A Fast Anti-jamming Decision Method Based on the Rule-Reduced Genetic Algorithm

Abstract

To cope with the complex electromagnetic environment of wireless communication systems, anti-jamming decision methods are necessary to keep the reliability of communication. Basing on the rule-reduced genetic algorithm (RRGA), an anti-jamming decision method is proposed in this paper to adapt to the fast channel variations. Firstly, the reduced decision rules are obtained according to the rough set (RS) theory. Secondly, the randomly generated initial population of the genetic algorithm (GA) is screened and the individuals are preserved in accordance with the reduced decision rules. Finally, the initial population after screening is utilized in the genetic algorithm to optimize the communication parameters. In order to remove the dependency on the weights, this paper deploys an anti-jamming decision objective function, which aims at maximizing the normalized transmission rate under the constraints of minimizing the normalized transmitting power with the pre-defined bit error rate (BER). Simulations are carried out to verify the performance of both the traditional genetic algorithm and the adaptive genetic algorithm. Simulation results show that the convergence rates of the two algorithms increase significantly thanks to the initial population determined by the reduced-rules, without losing the accuracy of the decision-making. Meanwhile, the weight-independent objective function makes the algorithm more practical than the traditional methods.

1. Introduction

In the last two decades, the wireless communication technology has developed sharply with its wide applications related to government agencies, commercial areas and daily life of all aspects. Yet wireless communication systems are confronted with various artificial jamming due to their open characteristic. For a long time, spread-spectrum communication is one of the major technical methods for anti-jamming in the frequency domain. With the increasingly scarce of spectrum resources, it becomes too expensive to occupy more spectrums for a larger jamming tolerance.

The cognitive radio (CR) [1-3] offers a new approach to solve this problem. The capability of learning, reasoning and reconfiguring communication parameters is the core of CR research. In this case, the concepts of cognition and decision-making are introduced into communication anti-jamming field. This new method enables the system to choose proper communication parameters according to environmental changes so as to adapt to the jamming situation [4]. In [5], the bit error rate (BER) performance function and the normalized objective function are introduced to evaluate the quality of communication in detail. It proposes a weight-based method by combining different objective functions into a multi-objective function.

Many decision-making methods based on evolutionary algorithms have been proposed. Those methods are typically based on the genetic algorithm (GA), which searches the optimized configuration in parameters’ configurable fields. However, an initial population needs to be generated randomly in the GA-based decision-making, which results in a very large search space in some cases. Traversing the entire space always requires quite long time, which then adversely affects the timely decision. Many scholars have improved the algorithm to compensate for this disadvantage [6-11].

Tim Newman et. al. [6] proposes a new method to initialize the population. As a CR environment changes smoothly, the decision engine adds previous cognitive results to the next initial population. This algorithm reduces the decision-making time required and improves the real-time performance. Some further achievements have been reported to cope with other disadvantages of the traditional GA. For example, adaptive genetic algorithm (AGA) which employs adaptive crossover probability and mutation probability has been proposed in [7]. According to population evolutionary situation, the evolutionary strategy could adjust at any time to avoid the "premature" problem. In [8], the authors propose a simulated annealing genetic algorithm (SAGA), which employs simulated annealing to decide whether to accept the chromosome after crossover and mutation or not. By admitting some bad chromosomes into the next generation, this algorithm enlarges the range of parameter optimization, improves the climbing ability and the optimal range. Furthermore, [10] proposes a quantum genetic algorithm (QGA), which employs a quantum bit to encode chromosomes. It also introduces a quantum revolving door to update the population and to make the algorithm more nonlinear and non-deterministic, in conformity with the evolutionary model of the social intelligent community. This method works without a priori and historical experience. However, it requires the parameters affecting the performance of the system to be expressed as a more accurate formula. In addition, it always takes several iterations to converge to the optimal target value. Therefore, the convergence rate is slow and the computational cost is quite large.

