Cognitive Radio Spectrum Assignment Based on Artificial Bee Colony Algorithm Xiaoya Cheng, Mingyan Jiang School of Information Science and Engineering Shandong University Jinan, Shandong 250100 P.R. China Email:
[email protected],
[email protected] Abstract-Artificial bee colony (ABC) algorithm is a biologicalinspired optimization algorithm, which has been shown to be competitive with some biological-inspired algorithms, such as differential evolution, genetic algorithm and particle swarm optimization. In this paper, the work in de¿ning a general framework for spectrum allocation in cognitive radio systems is described, and a method using ABC algorithm to optimize spectrum allocation for efficiency and fairness is presented. Simulation results show that the solutions produced by ABC algorithm are better than those produced by Genetic Algorithm.
cognitive radio systems is described, and a method using ABC algorithm to optimize spectrum allocation for efficiency and fairness is presented. The rest of the paper is organized as follows. In Section Ċ the context of ABC algorithm is described. Next Section ċ provides a mathematical model of cognitive radio and de¿nes the utility functions. Then in Section Č , ABC algorithm to optimize the utility functions is described. Simulation results are provided in Section č , and conclusions are given in section Ď.
Keywords-Artificial bee colony (ABC) algorithm; cognitive radio; spectrum allocation; efficiency and fairness
I.
II. ARTIFICIAL BEE COLONY ALGORITHM
INTRODUCTION
Artificial bee colony (ABC) algorithm is a swarm intelligent optimization algorithm inspired by honey bee foraging [1-3]. In ABC algorithm, the colony of the artificial bees contains three groups of bees: employed bees, onlookers and scouts. The first half of the colony consists of the employed bees and the second half includes the onlookers. Each employed bee is associated with a food source, in other words, the number of the employed bees is equal to the food sources. Onlooker bees share the information of the food sources found by employed bees to choose better ones and explore around them. If some food sources are not improved for several cycles, the scouts are translated into a few employed bees, which abandon their food sources and search new ones. By simulating the behaviors of bee swarm, Karaboga [1] proposed ABC algorithm for numerical function optimization. The nectar amount of a food source corresponds to the quality of the solution, while the locations of employed bees or onlookers represent solutions. The details can be described as follows.
The foraging behavior, learning, memorizing and information sharing characteristics of bees have recently been one of the most interesting research areas in swarm intelligence. Studies on honey bees are in an increasing trend in the literature during the last few years. Artificial bee colony (ABC) algorithm was proposed by Karaboga in 2005 [1-3]. It is an optimization algorithm based on particular intelligent behavior of honey bee swarms. According to the recent studies [4], ABC algorithm is better than or similar to other population-based algorithms with the advantage of employing fewer control parameters. Wireless devices are becoming ubiquitous, placing increased stress on the ¿xed radio spectrum available to all access technologies. To eliminate interference between different wireless technologies, current policies allocate a ¿xed spectrum slice to each technology. This static assignment prevents devices from ef¿ciently utilizing allocated spectrum, resulting in spectrum holes (no targeted devices in local area) and very poor utilization (6%) in other geographic areas [7]. Studies have shown that reuse of such “wasted” spectrum can provide an order of magnitude improvement in system capacity. So the technology called cognitive radio has been researched during the recent years. While maximizing spectrum utilization is the primary goal of open spectrum systems, a good allocation scheme also needs to provide fairness across devices. To the best of our knowledge, the question of best addressing these two goals in the context of spectrum allocation for cognitive radio systems has not been previously addressed. In this paper, the work in de¿ning a general framework for spectrum allocation in ___________________________________
min f
f ( x) , x
( x1 , x2 ,..., xm ) S , S
[ xiL , xiH ]
Where, f represents the objective function, x
(1)
is m -
dimensional variable, [ xiL , xiH ] indicates the upper and lower bounds of the i th-dimensional variable. Suppose that the number of the employed bees and onlooker bees all is N . The main steps of the algorithm are given below[13]: a) Initialization
