Proceedings of the 2009 IEEE 9th Malaysia International Conference on Communications 15 -17 December 2009 Kuala Lumpur Malaysia
Realization of Microcontroller-based Polarization Control System with Genetic Algorithm Ghazaleh Mamdoohi#1, Aida Esmailian#2, Ahmad Fauzi Abas#3, Khairulmizam Samsudin#4, Ariya Hidayat#5, Noor Hisham Ibrahim#6, Mohd Adzir Mahdi#7 Photonic and Fiber Optic System Laboratory, Centre of Excellence for Wireless and Photonics Network, Engineering and Technology Complex, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia. 1
[email protected] [email protected] 3
[email protected] 4
[email protected] 5
[email protected] 2
6 7
[email protected] [email protected]
Abstract— Realization of a PIC32 microcontroller-based polarization control system is described. Genetic algorithm is used for control purposes. The controller measures the signal intensity to estimate the genetic value. To reach optimum performance, the code is optimized by using the best genetic parameter to achieve the fastest execution time. This algorithm consumes low size of memory besides providing fast speed. The implementation of microcontroller allows for more economic polarization control solution. Keywords— Microcontroller, polarization controller, rotating wave plates, genetic algorithm, lithium niobate
I. INTRODUCTION In coherent optical communication systems, polarization matching between the transmitter and receiver must be guaranteed. The problem is mainly the instability of the SOP when light propagates along standard single mode fiber [1]. There have been many technologies proposed to solve this problem, such as polarization controller [2-6], polarization diversity [7], polarization scrambling [8], and polarization switching [9]. Among these techniques, polarization controller is preferable due to bit rate independency and simple receiver configuration [10]. For optimum performance transmission components such as coherent optical receivers [11]-[13], fast electro-optic switch arrays [14], and polarization demultiplexers [15] require polarization controllers with endless transformation ranges and fast control speed [1l], [12]. Highly accurate polarization control system is needed to manage polarization state variation in the received signal; while the tracking range of polarization controller system should be endless. In high-speed transmission, even a short time of undesired polarization mismatch may cause loss of data. There have been several technologies to realize polarization controller were introduced in the last two decades such as: mechanically rotating crystal wave plates or fiber loops, fiber squeezers or quartz with piezo electric elements[16], rotating
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wave plates [17], [13], [18], [11], variable retarder plates [19], liquid crystals [20], and waveguide devices such as LiNbO3 [13], [21], [11], [22]. To support the operation of the controller, algorithms are needed. There are different types of control algorithm for polarization control system. The main purpose of the algorithms is to provide fast and accurate response for unlimited transformation. Because of speed and complexity, polarization control algorithms are usually implemented in digital circuits [23]. There were polarization control algorithm that were executed on digital circuit such as microprocessor [13], a combination of basic digital blocks [24] and a dedicated digital signal processor [25]. In this paper, control algorithm is developed based on Genetic Algorithm and executed by using PIC32 Microcontroller. II. LINBO3 POLARIZATION CONTROLLER The polarization controller, schematically shown in Fig. 1, is manufactured on low-birefringence, X-cut, Z-propagation LiNbO3 crystal by diffusion from titanium waveguide [26]. It is a commercial electro-optic polarization transformer from EOSPACE consists of 8 cascade stages with a total insertion loss of 2.1 dB, low polarization dependent loss (PDL) and operates using different combination of drive voltages [27]. Each section consists of a centre electrode on the waveguide, which is connected to ground and two electrodes placed on both side of the waveguide [22]. It can transform any arbitrary input polarization state to any arbitrary output polarization state when suitable voltages are applied. Its function as a Quarter Wave Plate (QWP)−Half Wave Plate (HWP)−Quarter Wave Plate (QWP) is explored, which proves its potential to become a dynamic polarization control system.
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digital signal by using analog-to-digital converter (ADC). The driving signal from the microcontroller must be converted to analog by using digital-to-analog converter (DAC) to drive the 16 input pins of lithium-niobate polarization controller. In this paper, all eight stages were used to achieve fast operation and high accuracy. For converting digital signals to analog, DACS are required. The speed and the performance of the ADC and the DACs are very critical in this experiment.
