Evolutionary Algorithms for Radio Resource Management in Cognitive ...
Evolutionary Algorithms for Radio Resource Management in Cognitive Radio Network Muhammad Waheed, Anni Cai School of Information and Communication Engineering Beijing University of Posts and Telecommunications Beijing, People Republic of China [email protected] Abstract— Cognitive radio (CR) technology employing dynamic spectrum access (DSA) improves spectrum utilization by exploiting its unused portions and provides a solution to the apparent spectrum scarcity problem. In this paper we present binary particle swarm optimization (BPSO) and genetic algorithm (GA) for radio resource management (RRM) in OFDMA-based cognitive radio network (CRN). The simulation results show that BPSO-based RRM performs better than GA. Keywords- cognitive radio; orthogonal frequency division multiplexing; radio resource management; evolutionary algorithms.
I.
INTRODUCTION
Spectrum is scarce and precious resource in wireless communication systems and networks. But, the static spectrum allocation policy of assigning radio resources to license holders has lead to a scarcity of this precious resource. To meet with the ever increasing spectrum demands by mobile and wireless applications, this static assignment policy faces spectrum scarcity in particular spectrum bands [1]. The situation is particularly acute in hot spots such as airports and shopping malls. Despite the development of communication technologies operating with higher spectral efficiency and employing highly sophisticated signal processing techniques, there is a practical limit to the number of additional subcarriers that can be accommodated within a given bandwidth. The studies conducted in different parts of the world have shown that a large portion of this statically allocated spectrum is used only sporadically and that spectrum utilization is very low [2]. This finding coupled with the fact that spectrum scarcity will limit the development of future wireless communication services, urged for re-examination of FCC spectrum allocation policy. Hence, dynamic spectrum access techniques were recently proposed to solve these spectrum inefficiency problems and improve its utilization. The key enabling technology of dynamic spectrum access techniques is cognitive radio (CR) technology [3], which provides the capability to share the wireless channel with licensed user in an opportunistic manner. CR improves overall spectrum utilization by allowing unlicensed secondary users (SUs) (also referred as CR users or CRUs) to access those frequency bands which are not currently
being used by licensed primary users (PUs). In order to avoid unacceptable levels of interference to PUs, CRs have the ability to sense the environment and rapidly adapt their transmission parameters [4]. CR, with its ability to sense the unused bandwidth and adjust its transmission parameters accordingly, is an excellent candidate for improving spectrum utilization. Recognizing this, and to alleviate the looming spectrum shortage crisis, the FCC has suggested the use of CR technology in order to allow unlicensed users to share radio resources with licensed users while not unduly interfering with them [5]. Orthogonal frequency division multiplexing (OFDM) is a scheme that uses a large number of closely spaced orthogonal subcarriers to carry data. It has been considered an appropriate modulation candidate for CR systems [6], not only because of its high spectral efficiency, but also its flexibility in dynamically allocating radio resources to multiple users and its low interference between adjacent subcarriers. However, fast and efficient resource allocation (RA) algorithms are required, to enable secondary users in a multiuser OFDM-based CR system, to adapt their transmission parameters to the rapidly changing environment in a near optimal manner. We formulated resource optimization in OFDM-based CR system as integer programming problem. The main objective of this resource allocation problem is to assign OFDM carriers to users in such a manner that sum rate capacity of the cognitive radio network (CRN) is maximized under the interference and power constraints. But, optimal allocation of subcarriers, bits and powers in a multiuser (MU) OFDM-based CR system is computationally complex. Therefore, an intelligent approach is used to search for reasonable approximate solution with lesser computational complexity. In literature, Genetic Algorithm (GA) and Swarm Intelligence (SI) have successfully been applied for CR parameter adaptation and to the other combinatorial optimization problems of communication systems [4] [7]. In this paper we apply evolutionary techniques for resource allocation in MU OFDM-based CR system. Simulations results given ahead, show that both the evolutionary techniques Genetic algorithm (GA) and Binary Particle Swarm Optimization (BPSO) provide an efficient solution to the resource allocation problem in multiuser OFDM-based CR system. They maximize the system capacity while adhering to the interference and power constraints. Moreover, from the simulation results it is also
evident that BPSO-based resource allocation algorithm performs better than GA-based allocation method. The rest of this paper is organized as follows. In Section II, the system model is described and the problem of optimizing resource allocation is formulated. In Section III, resource allocation in OFDM systems is briefly discussed. In Section IV, evolutionary techniques for optimal allocation of transmit power, bit and subcarrier in MU OFDM-based CR system are proposed. Simulation results and analysis is given in Section V. Section VI finally concludes the paper. II.
