Radio communication method is useful concept and due more advantages for the wireless communication environment. Radio frequencies are used in many kind of application in today such as GSM, Wi-Fi, 3G (UMTS), and satellite communication. Impedance matching is most important factor to achieve maximum power transfer between transmitter (source) and antenna (load). That antenna impedance is varied with operating frequency and environment factors, such as lightning, rain, etc...
Impedance matching network is required to prevent effect of this impedance mismatch. Several impedance matching networks are used in industrial (L network, T network and p network). But here p network is used as matching network. Genetic algorithm is used select the optimum value for the p network component. Genetic algorithm is helpful to achieve fast and optimum solution to a problem.
Aim and Objectives
- Develop the impedance matching tuning algorithm using genetic algorithms.
- That algorithms operating frequency range should be relevant to GSM and UMTS (3G).
- Identify the limitation and problem of algorithms.
Wireless and mobile communication
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Wireless and mobile communication most helpful concept in today. That is used in many kind of application. That can be communicating information from few meters to thousands of Kilometres using radio waves. GSM and UMTS technologies are mainly used in mobile communication. GSM is defined the 2nd generation of mobile communication and which operating frequency band is 800 MHz and 1800 MHz. GSM 900 band Up-link frequency spread form 890 MHz to 915 MHz and Down-link frequency spread form 935 MHz to 960 MHz Also GSM 1800 band Up-link frequency spread form 1710 MHz to 1780 MHz and Down-link frequency spread form 1805 MHz to 1880 MHz.
UMTS is 3rd generation in mobile communication system which consists in HSUPA, HSDPA. UMTS is called as 3G technology. It use to high speed internet access, mobile video call and other related high speed data access purpose in mobile communication. That 3G (UMTS) Up-link frequency spread form 1920 MHz to 1980 MHz and Down-link frequency spread form 2110 MHz to 2170 MHz.
N.B. - Above frequency band can be vary with different country. GSM-900 and GSM-1800 are used in most parts of the world:Europe,Middle East,Africa,Oceaniaand most ofAsia.
Impedance Matching Network
Impedance matching network is very important to success project objectives. Performance of the antenna determine by the impedance. There are three type of impedance matching networks widely use. It will be discuss later. In this project describe how to match the impedance of antenna by using final Matlab programme. (Optimum component values are taken by using final programme for the matching network component).
In this project genetic algorithm is used to develop Matlab programming and get optimum value to the network component by using different parameters. A genetic algorithm (GA) is a search technique used in computing to find exact or approximate solutions to optimization and search problems. Under the chapter 2, describe more details about the genetic algorithm.
- Chapter 2 - introduce the Genetic Algorithms and it's operation. Also describe outline of GA and parameter of GA. Describe the operator of genetic algorithms.
- Chapter 3 - under this chapter introduce about impedance matching network and their function. Explain p - network and it's operation and characteristic. Further derivation of impedance matching equation.
- Chapter 4 - discuss about impedance tuning programme and their characteristic. Compare the Matlab software with C/ C++ programming language. Describe software flow chart and discuss behaviour of tuning programme with GA parameters.
- Chapter 5
Introduction of Genetic algorithms
Genetic algorithms are the part of evolutionary computing; it was invented by John Holland. Also it is powerful and broadly applicable stochastic search and optimization techniques. Algorithm is started with a set of solutions (represented by chromosomes) called population. Solutions from one population are taken and used to form a new population. This is motivated by a hope, that the new population will be better than the old one. Solutions which are selected to form new solutions (offspring) are selected according to their fitness - the more suitable they are the more chances they have to reproduce.
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In genetic algorithms, chromosomes can define as set of solution. That chromosome is consisted in collection of binary strings. Chromosomes are divided into parts. It is called as genes. The set of the initial chromosomes is called population.
In general, a genetic algorithm has five basic components.
- A genetic representation of solutions to the problem
- A way to create an initial population of solutions
- An evaluation function rating solutions in terms of their fitness
- Genetic operators that alter the genetic composition of children during reproduction
- Value for the parameters of genetic algorithms
Outline of the Basic Genetic Algorithm
In here describe the basic Genetic Algorithm operation with each steps.
- Start - initiate to generate random population of n chromosomes
- Fitness - score(evaluate) the fitness f(x) of each chromosome x in the population
- New population - implement the new population using following steps. Repeat the that process until the new population is complete
- Selection - Select two parent chromosomes from a population according to their fitness. If fitness is high, it has more chance to select.
- Crossover - exchange characteristic of chromosome with each other chromosome. If no crossover was occur, offspring is not change, it is an exact copy of their parents.
