Wireless Pers Commun (2012) 65:15–24 DOI 10.1007/s11277-011-0225-7
Cognitive Radio Engine Design Based on Ant Colony Optimization Nan Zhao · Shuying Li · Zhilu Wu
Published online: 3 February 2011 © Springer Science+Business Media, LLC. 2011
Abstract In this letter, a mutated ant colony optimization (MACO) cognitive radio engine is proposed, and it is the first time to apply ACO algorithm to this problem. The cognitive radio is a promising technology nowadays to alleviate the apparent scarcity of available radio spectrum, and the cognitive radio engine determines the optimal radio transmission parameters for the system. The cognitive engine problem is usually solved by genetic algorithm (GA), however, the GA converges slowly and its performance can still be improved. Hence, MACO algorithm with excellent performance is applied to the cognitive engine in this letter. Simulation results show that the fitness scores obtained by the MACO engine are much better than the ACO and GA engines in different scenarios. Keywords Cognitive radio · Decision engine · Ant colony optimization · Mutation mechanism · Genetic algorithm
1 Introduction Cognitive radio is receiving significant attention as an approach to overcome the apparent spectrum scarcity problem, as well as to improve the communication efficiency [1]. Three basic parts make it work cognitively, including the ability to sense, the capacity to learn and the capability to adapt within any layer of the radio communication system. The adaptive component of these parts is first solved by genetic algorithm (GA) engine in [2,3]. Afterwards, many other GA engines for cognitive radio have been proposed to improve the performance in decision [4,5].
N. Zhao (B) School of Information and Telecommunication Engineering, Dalian University of Technology, Dalian, Liaoning 116024, China e-mail:
[email protected] S. Li · Z. Wu School of Electronics and Information Technology, Harbin Institute of Technology, Harbin, Heilongjiang 50001, China
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Ant colony optimization (ACO) algorithms have already successfully been used in combinatorial optimization [6,7]; however, they have not been applied to the cognitive radio engine design. In this letter, ACO algorithm is analyzed and applied to cognitive engine design, and this is the first time to use ACO algorithm to solve the cognitive radio engine problem. In our former papers, mutated ant colony optimization (MACO) algorithm is proposed [8,9]. The MACO algorithm can enlarge searching range and avoid local minima, so it can achieve much better performance than ACO algorithm with almost the same computational complexity. Therefore MACO algorithm is also introduced to the design of cognitive engine. Plenty of simulations compare the performance of the GA, ACO and MACO in solving the cognitive engine design problem, and the MACO engine has the superior performance.
2 Cognitive Radio Parameters To develop a cognitive radio control system, each cognitive engine should be able to adaptively adjust the transmission parameters according to the environment information. Hence the key parameters, including environment and transmission parameters, should be defined. The environment parameters should be known in time to calculate the fitness functions and help cognitive radio engine make decision. The environment parameters used in this letter are bit-error rate (BER), signal-to-noise ratio (SNR), background noise power and channel loss. Cognitive radio engine becomes possible when the transmission parameters within the cognitive engine can be changed adaptively according to the environment. In the artificial intelligence cognitive engine, the transmission parameters are necessary to calculate the fitness functions and make the optimal decision. It’s impossible to define a complete list of transmission parameters in all radios, and the transmission parameters used in this letter are transmit power, modulation type and modulation index.
3 Fitness Functions In the optimization process of the cognitive engine, the fitness function should be defined to guide the searching direction. There are three single-objective fitness functions in this letter [5], and they are power consumption minimization, BER minimization and throughput maximization. The fitness function of power consumption minimization is defined as f min_power = 1 −
P Pmax
(1)
where P is the average transmit power of all the subcarriers, and Pmax is the maximum available transmit power. The fitness function of BER minimization is given as f min_ber = 1 −
log10 (0.5) log10 (Pbe )
(2)
where Pbe represents the average BER over all the channels. In this letter, we assume that the possible modulation types include BPSK, 4, 16, and 64 QAM, and the BER of these modulation types at given SNR in the Gaussian channel can be calculated using the BER equations given in [10].