SYSTEM MODEL
We consider a scenario where PU and SU may co-exist in side-by-side bands as assumed in [8]. It is assumed that band occupied by the PU is sensed by the CR system and is of width Wm Hz. The unoccupied bands sensed by CR system for its possible transmission are located on each side of the PU band. The available bandwidth for CR transmission is divided into N OFDM subcarriers, having N/2 subcarriers on each side and each occupying a band width of Δf Hz, as shown in Fig. 1.
2
I m ,n = hbs ,m Pn,k Ts ∫
Δf m ,n +Wm / 2
Δf m ,n −Wm / 2
where
2
⎛ sin π f Ts ⎞⎟ ⎜⎜ ⎟ df ⎜⎝ π f Ts ⎟⎟⎠
(2)
Pn ,k is the transmit power assigned to the nth
subcarrier for the kth secondary user and Ts is the symbol duration , Δfm ,n represents the spectral distance between the nth subcarrier of secondary user band and the mth primary user band. We assume that the transmission power assigned to the kth user at the nth carrier has finite number bs
bs
of levels between 0 and P , where P is the maximum allowable transmission power from BS. The main objective of this resource allocation is to assign the carriers to the users in such a manner that the sum rate capacity of the cognitive radio network is maximized under the interference and power constraints. Let
xn ,k is a binary subcarrier allocation indicator and is
defined as ⎧ ⎪1 if subcarrier n is assigned to user k xn , k = ⎪ ⎨ ⎪ otherwise ⎪ ⎩0
Figure 1. Side-by-side co-existance scenario of primary and secondary users, occupying neighbouring frequency bands.
We consider a downlink scenario in a multiuser OFDMbased CR system in which a CR base station (BS) transmits information to the CRU using radio spectrum which is unoccupied by the PU. For such downlink scenario interference introduced by CRU to PU’s band is the limiting factor, which limits the transmit power as well as the achievable transmission rate of the CRU. There is M=1 primary user, K secondary users and at most N OFDM subcarriers available for these secondary users. Assume a flat fading model and channel gains are known at the transmitters. We denote by f bs , k the fading gain between BS and the kth secondary user and hbs , m the fading gain between BS and the mth primary user (PU). The power spectral density (PSD) of nth subcarrier signal is assumed to have form [8].
The transmit power is adjusted for secondary user’s nth subcarrier with an ideal coding scheme. We denote by N o , the additive white Gaussian noise (AWGN) variance 1 and interference introduced by the PU’s band into OFDM subcarriers is assumed to be zero. The transmission rate at the nth subcarrier (b/s/Hz) for the kth secondary user is defined as
⎛ f bs , k ⎜ log 2 ⎜⎜1 + Pn , k ⎜⎜ No ⎝
2
⎟⎞ ⎟⎟⎟ ⎠⎟
(3)
We formulated the resource optimization problem as integer programming problem K
max
N
∑∑x
n ,k
k =1 n =1
⎛ f bs , k ⎜ log 2 ⎜⎜1 + Pn , k ⎜⎜ No ⎝
2
⎟⎟⎞ ⎟⎟ ⎟⎠
(4)
Subject to: 2
⎛ sin π f Ts ⎞⎟ ⎟ Φn ( f ) = Pn ,k Ts ⎜⎜ ⎜⎝ π f Ts ⎟⎟⎠
K
(1)
∑x
n, k
≤1
∀n = 1,", N
(5)
k =1
Then the interference introduced by the nth subcarrier assigned to kth user in SU band to the mth PU band is the integration of the PSD of the nth subcarrier across the mth primary user band and can be written as
1
The noise is assumed to be generated by a Gaussian process with a known variance. Since the variance of a Gaussian process is equivalent to its power, its conventional to call this variance the noise power.