Considering the shortcomings of the existing genetic algorithms, this paper proposes an algorithm named Rule-Reduced Genetic Algorithm (RRGA) by combining decision rules with GA [12-13]. The idea of reduced-rules is introduced into the algorithm to improve the convergence rate of GA, as well as to decrease the complexity of the algorithm and ensure timely decisions. The innovation of the proposed algorithm is as follows. Firstly, by condensing the decision space according to a certain criterion without influencing the decision results, the order of the decision space can be reduced from 104 to 102. This change reduces the time overhead for searching the decision space. Secondly, the RS theory that can be done offline without any a priori is employed to extract decision rules from the condensed space. Thirdly, by introducing these rules into the initialization of GA, the convergence rate can be improved remarkably. Finally, the anti-jamming decision objective function which maximizing the normalized transmission rate at the expense of minimizing the normalized transmitting power is applied so as to reduce the dependency on the weights.

Compared with the existing algorithms, pre-processing is necessary for the RS theory employed in the decision-making space reduction, which requires additional calculations. Fortunately, the pre-processing can be completed in advance and stored, and then the impact on the overall system complexity is negligible.

The remainder of the paper is organized as follows. The anti-jamming decision-making model is introduced in Section 2. The reduction of the decision space based on the RS theory and the extraction of decision rules are presented in Section 3. The objective function and RRGA algorithm are proposed in Section 4, where two genetic algorithms named traditional genetic algorithm and the adaptive genetic algorithm are utilized respectively. In Section 5, the simulations and analysis are provided. Finally, the paper is concluded in Section 6.

 

2. Anti-jamming Decision-making Model

The anti-jamming decision-making based on the RRGA approach condenses the decision space of the system at first, and then applies the RS theory to obtain decision rules. On one hand, the decision engine improves the initial population according to these rules. On the other hand, it identifies the objective function according to the parameters of the electromagnetic environment (such as the signal-to-jamming ratio (SJNR) of each channel), user’s requirements (such as the BER threshold), and the decision criterion. The GA searches throughout the decision space until it acquires the proper parameters. The anti-jamming decision-making model based on jamming cognitive is shown in Fig. 1.

Fig. 1.Anti-jamming decision-making model

According to the anti-jamming decision-making model shown in Fig. 1, we have the following assumptions:

(1) The number of modulation modes is M1, all these modes constitute a modulation subspace which is defined as

(2) The number of encoding rate is M2, all these rates constitute an encoding subspace that is defined as

(3) The minimum transmitting power is Psmin, while the maximum transmitting power is Psmax. The number of power grade is NP. All these grades constitute a power subspace that is defined as

(4) The system has K non-overlapping channels, where each communication occupies one channel. All these channels constitute a channel subspace that is defined as

(5) Use SJNR to represent the jamming state of the Kth channel. Each channel’s SJNR is decided by the jamming environment, which is out of control. All the jamming states constitute state space of decision-making defined as γ = {γ(1), γ(2),...,γ(K)}. All the states are to be provided by the cognitive model, which is known a priori.

(6) The system’s constraints are obtained from the user requirement Ureq, which defines the objective function together with the decision criterion. In this paper, user requirement is to keep the BER below a pre-defined threshold. The decision criterion is to maximize the normalized transmission rate at the expense of minimizing the normalized transmitting power.

Therefore, the decision space can be defined as which is the Cartesian product of all the parameters. The number of the space states is (M1M2NpK). For example, if there are 4 modulation schemes, 3 encoding schemes, 80 channels and 20 power grades, theoretically the total number of decision space states is 4 × 3 × 20 × 80 = 19200. Each decision-making is to choose the most suitable combination of the parameters Ψopt = opt, which decides the behavior of the decision engine in one communication under some certain criteria in the decision space Ψ.

 

3. Anti-Jamming Decision Rules with Condensed Decision Space

In view of the advantage that the RS theory needs no any a priori knowledge, it can be applied to wireless communication systems to solve the decision-making problems where no a priori information is available. And the RS theory is capable of dealing with uncertainty and inaccuracy issues.

