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Intelligent control of cognitive radio parameter adaption: Using evolutionary multi-objective algorithm based on user preference
Ad Hoc Networks 26 (2015) 3–16
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Ad Hoc Networks journal homepage: www.elsevier.com/locate/adhoc
Intelligent control of cognitive radio parameter adaption: Using evolutionary multi-objective algorithm based on user preference Wen Chen ⇑, Tao Li, Tao Yang Sichuan University, No.24 South Section 1, Yihuan Road, Chengdu, China
a r t i c l e
i n f o
Article history: Received 8 July 2013 Received in revised form 13 April 2014 Accepted 10 September 2014 Available online 16 October 2014 Keywords: Cognitive radio network Transmission parameter User preference Pareto front Selection pressure Cognitive engine
a b s t r a c t Cognitive radio (CR) is a promising technique for overcoming the spectrum scarcity problem. It must appropriately alter its transmission parameters according to predefined objectives in dynamic wireless environment. In this paper, we model the CR parameter adaptation problem as an unconstrained multi-objective optimization problem and then propose a non-dominated front searching algorithm based on user preference (NFSA-UP) to determine the optimal transmission parameters for a multicarrier system. The distances from individuals to the user preference direction are combined with the pareto ranks to determine the evolving direction as well as the survive selection of individuals. It is beneficial to increase selection pressure at the beginning of the evolving, and speed up convergence to the true pareto optimal front at end. The best individual which is obtained after final iteration is reported here as the middle point on the first pareto front, avoiding the secondary selection from a set of optimal solutions. We performed multi-objective optimization on a 64 subcarriers in CR network. NFSA-UP is compared with other pareto front searching algorithms NSGAII and NSGAII-LBS, and the results demonstrate that the optimal transmission parameters of CR can be got using NFSA-UP with any user preference direction, while better performance is observed. Ó 2014 Published by Elsevier B.V.
1. Introduction The increasing growth of wireless services over the last decade demonstrates the vast demand for radio bands. However, the spectrum resource is limited and mostly has been licensed to users which can work within a limited frequency band [26]. The studies by the Federal Communication Commission have found that the actual licensed spectrum is largely unoccupied most of the time [7]. In order to deal with the imbalance between spectrum scarcity and spectrum under utilization, cognitive radio technology was proposed [15].
⇑ Corresponding author. http://dx.doi.org/10.1016/j.adhoc.2014.09.006 1570-8705/Ó 2014 Published by Elsevier B.V.
Cognitive radio is a promising technique for overcoming the apparent spectrum scarcity problem, as well as improving the communications efficiency [27,9]). The IEEE has formed the 802.22 Working Group to develop a standard for wireless regional area networks (WRAN) based on cognitive radio technology [10]. Ideally a Cognitive Radio (CR) possesses the capability of sensing, perceiving, decision making, planning, and learning in a wireless environment [6]. Due to the time varying radio channel characteristics, as well as the spectrum band availability, cognitive radios need to support time varying Quality of Service (QoS) requirements. Even though the principal goal of dynamic spectrum access (DSA) is to improve the spectrum utilization efficiency, other goals such as minimizing the bit-error-rate (BER), maximizing the data throughput,
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minimizing the power consumption, also need to be met [1]. Therefore, cognitive radio (CR) must be able to sense the environment periodically and appropriately alter the transmission parameters according to the objectives and QoS requirements of the users [22]. To achieve these goals, CR needs a cognitive engine to be aware of its environment, including the transmission link, user demands, and regulatory regimes, and it must balance multiple objectives. This learning characteristic of CR makes it intelligent that adapts itself in the dynamic situations [6,1,22]. Evolutionary multi-objective optimization (EMO) algorithms are well suited to solving multi-objective optimization and decision problems [11,14], and it has been shown that a EMO based cognitive radio engine can support awareness-processing, decision-making, and learning elements of cognitive functionality [21]. Research done at Virginia Tech has developed a genetic algorithm (GA) engine for cognitive radios [1]. Their simulation results validate that the genetic algorithm implementation does in fact change the transmission parameters to different settings, based upon a set of objectives. A set of single carrier and multicarrier fitness functions have been derived and GA is used to search the optimal set of transmission parameters in [16]. Adaptive transmission in the context of cognitive radio networks is addressed in [28] where GA is used to optimize the CR parameters by considering several QoS and channel coding schemes. In order to reduce the convergence time and to improve the optimization results of spectrum utilization, in [17] a population adaptation technique for reducing the amount of time required to reach an optimal decision for a GA-based cognitive engine is proposed. And a technique using quantized variables with adaptive variable ranges, based on the knowledge gathered from previous experience, is studied in [1]. These two methods both assumed that the wireless channel environment changes slowly, such that the gathered knowledge can be reused in the near future. All the above works have attempted to solve the parameter adaptation problem in CR by formulating it into single objective functions using weighted sum approach. When a multi-objective optimization problem is solved by weight vector aggregate sum approach, the result will find a single value for each parameter and thus the behavior of solution space cannot be deduced with respect to multiple objective functions. For the real-time scenario, the performance of CR system depends on the choice of weights to specific objective functions which is hard and scenario dependent [6]. Therefore, Tosh et al. model the CR parameter adaptation problem as an unconstrained multi-objective optimization problem and perform optimization of more than one conflicting objectives at a time using Non-dominated Sortingbased Genetic Algorithm (NSGA-II) instead of weighted sum approach [6]. This helps to find a set of optimal solutions from the large range of solution space defined in terms of pareto optimal set. NSGA-II avoided the setting of the weight vectors and got more accurate solutions than GA. However, for NSGA-II there are a set of optimal solutions on the pareto-front, which are all non-dominated, thus the choice of best solution needs a further comparison, and it takes more time to get coverage [5].
In the real applications of multi-objective optimization, the decision makers usually have some preference on the fitness functions. For example, they may want the fitness functions to coverage to given target values, and these preference information can be used to direct the evolutionary procedure [24]. Fonseca and Fleming probably suggested the earliest attempt to incorporate preferences, and their proposal was to use EMO together with goal information as an additional criterion to assign ranks to the members of a population [8]. Shaw and Fleming incorporate the target information into the calculation of fitness to design a preference based multi-objective optimization algorithm to solve the production scheduling problem [23]. Pierro et al. proposed preference order mechanism to discriminate non-dominate solutions [20]. Cvetkovic and Parmee [3] used binary preference relations (translated into weights) to narrow the search. In [25], preferences were included through the use of reference points. Also a guided dominance scheme and a biased crowding scheme were suggested. Thiele et al. suggest a hybrid approach which combine ideas from both evolutionary and interactive multi-objective optimization [24]. The principle is first give a rough approximation, and then generates a more accurate approximation of the area where the decision maker’s most satisfactory solution lies. Deb and Kumar present an interactive methodology for finding a preferred set of solutions focused on a small nondominated region, instead of the complete pareto-optimal frontier [4]. All the aforementioned methods have got promising results after the user preference was incorporated into the EMO algorithms. In the paper, we introduce a non-dominated front searching algorithm based on user preference (NFSA-UP) to solve the parameter set problem of cognitive radio system. During the searching of pareto front of multi objects, the preference information is utilized to direct the evolutionary procedure. In each generation, the individuals are selected to the next generation based on the front orders and individual distances to the preference directions. The simulation results of 64 subcarriers in the CR network demonstrated that, based on the user preference, the optimal transmission parameters can be effectively found, under the predefined quality of service (QoS).
2. Problem definition Assuming a multicarrier dynamic wireless environment with N c subcarriers, the basic characteristic of CR is to sense the environmental parameters, and it learns itself to adjust the value of transmission parameters to achieve the predefined quality of service (QoS). In CR system, the environmental parameters act as input to the problem and the transmission parameters act as decision variables. Hence the problem can be defined as to find the set of transmission parameters by modeling the scenarios as multi-objective functions [6]. The proposed algorithm is based on user preference to solve the formulated multi-objective function to obtain the required solutions. The below subsection briefs about the radio parameters involved in CR engine.
W. Chen et al. / Ad Hoc Networks 26 (2015) 3–16
(a) p = 10%, C1 = 1, C2 = 1
(b) p = 30%, C1 = 1, C2 = 1
(c) p = 70%, C1 = 1, C2 = 1
(d) p = 90%, C1 = 1, C2 = 1
5
Fig. 1. The survive value with different prefer distance and pareto rank.
Fig. 2. The individuals selected at different pareto front. (a) Selected individuals in the 10th generation, (b) Selected individuals in the 90th generation. In the figure, the black circles represent individuals been dropped, and the red diamonds represent individuals been selected to the next generation. For simplicity only the first five pareto fronts are depicted, and C 1 ¼ 1; C 2 ¼ 1.
2.1. Input and output parameters Radio parameters of CR are categorized into environmental parameters and transmission parameters [18]. The former gives knowledge of environmental characteristics of multicarrier wireless environment which are used as inputs to the CR system, where different environmental
parameters include channel attenuation, noise power, signal-to-noise ratio (SNR), spectrum information, etc. Transmission parameters are the tunable parameters of CR system. The CR tunes its transmission knobs to corresponding values from the optimal parameter set. The transmission parameters [18] are listed as: transmit power ðPÞ, type of modulation (mod type) scheme used for the
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PNc
Table 1 Transmission parameters with their ranges.
f min
Parameter (x)
xmin
xmax
Transmit power (P) Modulation index (m) Bandwidth (B) Coding rate (Rc) Frame length (L) Time division Duplex (TDD) Symbol rate (Rs) Noise power (N)
1 dBm 2 2 MHz 1/2 94 Bytes 1% 125 Ksps 0.01 dBm
18 dBm 10 32 MHz 3/4 1504 Bytes 100% 1 Msps 0.1 dBm
communication, modulation index (m), bandwidth ðBÞ, channel coding rate ðRc Þ, size of transmission frame in byte ðLÞ, time division duplex in percentage (TDD), and symbol rate ðRs Þ. Modulation Index ðmÞ is defined as the total number of symbols in a modulation scheme and TDD represent the percentage of transmits time.