Pnk ≥ 0, N
∑I
m,n
∀n, k ≤I
m max
(6)
∀ m = 1, ", M
(7)
n=1 K
N
∑∑ P
n,k
≤ P bs
(8)
k =1 n=1
xn ,k ∈ {0,1} ,
∀n, k
(9)
m
Where I max is the maximum tolerable interference (interference temperature) for the mth PU. The first constraint in (5) shows that any given subcarrier can be assigned to at most one user at a time. The third constraint given in (7) is the maximum allowable interference to the primary user, while the fourth constraint in (8) is the maximum transmit power constraint. III.
RESOURCE ALLOCATION IN OFDM
The bit and power loading problem for single-user OFDM systems can be solved by using the well-known water filling algorithm if we assume that the number of bits to be loaded is a real number, or implement a greedy approach that assigns one bit at a time to the subcarrier that requires the least additional power for the integer bit case. To reduce computational complexity for the integer bit case, various low complexity algorithms have been proposed, for both optimal and suboptimal solutions [9]. In the case of the downlink transmission of a BS to multiple users, the subchannels need to be assigned to users exclusively [10]. Therefore, RA involves subchannel assignment in addition to power and bit allocation. When the goal is to maximize system throughput, the problem can be solved in two separate steps [10], namely, assigning each subchannel to the user with the best channel condition, followed by power and bit allocation. When there are QoS or fairness requirements, subchannel, bit, and power allocation becomes more complicated. Since optimal solutions are generally computationally complex, various sub-optimal solutions have been proposed. In [11], suboptimal solution is proposed to minimize the total transmit power while satisfying rate and BER requirements for real-time (RT) services. For non-real-time (NRT) services, maximizing system throughput while guaranteeing a certain level of fairness among users is a reasonable goal [12]. Most of these suboptimal solutions use a divide-and-conquer approach, in which the subcarrier, power, and bit allocation problem is broken down into two steps, i.e., allocate subcarriers to users and load appropriate power and bits to each subcarrier. During the first step, power is often assumed to be the same across all subcarriers so as to simplify the problem.
IV. EVOLUTIONARY TECHNIQUES FOR RESOURCE ALLOCATION IN MU OFDM-BASED CR SYSTEM In a CR system, besides the fading characteristics of wireless communication channels, the available transmission spectrum also changes over time. Resource allocation (RA) algorithms designed for conventional OFDM systems assume that the available spectrum is fixed, which is not the case in CR systems. Thus, in CR systems new RA algorithms are needed that take into account both the fading characteristics of the transmission channel and the timevarying nature of the available spectrum as well as protectively share the spectrum holes without generating undue interference to the PUs. However, the problem of optimal allocation of subcarriers, bits and powers in a multiuser OFDM-based CR system is computationally complex. Therefore, an intelligent approach is used to search for reasonable approximate solution with lesser computational complexity. In literature, Genetic Algorithm (GA) and Swarm Intelligence (SI) have successfully been applied for CR parameter adaptation and to the other combinatorial optimization problems of communication systems [4] [7]. In this work, we formulated resource optimization in OFDM-based CR system as integer programming problem in (4). The main objective of this resource allocation problem is to assign OFDM carriers to users in such a manner that sum rate capacity of the cognitive radio network (CRN) is maximized under the interference and power constraints. An optimal solution to this integer programming problem in (4) is computationally complex thus, not suitable for cognitive radio systems in which channel conditions are constantly changing. Evolutionary techniques proposed for solution of RA optimization problem in multiuser OFDM-based CR system are given below: A. Genetic Algorithm (GA) Genetic algorithms are a class of artificial reasoning whereby the search is performed in a manner similar to genetic evolution. In general, solutions to a problem set are represented by binary strings. These strings then are allowed to act in a manner similar to genetic growth; strings which are considered ‘good’ split and recombine with other good strings to form new solutions, while ‘poorer’ strings are allowed to ‘die’ out of the solution set. This decision is made by the fitness function which inputs the parameters and outputs a score, based on the specific goals of the radio. Strings undergo a process called mutation, that is, a random flipping of bits, to help prevent local minimization from occurring. GAs are typically used as method of problem optimization [13]. Therefore, given its random nature, fast computation time, and ability to spontaneously generate unique solutions, GAs are an appealing candidate for resource allocation in CR systems. Input and output parameters can easily be mapped to a binary form and the size of the genetic population is customizable to space available within any given configuration. GAs are used mainly when the search space is
too large to be simply brute force search to determine the optimal parameter set.
