position of cats. Simulation results prove superiority of the propose Cross-CSO as compare to original CSO. Steps of the algorithm are as follows: Generate ranom population of cats having initial position an velocities. The imensions of the cats must be same as weights of IIR filter. Evaluate fitness of each cat an best position of cat is store as P g. Accoring to MR, the cats go for tracing moe an accoring to SMP; the cats go for seeking moe. The inices of position matrix that unergo tracing moe are given by q =, L/(+MR), where L is population size. Evaluate the fitness of cats in seeking moe an store the best position. Divie cats in tracing moe into parent an parent cats an apply uniform crossover to prouce chil. Then mix chil cats an parent cats an calculate fitness values an store the best position as P lm. Compare the fitness of P g an P lm an Upate the P g. Check the termination conitions an if they o not satisfy then repeat steps 3 to 6. Propose Training Metho: Metho of training RBFNN using CSO an its moifie forms for optimization of each parameter of RBFNN is iscusse below in this section. Steps for the training algorithm use in this paper can be outline as: i. Initialize population of cats. Each cat efines a network an the associate centers an banwiths. Set the number of iterations as MaxIteration. Start the first iteration. ii. Decoe each cat into a network. Compute the connection weights between the hien layer an the output of the network by the pseuo inverse metho. Compute the fitness of each cat. iii. Run CSO to upate the position. Fig. : Flowchart for Cross-CSO.

5 5 Rabi K. Mohapatra et al, 06 Australian Journal of Basic an Applie Sciences, 0(5) Special 06, Pages: -6 i. Go to next iteration; ii. Go back to step ii until reaching the maximum number of iterations. In this work, RBFNN traine with original CSO is terme as CRBF, while traine Cross-CSO as CCRBF for convenience of the reaer. Simulation Results: The simulation of the propose algorithm is one in MATLAB to emonstrate the potential for equalization of communication channels. In this section of result analysis, the new hybri algorithm Cross-CSO is compare with two stanar effective algorithms i.e. GA, PSO, CSO. The initial population chosen for all the algorithms is 50. The simulation parameters for PSO are: inertia weight is linearly ecrease from 0.9 to 0.4, both the acceleration constants are taken as an the ranom numbers are chosen in the range [0 ]. The parameters for CSO are: SMP = 5, SRD = 0%, CDC = 80%, MR = 0.9, C =, inertia weight is linearly ecrease from 0.9 to 0.4 an r lies in the range [0 ]. The best feature of GA i.e. uniform crossover is use in Cross-CSO in aition to the same parameters as that of CSO. The algorithms are run a number of times to prouce better results. For evaluation of performance of propose CRBF equalizers, results of contemporary PSO traine RBFNN (PRBF) [8] base equalizers are reprouce for the purpose of comparison. Simulations were conucte for the most popular istorte channel with transfer function: H ( z) = z + 0.6z (0) The equalizer performance is affecte by channel nonlinearity. This effect stuie in this paper introucing the nonlinearity: y ( n ) = tanh [ x( n )] () For the comparisons, two parameters, MSE & BER, were taken as performance inex. For convergence comparison among RBF base equalizers, i.e., evaluation of MSE uner similar conitions, SNR is kept fixe at 0B. Fig. 3: MSE plot for RBFNN equalizers. Figure shows the error convergence at 0B for ifferent equalizers. It is observe from the figure that, propose CCRBF outperforms other equalizers. It is also seen that, RBFNN traine CSO are better than as traine with other nature inspire algorithms like GA an PSO. It is also observe that CCSO is a better metho for training of RBFNN equalizer as compare to original forms of CSO. It was observe that, CCRBF requires only 835 iterations to converge while other equalizers fail to converge within 000 iterations. BER comparison among RBFNN base equalizers is epicte in figure 3. It is seen from figure 3 that, performance of GRBF an PRBF are comparable to each other up to SNR of 8B. CRBF equalizers perform better than GRBF an PRBF. Once again CCRBF performs better than CRBF, Fig. 4: BER plot for RBFNN equalizers.

6 6 Rabi K. Mohapatra et al, 06 Australian Journal of Basic an Applie Sciences, 0(5) Special 06, Pages: -6 Summary An Future Work: This paper propose novel strategy for RBFNN training using CSO an its moifie form. This paper also propose some efficient approaches for channel equalization as evience by simulation results. Maor contributions by this paper are, RBFNN training using CSO an its moifie form, use of CRBF in channel equalization an comparison among CSO an its moifie forms while training RBFNN. Significance of the works carrie out in this paper as compare to existing RBF base equalizers is that of a better learning an generalization of the RBF network. Performance of CRBF base equalizer also better than the existing equalizers as seen from the simulations. REFERENCES Barreto, A.M.S., H.J.C. Barbosa an N.F.F. Ebecken, 00. Growing Compact RBF Networks Using A Genetic Algorithm, In Proceeings of the VII Brazilian Symposium on Neural Networks, pp: Bergh, V. an A.P. Engelbrecht, 00. A new locally convergent particle swarm optimizer, Proceeings of IEEE International Conference on Systems, Man, an Cybernetics, Burse, K., R.N. Yaav an S.C. Shrivastava, 00. Channel Equalization Using Neural Networks: A Review, IEEE Trans. On Systems, man an cybernetics-part C: Applications an Reviews, 40(3): Chu S.C. an P.W. Tsai, 007. Computational intelligence base on the behavior of cats. International Journal of Innovative Computing, Information an Control, 3: Alç, M. an E. Beṣok, 005. Using an Exact Raial Basis Function Artificial Neural Network for Impulsive Noise Suppression from Highly Distorte Image Databases, Lecture Notes in Computer Science, 36: Cui, M., H. Liu, Z. Li, Y. Tang an X. Guan, 04. Ientification of Hammerstein moel using functional link artificialneural Networks, Neurocomputing, 4: Feng, H.M., 006. Self-generating RBFNs Using Evolutional PSO Learning, Neurocomputing, 70: 4-5. Gan, M., H. Peng, an L. Chen, 0. Global local Optimization Approach to Parameter Estimation of RBF-type Moels. Information Sciences, 97: Kaur, H. an B. Dhaliwa, 03. Design of Low Pass FIR Filter Using Artificial Neural Network, International Journal of Information an Electronics Engineering, 3(): Ruan, X. an Y. Zhang, 04. Blin sequence estimation of MPSK signals using ynamically riven recurrent Neural Networks, Neurocomputing, 9: Sarangi, A., S.K. Sarangi, S.P. Panigrahi, 06. An approach to Ientification of Unknown IIR Systems using Crossover Cat Swarm Optimization, accepte for publication in ICEMS. Schilling, R.J., Carroll JJ Jr an A.F. Al-Alouni, 00. Approximation of Nonlinear Systems with Raial Basis Function Neural Networks, IEEE Trans. on Neural Network, (): -5. Subramanian, K., R. Savitha, M. Suresh, 04. A complex-value neuro-fuzzy inference system an its learning mechanism, Neurocomputing, 3: 0-0. Yavuz, O. An T. Yilirim, 008. Design of igital filters with bilinear transform using neural networks," 6 th IEEE Conference on Signal Processing, Communication an Applications, -4.