Pbe
2.2.1. Object function for bit-error-rate One of the most common goals in wireless communications is to get an error free signal, or to minimize the bit error rate of the transmission. Determining the theoretical bit error rate depends on several transmission parameters including the transmit power, modulation type, modulation index, signal power, and noise power. The goal is to create a fitness function with a valid output range of between 0 and 1. Mathematically, the normalized objective function for minimizing BER [18] is defined in (1).
(a)
i¼1 1
log10 ð0:5Þlog10 ðPbei Þ log ð0:5Þlog ð1012 Þ 10
10
ð1Þ
Nc
where N c is the number of subcarriers, Pbe represents the probability of a bit error or BER for a given modulation scheme and a given channel type, and it is normalized to the worst possible BER value of 0.5 and divided over the total possible range of BER values selected. In the paper, 1012 is chosen to be the best case BER. In this investigation, we assume the possible modulation types include QAM, PSK, and FSK. To apply this work to practical systems, we must determine the BER probability for each modulation. The following equations describe the BER probability of QAM, PSK, and FSK, using a graycoded bit assignment and assuming an AWGN channel model. For a BPSK signal constellation, the probability of a bit error is defined as [19].
2.2. Fitness functions Ideally the fitness function must be able to guide the system to one optimal parameter set. A cognitive radio must perform an action based on a set of parameters, which should be selected from the pareto front according to some preference information [6]. Preference information is used to rank the objectives in order to help the fitness function guide the evolutionary algorithm to one optimal solution. In this work three objective functions: Bit-Error-Rate minimization, system throughput maximization, power consumption minimization are considered. In the next subsections, we describe the objective functions in detail.
ber
¼
rffiffiffiffi! P ¼Q N
ð2Þ
Whereas for M-ary PSK, the probability of a bit error is given as
Pbe ¼
2 Q log2 ðmÞ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P 2 log2 ðmÞ c sin m
ð3Þ
For M-ary QAM, the probability of a bit error is defined as
Pbe ¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi! 4 1 3 log2 ðmÞ c 1 pffiffiffiffiffi Q log2 ðmÞ m1 m
ð4Þ
where Q is the Q-function in term of error function, c represents the energy per bit. 2.2.2. Object function for throughput By definition, throughput is defined as the amount of correct information received at the receiver. Maximizing throughput is a common aim in the multimedia environment. Determining the theoretical throughput depends on the parameters such as coding rate ðRc Þ, frame size ðLÞ, MAC and IP layer overhead H, PHY layers overhead O, probability of BER ðPbe Þ and percentage of transmit time ðTDDÞ. The normalized objective function for maximizing throughput [18] for N c subcarriers is defined as
(b)
(c)
Fig. 3. pareto optimal front generated by NSGA-II, (a)–(c) represent pareto optimal front of f1 and f2, f1 and f3, f2 and f3 respectively.
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(a) (0,-1)to(0.1,-0.3)
(b) (0,-1)to(0.14,-0.2)
(c) (0,-0.5)to(0.18,-0.45)
(d) (0,-1)to(0.1,-0.3)
(e) (0,-1)to(0.14,-0.2)
(f) (0,-0.5)to(0.18,-0.45)
Fig. 4. pareto front of f1 and f2. (a)–(c) are generated by NFSA-UP, (d)–(f) are generated by NSGA-LBS.
PN c f max
tp
¼
Li i¼1 Li þOþH
ð1 P bei ÞLi þO Rci TDDi Nc
ð5Þ
Find x ¼ hx1 ; x2 ; x3 ; . . . ; xn i Min y ¼ hf 1 ðxÞ; f 2 ðxÞ; f 3 ðxÞ; . . . ; f m ðxÞi
ð7Þ
Subject to li 6 xi 6 ui ; 1 6 i 6 m; x 2 X; y 2 Y 2.2.3. Object function for power Energy is the most important factor which must be spent optimally for the communication process. Hence minimum power should be consumed for all the tasks while communicating or computing. The parameters contribute to the fitness for power minimization are bandwidth ðBÞ, modulation index (m), symbol rate ðRs Þ and transmit power ðPÞ. The normalized objective function for minimizing power is expressed as.
" f min power ¼ 1 a
PN c
i¼1 ðP max þ Bmax Þ ðP i þ Bi Þ
Nc ðPmax þ Bmax Þ # PN c P log ðmmax Þ log2 ðmi Þ Nc ðRsmax Rsi ð6Þ þ k i¼1 þb i¼1 2 N c log2 ðmmax Þ þ Bmax Nc Rsmax 2.3. Multi-objective algorithm
In general, a multi-objective fitness function problem can be presented as trying to determine the correct mapping of a set of n parameters to a set of m objectives [24]. This can be seen algebraically as:
where x is the set of decision variables with X is the parameter space, and y is the set of objectives with Y as the objective space. In the case of a multiple objective evolutionary algorithm, each f i ðxÞ represents the fitness function for a single objective. If any f i ðxÞ is originally expected to find maximum value, then it can be changed as f i ðxÞ. GA based on optimization method usually combine f i ðxÞ using weight factors to get a single fitness function f ðxÞ, for example
f ðxÞ ¼
X
-i f i ðxÞ
ð8Þ
i
Usually, the weight vector is set by empirical, and in real world problems, such as the problem addressed in this thesis, the objectives under consideration might conflict with each other. For example, minimizing power and minimizing BER simultaneously creates a conflict due to the single parameter, transmit power, affecting each objective in a different way. Determining the optimal set of decision variables for a single objective, e.g. minimize power, often results in a non-optimal set with respect to other objectives, e.g. minimize BER and maximize throughput.
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(a) (0,0)to(0.5,0.5)
(b) (0,0)to(0.2,0.8)
(d) (0,0)to(0.5,0.5)
(e) (0,0)to(0.2,0.8)
(c) (0,0.1)to(0.3,0.5)
(f) (0,0.1)to(0.3,0.5)
Fig. 5. pareto front of f1 and f3. (a)–(c) are generated by NFSA-UP, (d)–(f) are generated by NSGA-LBS.
For pareto dominance based EMO algorithms, The optimal set for multiple objective functions lie on what is known as the pareto optimal front [5]. This front represents the set of solutions that cannot be improved upon in any dimension. The solutions on the pareto front are optimal and co-exist due to the trade-offs between the multiple objectives. When a possible solution s in the last generation is not dominated by any other feasible solutions, s is referred to as a pareto-optimal solution of the m-objective minimization problem in (7). The set of all pareto optimal solutions forms the tradeoff surface in the objective space. This tradeoff surface is referred to as the pareto front. EMO algorithms are designed to search for a set of well distributed non-dominated solutions that approximates the entire pareto front very well. Hisao Ishibuchi demonstrated that pareto dominance based EMO algorithms, including NSGAII and SPEA [11], suffered from the deterioration of the search ability. Under multi-objects, sometimes almost all solutions in each population become non-dominated. This severely weakens the pareto dominance-based selection pressure toward the pareto front. That is, the convergence property of EMO algorithms is severely deteriorated. 3. NFSA-UP for the optimization of multi parameters of CR network A straightforward idea for the scalability improvement of EMO algorithms to many-objective problems is to
increase the selection pressure toward the pareto front. One approach based on this idea is to modify pareto dominance in order to decrease the number of non-dominated solutions in each population [11]. Another approach is to assign different ranks to non-dominated solutions [2,13]. In this paper, we incorporate user preference information into the EMO algorithms to help the searching of pareto non-dominated fronts, and propose a Non-dominated Front Searching Algorithm Based on User Preference (NFSA-UP). Before the iteration, the decision maker is asked to give preference information in terms of reference points consisting of desirable aspiration and reservation points for multi-objective functions. The information is used in NFSA-UP to generate a new population by combining the fitness function and an achievement scalar function.
3.1. Basic definition Preference information is used to direct the evolution while EMO algorithm is used to find multiple non-dominated solutions on the pareto front. Jaszkiewicz and Slowinski proposed preference model [12], in the model, the aspiration point, reservation point, indifference threshold, preference threshold and veto threshold must be given. In this paper, the preference relationship is reduced, and only the aspiration point, reservation point are needed. The preference direction is decided by the aspiration point
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(a) (-0.4,0)to(-0.3,0.4)
(b) (-0.4,0)to(-0.3,0.8)
(c) (-0.9,0.3)to(-0.3,0.4)
(d) (-0.4,0)to(-0.3,0.4)
(e) (-0.4,0)to(-0.3,0.8)
(f) (-0.9,0.3)to(-0.3,0.4)
Fig. 6. pareto front of f2 and f3. (a)–(c) are generated by NFSA-UP, (d)–(f) are generated by NSGA-LBS.
and reservation point. Usually the aspiration point can be any point with lower object value, and the reservation has higher object value than the aspiration point, and for the CR parameter optimization problem, the objectives under consideration might conflict with each other. Therefore, the decision maker (user) set higher object value for the preference object, and lower value for the other object. Definition 1 (Preference distance). The preference distance is defined to evaluate the distance from a possible solution xA to the direction of preference.
j¼1
ð9Þ
where xA is an possible solution of the multiple object optimization problem defined in (7), f i is the ith fitness function, Fðxv Þ ¼ ½f 1 ðxv Þ; . . . ; f m ðxv Þ is the aspiration point, Table 2 The quantitative comparison results. Algorithm
NSGA-II NSGA-UP NFSA-LBS
Time (s) f1f2
f1f3
f2f3
16.29 16.76 16.78
18.11 16.01 17.25
17.87 15.5 16.93
Definition 2 (Middle point). The solution with least preference distance is the middle point. Definition 3 (Pareto dominate ). If xA ; xB are two possible solutions, if xA xB , then
8i ¼ 1; 2; . . . ; m; f i ðxA Þ 6 f i ðxB Þ ^ 9j ¼ 1; 2 . . . m; f j ðxA Þ < f j ðxB Þ ð10Þ
m X dðxA Þ ¼ max kj ðf j ðxA ÞÞ f j ðxv ÞÞ þ q ðf j ðxA Þ f j ðxv ÞÞ;
1 kj ¼ f j ðxr Þ f j ðxv Þ
Fðxr Þ ¼ ½f 1 ðxr Þ; . . . ; f m ðxr Þ is the reservation point, and satisfy f j ðxr Þ P f j ðxv Þ; j ¼ 1; 2; . . . ; m.