3.1 Condensed decision space

3.1.1 Reduction of modulation and coding combinations

Since there are M1 kinds of modulation and M2 encoding schemes, the number of valid transmission rates would be K1 = M1M2. Because the differences between the practical transmission rate of some modulation-coding combinations lead to poor BER performance or inappropriate SJNR interval, we can abandon certain combinations. We select K2(K2 < K1) combinations which have proper SJNR interval, the scale of the decision space condensed from K1 × Np × K to K2 × Np × K.

3.1.2 Reduction of alternative channels

Generally speaking, the large number of alternative channels also leads to the large decision space [12]. Therefore, we can further condense the space by aggregating individual channel states; this aggregation allows the system to make decisions according to several channel states instead of every channel state. After acquiring the best channel state, we select the ideal channel from channel set that corresponds to the channel state. The details are as follows:

As we supposed that the channel interference state γ(k) is arbitrary, and it goes against the state aggregation. Therefore, we employ the discrete channel state instead of the original randomly generated channel state, according to Eq. (1) and (2).

where Rmin(k) is the maximum transmission rate that can be achieved under the constraints of γmin(k) and user’s BER (e.g.≤10-4). Rmax(k) is the maximum transmission rate that can be achieved under the constraints of γmax(k) and user’s BER. So the channel state of the system in k can be expressed as Rc(k)[γmin(k), γmax(k)].

After the discretization of channel states, the channels with the same state are aggregated into one channel subspace. Eventually, all the k channels can be aggregated into G(G ≤ K1 + 1) channel subspaces CHA1, CHA2, ... , CHAG. Each channel state contains K3(0 ≤ K3 ≤ K) channels. In addition, channel subspace CHAi can be expressed as:

It should be noted that, all the channels with very low SJNR are aggregated into one channel subspace, whose state is recorded as 0.

Thanks to the channel state aggregation, the selection of anti-jamming decision-making changes into the selection of channel subspace. And then the decision space is further reduced to K2Np(K2 + 1) + K3, in which K3 stands for the number of channels in the selected channel state (K ≤ K3). For example, suppose K = 80, Np = 20 and K2 = 6, all these channels aggregate into K2 + 1 = 7 channel states. If choosing a channel state, which contains 23 channels, the decision space reduced from 4 × 3 × 20 × 80 = 19200 to 6 × 20 × 7 + 23 = 863. That is, its order decreases from 104 to 102, condensed more than 95%.

So far, the scale of the decision space has been condensed dramatically. Suppose the space contains N decision schemes. If for each scheme we define the modulation mode, the encoding rate, and the channel state as conditional attributes, while the transmitting power is the decision attribute, then we get an initial decision table. This table has two problems: 1) The probable existence of some relevance between different conditional attributes will cause attribute confusion during the decision-making, and then decrease the distinctiveness of the derived rules. 2) The scale of the decision table is still too large, as the rules derived directly are not universal. Therefore, it is necessary to reduce the conditional attributes and their values.

3.2 Reduction rule attributes

This work applies the RS theory [13] to reduce the decision space to obtain the minimized decision rules. We use a tetrad DT = (U, A, V, f) to represent the decision system, where U = {x1,x2,...xN} stands for the decision space, that is, the set of all attributes. A = C ∪ D is a set of the whole attributes. C = {C1,C2,C3} represents conditional attributes, while D = {d} stands for the decision attribute. Here, we define the transmitting power as a decision attribute; is a set of values for all the attributes, in which Va is the value domain of attribute a; f is the mapping function from U × A to V, which sets the value for every attribute of each scheme.

3.2.1 Definitions

For convenience, some definitions related to the RS theory are presented .