978-1-61284-307-0/11/$26.00 ©2011 IEEE
to a slow varying spectrum environment where users quickly adapt to environmental changes by re-performing network wide spectrum allocation. Therefore, a model for a fixed topology is focused on. A network of N secondary users indexed from 1 to N competing for M spectrum channels indexed 1 to M is assumed. Each secondary user can be a transmission link or a broadcast access point. The channel availability and rewards for each secondary user can be calculated based on the location and channel usage of nearby primary users. The key components of the model are defined as follows: 1) Channel availability: L {ln , m | ln ,m {0,1}}N uM is a N
Produce 2N locations randomly, evaluate them and move the employed bees onto the N food sources with the more nectar amounts. b) The employed bees explore new food sources around themselves by the (2)
Vij
xij Rij ( xij xkj )
(2)
Where Vij is a new location, Rij is a random number in the range [-1,1], k {1, 2, 3, ..., N } and k z i . c) Mark the N food sources with more nectar amounts from the candidate food sources between a) and b). d) Onlookers explore new food sources The onlookers are placed on food sources selected in the roulette wheel selection method. Then each onlooker bee explores the neighborhood of food source xi as (2). Probability Pi is calculated as follows:
Pi
fiti N
by M binary matrix representing the channel availability; ln ,m 1 , if and only if channel m is available at user n ; otherwise, ln , m
2) Channel reward: B
representing the channel reward: bn ,m represents the maximum
(3)
Obviously, bn ,m = 0 if ln , m
i 1
3)
Here, fiti is calculated using the following equation:
fiti
{bn , m }N uM is a N by M matrix
bandwidth/throughput that can be acquired (assuming no interference from neighbors) by user n using channel m .
¦ fiti
1 , fi t 0 ° ®1 fi °1 abs ( f ), f 0 ¯ i i
0.
C
0.
Interference constraint: Let {cn , k , m | cn , k , m {0,1}}N u N uM , is a N by N by M matrix,
represents the interference constraints among secondary users. If cn , k , m 1 , users n and k would interfere with each other if
(4)
they use channel m simultaneously. 4) Conflict free channel assignment: A {an , m | an , m {0,1}}N uM is a N by M binary matrix that
Where, fi is the fitness value of the solution. e) If a solution cannot be improved for “limit” trials, it will be abandoned. The scout randomly produces a solution to replace the old one. f) Select the N better solutions between candidate solutions generated in step c) and step d). g) Record the best solution obtained till now and repeat step b) to f) until the max iterations.
represents the assignment; an , m
1 , if channel m is assigned
to user n . A conflict free assignment needs to satisfy all the interference constraints defined by C , that is,
an , m ak , m d 1, if cn , k , m
1, n, k N , m M
(5)
Based on the above descriptions, the reward that each user gets for a given channel assignment is:
III. THE MATHEMATICAL MODEL OF COGNITIVE RADIO In this paper, the case where the collection of available spectrum ranges forms a spectrum pool, divided into nonoverlapping orthogonal channels is considered. Secondary users select communication channels and adjust transmit power accordingly to avoid interfering with primary users. Each secondary user keeps a list of available channels that it can use without interfering with neighboring primary users. The spectrum access problem becomes a channel allocation problem. In the model, it assumes that environmental conditions such as user location, available spectrum are static during the time that takes to perform spectrum assignment. This corresponds
R
{E n
M
¦ an , m u bn ,m }N u1
(6)
m 1
and the total reward of entire system is: N
U (R)
¦ En
n 1
N
M
¦ ¦ an ,m u bn ,m
(7)
n 1m 1
IV. SPECTRUM ALLOCATION IN COGNITIVE RADIO BASED ON ABC ALGORITHM
ª1 «0 « «0 « ¬0
L
0 1 0 1º 1 0 0 1 »» 1 0 0 0» » 0 0 1 0¼
x
>1, 0,1, 0,1,1, 0@
A
ª1 «0 « «0 « ¬0
0 0 0 1º 0 0 0 1 »» 1 0 0 0» » 0 0 0 0¼
Figure 1. Schematic of encode and decode (N=4, M=5)
to utilize from a pool of channels (e.g. 10 channels). For simplicity, primary users have uniform protection ranges, i.e. d p = const. Given the location and channel selection of
Given the model above, the spectrum access problem becomes a channel allocation problem. The channel allocation is to maximize network utilization. So the spectrum assignment problem can be de¿ned by the following optimization function:
max U ( R )
f1
N
max ¦ E n
d S [ d min , d max ] to avoid interference with primary users. Set
N
M
max ¦ ¦ an ,m u bn ,m
n 1
primary users, each secondary user n adjusts its transmit power (and hence interference range) on each channel m , i.e.