Failed ratio (%)
Num
0 0 17
45 31 8
The solution xA ; xB means for each object function, xA is at least as good as xB , and at least for one object, xA is better than xB . When xA and xB are not pareto dominate each other, both solutions belong to the same non-dominated front, which means if xA is better than xB in some objectives, then it must be worse at least in one other objective. Usually, as the increasing of object number, the number of pareto non-dominated solutions increasing too [11]. Under the worst situation almost all the solutions in one population are non-dominated, and no possible solutions can be selected, resulting in the difficult to convergence. To increase the selection pressure toward the non-dominated (pareto) front, Kalyanmoy and Abhay [4] proposed a light beam search based NSGA-II algorithm (NSGA-LBS for abbreviation), which founds a preferred set of solutions,
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Fig. 7. The ratio of first front elements of f1f2.
Fig. 8. The ratio of first front elements of f1f3.
Fig. 9. The ratio of first front elements of f2f3.
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instead of the complete pareto-optimal frontier by incorporating the user preference information of the decision maker. During the evolution procedure, all the solutions on the second and higher pareto front are directly dropped, resulting in the lost of some possible solutions which are near to the user preference direction; and the span of the user preference on the first pareto front is determined by the veto threshold v: compared to the middle point, only the solutions with maximum deterioration in each object less than v can be reserved to the next generation. It is clear that although their algorithm increased the selection pressure and largely reduced the number of nondominated solutions, but the range of possible solutions are also reduced, and the population have high risk to be trapped in a local optimal area. To solve this problem, we introduce the concept of survive value to help the selection of individuals to the next generation. Definition 4 (Survive value). The survive value of an individual xA is determined by its preference distance and front rank, as follows
SUVðxA Þ ¼ p eC1 rankðxA Þ þ ð1 pÞ eC 2 disðxA Þ
ð11Þ
where p is the ratio of completed evolution, the completed evolution number to the expected evolution number, disðxA Þ is the preference distance of xA , rank(xA ) is the pareto front number of xA ; C 1 and C 2 are adjustable values. As both the coverage and search ability are concerned by EMO algorithms, the definition of SUV is based on the following trues: at the beginning of the evolution, p is small, the searching of global optimum solution is more important, therefore, in our definition, the second part eC 2 disðxA Þ has bigger weight ð1 pÞ, and the solutions which are closer to the prefer direction, with less disðxÞ, will prior to be selected to the next generation; at the ending of the evolution, p is near to 1, we need to enhance the selection pressure to accelerate the coverage rate, therefore, the coverage property is more important, the first part eC 1 rankðxA Þ has bigger weight p, and the solutions which are on the lower pareto front have more chance to survive. As shown in Figs. 1 and 2, when the generation percentage p is small, individuals with less prefer distance have bigger survive value, therefore, in Fig. 2(a), the individuals near to the prefer direction have more chance to be selected to the next generation; as the increasing of p, the pareto rank has more impact on the survive vale, thus in Fig. 2(b), individuals at the lower pareto front are more likely to survive, accelerating the coverage to the first front. 3.2. Maintaining diversity of population based on e-dominate Along with convergence to the pareto-optimal set, it is also desired that an EMO maintains a good spread of solutions in the obtained set of solutions. The original NSGA used the well-known sharing function approach, which has been found to maintain sustainable diversity in a population with appropriate setting of its associated parameters. The sharing function method involves a sharing
11
parameter r, which sets the extent of sharing desired in a problem. In NSGA-II, the sharing function is replaced by a crowded-comparison approach that an overall crowding-distance value of every solution is calculated as the sum of individual distance values corresponding to each objective, and the approach is used to eliminate similar or redundant solutions [5]. In this paper, we utilize e-dominate mechanism to maintain the diversity of population. For m-object optimization problems, e-dominate mechanism divide the target search space into ððK 1Þ=eÞm super lattices. In each lattice, there is only one possible solution, which is closest to the identification vector of the lattice, is allowed to left, and other possible solutions in that lattice are deleted to reduce individual redundancy. First the identification vector BðxA Þ of each solution xA is calculated by (12).
BðxA Þ ¼ ðB1 ðxA Þ; B2 ðxA Þ . . . Bm ðxA ÞÞ; where Bi ðxA Þ ¼ f i ðxA Þ=ei ; i ¼ 1; 2 . . . m
ð12Þ
And then solutions with same identification vector (in the same lattice) compete to left according to (13), the one won all the competitions will left in the lattice.
8xA ; xB 2 S; if BðxA Þ ¼ BðxB Þ;
then
delete xA ; if disðxA ; BðxA Þ P disðxB ; BðxB ÞÞ
ð13Þ
deletex xB ; otherwise
As the designer maker does not know the e-dominate mechanism is sensitive to the geometry distribution of pareto front, if two possible solutions are similar with each other in multi objects, then these two solutions make no difference to the decision maker, thus the e-dominate mechanism is appropriate to be utilized. 3.3. The detail of NFSA-UP To implement the procedure, the user preference needed to be given at first, and it is utilized to direct the evolution process of individuals during the evolution. We use the same way as in NSGA-II to calculate the pareto front in each generation, however, the individual selection, evolution direction, and diversity maintaining procedures are redesigned using our mechanisms. The detail of NFSA-UP is as following. Step 1 define the aspiration point a and reservation point r, population size N, Survive ratio Sp, maximum generation number m. Step 2 initialize the population P, each element in P represent a feasible solution; Step 3 Utilize some usual recombination, mutation, cross-over operators on P to generate new population Q, and let S ¼ P [ Q , then delete redundant individuals by e-dominate mechanism; Step 4 calculate the pareto front in S by the pareto partial ordering relation, set i ¼ 1: Step 4. 1 8s 2 S; if :s0 2 S; s0 s , add s into set Fronti , and remove s from S; Step 4. 2 calculate the survive vale of each solution in Fronti ;
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Step 4. 3 if the ith front is the last pareto front, goto step 5, else increase i, goto step 4.1. Step 5 select the first N Sp solutions with big survive vale into temporary set P0 . Step 6 if the number of P 0 is less than N, then new solutions will be randomly generated to search more solution place, and the new solutions will be incorporated into P0 until the size of P0 equals N. Step 7 If the maximum number of generations is reached, then exit, otherwise update P with P 0 , and go to step 3;
4. Simulation and results We simulated the multi-objective optimization problems, including minimization of BER (f1), maximization of throughput (f2), minimization of power consuming (f3) for CR network, using NFSA-UP, NSGA-LBS [4], and NSGAII [6,5]. We tried to address the problem by taking two conflicting objectives at a time and perform the optimization by assuming 64 subcarriers in CR network. The parameter list with their labels and range of values are
Channel Attenuation
The most difference between NFSA-UP and traditional NSGAII are in the selection process of individuals. In NFSA-UP, the solutions which have bigger survive value, in which both front rank and prefer distance are take into consideration, are more likely to survive. Therefore optimal solutions can be searched in a wider space to find global optimal transmission parameters. Furthermore, at the end of evolutions, the middle point on the first front can be automatically recommend to the decision maker, avoiding the second selection process in NSGA-II, that the decision makers have to manually choice ultimate solution from the first front. The time cost of step 1–3 could be constant OðCÞ, and the pareto fronts are recursively calculated in step 4, and the time complexity of this step can be analyzed as:For
each solution in the second or higher level of non-domination, the domination count can be at most 2N 1(there is at least 1 solution on the first front). Thus, each solution xA will be visited at most 2N 1 times before there is no other solutions dominate xA . At this point, xA is assigned a nondomination level and will never be visited again. Since there are at most ð2N 1Þ such solutions, the total complexity is OðMN2 Þ, where M is the number of objects and N is the population size. The time complexity of steps 5 to find N Sp individuals with big survive value is OðN 2 Þ, and the time complexity of step 6 and 7 is also constant OðCÞ, which can be ignored as well as that in steps 1–3. Therefore, the time complexity of NFSA-UP is OðMN 2 Þ, and the time cost of the calculation of non-dominate solutions dominate the whole time complexity.
Subcarrier Index
Throughput (bits/symbol)
(a)
Subcarrier Index
Transmit Power (mW)
(b)
Subcarrier Index
(c) Fig. 10. Sample final decision for low power mode for channel attenuation (a), throughput (b), and transmit power (c).