Definition 1: Division and Equivalence Class

Assuming that P ⊆ A is a random attribute subset of the decision system, if the whole system is traversed and all the schemes which have an equal attribute value to any attribute in the subset P are put in a set, all those sets form a set cluster, namely a division of U under P, This can be expressed algebraically as:

Given x ∈ U, y ∈ U, P ⊆ A for ∀a ∈ P, if x, y satisfies with

Then, sets of y, y in (5) constitute the division of U under P, denoted as U/P, y is the equivalence class of x, denoted as [x]P.

Definition 2: Positive Domain

Assuming that P ⊆ C is a random conditional attribute subset of decision system, and D is the decision attribute, if Yi is a subset in the set cluster U/D, at the same time, it is a set in the set cluster U/P, then, all these Yi are termed the P positive domain of D, denoted as POSP(D). This can be expressed like:

Definition 3: Core

Based on definition 2, for any individual pi ∈ P, if pi satisfies POPP-pi(D) ≠ POSP(D), pi is necessary for D within the range of P, all these pi constitute a set called the relative-D-core of P, denoted as CORED(P).

Definition 4: Significance

Assuming that C is the set of the whole conditional attributes, ∀B ⊆ C and ∀α ∈ C−B, define

as the significance of the attribute α to subset B, in which card(X) is the number of the individuals in set X.

3.2.2 Attributing reduction algorithm based on RS theory

The procedure of the algorithm is as follows:

Input: Elements of the decision system: U, A, V, f.

Output: The reduction of C with regard to the decision attribute D , denoted as REDD(C).

Step 1: Calculate the division of U under the set of condition attribute C with definition 1, which means classifying all the schemes according to C, suppose the total number of the resulting class is H1, i.e. U/C = {X1, X2,...,XH1}.

Step 2: Calculate the division of U under decision attribute D, suppose the total number of the resulting class is H2, i.e. U/D = {X1, X2,...,XH2}.

Step 3: Remove one condition attribute Ci ∈ C at a time, in succession. Recalculate the division of U under the other conditions, suppose the corresponding number of the class is Li, i.e. U/(C-Ci) = {X1, X2,...,XLi}.

Step 4: Calculate the D positive domain of the set of condition attributes C and ∀(C-Ci) with definition 2, and compare every POSC-Ci(D) to POSC(D) according to definition 3, if the two are not equal, condition attribute Ci is necessary to D, all these necessary condition attributes constitute the relative-D-core of C. Suppose the number of the attribute in the core is l, i.e. CORED(C) = {C1,...,Cl}.

Step 5: If the number of the individuals in the set CORED(C) equals to the number of individuals in set C, let REDD(C) = CORED(C) and go to Step 6. Otherwise, calculate the significance of the individuals that appear in the difference set between C, CORED(C) and D. Cm is the one that has the largest significance value. Let REDD(C) = Cm ∪ CORED(C).

Step 6: Output REDD(C).

3.3 Attributing value reduction algorithm based on RS theory

Now the decision system becomes DT' = (U, A', V, f), A' = REDD(C) ∪ D. Set each ordered pair of conditional attribute and its value to be a category. Several categories compose a category cluster.

For the i-th scheme, all the conditional attribute and its value constitute a category cluster In which, is the j-th condition attribute in REDD(C), vij is its value of the i-th scheme. Adding decision attribute and its value to each category cluster, we define every scheme as one decision rule. The algorithm proceeds as follows:

Input: Elements of the current decision system: U, A, V, f.

Output: A set of simplified decision rules R*.

Step1: Change each category cluster into corresponding decision rule ri, i.e. in which, “∧”represents “and”, “→”represents “derive”, is the value of decision attribute of i-th decision scheme.

Step2: For each ri, obtain a new rule after removing some of the schemes also need to remove the attribute value that corresponds to. If there are no rules which have the same conditional attributes but a different decision value with ri, the value vij corresponding to attribute is not necessary for the decision attribute D, and then we can remove it. Apply to all the condition attribute values in ri to obtain a reduction of ri as Apply this method while traversing all the decision rules.