Fig. 1 Structure of polarization controller and electrode configuration
By applying voltage V1 and V2 to the two outer electrodes, TE ↔ TM mode conversion and TE−TM phase shifting is induced [26]. Due to electro-optic effect, state of polarization is changed. Fig. 2 demonstrates the transformation of light after passing through different combination of quarter and half wave plate. Fig. 2 shows that a linear 450 input signal is transformed into circular polarization output after QWPHWP-QWP. Fig. 3 shows that any input state is transformed into linear polarization state after passing through cascaded QWP-HWP.
Fig. 4 Schematic diagram of the complete control system
The setup for the polarization control system is schematically demonstrated in Fig. 4. The controller is implemented in a PIC32MX360F512L microcontroller. This microcontroller has an onboard ADC. One of the analog pin is connected to the photo detector. The DACs are connected to pins of the PIC32MX microcontroller. For troubleshooting and debugging, the computer is used to retrieve additional information for the controller operation. PIC32MX starter kit board is connected to the computer by the USB cable. The analyser is used to display the state of polarization. By changing the voltages, which is fully determined by the control algorithm, the state of polarization is changed.
Fig. 2 Linear 450 polarizations after QWP-HWP-QWP
Fig. 3 Linear 450 polarizations after QWP-HWP
Several hardware components are required to implement a digital polarization control system. The feedback signal must be detected by a photo detection circuit and then converted to
III. GENETIC ALGORITHM An artificial algorithm is needed to control an endless polarization controller. There are various algorithms that can be used to control the polarization controller. In this paper, the Genetic Algorithm (GA) is embedded in a PIC32MX microcontroller. GA was first developed by John Holland [28] and are mainly used in search and optimization process [29] and also an effective technique for machine learning applications. GA is called “blind” because they have no knowledge of the problem [30], [31]. It based on the scheme of natural selection. They can be parameterized in such a way for solving optimization problems that is based on natural selection [32], [33]. In nature, GA attempts to copy the natural principle by coding the possible alternative solution of a problem, which features similar to chromosome [32]. In general, chromosomes are any point that is applied to the
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fitness function. Fitness function is an objective function we want to minimize. Each chromosome is assigned a "fitness score" according to how good a solution to the problem it provides. Chromosomes consist of a string of gene. The genes can be bits, integers, or any data structure. The chromosome is also called individual and structure. All possible solution to a given problem can be represented as population. In other words, a population is an array of individuals. In every iteration the genetic algorithm performs a series of computations on the current population to produce a new population. Each successive population is called a new generation [33]. Since the different individual has to be evaluated and compared again to each other, the concept of fitness is introduced. The fitness value is the value of a particular solution. In our case, intensity of photodiode is the fitness value. A. Genetic Algorithm Operator Genetic algorithms operate on the chromosomes. The following three basic operators are applied: • • •
Reproduction Crossover Mutation
The reproduction process creates a new generation. To create the next generation from the current generation two steps process are needed. It starts with the initial population, which is randomly produced. Selection is applied to the initial population to create an intermediate population. In the intermediate population, chromosomes that are called parents that contribute to the population at the next generation are chosen. These chromosomes are selected by one of parent selection techniques, where children are produce from the parents [33], [34]. Children are produced either by making random changes to a single parent (mutation) or by combining the two parents (crossover) to the intermediate population to create the next population. The process of going from the current population to the next population constitutes one generation in the implementation of a genetic algorithm [3537]. In the first generation the current population is also the initial population. Fig. 5 illustrates the reproduction concept. The new population is generated and replace the old population.
Fig.5 Reproduction process
The mutation operator applies random changes to genes of individual parents to form children. Below is the example of mutation operator.