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Channel Attenuation
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Subcarrier Index
Throughput (bits/symbol)
(a)
Subcarrier Index
Transmit Power (mW)
(b)
Subcarrier Index
(c) Fig. 11. Sample final decision for low bit error mode for channel attenuation (a), throughput (b), and transmit power (c).
shown in Table 1. A population size of 100 and iterations of 100 is considered during simulation. To obtain an optimal front, the objective functions need to be conflicting with each other, that means there should be some common parameters that guide both fitness functions towards optimality. We have taken all possible distinct combinations by taking two objectives at a time. The best individual fitness values which are obtained after final iteration are reported as the first pareto-front, and the individual nearest to the prefer direction on the first pareto front is the middle point. The pareto optimal fronts obtained by taking different combination of fitness functions are shown in Figs. 3–6. Figs. 3(a) and 4 represent the pareto-front between fitness for minimizing bit error rate (BER) and maximizing throughput. The probability Pbe is a common parameter in (1) and (5). It can be inferred from the equations that if P be increases then f min ber increases while f max tp decreases. Hence f min ber and f max tp exhibit an inverse relationship which is depicted in Figs. 3(a) and 4. In Figs. 3(b) and 5 the typical nature of minimization of BER and power fitness is depicted. In practice, if transmit power (P) decreases, then probability of BER increases. Hence if the f min power in (6) decreases then f min ber in (1) will increase. Figs. 3(c) and 6 show optimal pareto-front between fitness for maximization of throughput (5) and fitness for minimization of power consuming. In both fitness functions,
power (P) and modulation index (m) are the common parameters which oppositely affect max throughput and minimization power fitness. Comparing the first pareto optimization front in Figs. 3–6, we can see that, for NSGA-II, the whole first pareto front is depicted, even though only one solution is needed by the decision maker; furthermore as there are many optimal solutions distributed on the whole front, the decision maker have to manually choice one solution from them. For NFSA-UP, only some first front fragments near to the preference direction are depicted, and the solution nearest to the direction is marked with red pentacle, which can be the best solution that satisfies the user requirement. Figs. 4–6 demonstrated that, under different preference direction, the final depicted first front is different. The reason for this can be attributed to the difference of evolution direction controlled by the selection function of individuals based on the user preference. Therefore, the individuals, satisfying the user preference, have more chance to survive and mutate, and the solution space near to the user preference direction can be exhaustively searched to find best solution. Comparing Figs. 3–6, we can see that, the first pareto front of NFSA-UP is more similar to that of NSGA-II; for the result of NSGA-LBS, there are less individuals (solutions) on the first pareto front and the front is much deteriorated, resulting in the middle point trapped in local optimal area. Furthermore, as Table 2 shows, for the prob-
W. Chen et al. / Ad Hoc Networks 26 (2015) 3–16
Channel Attenuation
14
Subcarrier Index
Throughput (bits/symbol)
(a)
Subcarrier Index
Transmit Power (mW)
(b)
Subcarrier Index
(c) Fig. 12. Sample final decision for max throughput mode for channel attenuation (a), throughput (b), and transmit power (c).
lem of optimization of cognitive radio parameters, the time cost of NFSA-UP to search the first pareto front is similar with or less than that of NSGAI-II and NSGA-LBS. In the table, num represents average individual number on the first front, For NSGA-LBS there are little number of individuals on the first front and it has higher failed ratio to generate the first front. The reason is that only the individuals located on the first front and near to the middle point less than the veto threshold are permitted to survive during the evolution process of NSGA-LBS, which has seriously restricted the searching zone of individuals. From Figs. 7–9 we can see that as the evolution proceeds, more individuals generated by NSGA-II are on the first front. As the increasing of the ratio of individuals on the first front, the selection pressure is decreased, resulting in the deterioration of the search ability of pareto dominance. For NFSA-UP, the suppression mechanism of similar individuals is utilized to maintain the diversity of population, and the preference distance, not just the front number as in NSGA-II, is also take into consideration while the selection of individuals to the next generation, so the percentage of non-dominated solutions is much lower. While fewer solutions are on the first front, more solutions can be searched in wider solution space to find global optimum solutions. However, for NSGA-LBS, the size of the individuals on the first front is too small, resulting the final solutions trapped in some local optimal area or even failed to found the first pareto front.
The above-mentioned experimental results validate NFSA-UP by demonstrating that the multi-objects optimization algorithms properly generate first front fragment directed by the user preference. However, a more important result is the transmission parameter values to which they converge. Fig. 10 shows a set of attributes corresponding to a snapshot of a final output at generation 100 of a simulation run, for the low power mode scenario that the user preference direction for f 1 ; f 2 ; f 3 is from (1, 0, 0) to (1, 0, 1). The random channel attenuation is shown, along with the final values of throughput and power for each of the 64 subcarriers. The bottom windows in Fig. 10 shows that all transmit powers on the subcarriers are below 2 mW. The average transmit power in this specific case is 1.54 mW per subcarrier while the average throughput (modulation index) is at 2.0064 which consistent with the real situation that when the transmit power is lower, the throughput will be limited. The low average power indicates that the primary goal of the scenario, minimize power, was achieved. Figs. 11 and 12 also show similar information for both the low bit error mode, preference direction is from (0, 0, 1) to (1, 0, 1) and the max throughput mode, preference direction is from (1, 1, 1) to (1, 0, 1). The low bit error mode scenario, Fig. 11 shows that the final decision provided a low modulation index 2 over all the subcarriers. The transmit power over all the subcarriers with an average of 25 mW. This configuration yields a low BER due to
W. Chen et al. / Ad Hoc Networks 26 (2015) 3–16
the low modulation index, while using a high transmit power on each subcarrier. The middle window in the max throughput mode scenario, Fig. 12 validates that the maximum throughput is the primary objective for this scenario. All subcarriers are set to a big modulation index of 8 providing for the maximum possible throughput, while keeping small balance on the minimize power objective. 5. Conclusion Usually, CR parameter adaptation problem is molded as an unconstrained multi-objective optimization problem, and EMO algorithms are applied to determine the transmission parameters for a multicarrier CR network. The difficulties of current multi-objective optimization of CR transmission parameters lie in the lacking of enough selection pressure toward the non-dominated pareto front, and the secondary selection of the optimal suitable solution from the front. In this paper, we have used an EMO procedure along with the concept of user preference direction search strategy for finding a preferred set of pareto-optimal solutions. By specifying an aspiration point and a reservation point, the search results is focusing on the concerned part of pareto-optimal front based on the survive selection mechanism which combines preference distances and pareto ranks to determine the selection of individuals as well as the evolving direction. At the beginning of evolving, the distribution of the solutions in the focused region is controlled by a big weight of preference distance, and the convergence to the first pareto front is speed up by increase the weight of front rank at the ending. Using the above procedure, the decision maker can also obtain more than one set of preferred transmission parameters simultaneously by simply choosing multiple preference direction. Its strength is evident from its ability to converge satisfactorily to the true pareto-optimal front for a transmission parameters optimization problem in a 64 subcarriers CR network. Acknowledgement This research is supported by the National Natural Science Foundation of China (Nos. 61402308, 61173159). References [1] S. Chen, T.R. Newman, J.B. Evans, A.M. Wyglinski, Genetic algorithmbased optimization for cognitive radio networks, in: IEEE Sarnoff Symposium, 2010, pp. 1–26. [2] D. Corne, J. Knowles, Techniques for highly multiobjective optimization: some non-dominated points are better than others, in: Genetic and Evolutionary Computation Conference, 2007, pp. 773–780. [3] D. Cvetkovik, I.C. Parmee, Genetic algorithm based multi-objective optimization and conceptual engineering design. in: Congress on Evolutionary Computation, 1999, pp. 29–36. [4] K. Deb, A. Kumar, Light Beam Search Based Multi-Objective Optimization Using Evolutionary Algorithms, 2007. [5] K. Deb, A. Pratap, S. Agarwal, T. Meyarivan, A fast and elitist multiobjective genetic algorithm: Nsga-ii, IEEE Trans. Evol. Comput. 6 (2) (2002) 182–197. [6] K.T. Deepak, K.U. Siba, L.S. Samrat, Cognitive radio parameter adaptation using multi-objective evolutionary algorithm, Adv. Intell. Soft Comput. 130 (2012) 737–748. [7] FCC, Spectrum policy task force report, in: Proceedings of the Federal Communications Commission, 2002, pp. 21–35.
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[8] C.M. Fonseca, P.J. Fleming, Genetic algorithms for multiobjective optimization: formulation, discussion and generalization, in: International Conference on Genetic Algorithms, 1993, pp. 416–423. [9] S. Haykin, Cognitive radio: brain-empowered wireless communications, EEE Trans. Commun. 23 (2) (2005) 201–220. [10] IEEE, Standard for wireless regional area networks, IEEE P802.22/ D0.1 Draft 23(2) (2006) 201–220. [11] H. Ishibuchi, N. Tsukamoto, Y. Nojima, Evolutionary many-objective optimization: a short review, in: IEEE Congress on Evolutionary Computation, 2008, pp. 2424–2431. [12] A. Jaszkiewicz, R. Slowinski, The light beam search approach-an overview of methodology and applications, Eur. J. Oper. Res. 113 (2) (1999) 300–314. [13] S. Kukkonen, J. Lampinen, Ranking-dominance and many objective optimization, in: IEEE Congress on Evolutionary Computation, 2007, pp. 3983–3990. [14] J. Lee, Y.S. Kwon, Conservative multi-objective optimization considering design robustness and tolerance a quality engineering design approach, Struct. Multidisc. Optim. 47 (2013) 259–272. [15] J. Mitola, G.Q. Maguire, Cognitive radio: making software radios more personal, IEEE Pers. Commun 6 (1999) 13–18. [16] T.R. Newman, B.A. Barker, A.M. Wyglinski, A. Agah, J.B. Evans, G.J. Minden, Cognitive engine implementation for wireless multicarrier transceivers, Wireless Commun. Mobile Comput. 7 (9) (2007) 1129– 1142. [17] T.R. Newman, R. Rajbanshi, A.M. Wyglinski, J.B. Evans, G.J. Minden, Population adaptation for genetic algorithm-based cognitive radios, Mobile Networks Appl. 13 (5) (2008) 442–451. [18] T.R. Newmann, Dissertation on Multiple Objective Fitness Functions for Cognitive Radio Adaptation, 2008. [19] A.V. Oppenheim, R.W. Schafer, J.R. Buck, Discreate-Time Signal Processing, Prentice Hall, 1999. [20] F.d. Pierro, S.-T. Khu, D.A. Savic, An investigation on preference order ranking scheme for multi-objective evolutionary optimization, IEEE Trans. Evol. Comput. 11 (1) (2007) 17–45. [21] C.J. Rieser, T.W. Rondeau, C.W. Bostian, T.M. Gallagher, Cognitive Radio Testbed: Further Details and Testing of a Distributed Genetic Algorithm Based Cognitive Engine for Programmable Radios, 2004. [22] T.W. Rondeau, B. Le, C.J. Rieser, C.W. Bostian, Cognitive radios with genetic algorithms: intelligent control of software defined radios, in: Proceeding of the Software defined radio Technical Conference, 2004, pp. 3–8. [23] K.J. Shaw, P.J. Fleming, Including real-life preferences in genetic algorithms to improve optimization of production schedules, in: Proc. of the Genetic Algorithms in Engineering Systems Innovations and Applications, 1997, pp. 239–244. [24] L. Thiele, K. Miettinen, P.J. Korhonen, J. Molina, A preference-based evolutionary algorithm for multi-objective optimization, Evol. Comput. 17 (3) (2009) 411–436. [25] D.K. Tosh, S.K. Udgata, S.L. Sabat, Cognitive radio parameter adaptation using multi-objective evolutionary algorithm, Adv. Intell. Soft Comput. 130 (2012) 737–748. [26] B. Wang, K.J.R. Liu, Advances in cognitive radio networks: a survey, IEEE J. Sel. Topics Signal Process. 5 (1) (2011) 5–23. [27] T. Yucek, H. Arslan, A survey of spectrum sensing algorithms for cognitive radio applications, IEEE Commun. Surveys Tutorials 11 (1) (2009) 116–130. [28] Y. Zhang, F. Zhang, W. He, Adaptive transmission in cognitive radio networks, in: Chinese Control and Decision Conference, 2009, pp. 1951–1953.
