3. Problem Formulation and Assumptions

In this paper, we assume that inputs are collected from the radio environment (using a sensor) or secondary user. A Cognitive Radio must be including intelligence so that it can detect the spectrum accurately. According to [7], there are possible scenarios for an inaccurate decision, a “false alarm” when there’s no active primary user in the radio environment but the CR observes that there’s a present primary user. And “missed detection” is the opposite of “false alarm”; the CR observes that a PU is not present and the PU is using the spectrum. Both scenarios lead to interferences or missing the opportunity to allocate freer frequencies.

We also suppose that QoS requirements have been specified for each type of application. The purpose of optimization in spectrum allocation is assigning the free frequency spaces in the shared spectrum to the SU. So defining derived fitness function from performance objectives is the key of successful QoS management and result optimal spectrum utilization. Every CR device controls the power to reduce noise and guarantee the required power consumption, also adaptive modulation and coding scheme present important factor to compensate variation in the channel and results satisfied throughput and bit error rate requirements. Carrier frequency must also be

well chosen to prevent any vibration.

The dependence between all parameters and performance objectives made the optimization problem more complex. The quality of optimization solutions will depend on the quality of the algorithm used, algorithm operators, population size, execution time, optimality of solutions, CPU/RAM use, etc. In this paper we have chosen four performance objectives: minimizing power consumption/bit error rate, and maximizing throughput/ spectral efficiency. The genes considered in this paper are listed in table 1, we’ll use values from parameters of CR network as IEEE 802.22 discussed in paper [8]. Each fitness function must be normalized in the same range. So multi-objective weighted sum approach is more appropriate, it allows applying weights to normalized objectives. Weights have been choosing accordingly, and they depend on the QoS required from the end application. Derived fitness function for each parameter is initially used in [4].

The power consumption is the supplied power to maintain device operation, the total fitness include derived and normalized power consumption.

All technologies used in telecommunications have a fixed and important goal, to have free error rate or to minimize the bit error rate of transmission. To calculate the bit error rate, we assume AWGN channel model and using a gray-coded assignment, M-QAM and M-PSK are also considered as the set of Modulation types considered in this paper. Energy per bit to the noise spectral density is the second important factor to determine BER.

(1)

Where P transmitted power assuming that no Path Loss is considered, B channel bandwidth, N measured noise power, symbol rate and modulation index. According to the modulation type, we get different formula of BER [9].

For M-QAM:

(2)

For M-PSK:

(3)

Most wireless applications require free error rate or minimized BER. Using the approximation [10] and assuming QoS requirement of BER <= 0.001, mi >= 2:

(4)

Throughput formula depends on the definition used; it illustrates the amount of information received

(5)

where number of sub-carriers.

The spectral efficiency is defined as the amount of information that can be transmitted over a given bandwidth:

(6)

The cumulative sum of all performance function with the percentage of required QoS of each KPI is iluustrated using “” weight associated to the performance objective “”.

(7)

The percentage of Total fitness:

(8)

Weights differ according to application modes

4. Genetic Algorithm

GA is robust search and optimization technique inspired from nature [11,12] by mimicking processes nature used to evolve solution to complex optimization problems. GA is adaptive heuristic search based on evolutionary concepts. Even the fact that GA starts with randomized solutions, it exploits historical information to direct search into the space of better performance within the search space. Rechenberg is the first scientist describing the evolutionary computation and John Holland is the inventor of GA, published in 1975 on his book “Adaptation in Natural and Artificial Systems” [13]. Since the invention of GA, It has been solved difficult problems. It’s mainly used for parallelism purpose and the primary advantage is the fact that they work to with a population of solutions. Consolidated with operators, It explores the search space and less likely to get stuck in local extreme According to the same principle as evolutionary concepts, the GA starts with randomized population of solutions, and reproduces new population based on the best fitness. By repeating this cycle several times, ended population will include best solutions. Figure 1" target="_self"> Figure 1 illustrates pseudocode of general scheme of evolutionary process in GA.

4.1. The Glossary Used in GA Literature

4.1.1. Individual

Individuals are the solutions of the problem to be optimized. All solutions must be coded so that the treatment can be carried out by the genetic algorithm. The encoded representation is called a chromosome, and is composed of genes. Each gene can be a variable, an element of the solution, or a more abstract part. In the most used coding genetic algorithm is the encoding vector. Each solution is represented by a vector. This vector can be binary, integer, real, character, etc... Different types of coding are used, binary coding, gray coding, real and coding tree.