vidt +1 = vidt + c1r1( pidt − xidt ) + c2r2( pgdt − xgdt )
(10)
1 1+
e
(11)
t − vid
The resulting change in position is then defined by the following rule: If r< s (vid ) , then t
vid t
xidt =1; else xidt =0
(12)
The continuous-valued particle swarm algorithm limits by a value Vmax. Whereas, in binary version Vmax is
retained to avoid
s (vidt ) approaching 0 or 1, and a smaller
Vmax allows a higher mutation rate. The fitness function used by BPSO algorithm to converge to optimal solution is (4). BPSO algorithm proceeds as follows: Step 1. Initialize t=0 and randomly generate xid and vid . Step 2. Compute fitness of every particle in the population using fitness function given in (4). Step 3. Update velocity of the particles according to (10). Step 4. Generate random number distributed in [0,1] and update position as per change in position rule described in (12). Step 5. Repeat step 2 and compare particle’s fitness values with its own previous best as well as population’s best and select the greater value. Step 6. Terminate iteration if t= no of predefined iterations; else go to step 3 and repeat. V.
SIMULATION RESULTS AND ANALYSIS
The simulation results present the performance of BPSO and GA algorithms for various scenarios. The number of primary users is set to one. The bands of primary and secondary users are 1MHz each. The channel between BS and secondary users as well as between BS and primary user 40 35
BPSO GA
30 Capacity (b/s/Hz)
B. Binary Particle Swarm Optimization (BPSO) Particle Swarm Optimization (PSO) is population based stochastic optimization technique which is inspired by social behavior of bird flocking or fish school. PSO is distinctly different from other evolutionary-type methods in that it does not use the filtering operation (such as crossover and/or mutation) and the members of the entire population are maintained throughout the search procedure. In PSO algorithm, each member is called “particle” and each particle flies around in the multi-dimensional search space with a velocity, which is constantly updated by the particle’s own experience and the experience of the particle’s neighbors. PSO has a very simple concept, easy to implement and is computationally efficient. Therefore, ever since it is invented by Kennedy [14], it has successfully been applied to a variety of optimization problems [4]. The initially developed continuous PSO was restricted in real number space. However, many real optimization problems which require ordering or rearrange of discrete elements are set in discrete number space e.g. combinatorial problems like scheduling and routing. Therefore, to meet the need Kennedy and Eberhart developed a binary version of PSO, which differs from continuous PSO [15]. In binary space, a particle may be seen to move to nearer and farther corners of the hypercube by flipping various number of bits; thus velocity of the particle overall may be described by number of bits changed per iteration, or hamming distance between particle at time t and at t+1. A particle with zero bits flipped doesn’t move, while it moves the “farthest” by reversing all of its binary coordinates. Using BPSO, potential solution to an optimization problem such as CR parameter optimization is represented as a particle having coordinate xid and rate of change vid in a D-dimensional space. Each particle i maintains a record of its previous best performance in a vector called pid. An iteration comprises evaluation of each particle, then stochastic adjustment of vid in the particle i’s best previous position and the best previous position of any particle in the neighborhood. The variable “g” is assigned the value of the index of the particle with the best performance so far in the neighborhood. The current velocity of the dth bit of the ith particle at a time t+1 is updated as:
s (vidt ) =
25 20 15 10 5
Where, c1 and c2 are acceleration coefficients, and r1and r2 are random numbers uniformly distributed in [0, 1], pid and xid are the integers in {0, 1} and since vid is a probability, it must be constrained to the interval [0.0, 1.0] by using a sigmoid function :
0 -5 10
-4
10
-3
10 Interference Threshold
-2
10
Figure 2. System capacity versus maximum tolerable interference power (Ith Watts), with Pcarrier = 5mW , Ptotal =100 mW, N=16 and K=4.