Step3: Output

At this time, we have the simplified decision rules, which minimize the transmitting power under the BER constraint.

It shall be noted that the decision rules can be extracted offline, thus brings no additional computational burden during the system operation.

 

4. Objective Function Design and RRGA Algorithm

For the anti-jamming communication system shown in Fig. 1, the most common decision objectives are minimal transmitting power, maximal transmission rate, and minimal BER. All the objectives interfere with each other and cannot reach optimum for all of them at the same time. Currently, the GA-based methods always transform the above three decision objectives into objective functions respectively, and then weight them. However, without having a scientific foundation to determine the weights, the choice of weights depends on a certain subjectivity. Furthermore, this differs greatly from the actual situation of a communication system. For these reasons, we design a new objective function according to the following considerations. Try to meet the user’s BER requirement, minimize the transmitting power first, and on that base maximize the transmission rate. In this case, the resulting objective function is closer to the requirements of a practical application. After designing the objective function, combine the decision rules in Section 3 with the traditional genetic algorithm [6,12] or adaptive genetic algorithm [7], and adaptively select the transmitting power, the channel state, the modulation mode and the coding rate.

4.1 Objective function

In this paper, modulation schemes of PSK, QAM and LDPC with different orders are employed. However, when the BER is under certain threshold (i.e. waterfall region), the index value of the BER of each combination has an approximately linear relationship with the corresponding SJNR. Thus, a straight-line approximation is used to match this curve to get a simple BER formula. The normalized transmitting power fnorm-power and the normalized transmission rate fnorm-put are defined as follows respectively:

where pi represents the transmitting power of the i-th scheme and pmax represents the maximum transmitting power. Ci represents the coding rate of the i-th scheme and Mi represents the modulation mode of the i-th scheme, Cmax represents the maximum coding rate, while Mmax represents the maximum modulation mode. Then the objective function f can be defined as:

where fmin-power represents the minimum of fnorm-power the algorithm can find under the requirement of a pre-defined target BER, while fmax-put represents the maximum of fnorm-put the algorithm can find under the condition of fmin-power. The target of anti-jamming decision-making procedure is to adapt the communication parameters to maximize f as defined in Eq.(10).

4.2 Adaptive genetic algorithm

The procedure of the traditional GA (Tra GA) contains coding, fitness calculation, selection, crossover and mutation [12]. But adaptive genetic algorithm [7] (AGA) has proportional selection. It is the abbreviation of genetic algorithm with adaptive crossover and mutation operation. The convergence of the genetic algorithms primarily depends on their core operations of crossover and mutation operator because crossover operator offers the global search capability and mutation operator offers the local search capability. AGA adjusts the crossover and mutation rate to improve the traditional genetic algorithm.

where pc represents crossover probability, pc_max and pc_min are the maximum and minimum crossover probability respectively, pm represents mutation probability, pm_max and pm_min are the maximum and minimum mutation probability respectively, itmax represents the maximum generation, iter represents current generation, favg represents the average fitness of population, f′ represents the bigger fitness in two individuals to crossover, f represents the fitness in individual to mutation.

Eq. (11) and (12) show that if the individual is poor (that is, fitness value is less than the average fitness), it would give larger crossover probability and smaller mutation probability; if the individual is good (fitness value is greater than the average fitness value), the crossover probability and the mutation probability will be adjusted. This measure contributes to protect the individual an effective model of good, easy to find the global optimum and prevent "premature" phenomenon.

In addition, comparison of individual fitness values is increased or decreased after crossover and mutation. Compared with the traditional algorithm, this measure ensures that the new individual generated by genetic manipulation is excellent and accelerates the speed of the evolution of the genetic algorithm so that it can avoid the evolution of individual self-degradation.