Wen Chen was born in 1983. He received his Ph.D. in computer science from the Sichuan University, Chengdu, in 2011. Currently, he is a Senior Engineer at the Information Security Laboratory, Sichuan University. His research interests include cognitive radio network, wireless sensor network, information security and machine learning. He is a member of IEEE, as well as IEICE.
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W. Chen et al. / Ad Hoc Networks 26 (2015) 3–16 Tao Li born in 1965. He received the Ph.D. degree in Computer Science from the University of Electronic Science and Technology of China in 1994. From 1994 to 1995, he was a visiting scholar in University of California at Berkeley for neural networks theory. Now, he is a IEEE fellow and working as a professor in the Department of Computer Science at Sichuan University, China. His current research interests include wireless sensor network, network security, artificial immune theory and disaster recovery application.
Tao Yang was born in 1982. He received the M.S. degree in computer science from the Western China normal University. Now, he is a associate professor in the Department of Computer Science at Sichuan University, China. Her current research interests include wireless network, network security, artificial intelligence and disaster recovery application.
Contents lists available at ScienceDirect
Ad Hoc Networks journal homepage: www.elsevier.com/locate/adhoc
Intelligent control of cognitive radio parameter adaption: Using evolutionary multi-objective algorithm based on user preference Wen Chen ⇑, Tao Li, Tao Yang Sichuan University, No.24 South Section 1, Yihuan Road, Chengdu, China
a r t i c l e
i n f o
Article history: Received 8 July 2013 Received in revised form 13 April 2014 Accepted 10 September 2014 Available online 16 October 2014 Keywords: Cognitive radio network Transmission parameter User preference Pareto front Selection pressure Cognitive engine
a b s t r a c t Cognitive radio (CR) is a promising technique for overcoming the spectrum scarcity problem. It must appropriately alter its transmission parameters according to predefined objectives in dynamic wireless environment. In this paper, we model the CR parameter adaptation problem as an unconstrained multi-objective optimization problem and then propose a non-dominated front searching algorithm based on user preference (NFSA-UP) to determine the optimal transmission parameters for a multicarrier system. The distances from individuals to the user preference direction are combined with the pareto ranks to determine the evolving direction as well as the survive selection of individuals. It is beneficial to increase selection pressure at the beginning of the evolving, and speed up convergence to the true pareto optimal front at end. The best individual which is obtained after final iteration is reported here as the middle point on the first pareto front, avoiding the secondary selection from a set of optimal solutions. We performed multi-objective optimization on a 64 subcarriers in CR network. NFSA-UP is compared with other pareto front searching algorithms NSGAII and NSGAII-LBS, and the results demonstrate that the optimal transmission parameters of CR can be got using NFSA-UP with any user preference direction, while better performance is observed. Ó 2014 Published by Elsevier B.V.
1. Introduction The increasing growth of wireless services over the last decade demonstrates the vast demand for radio bands. However, the spectrum resource is limited and mostly has been licensed to users which can work within a limited frequency band [26]. The studies by the Federal Communication Commission have found that the actual licensed spectrum is largely unoccupied most of the time [7]. In order to deal with the imbalance between spectrum scarcity and spectrum under utilization, cognitive radio technology was proposed [15].
⇑ Corresponding author. http://dx.doi.org/10.1016/j.adhoc.2014.09.006 1570-8705/Ó 2014 Published by Elsevier B.V.
Cognitive radio is a promising technique for overcoming the apparent spectrum scarcity problem, as well as improving the communications efficiency [27,9]). The IEEE has formed the 802.22 Working Group to develop a standard for wireless regional area networks (WRAN) based on cognitive radio technology [10]. Ideally a Cognitive Radio (CR) possesses the capability of sensing, perceiving, decision making, planning, and learning in a wireless environment [6]. Due to the time varying radio channel characteristics, as well as the spectrum band availability, cognitive radios need to support time varying Quality of Service (QoS) requirements. Even though the principal goal of dynamic spectrum access (DSA) is to improve the spectrum utilization efficiency, other goals such as minimizing the bit-error-rate (BER), maximizing the data throughput,
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minimizing the power consumption, also need to be met [1]. Therefore, cognitive radio (CR) must be able to sense the environment periodically and appropriately alter the transmission parameters according to the objectives and QoS requirements of the users [22]. To achieve these goals, CR needs a cognitive engine to be aware of its environment, including the transmission link, user demands, and regulatory regimes, and it must balance multiple objectives. This learning characteristic of CR makes it intelligent that adapts itself in the dynamic situations [6,1,22]. Evolutionary multi-objective optimization (EMO) algorithms are well suited to solving multi-objective optimization and decision problems [11,14], and it has been shown that a EMO based cognitive radio engine can support awareness-processing, decision-making, and learning elements of cognitive functionality [21]. Research done at Virginia Tech has developed a genetic algorithm (GA) engine for cognitive radios [1]. Their simulation results validate that the genetic algorithm implementation does in fact change the transmission parameters to different settings, based upon a set of objectives. A set of single carrier and multicarrier fitness functions have been derived and GA is used to search the optimal set of transmission parameters in [16]. Adaptive transmission in the context of cognitive radio networks is addressed in [28] where GA is used to optimize the CR parameters by considering several QoS and channel coding schemes. In order to reduce the convergence time and to improve the optimization results of spectrum utilization, in [17] a population adaptation technique for reducing the amount of time required to reach an optimal decision for a GA-based cognitive engine is proposed. And a technique using quantized variables with adaptive variable ranges, based on the knowledge gathered from previous experience, is studied in [1]. These two methods both assumed that the wireless channel environment changes slowly, such that the gathered knowledge can be reused in the near future. All the above works have attempted to solve the parameter adaptation problem in CR by formulating it into single objective functions using weighted sum approach. When a multi-objective optimization problem is solved by weight vector aggregate sum approach, the result will find a single value for each parameter and thus the behavior of solution space cannot be deduced with respect to multiple objective functions. For the real-time scenario, the performance of CR system depends on the choice of weights to specific objective functions which is hard and scenario dependent [6]. Therefore, Tosh et al. model the CR parameter adaptation problem as an unconstrained multi-objective optimization problem and perform optimization of more than one conflicting objectives at a time using Non-dominated Sortingbased Genetic Algorithm (NSGA-II) instead of weighted sum approach [6]. This helps to find a set of optimal solutions from the large range of solution space defined in terms of pareto optimal set. NSGA-II avoided the setting of the weight vectors and got more accurate solutions than GA. However, for NSGA-II there are a set of optimal solutions on the pareto-front, which are all non-dominated, thus the choice of best solution needs a further comparison, and it takes more time to get coverage [5].
In the real applications of multi-objective optimization, the decision makers usually have some preference on the fitness functions. For example, they may want the fitness functions to coverage to given target values, and these preference information can be used to direct the evolutionary procedure [24]. Fonseca and Fleming probably suggested the earliest attempt to incorporate preferences, and their proposal was to use EMO together with goal information as an additional criterion to assign ranks to the members of a population [8]. Shaw and Fleming incorporate the target information into the calculation of fitness to design a preference based multi-objective optimization algorithm to solve the production scheduling problem [23]. Pierro et al. proposed preference order mechanism to discriminate non-dominate solutions [20]. Cvetkovic and Parmee [3] used binary preference relations (translated into weights) to narrow the search. In [25], preferences were included through the use of reference points. Also a guided dominance scheme and a biased crowding scheme were suggested. Thiele et al. suggest a hybrid approach which combine ideas from both evolutionary and interactive multi-objective optimization [24]. The principle is first give a rough approximation, and then generates a more accurate approximation of the area where the decision maker’s most satisfactory solution lies. Deb and Kumar present an interactive methodology for finding a preferred set of solutions focused on a small nondominated region, instead of the complete pareto-optimal frontier [4]. All the aforementioned methods have got promising results after the user preference was incorporated into the EMO algorithms. In the paper, we introduce a non-dominated front searching algorithm based on user preference (NFSA-UP) to solve the parameter set problem of cognitive radio system. During the searching of pareto front of multi objects, the preference information is utilized to direct the evolutionary procedure. In each generation, the individuals are selected to the next generation based on the front orders and individual distances to the preference directions. The simulation results of 64 subcarriers in the CR network demonstrated that, based on the user preference, the optimal transmission parameters can be effectively found, under the predefined quality of service (QoS).
2. Problem definition Assuming a multicarrier dynamic wireless environment with N c subcarriers, the basic characteristic of CR is to sense the environmental parameters, and it learns itself to adjust the value of transmission parameters to achieve the predefined quality of service (QoS). In CR system, the environmental parameters act as input to the problem and the transmission parameters act as decision variables. Hence the problem can be defined as to find the set of transmission parameters by modeling the scenarios as multi-objective functions [6]. The proposed algorithm is based on user preference to solve the formulated multi-objective function to obtain the required solutions. The below subsection briefs about the radio parameters involved in CR engine.