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Cognitive Radio Engine Design Based on Ant Colony Optimization Table 1 Example weighting scenarios, ω1 , ω2 andω3 determine the importance of power minimization, BER minimization and throughput minimization objectives
Scenario
17 Weight vector [ω1 , ω2 , ω3 ]
Low power mode (minimize power)
[0.80 0.05 0.15]
Emergency mode (minimize BER)
[0.15 0.80 0.05]
Multimedia mode (maximize throughput)
[0.05 0.15 0.80]
Balanced mode (equal weight)
[1/3 1/3 1/3]
The fitness function of throughput maximization is described as f max_throughput =
log2 (M) log2 (Mmax )
(3)
where M is the average modulation index of all the subcarriers, and Mmax is the maximum modulation index equal to 64. The three signal-objective fitness functions are in conflict with each other, for example the minimization of power consumption usually results in an increase of the BER. Therefore, the actual results of optimization should strike a balance between these signal-objective fitness functions, which can meet the communication requirements of the system and improve the other performance as high as possible. Therefore, we can define the multiple-objective fitness function of the whole network as f = ω1 × f min_power + ω2 × f min_ber + ω3 × f max_throughput
(4)
where the weight vector W determines the importance of the three control objectives, and it should meet the requirement ω1 + ω2 + ω3 = 1. Therefore several weight vectors as examples representing some common scenarios are defined, and they are shown in Table 1 [4]. The weight vectors in Table 1 determine the searching direction of the cognitive engine, and the selection of the proper weight vector should follow the requirements of the communication system.
4 MACO Cognitive Radio Engine 4.1 Problem Description In the simulation of this letter, there are 10 subcarriers. The transmit power of each subcarrier ranges from 5 to 250 mW with increment of 5 mW. So there are 50 possible values of the transmit power to be chosen. The modulation type of each subcarrier can be BPSK, 4, 16, and 64 QAM; hence there are 4 possible values of the modulation type to be chosen. Therefore the total searching space of the system is 1.024 × 1023 . The problem described above can be seemed as a traveling salesman problem (TSP) solved by ACO engine, in which there are 20 cities to be visited (10 for transmit power of each channel, and 10 for modulation type of each channel). The ants travel from the 1st city to the 20th city, and 10 of the cities have 50 possible values to choose, and the other 10 of the cities have 4 possible values to choose. The aim of the TSP is to find the path consisting of the 20 cities that can maximize the multiple-objective fitness function defined in (4).
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4.2 MACO Algorithm ACO algorithm has gained a great success in solving combinatorial optimization problems; however its performance still can be improved. The MACO algorithm [8,9] is proposed by introducing the mutation mechanism to ACO algorithm, and it can enlarge searching range and avoid local minima by randomly changing one or more elements of the local best solution after each iteration, which can improve the performance of ACO efficiently. In the iteration of MACO algorithm, assuming that the local best solution after the nth iteration is snbest = (s1nbest,..., s K nbest )T . Randomly choose one or more elements in the snbest , change them in a certain manner, and keep the other elements unchanged. Through this mutation operation, the mutated solution snbest ’ of snbest can be got. If snbest ’ is better than snbest , replace snbest by snbest ’. Otherwise the local best solution remained unchanged. The number of the mutated elements is decided by the number K of all the elements in the solution of the problem, and the larger K is, the more elements can be mutated. If K is extremely large, the number of mutated elements can be set to decrease as iterations carried on. 4.3 MACO Cognitive Engine In this letter, the MACO algorithm is applied to the design of cognitive radio engine, and it is the first time to use ACO algorithm to solve this problem. The MACO cognitive engine can be represented by the following steps: Step 1 Initialize the parameters, including the number of iterations Nc , the number of the cities K , the population of the ant colony M, the evaporation rate ρ, and the initial value of the pheromone τ0 . Step 2 Assume that the set Sk contains all the possible values for the kth cities, which is described in Sect. 4.1. The probability of what value the kth city is from the ant m at the time t is given by pkmj (t) =
τk j (t) , k = 1, 2, . . . , K , j ∈ Sk s∈Sk τks (t)
(5)
M ants travel from the 1st city to the K th city following Eq. (5), and then we can get M solutions. Step 3 Compare the M solutions based on the Eq. (4), and set the solution that has the largest value (equal to Cn ) of Eq. (4) as the local best solution snbest in this iteration. Step 4 Calculate the mutated solution snbest ’ of snbest following the mutation mechanism described above and get the value of Eq. (4) Cn ’ using snbest ’. Compare Cn and Cn ’. If Cn ’ is larger than Cn , replace snbest by snbest ’ and replace Cn by Cn ’. Step 5 Update the pheromone as follows: τk j (t + 1) = (1 − ρ) · τk j (t) + τk j , k = 1, 2, . . . , K , j ∈ Sk (Cn + Q)/r (k, j) ∈ snbest , τk j = 0 otherwise
(6) (7)
where τk j is the quantity of pheromone laid on edge (k, j) of the kth user with the value j, Q is a positive constant to ensure (Cn + Q) ≥ 0, and r is a constant to adjust the value of τk j .