- Mutation - With a mutation probability mutate new offspring at each locus (position in chromosome).
- Accepting - Place new offspring in a new population
- Replace - new population is reinsert to initial population for a further run of algorithm.
- Test - If the end condition is satisfied, stop, and return the best solution in current population
- Loop - Go to step 2, repeat the process until satisfy the condition
Operators of Genetic Algorithms
Under that part describe the how to work genetic algorithms to solve the problems. In here operation of the GA describe clearly under the three separate parts (Selection, Crossover, Mutation). Crossover and mutation are most important part of the genetic algorithms. The performance of the genetic algorithm is influenced mainly by these crossover and mutation operators.
Function of the selection; choose the chromosomes from current generation's population for reproduction. Each chromosome is scored and assigns according to their fitness. According to Darwin's evolution theory the best ones should survive and create new offspring. There are several types of selection method available, Roulette Wheel selection, Rank selection, Tournament selection, Fitness Proportionate selection and Elitism.
Roulette selection is simplest selection scheme. Process of the roulette selection is creating a set of chromosome strings each with a fitness score and then creates a biased roulette wheel where each current string in the population has a roulette slot sized in proportion to its fitness. Parents are selected according to their fitness. The better the chromosomes are, the more chances to be selected they have. Imagine a roulette wheel where are placed all chromosomes in the population.
Roulette selection will have problems when the fitnesses differ very much. For example, if the best chromosome fitness is 90% of all the roulette wheel then the other chromosomes will have very few chances to be selected.
Rank selection first ranks the population and then every chromosome receives fitness from this ranking. The worst will have fitness 1, second worst 2 etc. and the best will have fitness N (number of chromosomes in population).
In tournament selection a number Tour of individuals is chosen randomly from the population and the best individual from this group is selected as parent. This process is repeated as often as individuals must be chosen. These selected parents produce uniform at random offspring. The parameter for tournament selection is the tournament size Tour. Tour takes values ranging from 2 to Nind (number of individuals in population).
- Fitness- Proportionate selection
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Function of the crossover operator is creating the new offspring chromosome using two parent chromosomes. First select the two parent chromosome and both are split in part and exchange their part in each other and create new offspring chromosome. The idea behind crossover is that the new chromosome may be better than both of the parents if it takes the best characteristics from each of the parents. There is much type of crossover method, single point crossover, two point crossover, multipoint crossover, and uniform crossover. In this project describe about single point crossover, two point crossover, and uniform crossover only.
Single point crossover
Single point crossover is simplest crossover method than others. First select the two parent chromosomes in the population and randomly select the crossover position and then interchanges the two parent chromosomes at this point to produce two new offspring. Following figures explain this process.
Two point crossover
Two point crossover operations is similar to single point crossover. Main different is it chose randomly two crossover position. Then interchanges the two parent chromosomes at these two points and produce two new offspring. This is more accurate than single point crossover.
Operation of the uniform crossover is selected the two parent chromosome and then exchange bit string according to mixing ratio. Uniform crossover is similar to multi-point crossover. That Uniform crossover generalizes this scheme to make every locus a potential crossover point. A crossover mask, the same length as the individual structure is created at random and the parity of the bits in the mask indicate which parent will supply the offspring with which bits.
Mutation is a genetic operator that alters one or more gene values in a chromosome from its initial state. This can result in entirely new gene values being added to the gene pool. With these new gene values, the genetic algorithm may be able to arrive at better solution than was previously possible. Mutation is an important part of the genetic search as help helps to prevent the population from stagnating at any local optima.
Randomly change the 0 to 1, and 1 to 0.
Parameters of Genetic Algorithms
Parameters of genetic algorithms are used to increase the ability of the programme. There are two basic parameter is used in genetic algorithms, Crossover probability and Mutation probability. There are also some other parameters of genetic algorithms. Population size and Generation number are other parameters in genetic algorithms.
Crossover probability is most important parameter in GA. If crossover probability is equal to zero, new offspring is exact copy of chromosomes from old population. It mean that new offspring is identical with their parents. If crossover probability is 1, (it is mean 100%) all new offspring is produced by parent chromosomes.
Crossover is made in hope that new chromosomes will have good parts of old chromosomes and maybe the new chromosomes will be better. However it is good to leave some part of population survive to next generation. In this project crossover probability value is used in 0.8 - 0.9 range.