Before: After:
(1 0 1 1 0 1 1 0) (1 0 1 0 0 1 1 0)
The crossover operator exchanges the information between two chromosomes [33]. It greatly accelerates search early in evolution of a population. The two chromosomes, which are selected in one of selection techniques, are broken up at random crossover point. All data beyond that point is swapped between the two parents. One hopes that two new chromosomes have good properties than previous one. Follows is the example of crossover operator. P1 (0 1 1 0 1 0 0 0) P2 (1 1 0 1 1 0 1 0)
(0 1 0 1 1 0 1 0) C1 (1 1 1 0 1 0 0 0) C2
Both processes are essential to the GA. Crossover enables the algorithm to extract the best index from different voltages and recombine them into potentially superior children [34]. Mutation adds to the diversity of a population and thus increases the chance that the algorithm will generate voltages with lower intensity. In this research, we use two ways to call mutation function, in the first method, in the conditional command that define probability of mutation optionally, if probability of mutation happens, mutation operator is alerted. In this method there could be more than 1000 times mutation is repeated which may takes a long time, but in the second method, the number of mutation is calculated by the following formula: Number of Mutation = (populationsize - 1) × number of variables × mutation rate. Where population size is 20, the number of variables is 16, and mutation rate is 0.2. All these values are defined by the user. Mutation operator selects the index of gene randomly, and replaces the previous one. B. Selection techniques There are several techniques for selecting the parents. Among them are: • • • •
Random selection Roulette wheel selection Ranking selection Tournament selection
Roulette wheel and tournament selection are simply the most commonly employed [38]. The principal duty of all selection methods is to measure the relative fitness of each chromosome [38]. In this paper, to reach optimum performance and fastest execution time, the code is optimized by using the best genetic parameter .to find the best selection methods, all selection methods are run on PIC32 microcontroller. Tournament is recognized as the best technique to allocate the low size of memory besides providing fast speed. Tournament selection imposed several tournaments among competitors. The winner of tournament is the individual with lower fitness among the 20 tournament
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competitors and the winner is inserted into the mating pool. The mating pool is comprised of tournament winner. C. Stopping Criteria The criteria for stopping the Genetic algorithm are: • After reaching maximum generation • After reaching the objective value. In our case, the objective value is 0.05 (minimum intensity) and maximum generation is defined as 100. D. Evaluation The evaluation function determines the fitness value of each population. In our case, after transfer data on DACs the evaluation is happen. E. Implementation of Genetic Algorithms The flow chart in Fig. 6 shows the sequence of the basic operators used in GA. We start with a randomly selected first generation. Every population in this generation is evaluated according to its value. Next, a new generation is produced by applying the reproduction operator. Pairs of individual of the new generation are selected and crossover is performed. With a certain probability, genes are mutated before all solutions are evaluated again. This process is repeated until stopping criteria is reached. The best solution is obtained at the end of the algorithm.
Initial population is randomly produced then the intensity of photodiode is evaluated. In our case, the size of initial population is the 20 by 16 matrix. Selection is applied to the initial population to create an intermediate population. In the intermediate population, voltages are chosen using "Tournament" to fill the intermediate population at the next generation. After selection has been carried out, the structure of the intermediate population completes and crossover occurs. This can be viewed as creating the next population from the intermediate population. Crossover is applied to pair voltages (parents) with a probability denoted as pc, which in our case is 0.5. These voltages are combined to form two new voltages (children) that are inserted into the next population. Mutation is applied to each child individually after crossover. In each generation, 16 voltages are randomly transformed, evaluated and stopping criteria is checked. The control algorithm is capable to execute maximum of 100 generation to provide 16 suitable voltages, which are swept between the ranges of -10V to +10V. These voltages should be sufficient to produce desired intensity in the photodiode. To achieve optimal performance, the algorithm is optimized to get the shortest possible execution time. In each generation if the stopping criteria are reached, the best solution is produced.
First generation (randomly)
Mutation Crossover
Evaluation
Fig. 7 Polarization controller setup
G. Comparison with Other Methods GA are probabilistic (stochastic) and not deterministic. It is adaptive and able to deal with highly nonlinear models and noisy data [28], [36], and [38]. It can rapidly check the solution set. GA does not need gradient information or smooth functions to estimates the solutions. In practical purposes they appear to work best in combination to optimise the parameters. In comparison to gradient search techniques, GA starts with an initial random population and allocates population of possible solutions to the regions of the search space. It is also less susceptible to getting 'stuck' at local optima than gradient search methods [39].
Selection No
Stoping criteria are reached?
Yes Return best
solution
Fig.6 Genetic algorithm flowchart
F. Development for Polarization Control System The polarization control setup is schematically shown in Fig. 7. The controller measures the intensity to infer the GA.
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H. Experimental Result
The output of polarization controller can be analysed on a Poincare sphere as shown in Fig. 8. This figure shows clearly how the state of polarization randomly changes. Different voltages are produced by the algorithm until stopping criteria is reached. In this figure, algorithm for 20 generations is executed until the minimum intensity is reached, which is achieved by changing voltages.