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Table 2 Computational complexity comparison of the engines Engine type
Traveling times by ants
Mutation times by ants
MOFF calculation times
GA
0
0
500 × 20 = 10,000
ACO
500 × 20 = 10,000
0
500 × 20 = 10,000
MACO
500 × 19 = 9,500
500
9, 500 + 500 = 10, 000
Table 3 Average fitness score comparison in different scenarios
Scenario
GA
ACO
MACO
Low power mode
0.9383
0.9107
0.9482
Emergency mode
0.8422
0.8485
0.8523
Multimedia mode
0.9395
0.9416
0.9422
Balanced mode
0.8305
0.8336
0.8460
Step 6 Compare the local best solution with the global best solution. If the local best solution is better than the global best solution, set the local best solution as the global best solution. Step 7 Output the global best solution if stopping criterion is satisfied, or return to Step 3.
5 Simulation Results In the simulation of this section, the performance of GA, ACO and MACO cognitive engines is compared. There are 10 sub carriers, so there are 20 cities to be traveled. The transmit power of each subcarrier ranges from 5 to 250 mW with increment of 5 mW. The modulation type of each subcarrier can be BPSK, 4, 16, and 64 QAM. The number of iterations in GA, ACO and MACO cognitive engines is 500. To ensure that the computational complexity in these GA, ACO, and MACO engines is almost the same, the parameters in these engines are set as follows. The number of ants in ACO is 20, the number of ants in MACO is 19, and the number of chromosomes in GA is 20. The total number of mutation times, traveling times by the ants, and calculating the value of the multiple-objective fitness function (MOFF) in Eq. (4) in GA, ACO, and MACO engines are listed in Table 2. From Table 2 we can see that MOFF calculation times of these engines is all equal to 10,000, hence, the computational complexity of these engines is almost the same. In ACO and MACO engines, the evaporation rate ρ is equal to 0.8, 0.85, and 0.9, respectively, to find the optimal parameter ρ. In GA engine, the probability for the crossover process between two chromosomes is set to 0.85, 0.9, and 0.95, respectively, to find the optimal crossover rate, and additionally, the mutation probability for each chromosome is 0.05 [2]. Each subcarrier has a random channel attenuation. Though simulations, it is shown that the optimal ρ in MACO engine is 0.9, also, the optimal crossover process in GA engine is 0.9. The GA, ACO and MACO engines with their optimal parameters are used to solve the cognitive engine problem respectively in different scenarios described in Table 1, and the average fitness scores obtained by these engines after 500 iterations over 20 simulations are shown in Table 3.
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0.9
ACO, evaporation rate=0.8 MACO, evaporation rate=0.8 MACO, evaporation rate=0.9
Fitness Score
0.85
MACO, evaporation rate=0.85 GA, crossover rate=0.85, mutation rate=0.05
0.8
GA, crossover rate=0.95, mutation rate=0.05 GA, crossover rate=0.9, mutation rate=0.05
0.75
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0
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(a) Convergence process in 0 to 500 iterations.
0.945
0.94
Fitness Score
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0.93
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0.925
0.92
0.915
0.91 470
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Iterations
(b) Local convergence process in 470 to 500 iterations. Fig. 1 Average fitness function convergence process comparison in the low power mode
In Table 3, we can see that, the fitness scores obtained by MACO cognitive engine in all the scenarios are larger than GA engine, while the fitness scores obtained by GA engine are better than ACO engine. To compare these three cognitive engines more explicitly, the average fitness function convergence process in the low power mode of these three cognitive engines with different parameters over 20 simulations is depicted in Fig. 1. In Fig. 1, the ACO engine converges most quickly, however, its fitness score is much smaller than the other two engines because it stops searching early. The fitness score of the
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Fig. 3 Final decisions of the transmit power, modulation type and BER under emergency mode. In modulation type sub-figure, 1, 2, 3 and 4 represent BPSK, 4, 16 and 64 QAM, respectively
MACO engine is the largest among the three engines with ρ = 0.9, and it converges more quickly than GA engine with the crossover rate equal to 0.85, 0.9, and 0.95. Hence, the MACO cognitive engine has the most excellent performance among these engines, and is suitable to be applied to the cognitive radio system. To further analyze the final decisions obtained by the MACO cognitive engine, the transmit power, modulation type and BER control results under low power mode, emergency mode, multimedia mode and balanced mode are depicted in Figs. 2–5. In the modulation type control results of these Figs. 1–4 represent BPSK, 4, 16, and 64 QAM, respectively. In Fig. 2, because it is under low power mode, the transmit power controlled by MACO cognitive engine is much lower, while the BER is relatively high. Figure 3 is for the case of emergency mode, and under this mode, the cognitive engine should minimize the BER in
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Transmit power (mW)
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Fig. 4 Final decisions of the transmit power, modulation type and BER under multimedia mode. In modulation type sub-figure, 1, 2, 3 and 4 represent BPSK, 4, 16 and 64 QAM, respectively
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Fig. 5 Final decisions of the transmit power, modulation type and BER under balanced mode. In modulation type sub-figure, 1, 2, 3 and 4 represent BPSK, 4, 16 and 64 QAM respectively
each channel, hence from Fig. 3 we can see that the BER of each channel is extremely low controlled by MACO cognitive engine at the cost of larger transmit power in each channel. In Fig. 4, it is under multimedia mode, therefore the modulation types of these channels are all set to 64 QAM by MACO cognitive engine, which maximize the throughput of the systems at the cost of large transmit power and high BER. Figure 5 depicts the case of balanced mode, and in this mode, the weights of the three control objectives are equal, and the transmit power, BER are relatively large with throughput relatively small.