4.3 RRGA Algorithm

In this paper, we encode working parameters in the form of binary, and then connect them to form a chromosome. After generating the initial population randomly, we screen it according to the decision rules, by utilizing the objective function as the criterion to choose superior ones. Then the superior ones are crossed over, recombined, and mutated. The process is iterated over the whole population. In this paper, we apply the form of roulette to choose the superior chromosomes, and then use the single-point crossover and basic-point mutation method. The population evolves during iteration, and generates chromosomes, which are close to the optimum gradually. The algorithm flow chart is shown in Fig. 2.

Fig. 2.Flow chart of RRGA algorithm

The procedure of RRGA is as follows:

Step 1: Set up the decision space, condense it under the condition of not influencing the decision result.

Step 2: Reduce the decision space and then obtain the simplified decision rules.

Step 3: Initialize the population according to the value range of each parameter; initialize the iteration counter.

Step 4: Screen the population according to the rules obtained in Step 2, acquiring a new population with all feasible schemes.

Step 5: Calculate the objective value of every chromosome according to Eq. (8), (9), and (10).

Step 6: Choose several chromosomes, which have superior objective value, then crossover, recombine, mutate them, and get child generation. Calculate BER (bit error ratio) of each chromosome according to its SJNR (signal to jamming and noise ratio) and the BER formula, and then reserve those chromosomes, which conform to user’s BER requirement. Return to Step 5, get the objective value of every chromosome in child generation, insert superior child chromosome into its father generation, and get the complete population.

Step 7: Complete one iteration, increment the iteration counter. If the number of iterations is smaller than a pre-defined threshold, return to Step 5 or Step 6, or stop the iteration.

 

5. Simulations and analysis

As shown in Table 1, six modulation-encoding combinations that have proper SJNR intervals are selected.

Table 1.Proper modulation-encoding combinations

The BER performance of the 6 types of modulation and coding combinations in the case of Rician channel is presented in Fig. 3.

Fig. 3.BER performance of different combinations of LDPC coding and modulation

Each SJNR interval of modulation and coding scheme can be achieved from Fig. 3, and is shown in Table 2.

Table 2.SJNR interval of each modulation-encoding combination

In order to obtain the minimum decision rules, firstly a decision table shall be set up, in which the decision schemes are the permutations and combinations of the 6 combinations as shown in Fig. 3 and the 7 channel states as shown in Table 2. The target BER is 10−4. We can obtain the channel state of each combination according to the BER target, and calculate the minimum value range of transmitting power. The minimum transmitting power is taken as the decision criterion. The value domain of each attribute in the decision table is expressed as follows: 1) Modulation mode (C1) : BPSK, QPSK, 8QAM, 32QAM. 2) Encoding rate (C2) :1/4,1/2,4/5. 3) Channel state (C3) : the channel states under the condition of minimum transmitting power, as shown in Table 2. 4) Transmitting power (d) : 0~20dBm, with intervals of 0.1dBm. Thus the size of decision space is 6 × 7 × 200 = 8400. Part of the decision table is given in Table 3. Different from the approach in Table 1, the BER target can be reached by increasing the transmitting power in case the channel state is 0.

Table 3.Anti-jamming decision table

By utilizing the method of Sec. 4, one can achieve the minimal decision table as shown in Table 4.

Table 4.The minimal decision table

The universal decision rules can then be achieved based on the core value table after the rules reduction, as given in Table 5.

Table 5.Decision Rules

In practice, the interference information is reflected in the channel states. As can be seen from the decision rule set, if the channel state is determined, one can still minimize the transmitting power without making a choice of all the condition attributes. To some extent, it reduces the complexity of the decision-making process. For example, (c1, BPSK) ∧ (c3 ≠ 0) → p = 0 (coverage rules 2-7). It means that as long as the selected channel is not 0 and when the modulation is BPSK, it can be determined without considering coding rate and that the minimum transmitting power is 0.