80
50 45
BPSO GA
70
BPSO GA
40 60 Capacity (b/s/Hz)
Capacity (b/s/Hz)
35 30 25 20
50 40 30
15 20
10 10
5 0 -5 10
-4
10
-3
10 Interference Threshold
Figure 3. System capacity versus maximum tolerable interference power (Ith Watts), with Pcarrier = 10mW , Ptotal =100 mW, N=16 and K=4. 50 45
0 -5 10
-2
10
-3
10 Interference Threshold
-2
10
Figure 5. System capacity versus maximum tolerable interference power (Ith Watts), with Pcarrier = 5mW , Ptotal =500 mW, N=32 and K=6. 120
BPSO GA
BPSO GA 100
40 35
80 Capacity (b/s/Hz)
Capacity (b/s/Hz)
-4
10
30 25 20 15 10
60
40
20
5
-4
10
-3
10 Interference Threshold
0 -5 10
-2
10
Figure 4. System capacity versus maximum tolerable interference power (Ith Watts), with Pcarrier = 15mW , Ptotal =100 mW, N=16 and K=4.
is assumed to be independent, identically distributed Rayleigh random variables. The value of No, is set 10-3 . The parameters for BPSO are, population size=10, c1=c2=2, Vmax +7 to -7, maximum number of iterations =10. Whereas, for GA the population size is 10 with a crossover rate and mutation probability of 0.9 and 0.1 respectively, the maximum number of generation was set to 10. Figures 2, 3 and 4 present the performance of BPSO and GA for a system with 16 subcarriers, 4 secondary users, and 100mW of total power. The carrier power is set to 5mW, 10mW and 15 mW for figures 2, 3 and 4 respectively. The interference threshold is set to 10uW, 100uW, 1mW and 10 mW. The figures depict that the BPSO-based RA method provides higher average system capacity than GA-based method. It is also observe that the gap between these two algorithms increases with increase in the interference threshold level. The figures 5, 6 and 7 present the performance of BPSO and GA for a system with 32 subcarriers, 6 secondary users, and 500mW of total power. The carrier power is set to 5mW, 15mW and 25 mW for figures 5, 6 and 7 respectively.
-4
10
-3
10 Interference Threshold
-2
10
Figure 6. System capacity versus maximum tolerable interference power (Ith Watts), with Pcarrier = 15mW , Ptotal =500 mW, N=32 and K=6. 140 BPSO GA 120
100 Capacity (b/s/Hz)
0 -5 10
80
60
40
20
0 -5 10
-4
10
-3
10 Interference Threshold
-2
10
Figure 7. System capacity versus maximum tolerable interference power (Ith Watts), with Pcarrier = 25mW , Ptotal =500 mW, N=32 and K=6.
The interference threshold is set to 10uW, 100uW, 1mW and 10 mW. These figures also depict that the BPSO-based RA method provides higher average system capacity than
GA-based method. It is also observe that by increasing the subcarriers a higher average system capacity is achieved. VI.
CONCLUSION
Cognitive radio (CR) technology employing dynamic spectrum access (DSA) improves spectrum utilization by exploiting its unused portions and provides a solution to the apparent spectrum scarcity problem. However, fast and efficient resource allocation (RA) algorithms are required to enable secondary users in a multiuser cognitive radio network (CRN) to adapt their transmission parameters to the rapidly changing environment. We formulated resource optimization in OFDM-based CR system as integer programming problem and applied evolutionary techniques for its solution. Simulations results show that proposed evolutionary techniques, genetic algorithm (GA) and binary particle swarm optimization (BPSO) provide an efficient solution for radio resource management (RRM) in multiuser OFDM-based CR system. They maximize the system capacity while adhering to the interference and power constraints. Moreover, from the simulation results it is also evident that BPSO-based RA algorithm performs better and provides higher average system capacity than GA-based method.
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
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[2]
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[4]
National Telecommunications and Information Administration, “United states frequency allocation chart." [Online]. Available: http://www.ntia.doc.gov/osmhome/allochrt.html D. Cabric, S. M. Mishra, D. Willkomm, R. Brodersen, and A. Wolisz, “A cognitive radio approach for usage of virtual unlicensed spectrum," in Proc. of 14th IST Mobile Wireless Communications Summit, Dresden, Germany, June 2005. S. Haykin, “Cognitive radio: brain-empowered wireless communications," IEEE Journal on Selected Areas in Communications, vol. 23, no. 2, pp. 201-220, February 2005. M. Waheed and A. Cai, “Evolutionary Schemes for Cognitive Radio Adaptation.” in Proc. of The Fifth International Confrence on Wireless Communications, Networking and Mobile Computing, WiCOM 2009.