W. Chen et al. / Ad Hoc Networks 26 (2015) 3–16
(a) p = 10%, C1 = 1, C2 = 1
(b) p = 30%, C1 = 1, C2 = 1
(c) p = 70%, C1 = 1, C2 = 1
(d) p = 90%, C1 = 1, C2 = 1
5
Fig. 1. The survive value with different prefer distance and pareto rank.
Fig. 2. The individuals selected at different pareto front. (a) Selected individuals in the 10th generation, (b) Selected individuals in the 90th generation. In the figure, the black circles represent individuals been dropped, and the red diamonds represent individuals been selected to the next generation. For simplicity only the first five pareto fronts are depicted, and C 1 ¼ 1; C 2 ¼ 1.
2.1. Input and output parameters Radio parameters of CR are categorized into environmental parameters and transmission parameters [18]. The former gives knowledge of environmental characteristics of multicarrier wireless environment which are used as inputs to the CR system, where different environmental
parameters include channel attenuation, noise power, signal-to-noise ratio (SNR), spectrum information, etc. Transmission parameters are the tunable parameters of CR system. The CR tunes its transmission knobs to corresponding values from the optimal parameter set. The transmission parameters [18] are listed as: transmit power ðPÞ, type of modulation (mod type) scheme used for the
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PNc
Table 1 Transmission parameters with their ranges.
f min
Parameter (x)
xmin
xmax
Transmit power (P) Modulation index (m) Bandwidth (B) Coding rate (Rc) Frame length (L) Time division Duplex (TDD) Symbol rate (Rs) Noise power (N)
1 dBm 2 2 MHz 1/2 94 Bytes 1% 125 Ksps 0.01 dBm
18 dBm 10 32 MHz 3/4 1504 Bytes 100% 1 Msps 0.1 dBm
communication, modulation index (m), bandwidth ðBÞ, channel coding rate ðRc Þ, size of transmission frame in byte ðLÞ, time division duplex in percentage (TDD), and symbol rate ðRs Þ. Modulation Index ðmÞ is defined as the total number of symbols in a modulation scheme and TDD represent the percentage of transmits time.
Pbe
2.2.1. Object function for bit-error-rate One of the most common goals in wireless communications is to get an error free signal, or to minimize the bit error rate of the transmission. Determining the theoretical bit error rate depends on several transmission parameters including the transmit power, modulation type, modulation index, signal power, and noise power. The goal is to create a fitness function with a valid output range of between 0 and 1. Mathematically, the normalized objective function for minimizing BER [18] is defined in (1).
(a)
i¼1 1
log10 ð0:5Þlog10 ðPbei Þ log ð0:5Þlog ð1012 Þ 10
10
ð1Þ
Nc
where N c is the number of subcarriers, Pbe represents the probability of a bit error or BER for a given modulation scheme and a given channel type, and it is normalized to the worst possible BER value of 0.5 and divided over the total possible range of BER values selected. In the paper, 1012 is chosen to be the best case BER. In this investigation, we assume the possible modulation types include QAM, PSK, and FSK. To apply this work to practical systems, we must determine the BER probability for each modulation. The following equations describe the BER probability of QAM, PSK, and FSK, using a graycoded bit assignment and assuming an AWGN channel model. For a BPSK signal constellation, the probability of a bit error is defined as [19].
2.2. Fitness functions Ideally the fitness function must be able to guide the system to one optimal parameter set. A cognitive radio must perform an action based on a set of parameters, which should be selected from the pareto front according to some preference information [6]. Preference information is used to rank the objectives in order to help the fitness function guide the evolutionary algorithm to one optimal solution. In this work three objective functions: Bit-Error-Rate minimization, system throughput maximization, power consumption minimization are considered. In the next subsections, we describe the objective functions in detail.
ber
¼
rffiffiffiffi! P ¼Q N
ð2Þ
Whereas for M-ary PSK, the probability of a bit error is given as
Pbe ¼
2 Q log2 ðmÞ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P 2 log2 ðmÞ c sin m
ð3Þ
For M-ary QAM, the probability of a bit error is defined as
Pbe ¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi! 4 1 3 log2 ðmÞ c 1 pffiffiffiffiffi Q log2 ðmÞ m1 m
ð4Þ
where Q is the Q-function in term of error function, c represents the energy per bit. 2.2.2. Object function for throughput By definition, throughput is defined as the amount of correct information received at the receiver. Maximizing throughput is a common aim in the multimedia environment. Determining the theoretical throughput depends on the parameters such as coding rate ðRc Þ, frame size ðLÞ, MAC and IP layer overhead H, PHY layers overhead O, probability of BER ðPbe Þ and percentage of transmit time ðTDDÞ. The normalized objective function for maximizing throughput [18] for N c subcarriers is defined as
(b)
(c)
Fig. 3. pareto optimal front generated by NSGA-II, (a)–(c) represent pareto optimal front of f1 and f2, f1 and f3, f2 and f3 respectively.
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(a) (0,-1)to(0.1,-0.3)
(b) (0,-1)to(0.14,-0.2)
(c) (0,-0.5)to(0.18,-0.45)
(d) (0,-1)to(0.1,-0.3)
(e) (0,-1)to(0.14,-0.2)
(f) (0,-0.5)to(0.18,-0.45)
Fig. 4. pareto front of f1 and f2. (a)–(c) are generated by NFSA-UP, (d)–(f) are generated by NSGA-LBS.
PN c f max
tp
¼
Li i¼1 Li þOþH
ð1 P bei ÞLi þO Rci TDDi Nc
ð5Þ
Find x ¼ hx1 ; x2 ; x3 ; . . . ; xn i Min y ¼ hf 1 ðxÞ; f 2 ðxÞ; f 3 ðxÞ; . . . ; f m ðxÞi
ð7Þ
Subject to li 6 xi 6 ui ; 1 6 i 6 m; x 2 X; y 2 Y 2.2.3. Object function for power Energy is the most important factor which must be spent optimally for the communication process. Hence minimum power should be consumed for all the tasks while communicating or computing. The parameters contribute to the fitness for power minimization are bandwidth ðBÞ, modulation index (m), symbol rate ðRs Þ and transmit power ðPÞ. The normalized objective function for minimizing power is expressed as.
" f min power ¼ 1 a
PN c
i¼1 ðP max þ Bmax Þ ðP i þ Bi Þ
Nc ðPmax þ Bmax Þ # PN c P log ðmmax Þ log2 ðmi Þ Nc ðRsmax Rsi ð6Þ þ k i¼1 þb i¼1 2 N c log2 ðmmax Þ þ Bmax Nc Rsmax 2.3. Multi-objective algorithm
In general, a multi-objective fitness function problem can be presented as trying to determine the correct mapping of a set of n parameters to a set of m objectives [24]. This can be seen algebraically as:
where x is the set of decision variables with X is the parameter space, and y is the set of objectives with Y as the objective space. In the case of a multiple objective evolutionary algorithm, each f i ðxÞ represents the fitness function for a single objective. If any f i ðxÞ is originally expected to find maximum value, then it can be changed as f i ðxÞ. GA based on optimization method usually combine f i ðxÞ using weight factors to get a single fitness function f ðxÞ, for example
f ðxÞ ¼
X
-i f i ðxÞ
ð8Þ
i
Usually, the weight vector is set by empirical, and in real world problems, such as the problem addressed in this thesis, the objectives under consideration might conflict with each other. For example, minimizing power and minimizing BER simultaneously creates a conflict due to the single parameter, transmit power, affecting each objective in a different way. Determining the optimal set of decision variables for a single objective, e.g. minimize power, often results in a non-optimal set with respect to other objectives, e.g. minimize BER and maximize throughput.
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(a) (0,0)to(0.5,0.5)
(b) (0,0)to(0.2,0.8)
(d) (0,0)to(0.5,0.5)
(e) (0,0)to(0.2,0.8)
(c) (0,0.1)to(0.3,0.5)
(f) (0,0.1)to(0.3,0.5)
Fig. 5. pareto front of f1 and f3. (a)–(c) are generated by NFSA-UP, (d)–(f) are generated by NSGA-LBS.
For pareto dominance based EMO algorithms, The optimal set for multiple objective functions lie on what is known as the pareto optimal front [5]. This front represents the set of solutions that cannot be improved upon in any dimension. The solutions on the pareto front are optimal and co-exist due to the trade-offs between the multiple objectives. When a possible solution s in the last generation is not dominated by any other feasible solutions, s is referred to as a pareto-optimal solution of the m-objective minimization problem in (7). The set of all pareto optimal solutions forms the tradeoff surface in the objective space. This tradeoff surface is referred to as the pareto front. EMO algorithms are designed to search for a set of well distributed non-dominated solutions that approximates the entire pareto front very well. Hisao Ishibuchi demonstrated that pareto dominance based EMO algorithms, including NSGAII and SPEA [11], suffered from the deterioration of the search ability. Under multi-objects, sometimes almost all solutions in each population become non-dominated. This severely weakens the pareto dominance-based selection pressure toward the pareto front. That is, the convergence property of EMO algorithms is severely deteriorated. 3. NFSA-UP for the optimization of multi parameters of CR network A straightforward idea for the scalability improvement of EMO algorithms to many-objective problems is to
increase the selection pressure toward the pareto front. One approach based on this idea is to modify pareto dominance in order to decrease the number of non-dominated solutions in each population [11]. Another approach is to assign different ranks to non-dominated solutions [2,13]. In this paper, we incorporate user preference information into the EMO algorithms to help the searching of pareto non-dominated fronts, and propose a Non-dominated Front Searching Algorithm Based on User Preference (NFSA-UP). Before the iteration, the decision maker is asked to give preference information in terms of reference points consisting of desirable aspiration and reservation points for multi-objective functions. The information is used in NFSA-UP to generate a new population by combining the fitness function and an achievement scalar function.