For the convenience of binary-coded GA, it is supposed that the transmitting power is in the range 0~25.5dBmwith a 0.1dBminterval, and encoded in 8-bit binary. The SJNR is -4~21.5dBm− with a 0.1dBminterval, and encoded with 8-bit binary as well. In addition to the 6 modulation-encoding combinations shown in Fig. 2, and encoded with 3-bit binary. After generating the initial population, we screen it with the rules shown in Table 4 , and integrated the chromosomes that meet the rules into the new population, then evolved it to reach the optimum. The parameter settings in the GA are as follows: the selection probability is 0.8, the crossover probability is 0.8, the mutation probability is0.01, the amount of population is 150, and the maximum evolutionary generation is 300.

Fig. 4 and Fig. 5 illustrate the design of objective function according to 4.1 and three operational parameters selection results that the anti-jamming decision-making system uses before and after the reduction in GA. In the implementation of RRGA, the use of the Tra GA is named RRGA1; the use of the AGA is named RRGA2.

Fig. 4.Comparison of Tra GA with RRGA1

Fig. 5.Comparison of AGA with RRGA2

The overlapping part of the two curves in Fig. 4 and Fig. 5 means the same results are obtained using these two different methods. In the later stage of evolution, all curves tended to be stable, which means parameters-adaptation had reached the optimum. During the evolution, the value of a parameter changed within its domain and stayed on a fixed value eventually. The parameter-adaptation results are SJNR=21.4dBm; modulation-encoding combination is (32QAM, 4/5).

The smaller number of evolutionary generation is needed to reach the same objective value, the higher the convergence rate of an algorithm. RRGA has a much higher convergence rate than the traditional GA, which results from screening the initial population by decision rules, and by decreasing the scale of the population on the condition of not losing feasible schemes. The computational complexity of GA is mainly in the calculation of objective function. AGA algorithm is mainly concentrated in the calculation of the objective function out of local optimal to overcome "premature". By designing a simplified objective function than those weight-based, the convergence rate can be improved significantly.

The experiment is repeated for 100 times independently, and the objective function is optimized by using the Tra GA, AGA and two types of proposed RRGA (named RRGA1 and RRGA2). Tra GA parameters are normalized as the benchmark and the other algorithms (AGA, RRGA1 and RRGA2) are compared with it.

Fig. 6 shows the comparison of population before and after the reduction. It can be seen from Fig. 6, the initial population of two genetic algorithms (Tra GA and AGA) is the same. That means the initial population of RRGA1 and RRGA2 are the same after using reduced- rules. The population after reduction is only the 43.754% of the original one.

Fig. 6.Normalized anti-jamming decision’s initial population in different algorithms

Fig. 7 and Fig. 8 are the comparison of generation and the average SJNR of each algorithm to Tra GA before convergence.

Fig. 7.Normalized evolution generation comparison chart

Fig. 8.Normalized average SJNR comparison chart

As can be seen from the results of the Fig. 7 and Fig. 8, when the objective function optimized, the results of RRGA1 and RRGA2 are much better than the Tra GA and AGA. The results demonstrated that compared with Tra GA and AGA, RRGA1 and RRGA2 have strongly improved in search efficiency and convergence speed.

 

6. Conclusions

In this paper, an anti-jamming decision-making method named RRGA is proposed, which combines the reduced decision rules and GA, and utilizes the adaptation of communication parameters. Without loss of generality, two typical genetic algorithms (Tra GA and AGA) are simulated separately. Simulation results prove that RRGA1 and RRGA2 are superior to Tra GA and AGA in terms of search efficiency, convergence rate and algorithm stability. The proposed method condenses the decision space at first, then evolves the resulting population under the condition of not losing feasible schemes, which finally reduces the decision time under the condition of not influencing the decision accuracy. As in practice, each decision objective weight value cannot be given accurately, we also proposes the criteria of minimizing the normalized transmitting power and maximizing the normalized transmission rate, in the presence of the BER constraint. Therefore, it is also more applicable than traditional methods. In the future, other evolutionary algorithms can also be considered.