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6 Conclusion In this letter, we propose a MACO cognitive radio engine, and it can adapt the radio parameters according to the changing environment and requirements of the system. The MACO algorithm is proposed by introducing the mutation mechanism to the ACO algorithm, and it can enlarge the searching range and avoid local minima, so its performance is much better than the ACO algorithm. Simulation results show that the fitness scores gained by the MACO engine in different scenarios are larger than the ACO engine and the conventional GA engine, and the MACO engine also converges quickly enough.
References 1. Haykin, S. (2005). Cognitive radio: Brain-empowered wireless communications. IEEE Journal on Selected Areas in Communications, 23(2), 201–220. 2. Goldberg, D. E. (1989). Genetic algorithms in search, optimization and machine learning. Reading, MA: Addison-Wesley. 3. Rondeau, T., Le, B., Rieser, C., & Bostian, C. (2004). Cognitive radios with genetic algorithms: Intelligent control of software defined radios. In Software defined radio forum technical conference (pp. C3–C8). 4. Newman, T. R., Barker, B. A., Wyglinski, A. M., & Agah, A. (2007). Cognitive engine implementation for wireless multicarrier transceivers. Wireless Communications and Mobile Computing, 7(9), 1129–1142. 5. Newman, T. R., Rajbanshi, R., Wyglinski, A. M., & Evans, J. B. (2008). Population adaptation for genetic algorithm-based cognitive radios. Mobile Networks and Applications, 13(5), 442–451. 6. Dorigo, M., Birattari, M., & Stüzle, T. (2006). Ant colony optimization. IEEE Computational Intelligence Magazine, 1(4), 28–39. 7. Zhao, N., Wu, Z. L., Zhao, Y. Q., & Quan, T. F. (2010). Population declining ant colony optimization multiuser detection in asynchronous CDMA communications. Wireless Personal Communications, to be published. 8. Zhao, N., Wu, Z. L., Zhao, Y. Q., & Quan, T. F. (2010). Ant colony optimization algorithm with mutation mechanism and its applications. Expert Systems with Applications, 37(7), 4805–4810. 9. Zhao, N., Wu, Z. L., Zhao, Y. Q., & Quan, T. F. (2010). A population declining mutated ant colony optimization multiuser detector for MC-CDMA. IEEE Communications Letters, 14(6), 497–499. 10. Proakis, J. G. (2000). Digital communications. New York: McGraw-Hill.
Author Biographies Nan Zhao was born in Dalian, China, in 1982. He received the B.S. degree in electronics and information engineering in 2005, the M.E. degree in signal and information processing in 2007, and the Ph. D. degree in Information and communication engineering in 2011 from Harbin Institute of Technology, Harbin, China. He is currently a lecturer at School of Information and Telecommunication Engineering, Dalian University of Technology. His research interests are multiuser detection and power control in CDMA, spectrum sensing in cognitive radio, cognitive radio engine design, chaotic theory, and ant colony optimization.
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N. Zhao et al. Shuying Li was born in Hebei, China, in 1984. He received the M.E. degree in signal and information processing in 2010 from Harbin Institute of Technology (HIT), Harbin, China. He is currently a Ph.D. in Information and communication engineering in HIT. And now, he does his research as a visiting student in Electrical Engineering Department, Columbia University, New York, US. His research interest is spectrum sensing in cognitive radio, and cognitive radio engine design.
Zhilu Wu was born in Harbin, China, in 1961. He is a professor with the School of Electronics and Information Technology and the dean of the Information Engineering Department at Harbin Institute of Technology, Harbin, China. He received the B.S. degree in electronic instrument and measurement technology in 1983, the M.S. degree in signal and information processing in 1989, and the Ph.D. in information and communication engineering in 2008 from Harbin Institute of Technology. His research interests are wireless communication, spectrum sensing in cognitive radio, cognitive radio engine design, software radio, and artificial neural networks.
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