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Federal Communications Commission, “Facilitating opportunities for flexible, efficient, and reliable spectrum use employing cognitive radio technologies," notice of proposed rulemaking and order, FCC 03-322, 2003. T. A. Weiss and F. K. Jondral, “Spectrum pooling: an innovative strategy for the enhancement of spectrum efficiency," IEEE Communications Magazine, vol. 42, no. 3, pp. S8-S14, March 2004. I. Kassabalidis, M. A. EI-Sharkawi, R. J. Marks II, P. Arabshahi, A. A. Gray, “Swarm Intelligence for Routing in Communication Networks,” Proc. IEEE Globecom, Nov. 25-29, 2001. T. Weiss, J. Hillenbrand, A. Krohn, and F. K. Jondral, “Mutual interference in OFDM-based spectrum pooling systems," in Proc. of IEEE 59th Vehicular Technology Conference (VTC 2004-Spring), vol. 4, Milan, Italy, May 2004, pp. 1873-1877. B. S. Krongold, K. Ramchandran, and D. L. Jones, “Computationally efficient optimal power allocation algorithms for multicarrier communication systems," IEEE Transactions on Communications, vol. 48, no. 1, pp. 23{27, January 2000. J. Jang and K. B. Lee, “Transmit power adaptation for multiuser OFDM systems," IEEE Journal on Selected Areas in Communications, vol. 21, no. 2, pp. 171-178, February 2003. G. Yu, Z. Zhang, Y. Chen, J. Shi, and P. Qiu, “A novel resource allocation algorithm for real-time services in multiuser OFDM systems," in Proc. of IEEE 63rd Vehicular Technology Conference (VTC 2006-Spring), vol. 3, Melbourne, Australia, May 2006, pp. 1156-1160. G. Yu, Z. Zhang, Y. Chen, P. Cheng, and P. Qiu, “Subcarrier and bit allocation for OFDMA systems with proportional fairness," in Proc. of IEEE Wireless Communications and Networking Conference (WCNC 2006), vol. 3, Las Vegas, NV, USA, April 2006, pp. 17171722. T. R. Newman, B. A. Barker, M. Alexander, Wyglinski, A. Arvin, J. B. Evans and G. J. Minden, “Cognitive engine implementation for wireless multicarrier transceivers,” Wiley Journal on Wireless Commu nications and Mobile Computing, 2007, 7: 1129–1142. J. Kennedy and R. C. Eberhart, “Particle swarm optimization,” in Proceedings of IEEE International Conference on Neural Networks, 1995, pp. 1942–1948. J. Kennedy and R. C. Eberhart, “A discrete binary version ofthe particle swarm algorithm,” in Proceedings of the World Multiconference on Systemics, Cybernetics and Informatics,1997, pp. 4104–4109.
I.
