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Populationadaptive differential evolutionbased power allocation algorithm for cognitive radio networks
 Xiu Zhang^{1, 2} and
 Xin Zhang^{1, 2}Email authorView ORCID ID profile
https://doi.org/10.1186/s1363801607221
© The Author(s) 2016
 Received: 14 July 2016
 Accepted: 6 September 2016
 Published: 15 September 2016
Abstract
Cognitive radio (CR) networks have drawn great attention in wireless communication fields. Efficient and reliable communication is a must to provide good services and assure a highquality life for human beings. Resource allocation is one of the key problems in information transmission of CR networks. This paper studies power allocation in cognitive multiple input and multiple output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. Power allocation is modeled as a minimization problem with three practical constraints. To deal with the problem, a populationadaptive differential evolution (PADE) algorithm is proposed. All algorithmic parameters are adaptively controlled in PADE. In numerical experiment, three test cases are simulated to study the performance of the proposed algorithm. Particle swarm optimization, differential evolution (DE), an adaptive DE, and artificial bee colony algorithms are taken as baseline. The results show that PADE presents the best performance among all test algorithms over all test cases. The proposed PADE algorithm can also be used to tackle other resource allocation problems.
Keywords
 Cognitive radio networks
 Differential evolution
 Power allocation
 Resource allocation
 Parameter control
1 Introduction
In radar networks [1–3], power allocation is important to ensure the quality of services (QoS) under the limited power resources. In [1], the power allocation and sensor selection scheme in radar networks was studied based on opportunistic sensing. In [4], knowledgebased radar sensor network was studied to improve threat assessment based on different antecedents where higher power was allocated for suspicious scenario. Waveform design and diversity in radar networks to maximize the receiving power was studied in [5]. Similarly, power allocation could be applied to cognitive radio networks to increase spectrum efficiency without losing QoS.
With the development of wireless communication techniques, advanced radio interface technology and code modulation mode provide good support for utilizing radiowave spectrum. However, recent study reports reveal that radiowave spectrum becomes scarce resource with the sharp increase of mobile users and services. On the other hand, researchers observe that the allocated spectrum resources were not fully used and the utilization ratio is usually between 15 and 85 % [6]. The imbalance problem of spectrum utilization becomes more and more prominent. For example, some unauthorized frequency bands are often crowded and congested, while some authorized frequency bands are often in idle status. Thus, how to effectively enhance the utilization ratio of radiowave spectrum becomes a tough problem in the nextgeneration wireless communication.

Spectrum pooling system was proposed by Jondral et al. [7]. It is a centralized network architecture based on orthogonal frequency division multiplexing (OFDM). Its suitable scenarios include spectrum share in OFDM wireless local area network (WLAN) and global system for mobile communication (GSM) network. The architecture involves both authorized and unauthorized users, in which unauthorized users could detect authorized users through sensors and send collected information to base station so that base station could periodically broadcast the usage conditions to all users.

Zheng and his collaborators sponsored the Nautilus project [8]. It emphasizes the spectrum share in a distributed and cooperated manner. They provide three spectrum access patterns including cooperationbased access, local bargaining distributed access, and priori negotiation access. This project focuses on selecting optimal data transmission channel in the foundation of architecture.