3.1. Basic definition Preference information is used to direct the evolution while EMO algorithm is used to find multiple non-dominated solutions on the pareto front. Jaszkiewicz and Slowinski proposed preference model [12], in the model, the aspiration point, reservation point, indifference threshold, preference threshold and veto threshold must be given. In this paper, the preference relationship is reduced, and only the aspiration point, reservation point are needed. The preference direction is decided by the aspiration point
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(a) (-0.4,0)to(-0.3,0.4)
(b) (-0.4,0)to(-0.3,0.8)
(c) (-0.9,0.3)to(-0.3,0.4)
(d) (-0.4,0)to(-0.3,0.4)
(e) (-0.4,0)to(-0.3,0.8)
(f) (-0.9,0.3)to(-0.3,0.4)
Fig. 6. pareto front of f2 and f3. (a)–(c) are generated by NFSA-UP, (d)–(f) are generated by NSGA-LBS.
and reservation point. Usually the aspiration point can be any point with lower object value, and the reservation has higher object value than the aspiration point, and for the CR parameter optimization problem, the objectives under consideration might conflict with each other. Therefore, the decision maker (user) set higher object value for the preference object, and lower value for the other object. Definition 1 (Preference distance). The preference distance is defined to evaluate the distance from a possible solution xA to the direction of preference.
j¼1
ð9Þ
where xA is an possible solution of the multiple object optimization problem defined in (7), f i is the ith fitness function, Fðxv Þ ¼ ½f 1 ðxv Þ; . . . ; f m ðxv Þ is the aspiration point, Table 2 The quantitative comparison results. Algorithm
NSGA-II NSGA-UP NFSA-LBS
Time (s) f1f2
f1f3
f2f3
16.29 16.76 16.78
18.11 16.01 17.25
17.87 15.5 16.93
Definition 2 (Middle point). The solution with least preference distance is the middle point. Definition 3 (Pareto dominate ). If xA ; xB are two possible solutions, if xA xB , then
8i ¼ 1; 2; . . . ; m; f i ðxA Þ 6 f i ðxB Þ ^ 9j ¼ 1; 2 . . . m; f j ðxA Þ < f j ðxB Þ ð10Þ
m X dðxA Þ ¼ max kj ðf j ðxA ÞÞ f j ðxv ÞÞ þ q ðf j ðxA Þ f j ðxv ÞÞ;
1 kj ¼ f j ðxr Þ f j ðxv Þ
Fðxr Þ ¼ ½f 1 ðxr Þ; . . . ; f m ðxr Þ is the reservation point, and satisfy f j ðxr Þ P f j ðxv Þ; j ¼ 1; 2; . . . ; m.
Failed ratio (%)
Num
0 0 17
45 31 8
The solution xA ; xB means for each object function, xA is at least as good as xB , and at least for one object, xA is better than xB . When xA and xB are not pareto dominate each other, both solutions belong to the same non-dominated front, which means if xA is better than xB in some objectives, then it must be worse at least in one other objective. Usually, as the increasing of object number, the number of pareto non-dominated solutions increasing too [11]. Under the worst situation almost all the solutions in one population are non-dominated, and no possible solutions can be selected, resulting in the difficult to convergence. To increase the selection pressure toward the non-dominated (pareto) front, Kalyanmoy and Abhay [4] proposed a light beam search based NSGA-II algorithm (NSGA-LBS for abbreviation), which founds a preferred set of solutions,
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Fig. 7. The ratio of first front elements of f1f2.
Fig. 8. The ratio of first front elements of f1f3.
Fig. 9. The ratio of first front elements of f2f3.
W. Chen et al. / Ad Hoc Networks 26 (2015) 3–16
instead of the complete pareto-optimal frontier by incorporating the user preference information of the decision maker. During the evolution procedure, all the solutions on the second and higher pareto front are directly dropped, resulting in the lost of some possible solutions which are near to the user preference direction; and the span of the user preference on the first pareto front is determined by the veto threshold v: compared to the middle point, only the solutions with maximum deterioration in each object less than v can be reserved to the next generation. It is clear that although their algorithm increased the selection pressure and largely reduced the number of nondominated solutions, but the range of possible solutions are also reduced, and the population have high risk to be trapped in a local optimal area. To solve this problem, we introduce the concept of survive value to help the selection of individuals to the next generation. Definition 4 (Survive value). The survive value of an individual xA is determined by its preference distance and front rank, as follows
SUVðxA Þ ¼ p eC1 rankðxA Þ þ ð1 pÞ eC 2 disðxA Þ
ð11Þ
where p is the ratio of completed evolution, the completed evolution number to the expected evolution number, disðxA Þ is the preference distance of xA , rank(xA ) is the pareto front number of xA ; C 1 and C 2 are adjustable values. As both the coverage and search ability are concerned by EMO algorithms, the definition of SUV is based on the following trues: at the beginning of the evolution, p is small, the searching of global optimum solution is more important, therefore, in our definition, the second part eC 2 disðxA Þ has bigger weight ð1 pÞ, and the solutions which are closer to the prefer direction, with less disðxÞ, will prior to be selected to the next generation; at the ending of the evolution, p is near to 1, we need to enhance the selection pressure to accelerate the coverage rate, therefore, the coverage property is more important, the first part eC 1 rankðxA Þ has bigger weight p, and the solutions which are on the lower pareto front have more chance to survive. As shown in Figs. 1 and 2, when the generation percentage p is small, individuals with less prefer distance have bigger survive value, therefore, in Fig. 2(a), the individuals near to the prefer direction have more chance to be selected to the next generation; as the increasing of p, the pareto rank has more impact on the survive vale, thus in Fig. 2(b), individuals at the lower pareto front are more likely to survive, accelerating the coverage to the first front. 3.2. Maintaining diversity of population based on e-dominate Along with convergence to the pareto-optimal set, it is also desired that an EMO maintains a good spread of solutions in the obtained set of solutions. The original NSGA used the well-known sharing function approach, which has been found to maintain sustainable diversity in a population with appropriate setting of its associated parameters. The sharing function method involves a sharing
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parameter r, which sets the extent of sharing desired in a problem. In NSGA-II, the sharing function is replaced by a crowded-comparison approach that an overall crowding-distance value of every solution is calculated as the sum of individual distance values corresponding to each objective, and the approach is used to eliminate similar or redundant solutions [5]. In this paper, we utilize e-dominate mechanism to maintain the diversity of population. For m-object optimization problems, e-dominate mechanism divide the target search space into ððK 1Þ=eÞm super lattices. In each lattice, there is only one possible solution, which is closest to the identification vector of the lattice, is allowed to left, and other possible solutions in that lattice are deleted to reduce individual redundancy. First the identification vector BðxA Þ of each solution xA is calculated by (12).
BðxA Þ ¼ ðB1 ðxA Þ; B2 ðxA Þ . . . Bm ðxA ÞÞ; where Bi ðxA Þ ¼ f i ðxA Þ=ei ; i ¼ 1; 2 . . . m
ð12Þ
And then solutions with same identification vector (in the same lattice) compete to left according to (13), the one won all the competitions will left in the lattice.
8xA ; xB 2 S; if BðxA Þ ¼ BðxB Þ;
then
delete xA ; if disðxA ; BðxA Þ P disðxB ; BðxB ÞÞ
ð13Þ
deletex xB ; otherwise
As the designer maker does not know the e-dominate mechanism is sensitive to the geometry distribution of pareto front, if two possible solutions are similar with each other in multi objects, then these two solutions make no difference to the decision maker, thus the e-dominate mechanism is appropriate to be utilized. 3.3. The detail of NFSA-UP To implement the procedure, the user preference needed to be given at first, and it is utilized to direct the evolution process of individuals during the evolution. We use the same way as in NSGA-II to calculate the pareto front in each generation, however, the individual selection, evolution direction, and diversity maintaining procedures are redesigned using our mechanisms. The detail of NFSA-UP is as following. Step 1 define the aspiration point a and reservation point r, population size N, Survive ratio Sp, maximum generation number m. Step 2 initialize the population P, each element in P represent a feasible solution; Step 3 Utilize some usual recombination, mutation, cross-over operators on P to generate new population Q, and let S ¼ P [ Q , then delete redundant individuals by e-dominate mechanism; Step 4 calculate the pareto front in S by the pareto partial ordering relation, set i ¼ 1: Step 4. 1 8s 2 S; if :s0 2 S; s0 s , add s into set Fronti , and remove s from S; Step 4. 2 calculate the survive vale of each solution in Fronti ;
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Step 4. 3 if the ith front is the last pareto front, goto step 5, else increase i, goto step 4.1. Step 5 select the first N Sp solutions with big survive vale into temporary set P0 . Step 6 if the number of P 0 is less than N, then new solutions will be randomly generated to search more solution place, and the new solutions will be incorporated into P0 until the size of P0 equals N. Step 7 If the maximum number of generations is reached, then exit, otherwise update P with P 0 , and go to step 3;
4. Simulation and results We simulated the multi-objective optimization problems, including minimization of BER (f1), maximization of throughput (f2), minimization of power consuming (f3) for CR network, using NFSA-UP, NSGA-LBS [4], and NSGAII [6,5]. We tried to address the problem by taking two conflicting objectives at a time and perform the optimization by assuming 64 subcarriers in CR network. The parameter list with their labels and range of values are
Channel Attenuation
The most difference between NFSA-UP and traditional NSGAII are in the selection process of individuals. In NFSA-UP, the solutions which have bigger survive value, in which both front rank and prefer distance are take into consideration, are more likely to survive. Therefore optimal solutions can be searched in a wider space to find global optimal transmission parameters. Furthermore, at the end of evolutions, the middle point on the first front can be automatically recommend to the decision maker, avoiding the second selection process in NSGA-II, that the decision makers have to manually choice ultimate solution from the first front. The time cost of step 1–3 could be constant OðCÞ, and the pareto fronts are recursively calculated in step 4, and the time complexity of this step can be analyzed as:For
each solution in the second or higher level of non-domination, the domination count can be at most 2N 1(there is at least 1 solution on the first front). Thus, each solution xA will be visited at most 2N 1 times before there is no other solutions dominate xA . At this point, xA is assigned a nondomination level and will never be visited again. Since there are at most ð2N 1Þ such solutions, the total complexity is OðMN2 Þ, where M is the number of objects and N is the population size. The time complexity of steps 5 to find N Sp individuals with big survive value is OðN 2 Þ, and the time complexity of step 6 and 7 is also constant OðCÞ, which can be ignored as well as that in steps 1–3. Therefore, the time complexity of NFSA-UP is OðMN 2 Þ, and the time cost of the calculation of non-dominate solutions dominate the whole time complexity.