The convergence of GA may need time to obtain an optimal solution but normally do nottake much time to give very good solutions [11]. Bellow we describe words used in GA literature [11-17]

4.1.2. Population

The set of chromosomes is within the same generation. Usually, the size of the population remains constant during GA process

4.1.3. Selection

Depending on individual fitness, each individual is assigned a percentage chance of being selected for reproduction, which is the relative importance of the quality of the individual in relation to the overall quality of the population. Many selection methods are used in GA literature, the most commonly used methods of selecting chromosomes for parents to crossover are Roulette wheel Selection, Tournament selection, Rank selection and other heuristic methods.

4.1.4. Reproduction

Reproduction is usually done by crossing two individuals, which produces two new individuals to be placed in the new population. The two common genetic operators are crossover and mutation:

• Crossover: Each child chromosome receives a percentage of genes from each parent selected in crossover operation. The probability of crossover is almost always greater than 50%. According to this probability, we exchange homologous genes from both chromosomes.

• Mutation: despite lower mutation probability (usually less than 0.1). It plays a very important role. A reproduction using only crossover is a hill-climbing method which is limited by the achievement of local maxima. Indeed, the genes of children are limited by the genes of the parents, and if a gene is not present in the initial population (or it disappears because of reproductions), it will never grow in the offspring. The mutation operator is to circumvent this problem and ensure diversity.

4.1.5. Validity and Consistency

According to the encoding method and its meaning, we must always be sure that the individuals in the population arevalid (feasible solution). Indeed, GA operators could produce solution resulting best fitness, but has no practical meaning when interpreted. We must therefore ensure that the function of creating individuals always creates valid individuals, and genetic operators maintain the validity of treated individuals. This is to maintain the overall consistency of the algorithm.

4.1.6. Termination Criterion:

Generally, a genetic algorithm terminates after a number of generations, but it can also end the execution of the algorithm when a certain condition is reached, such as when the quality of an individual exceeds a certain threshold…

Many types of crossover operators are used in GA literature: One-Point crossover, Two Point, Uniform, Arithmetic and heuristic crossovers.

The Combined Single-Heuristic Crossover (CSHC) used in this paper combines both Single point crossover and the heuristic crossover which uses the fitness values of the two parents’ chromosomes to determine the direction of search [14]:

where rand is random number selected between 0 and 1.

The adaptive heuristics consists of selecting the best child resulted from both heuristic crossover and single point crossover.

Single crossover is the most commonly used in GA, when performing crossover, new child is created with a part from parent 1 and second part from parent 2. Both parent’s part are split randomly. Heuristic crossover uses the adaptation of the parents to generate the new offspring. Based on the fitness values of the two parents, the direction of search is fixed.

The combination of two methods guarantees the exploration and exploitation of space search.

5. Simulation and Results

To evaluate the proposed model, we have tested several GA parameters. The GA initialized with 60 Best chromosomes selected from 100 chromosomes. The GA processes will be iterated 1000 times. Selection remainder, selection roulette and tournament selection were tested. A population of 60 chromosomes is used to evaluate all GA operators. And single point crossover, heuristic crossover are implemented with probability 0.9 and mutation 0.01. Table 2 resumes the values of GA parameters.

One Mode is tested in this paper, throughput mode for applications that need big data and tolerated level of errors.

Evolution of average and max fitness is illustrated in figure 2, it shows the stability of evolution of the mean and best values of fitness. The stability started from the 100th generation.

The figure 3 shows the enhancement of the quality of best solution obtained when combining both single and heuristic crossover The results clearly show the enhancement of obtained fitness value. Our result shows that the best total fitness value turns out to be 90%.

6. Conclusion

This work shows the flexibility of GA in terms of implementation but also the possibility of adapting and combining operators. It can also be used with other metaheuristic to enhance the quality of solution without penalizing the complexity and time of execution. In this work, we have used four performance objectives, but using more performance objectives will help to approach real model and give more QoS control. The dynamic optimization problem presents another aspect of research, so the future work can be focused on the dynamic optimization and proposing new meta-heuristic fully thought to resolve the spectrum management problem.

REFERENCES