The nextgeneration (XG) project sponsored by defense advanced research projects agency of USA planned to provide a complete solution for dynamic spectrum access in order to realize dynamic spectrum access and share [9]. The network architecture of this project is divided to main network and XG network, where XG network supports heterogeneous.
It is observed that selfadaptive OFDM technology is capable to enhance spectrum efficiency and system transmission speed. CR system supported by selfadaptive OFDM technology is a must in nextgeneration mobile communication system. In the CR system, available frequency bands are usually discontinuous, while OFDM technology could flexibly combine or split available bands. This property promotes the usage of OFDM in power allocation in CR system. Given secondary users did not disturb the communication of main users, secondary users could opportunistically occupy available bands of main users. Based on the damping of every carrier channel, OFDM would reallocate the power energy assigned to each subcarrier. Thus, the utilization ratio of spectrum and system efficiency are improved, and the throughput capacity of secondary users can then be maximized.
To use spectrum resource more wisely and improve data transmission rate and reliability, dynamic resource allocation in OFDMbased CR systems is the key technique. Observe that computational intelligence algorithms have been successfully applied to deal with optimization problems in wireless communication. This paper concentrates on tackling dynamic power allocation problem in OFDMbased CR systems. The allocation problem is optimized by evolutionary computing (EC) approaches. Moreover, a populationadaptive differential evolution algorithm is proposed to gain a better allocation solution than standard EC approaches.
The organization of this paper is as follows: Section 2 reports the power allocation problem and related works. Section 3 gives three popular EC approaches and the proposed algorithm. Section 4 shows the numerical simulation results and discussions. Section 5 concludes the paper.
2 Problem overview and related works
3 Optimization algorithms
Power allocation techniques in CR systems can roughly be classified to equal power allocation methods and unequal power allocation ones. The former means each subcarrier is allowed the same power energy, which is very simple and commonly used in reality. Clearly, equal power allocation methods do not effectively exploit channel status and thus its resulting system performance is not satisfactory. Unequal power allocation could overcome this shortcoming and draw great attention in present research field. Waterfilling algorithm is the most famous unequal power allocation methods. The finding of optimal waterfilling factor is the essential work in waterfilling algorithm. The near optimal factor could be obtained by line search methods, though the computational cost may rapidly grow in case line search method did work properly. Many researchers attempt to modify waterfilling method to attain good solution.
EC approaches are applied to deal with problem (3) including PSO, DE, and artificial bee colony (ABC). PSO and ABC are typical swarm intelligence paradigms where the standard algorithms do not contain recombination operators. DE was not inspired from observation of natural species. In fact, it was proposed based on the empirical experience of Storn and his collaborators [19]. DE consists of both mutation and recombination operators. So far, various operators have been proposed for the three paradigms [20–23].
3.1 Three classical evolutionary computing algorithms
where w is inertia weight factor, c _{1} and c _{2} are learning factor, r _{1} and r _{2} are two randomly numbers between 0 and 1. \(\mathbf {p}_{t}^{l}\) is the local best solution associated with x _{ t }, while \(\mathbf {p}_{t}^{g}\) is the global best solution of whole population.
where rand(0,1) returns a randomly number ∈(0,1); Cr is crossover rate which needs to be provided by users.
where ϕ _{ t,j1}∈[−1,1] is a random real number, and j1∈[1,D] is a random integer. x _{ r1} has to be a different solution from x _{ t }.
Survivor selection step of the three algorithms is quite similar. Candidate solution x _{ t+1} competes with its parent x _{ t }. The winner survives and the other is discarded. For PSO, the local and global best solution are updated in this step. For DE and ABC, the global best solution are also recorded so that it can be returned once the algorithm terminates.
3.2 Populationadaptive differential evolution algorithm
In the viewpoint of algorithmic parameters, PSO contains the largest number of parameters to be tuned by users than DE and ABC, while ABC has the least number of parameters (i.e., two parameters). Algorithmic parameter brings notorious impression to EC approaches since users have to think out how to set them before using the algorithms. Some parameters may be sensitive to the performance of the algorithm [24].
To alleviate the overhead of algorithmic parameter setting, a populationadaptive method is proposed for DE, which is called PADE algorithm. As suggested in [19], the initial population size Np ^{init} is set to 4D (i.e., Np=Np ^{init} in the beginning). At each generation, the search status of the algorithm is monitored. If the best solution so far is improved at generation t, population size should not be changed as the population performs good in finding good solutions; otherwise, population size is reduced by size 2. When eliminating a solution from population, a binary tournament selection is used. That is randomly choosing two solution and the one with less fitness is discarded. In this way, the best solution so far always survives in population. This progress continues until Np=4. Observed from (6), the mutation of DE needs at least 4 solutions; hence, Np must not be less than 4. Once Np=4, population size starts to increase by size 2 under the condition that fitness is not improved at a generation. Two new solutions are randomly created in search space as in initialization. In the population size increase stage, a maximum threshold Np ^{init}/2 is set based on empirical experience [25].
where rand _{ j }∈(0,1),j∈{1,2,3,4} are independently sampled random numbers, τ _{1} and τ _{2} are probabilities to adjust the control parameters, F ^{ l }=0.1 and F ^{ u }=0.9 delimit the range of F values ∈[0.1,1]. Brest et al. used τ _{1}=τ _{2}=0.1 and named the adaptive algorithm as jDE. In this scheme, each solution is extended by two dimensions standing for F and Cr. Then, both parameters are modified the same as candidate solutions. The main procedures of the PADE algorithm are given in Algorithm 1.
Observed from Algorithm ??, all algorithmic parameters are adapted. This saves the effort of users to set any parameter except their own optimization problem. Unlike the existing algorithms as in [27–29], the PADE algorithm does not introduce any new parameter and does not increase the burden of algorithmic parameter control.
4 Numerical experiment
In this section, the proposed PADE algorithm is applied to deal with problem (3).
4.1 Simulation setting
Simulation configuration is described as follows. Suppose the number of transmitter antennas of secondary user is MT=4, the number of receptor antennas of secondary user is MR=4, and main user has a receptor antenna. The number of subcarriers is 128, i.e., N=128. Noise power σ=0.001; subcarrier interval is 1000 Hz. The channel gain noise ratio from secondary user’s transmitter to its receptor is 10 dB. The channel gain noise ratio from secondary user’s transmitter to main user’s receptor is 15 dB.
Thus, the gain of separate subchannel flow over subcarrier n is \(g_{ss,n} = \left [g_{ss,1,n}^{2},\ldots, g_{ss,MT,n}^{2}\right ]\). The total channel gain over all subcarriers is g=[g _{ ss,1},g _{ ss,2},…,g _{ ss,N }]. Hence, the objective function value f could be computed given an allocation p _{ m,n }.
Configuration of PSO, DE, ABC, jDE, and PADE algorithms
Algorithm  Parameters 