Mutation probability is useful concept in when produce the new offspring. If mutation probability is equal to zero, new offspring is produced without any change. If mutation probability is equal to 1 (100%), it is mean whole chromosomes is changed. Problem is when increase mutation probability optimum chromosome can be destroyed. The recommended value of the mutation probability is used in this programme between 0.005 - 0.03.
Population size is representing how many chromosomes are in population (in one generation). If population size is small, it has little chance to achieve the optimum solution to a problem. When increase the population size, it has better chance to achieve the optimum solution to a problem. But when increase the population size it has taken long time to solving the problem. The recommended value of the population size is used in this programme between "20-150".
Generation number is representing number of times the genetic algorithm operation occurs. If generation number is high, result is more accurate and it will take long time to solving the problem. If Generation number is small, result is not achieving the optimum solution to a problem. High generation number is used in that programme.
Impedance matching network
Impedance matching is more helpful concept to achieve the maximum power transfer from source (transmitter) to load (Antenna) through transmission line. Input impedance of the load is should equal to output impedance of source to succeed maximum power transfer. But problem, that load impedance is vary with operating frequency and according to environment factor. To match the impedance in load and source, engineers use combinations of transformers, resistors, inductors and capacitors. These passive and active impedance matching devices are optimized for different applications, and are called baluns, antenna tuners (sometimes called ATUs or roller coasters because of their appearance), acoustic horns, matching networks, and terminators.
In this project impedance matching network is used to matching the impedance. There are several types of impedance matching network as follows.
- L - Network
- T - Network
- Π - Network
π - Network and fitness function
In this project p - Network is used as matching network. It is simplest network and it is consisted on two capacitors and one inductor. It has more advantage when compare other network. p - Network has three variables, it is help to tune more range easily. But L - Network has only two variables. When compare these two network p - Network will given more accurate result than other. p - Network has good characteristic, it can match any impedance at any frequency by modifying component value in network.
Basic diagram of π - Network
- C1, C2 - capacitors
- L - inductor
- RS - source impedance, it is often configure at 50Ω
- RL - Antenna impedance, it is vary with operating frequency and environment factors.
- Z1 - impedance of RL and C2
- Z2 - impedance of Z1 and L
- Zin - impedance of Z2 and C1
When Zin equal to RS or close 50Ω, it will given maximum effective power transfer from source to load. That Zin produce by component value in p- Network. Main purpose of this project is produce Zin value equal or close to RS (50Ω) by changing C1, C2, L value in p- Network. Different between Zin and RS is introduced as error. That error is used describe the fitness function of the genetic algorithms. That error value should always close to 0 to achieve the good impedance matching.
The Quality factor
Quality factor is help to determine the required component value range in p - network and determine the losses of network.
Zin input impedance is can be calculate using above equation. According to above equation Zin input impedance depends on following variable.
C1, C2 - capacitors value
L - Inductor value
RL - load resistance
ω = 2πf - angular frequency, that f is depend on user input frequency value
RL( load resistance) and f (frequency) are fixed value. Zin value of p- network is depending on C1, C2, and L component value. Function of the software is matching Zin value changing the C1, C2, L. that tuning algorithms is always try to equal the Zin value and RS (source resistance) value.
Under this chapter describe about the implementation of impedance tuning programme software. Main purpose of this tuning programme is match optimum value for the p - network component by satisfying impedance matching between source impedance (RS) and input impedance of load (Zin). Genetic Algorithms is used choose the find optimum component value for C1, C2, L by changing their parameters. That final tuning programme was developed using Matlab software. That final tuning programme is worked with GSM 900, GSM 1800, and UMTS (3G) frequency band without changing any parameters of software coding. Under following topic describe tuning programme implementation, how to work the tuning programme with each parameters and full description about a tuning programme.
There are many programming software can be used to develop this tuning programme such as C/ C++ or Matlab. In this project Matlab software was used to develop the tuning programme. That final programme is user friendly and easier to use the user. It has graphical user interface when enter require input parameters (e.g. frequency, load impedance and genetic algorithms parameters) programme will be display matching error graph, Zin vs. Source impedance graph and final C1, C2, L component value. Referring these two graph user can determine best optimum component value for the relevant frequencies. If Zin is not matching to RS user can be run the programme until find the best optimum value for the component.
That tuning programme was developed using Matlab software, reason for use the Matlab software describe as follows.
- When compare the C/ C++, Matlab more accurate and faster than others for solving the problem.
- Matlab is easy to learn than other programming language.
- Using Matlab software easy to create graphical user interface than others.
- More tutorial and details can be found about the matlab coding than others.
- Arrays and matrices are easy to use which is required the most to develop the algorithms.