Subcarrier Index
Throughput (bits/symbol)
(a)
Subcarrier Index
Transmit Power (mW)
(b)
Subcarrier Index
(c) Fig. 10. Sample final decision for low power mode for channel attenuation (a), throughput (b), and transmit power (c).
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Channel Attenuation
W. Chen et al. / Ad Hoc Networks 26 (2015) 3–16
Subcarrier Index
Throughput (bits/symbol)
(a)
Subcarrier Index
Transmit Power (mW)
(b)
Subcarrier Index
(c) Fig. 11. Sample final decision for low bit error mode for channel attenuation (a), throughput (b), and transmit power (c).
shown in Table 1. A population size of 100 and iterations of 100 is considered during simulation. To obtain an optimal front, the objective functions need to be conflicting with each other, that means there should be some common parameters that guide both fitness functions towards optimality. We have taken all possible distinct combinations by taking two objectives at a time. The best individual fitness values which are obtained after final iteration are reported as the first pareto-front, and the individual nearest to the prefer direction on the first pareto front is the middle point. The pareto optimal fronts obtained by taking different combination of fitness functions are shown in Figs. 3–6. Figs. 3(a) and 4 represent the pareto-front between fitness for minimizing bit error rate (BER) and maximizing throughput. The probability Pbe is a common parameter in (1) and (5). It can be inferred from the equations that if P be increases then f min ber increases while f max tp decreases. Hence f min ber and f max tp exhibit an inverse relationship which is depicted in Figs. 3(a) and 4. In Figs. 3(b) and 5 the typical nature of minimization of BER and power fitness is depicted. In practice, if transmit power (P) decreases, then probability of BER increases. Hence if the f min power in (6) decreases then f min ber in (1) will increase. Figs. 3(c) and 6 show optimal pareto-front between fitness for maximization of throughput (5) and fitness for minimization of power consuming. In both fitness functions,
power (P) and modulation index (m) are the common parameters which oppositely affect max throughput and minimization power fitness. Comparing the first pareto optimization front in Figs. 3–6, we can see that, for NSGA-II, the whole first pareto front is depicted, even though only one solution is needed by the decision maker; furthermore as there are many optimal solutions distributed on the whole front, the decision maker have to manually choice one solution from them. For NFSA-UP, only some first front fragments near to the preference direction are depicted, and the solution nearest to the direction is marked with red pentacle, which can be the best solution that satisfies the user requirement. Figs. 4–6 demonstrated that, under different preference direction, the final depicted first front is different. The reason for this can be attributed to the difference of evolution direction controlled by the selection function of individuals based on the user preference. Therefore, the individuals, satisfying the user preference, have more chance to survive and mutate, and the solution space near to the user preference direction can be exhaustively searched to find best solution. Comparing Figs. 3–6, we can see that, the first pareto front of NFSA-UP is more similar to that of NSGA-II; for the result of NSGA-LBS, there are less individuals (solutions) on the first pareto front and the front is much deteriorated, resulting in the middle point trapped in local optimal area. Furthermore, as Table 2 shows, for the prob-
W. Chen et al. / Ad Hoc Networks 26 (2015) 3–16
Channel Attenuation
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Subcarrier Index
Throughput (bits/symbol)
(a)
Subcarrier Index
Transmit Power (mW)
(b)
Subcarrier Index
(c) Fig. 12. Sample final decision for max throughput mode for channel attenuation (a), throughput (b), and transmit power (c).
lem of optimization of cognitive radio parameters, the time cost of NFSA-UP to search the first pareto front is similar with or less than that of NSGAI-II and NSGA-LBS. In the table, num represents average individual number on the first front, For NSGA-LBS there are little number of individuals on the first front and it has higher failed ratio to generate the first front. The reason is that only the individuals located on the first front and near to the middle point less than the veto threshold are permitted to survive during the evolution process of NSGA-LBS, which has seriously restricted the searching zone of individuals. From Figs. 7–9 we can see that as the evolution proceeds, more individuals generated by NSGA-II are on the first front. As the increasing of the ratio of individuals on the first front, the selection pressure is decreased, resulting in the deterioration of the search ability of pareto dominance. For NFSA-UP, the suppression mechanism of similar individuals is utilized to maintain the diversity of population, and the preference distance, not just the front number as in NSGA-II, is also take into consideration while the selection of individuals to the next generation, so the percentage of non-dominated solutions is much lower. While fewer solutions are on the first front, more solutions can be searched in wider solution space to find global optimum solutions. However, for NSGA-LBS, the size of the individuals on the first front is too small, resulting the final solutions trapped in some local optimal area or even failed to found the first pareto front.
The above-mentioned experimental results validate NFSA-UP by demonstrating that the multi-objects optimization algorithms properly generate first front fragment directed by the user preference. However, a more important result is the transmission parameter values to which they converge. Fig. 10 shows a set of attributes corresponding to a snapshot of a final output at generation 100 of a simulation run, for the low power mode scenario that the user preference direction for f 1 ; f 2 ; f 3 is from (1, 0, 0) to (1, 0, 1). The random channel attenuation is shown, along with the final values of throughput and power for each of the 64 subcarriers. The bottom windows in Fig. 10 shows that all transmit powers on the subcarriers are below 2 mW. The average transmit power in this specific case is 1.54 mW per subcarrier while the average throughput (modulation index) is at 2.0064 which consistent with the real situation that when the transmit power is lower, the throughput will be limited. The low average power indicates that the primary goal of the scenario, minimize power, was achieved. Figs. 11 and 12 also show similar information for both the low bit error mode, preference direction is from (0, 0, 1) to (1, 0, 1) and the max throughput mode, preference direction is from (1, 1, 1) to (1, 0, 1). The low bit error mode scenario, Fig. 11 shows that the final decision provided a low modulation index 2 over all the subcarriers. The transmit power over all the subcarriers with an average of 25 mW. This configuration yields a low BER due to
W. Chen et al. / Ad Hoc Networks 26 (2015) 3–16
the low modulation index, while using a high transmit power on each subcarrier. The middle window in the max throughput mode scenario, Fig. 12 validates that the maximum throughput is the primary objective for this scenario. All subcarriers are set to a big modulation index of 8 providing for the maximum possible throughput, while keeping small balance on the minimize power objective. 5. Conclusion Usually, CR parameter adaptation problem is molded as an unconstrained multi-objective optimization problem, and EMO algorithms are applied to determine the transmission parameters for a multicarrier CR network. The difficulties of current multi-objective optimization of CR transmission parameters lie in the lacking of enough selection pressure toward the non-dominated pareto front, and the secondary selection of the optimal suitable solution from the front. In this paper, we have used an EMO procedure along with the concept of user preference direction search strategy for finding a preferred set of pareto-optimal solutions. By specifying an aspiration point and a reservation point, the search results is focusing on the concerned part of pareto-optimal front based on the survive selection mechanism which combines preference distances and pareto ranks to determine the selection of individuals as well as the evolving direction. At the beginning of evolving, the distribution of the solutions in the focused region is controlled by a big weight of preference distance, and the convergence to the first pareto front is speed up by increase the weight of front rank at the ending. Using the above procedure, the decision maker can also obtain more than one set of preferred transmission parameters simultaneously by simply choosing multiple preference direction. Its strength is evident from its ability to converge satisfactorily to the true pareto-optimal front for a transmission parameters optimization problem in a 64 subcarriers CR network. Acknowledgement This research is supported by the National Natural Science Foundation of China (Nos. 61402308, 61173159). References [1] S. Chen, T.R. Newman, J.B. Evans, A.M. Wyglinski, Genetic algorithmbased optimization for cognitive radio networks, in: IEEE Sarnoff Symposium, 2010, pp. 1–26. [2] D. Corne, J. Knowles, Techniques for highly multiobjective optimization: some non-dominated points are better than others, in: Genetic and Evolutionary Computation Conference, 2007, pp. 773–780. [3] D. Cvetkovik, I.C. Parmee, Genetic algorithm based multi-objective optimization and conceptual engineering design. in: Congress on Evolutionary Computation, 1999, pp. 29–36. [4] K. Deb, A. Kumar, Light Beam Search Based Multi-Objective Optimization Using Evolutionary Algorithms, 2007. [5] K. Deb, A. Pratap, S. Agarwal, T. Meyarivan, A fast and elitist multiobjective genetic algorithm: Nsga-ii, IEEE Trans. Evol. Comput. 6 (2) (2002) 182–197. [6] K.T. Deepak, K.U. Siba, L.S. Samrat, Cognitive radio parameter adaptation using multi-objective evolutionary algorithm, Adv. Intell. Soft Comput. 130 (2012) 737–748. [7] FCC, Spectrum policy task force report, in: Proceedings of the Federal Communications Commission, 2002, pp. 21–35.
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Wen Chen was born in 1983. He received his Ph.D. in computer science from the Sichuan University, Chengdu, in 2011. Currently, he is a Senior Engineer at the Information Security Laboratory, Sichuan University. His research interests include cognitive radio network, wireless sensor network, information security and machine learning. He is a member of IEEE, as well as IEICE.
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W. Chen et al. / Ad Hoc Networks 26 (2015) 3–16 Tao Li born in 1965. He received the Ph.D. degree in Computer Science from the University of Electronic Science and Technology of China in 1994. From 1994 to 1995, he was a visiting scholar in University of California at Berkeley for neural networks theory. Now, he is a IEEE fellow and working as a professor in the Department of Computer Science at Sichuan University, China. His current research interests include wireless sensor network, network security, artificial immune theory and disaster recovery application.
Tao Yang was born in 1982. He received the M.S. degree in computer science from the Western China normal University. Now, he is a associate professor in the Department of Computer Science at Sichuan University, China. Her current research interests include wireless network, network security, artificial intelligence and disaster recovery application.