n 1m 1
K=20, N=10, M=10, d p
(8)
max U fair
N
max E n 1e 4 n 1
1/ N
(9)
Here, the fairness will not become 0 by assuming a baseline reward of 1e í 4 at each secondary user, if there exists a secondary user without any channels assigned, i.e. a starved user. The objective function is getted by weighted summation method, that is,
f
Z1 u f1 Z2 u f 2 , and Z1 Z2
1
1 , d max
4 . Channel
availability, reward and interference constraints are derived according to Section ċ . The parameters L , B , C are generated by the pseudo-code of Appendix 1 in [6]. The statistical performance of spectrum allocation over 10 different topologies is studied. To compare the performance, the experiments are simulated by ABC algorithm and Genetic Algorithm (GA), respectively. The parameters of ABC algorithm are set as follows: population size NP=20, Limit=100, Max_iter=2500. In GA: population size N=100, max_iter=1000, probability of crossover=0.8, probability of mutation=0.05. In addition, Z1 0.06 , Z2 =0.94 in the objective function.
Consistent with prior work [8,9,10,11], fairness of users is simultaneously considered and addressed. The corresponding fairness-driven utility optimization problem is expressed as:
f2
2 , d min
Each of the experiments in this section is repeated 10 trials under 10 different topologies. For a certain topology, get the mean value of the 10 experiments. Fig. 2 illustrates the value of objective function corresponding to each of the 10 topologies. The results con¿rm that the system performance optimizing by the proposed algorithm outperforms GA, while taking into account the fairness, effectiveness also is increased. The convergence curve under a certain topology is given in Fig. 3 and Fig. 4, by ABC algorithm and GA, respectively. From the figures, it can be seen that not only the optimal value of objective function is better, but also the runtime of program is shorter. So ABC algorithm is obviously superior to GA in terms of convergence speed, success rate and solution accuracy. Although simulations are only conducted in static scenarios, it is applicable to the dynamic environment. Only if users quickly get the channel assignment A , according to the proposed method, so as to adapt to environmental changes by re-performing network wide spectrum allocation.
(10)
In the proposed algorithm, the location of one employed bee or onlooker corresponds to channel assignment A . For a network of N secondary users competing for M spectrum channels, the location of one employed bee or onlooker can be encoded to a N by M matrix. To reduce the computation complexity, the encoded mode adopts the same mode in [5]. An example is given in Fig. 1. V. SIMULATION RESULTS AND DISCUSSIONS The simulations are conducted under the assumption of a noiseless, immobile radio network. Place randomly K primary and N secondary users in a given area (10 × 10). M channels are available. Each primary user randomly selects one channel
35
VI. CONCLUSION
The value of Objective function
The artificial bee colony (ABC) algorithm is a new swarm optimization algorithm with good numerical optimization results. In this paper, a general model and utility functions for optimizing efficiency and fairness in spectrum allocation of cognitive radio by ABC algorithm are de¿ned. The experimental results show that not only can the proposed algorithm drastically improve network performance, but also the proposed algorithm provides bene¿ts comparable to the Genetic Algorithm in terms of convergence speed, success rate and solution accuracy, meanwhile drastically reducing computation complexity. The proposed algorithm is very simple and flexible, especially suitable for engineering application.
ABC GA
30
25
20
15
10
1
2
3
4
5 6 7 10 different topologies
8
9
10
Figure 2. The curve under 10 different topologies
ACKNOWLEDGMENT This work is supported by the Natural Science Foundation of Shandong Province (No. ZR2010FM040 ).
Optimal value:25.9739,time:13.547seconds 26
REFERENCES The value of objective function
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[2] 20
[3] 18
[4]
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[5] 14
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[6] 0
500
1000
1500
2000
2500
Iterations
[7]
Figure 3. The convergence curve by ABC
[8] Optimal value:23.8272,time:18.484seconds 24
[9]
The value of objective function
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[10]
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[11] 20
[12]
19 18
[13]
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0
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500 600 Iterations
700
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1000
Figure 4. The convergence curve by GA
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