PSO  Np=10, c _{1}=c _{2}=1.49, w ^{min}=0.4, w ^{max}=0.9, K=3 
DE  Np=10, F=0.5, Cr=0.9 
ABC  Np=4, limit=0.5NpD 
jDE  Np=10, F ^{ l }=0.1, F ^{ u }=0.9, τ _{1}=τ _{2}=0.1 
PADE  Np ^{init}=4D 

(1) The maximum number of function evaluations (MFE) is reached, where MFE =1000;

(2) f(x ^{best}) is stagnated for an interval of five, where f(x ^{best}) stands for the best value found by an algorithm.
The CR system and algorithms are implemented in MATLAB and executed on a personal computer with 4core 2.50 GHz CPU and 4 GB of memory. Thus, a fair comparison can be conducted under the same running environment.
4.2 Simulation results
Results found by the test algorithms with R _{min}=150 Mbps and I _{max}=8.0e−4 W
Algorithm  f(x ^{best})  R  I  f _{eval} 

PSO  1.7976  164.20  4.449e −04  105.52 
DE  1.6108  151.81  3.998e −04  110.20 
ABC  1.6112  151.76  3.889e −04  116.24 
jDE  1.6173  153.60  3.9253e −04  130.00 
PADE  1.5825  150.58  3.875e −04  106.26 
The average number of function evaluations cost by the test algorithms to deal with power allocation instances
Algorithm  PSO  DE  ABC  jDE  PADE 

\(R_{\text {min}}^{1}\)  0.00  0.00  0.00  0.00  0.00 
\(R_{\text {min}}^{2}\)  106.40  115.10  127.66  119.20  113.12 
\(R_{\text {min}}^{3}\)  105.80  136.40  144.08  124.40  114.32 
\(R_{\text {min}}^{4}\)  105.60  128.40  143.78  114.60  105.76 
\(R_{\text {min}}^{5}\)  105.44  120.60  146.42  116.40  109.84 
\(R_{\text {min}}^{6}\)  105.92  122.90  141.74  123.90  114.08 
\(R_{\text {min}}^{7}\)  104.00  115.50  180.58  120.50  105.08 
\(R_{\text {min}}^{8}\)  104.72  154.90  201.88  176.70  115.28 
\(R_{\text {min}}^{9}\)  106.60  235.44  301.66  300.50  191.30 
\(R_{\text {min}}^{10}\)  439.76  502.64  543.70  487.50  444.00 
\(R_{\text {min}}^{11}\)  702.92  799.30  814.80  745.20  727.60 
In case 3, the result comparison of FEs’ cost by each algorithm is similar to that in case 2. That is, PSO consumes the least FEs among the four algorithms, though its allocation solution is the worst; PADE costs less FEs than DE, ABC, and jDE; its solution is the best compared with PSO, DE, jDE, and ABC. Therefore, the above three cases demonstrate that the proposed PADE algorithm is very useful to tackle power allocation problems in cognitive MIMOOFDM systems.
5 Conclusions
Efficient and robust communication networks require strong resource allocation schemes, especially for ad hoc networks or sensor networks in which power energy is rare and limited. Selfadaptive OFDM technology is capable to enhance spectrum efficiency and system transmission speed. Moreover, the combination of MIMO and OFDM is useful to exploit frequency domain and space domain resources. Hence, this paper focuses on power allocation in cognitive MIMOOFDM systems.
Power allocation problem is formulated to a minimization under the conditions that a minimal speed bound is set for secondary user’s data transmission and a maximal threshold is set to restrict the average interference power caused by secondary user to main user. Also, the power energy allocated on each subcarrier has to be nonnegative.
The main contribution of this paper is to propose a populationadaptive differential evolution (PADE) algorithm for tackling power allocation problem. PADE is a fully adaptive algorithm and saves user efforts to set algorithmic parameters. Moreover, PSO, DE, jDE, and ABC are also taken as baseline in numerical experiments. Three test cases are illustrated to study the performance of the proposed algorithm. Based on the results, we can conclude that the PADE algorithm is good at dealing with power allocation problems than PSO, DE, jDE, and ABC.
The same termination condition is used for all test algorithms for a fair comparison. In practical applications, users could revise the criterion based on their empirical experience, computational time, or any other prior knowledge. The expected running time of PADE could be reduced by using more powerful mutation formula or by identifying search patterns in archive solutions, which we would investigate further in the future.
Declarations
Acknowledgements
This research was supported in part by the Tianjin Thousand Youth Talents Plan Project of Tianjin Normal University (ZX110023), the National Science Foundation of China (61603275, 61601329), and the Applied Basic Research Program of Tianjin (15JCYBJC51500, 15JCYBJC52300).
Competing interests
The authors declare that they have no competing interests.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License(http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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