INTRODUCTION
Spectrum is scarce and precious resource in wireless communication systems and networks. But, the static spectrum allocation policy of assigning radio resources to license holders has lead to a scarcity of this precious resource. To meet with the ever increasing spectrum demands by mobile and wireless applications, this static assignment policy faces spectrum scarcity in particular spectrum bands [1]. The situation is particularly acute in hot spots such as airports and shopping malls. Despite the development of communication technologies operating with higher spectral efficiency and employing highly sophisticated signal processing techniques, there is a practical limit to the number of additional subcarriers that can be accommodated within a given bandwidth. The studies conducted in different parts of the world have shown that a large portion of this statically allocated spectrum is used only sporadically and that spectrum utilization is very low [2]. This finding coupled with the fact that spectrum scarcity will limit the development of future wireless communication services, urged for re-examination of FCC spectrum allocation policy. Hence, dynamic spectrum access techniques were recently proposed to solve these spectrum inefficiency problems and improve its utilization. The key enabling technology of dynamic spectrum access techniques is cognitive radio (CR) technology [3], which provides the capability to share the wireless channel with licensed user in an opportunistic manner. CR improves overall spectrum utilization by allowing unlicensed secondary users (SUs) (also referred as CR users or CRUs) to access those frequency bands which are not currently
being used by licensed primary users (PUs). In order to avoid unacceptable levels of interference to PUs, CRs have the ability to sense the environment and rapidly adapt their transmission parameters [4]. CR, with its ability to sense the unused bandwidth and adjust its transmission parameters accordingly, is an excellent candidate for improving spectrum utilization. Recognizing this, and to alleviate the looming spectrum shortage crisis, the FCC has suggested the use of CR technology in order to allow unlicensed users to share radio resources with licensed users while not unduly interfering with them [5]. Orthogonal frequency division multiplexing (OFDM) is a scheme that uses a large number of closely spaced orthogonal subcarriers to carry data. It has been considered an appropriate modulation candidate for CR systems [6], not only because of its high spectral efficiency, but also its flexibility in dynamically allocating radio resources to multiple users and its low interference between adjacent subcarriers. However, fast and efficient resource allocation (RA) algorithms are required, to enable secondary users in a multiuser OFDM-based CR system, to adapt their transmission parameters to the rapidly changing environment in a near optimal manner. We formulated resource optimization in OFDM-based CR system as integer programming problem. The main objective of this resource allocation problem is to assign OFDM carriers to users in such a manner that sum rate capacity of the cognitive radio network (CRN) is maximized under the interference and power constraints. But, optimal allocation of subcarriers, bits and powers in a multiuser (MU) OFDM-based CR system is computationally complex. Therefore, an intelligent approach is used to search for reasonable approximate solution with lesser computational complexity. In literature, Genetic Algorithm (GA) and Swarm Intelligence (SI) have successfully been applied for CR parameter adaptation and to the other combinatorial optimization problems of communication systems [4] [7]. In this paper we apply evolutionary techniques for resource allocation in MU OFDM-based CR system. Simulations results given ahead, show that both the evolutionary techniques Genetic algorithm (GA) and Binary Particle Swarm Optimization (BPSO) provide an efficient solution to the resource allocation problem in multiuser OFDM-based CR system. They maximize the system capacity while adhering to the interference and power constraints. Moreover, from the simulation results it is also
evident that BPSO-based resource allocation algorithm performs better than GA-based allocation method. The rest of this paper is organized as follows. In Section II, the system model is described and the problem of optimizing resource allocation is formulated. In Section III, resource allocation in OFDM systems is briefly discussed. In Section IV, evolutionary techniques for optimal allocation of transmit power, bit and subcarrier in MU OFDM-based CR system are proposed. Simulation results and analysis is given in Section V. Section VI finally concludes the paper. II.
SYSTEM MODEL
We consider a scenario where PU and SU may co-exist in side-by-side bands as assumed in [8]. It is assumed that band occupied by the PU is sensed by the CR system and is of width Wm Hz. The unoccupied bands sensed by CR system for its possible transmission are located on each side of the PU band. The available bandwidth for CR transmission is divided into N OFDM subcarriers, having N/2 subcarriers on each side and each occupying a band width of Δf Hz, as shown in Fig. 1.
2
I m ,n = hbs ,m Pn,k Ts ∫
Δf m ,n +Wm / 2
Δf m ,n −Wm / 2
where
2
⎛ sin π f Ts ⎞⎟ ⎜⎜ ⎟ df ⎜⎝ π f Ts ⎟⎟⎠
(2)
Pn ,k is the transmit power assigned to the nth
subcarrier for the kth secondary user and Ts is the symbol duration , Δfm ,n represents the spectral distance between the nth subcarrier of secondary user band and the mth primary user band. We assume that the transmission power assigned to the kth user at the nth carrier has finite number bs
bs
of levels between 0 and P , where P is the maximum allowable transmission power from BS. The main objective of this resource allocation is to assign the carriers to the users in such a manner that the sum rate capacity of the cognitive radio network is maximized under the interference and power constraints. Let
xn ,k is a binary subcarrier allocation indicator and is
defined as ⎧ ⎪1 if subcarrier n is assigned to user k xn , k = ⎪ ⎨ ⎪ otherwise ⎪ ⎩0
Figure 1. Side-by-side co-existance scenario of primary and secondary users, occupying neighbouring frequency bands.