Stable Point
Stopping
Best
Random
Mutation
index ⎡− 0.26⎤ ⎢− 6.90⎥ ⎢ ⎥ ⎢ 4.56 ⎥ ⎢ ⎥ ⎢ 6 ⎥⇒ ⎢ 3.78 ⎥ ⎢ ⎥ ⎢ − 9.45⎥ ⎢ 0.932 ⎥ ⇒ ⎢ ⎥ ⎢ 4.9 ⎥ ⇒ ⎢ # ⎥ ⎢ ⎥ ⎢⎣− 3.56⎥⎦
solution criteria ⎡− 0.26⎤ ⎡ when Gen = 2 ⎤ ⎡ − 0.7 ⎤ ⎢− 6.90⎥ ⎢ int ensity is ⎥ ⎢− 4.46⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ 4.56 ⎥ ⎢ ⎥ ⎢ − 8.36 ⎥ 0.05 ⎢ ⎥ Fitness ⎢ ⎥ ⎢ ⎥ ⎢ 6 ⎥ =0.09 ⎢ the genetic ⎥ ⎢ 6.45 ⎥ ⎢ 3.78 ⎥ ⎯⎯ ⎯⎯→ ⎢ ⎥ → ⎢ 0.4 ⎥ select ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ − 9.45⎥ ⎢the last voltages ⎥ ⎢ 7.55 ⎥ ⎢ 5.76 ⎥ ⎢ as a solution ⎥ ⎢ − 3.53⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ 4.9 ⎥ ⎢ ⎥ ⎢ − 9.54⎥ ⎢ # ⎥ ⎢ ⎥ ⎢ # ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢⎣− 3.56⎥⎦ ⎢⎣ ⎥⎦ ⎢⎣ 3 ⎥⎦
Fig.9 Arrangement of genetic algorithm for one population
Fig.8 Genetic algorithm executed on PIC32 microcontroller
The generated voltages for the first generation of genetic algorithm are shown in Fig. 9. At first the initial population is generated randomly, and transfer those voltages on to the DACs. If the stopping criterion is not reached, the algorithm possesses tournament selection. After selection has been carried out, the Crossover is applied to pair voltages (parents); these new voltages (children) are inserted into the next population. In the crossover, two random indexes of individuals are chosen to perform the crossover operator. Mutation is applied to each child individually after crossover for 61 times. In each generation, 16 voltages are transformed, evaluated and stopping criteria is checked. In this figure, the winner population is selected to possess the genetic operator on it.
IV. CONCLUSIONS We have demonstrated an accurate endless polarization control system algorithm with the digital processing realized in a PIC32 Microcontroller. The controller is able to stabilize polarization changes. This controller is able to support the operation of polarization demultiplexer, Polarization Mode Dispersion compensator and coherent receiver.
Initial population ⎡− 0.903 ⎢ 0.978 ⎢ start ⎢ # ⎯⎯ ⎯→ ⎢ ⎢ − 7 .3 ⎢ ⎢ ⎢ # ⎢ ⎢ ⎢⎣− 8.877
" " "
"
Tournoment Crossover selection 3.966 ⎤ ⎡− 0.26⎤ ⎡− 0.26⎤ ⎥ ⎢ ⎥ ⎢− 6.90⎥ 2.78 ⎥ 6.90 ⎢− ⎥ ⎢ ⎥ fitness ⎥ =0.1 ⎢ 4.56 ⎥ ⎢ 4.56 ⎥ ⎥ ⎯⎯ ⎯→ ⎢ ⎥ ⎢ ⎥ 4.92 ⎥ ⎢ 10 ⎥ ⇒ ⎢ 6 ⎥ ⎥ ⎢ 3.37 ⎥ ⎢ 3.37 ⎥ ⎥ ⎢ ⎥ ⎢ ⎥ 9 . 45 − ⎥ ⎢ ⎥ ⎢ − 9.45⎥ ⎥ ⎢ 0.932 ⎥ ⎢ 0.932 ⎥ ⎥ ⎢ ⎥ ⎢ ⎥ − 5.76⎥⎦ ⎢⎣− 7.45⎥⎦ ⇒ ⎢⎣ 4.9 ⎥⎦
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