We consider a downlink scenario in a multiuser OFDMbased CR system in which a CR base station (BS) transmits information to the CRU using radio spectrum which is unoccupied by the PU. For such downlink scenario interference introduced by CRU to PU’s band is the limiting factor, which limits the transmit power as well as the achievable transmission rate of the CRU. There is M=1 primary user, K secondary users and at most N OFDM subcarriers available for these secondary users. Assume a flat fading model and channel gains are known at the transmitters. We denote by f bs , k the fading gain between BS and the kth secondary user and hbs , m the fading gain between BS and the mth primary user (PU). The power spectral density (PSD) of nth subcarrier signal is assumed to have form [8].
The transmit power is adjusted for secondary user’s nth subcarrier with an ideal coding scheme. We denote by N o , the additive white Gaussian noise (AWGN) variance 1 and interference introduced by the PU’s band into OFDM subcarriers is assumed to be zero. The transmission rate at the nth subcarrier (b/s/Hz) for the kth secondary user is defined as
⎛ f bs , k ⎜ log 2 ⎜⎜1 + Pn , k ⎜⎜ No ⎝
2
⎟⎞ ⎟⎟⎟ ⎠⎟
(3)
We formulated the resource optimization problem as integer programming problem K
max
N
∑∑x
n ,k
k =1 n =1
⎛ f bs , k ⎜ log 2 ⎜⎜1 + Pn , k ⎜⎜ No ⎝
2
⎟⎟⎞ ⎟⎟ ⎟⎠
(4)
Subject to: 2
⎛ sin π f Ts ⎞⎟ ⎟ Φn ( f ) = Pn ,k Ts ⎜⎜ ⎜⎝ π f Ts ⎟⎟⎠
K
(1)
∑x
n, k
≤1
∀n = 1,", N
(5)
k =1
Then the interference introduced by the nth subcarrier assigned to kth user in SU band to the mth PU band is the integration of the PSD of the nth subcarrier across the mth primary user band and can be written as
1
The noise is assumed to be generated by a Gaussian process with a known variance. Since the variance of a Gaussian process is equivalent to its power, its conventional to call this variance the noise power.
Pnk ≥ 0, N
∑I
m,n
∀n, k ≤I
m max
(6)
∀ m = 1, ", M
(7)
n=1 K
N
∑∑ P
n,k
≤ P bs
(8)
k =1 n=1
xn ,k ∈ {0,1} ,
∀n, k
(9)
m
Where I max is the maximum tolerable interference (interference temperature) for the mth PU. The first constraint in (5) shows that any given subcarrier can be assigned to at most one user at a time. The third constraint given in (7) is the maximum allowable interference to the primary user, while the fourth constraint in (8) is the maximum transmit power constraint. III.
RESOURCE ALLOCATION IN OFDM
The bit and power loading problem for single-user OFDM systems can be solved by using the well-known water filling algorithm if we assume that the number of bits to be loaded is a real number, or implement a greedy approach that assigns one bit at a time to the subcarrier that requires the least additional power for the integer bit case. To reduce computational complexity for the integer bit case, various low complexity algorithms have been proposed, for both optimal and suboptimal solutions [9]. In the case of the downlink transmission of a BS to multiple users, the subchannels need to be assigned to users exclusively [10]. Therefore, RA involves subchannel assignment in addition to power and bit allocation. When the goal is to maximize system throughput, the problem can be solved in two separate steps [10], namely, assigning each subchannel to the user with the best channel condition, followed by power and bit allocation. When there are QoS or fairness requirements, subchannel, bit, and power allocation becomes more complicated. Since optimal solutions are generally computationally complex, various sub-optimal solutions have been proposed. In [11], suboptimal solution is proposed to minimize the total transmit power while satisfying rate and BER requirements for real-time (RT) services. For non-real-time (NRT) services, maximizing system throughput while guaranteeing a certain level of fairness among users is a reasonable goal [12]. Most of these suboptimal solutions use a divide-and-conquer approach, in which the subcarrier, power, and bit allocation problem is broken down into two steps, i.e., allocate subcarriers to users and load appropriate power and bits to each subcarrier. During the first step, power is often assumed to be the same across all subcarriers so as to simplify the problem.
IV. EVOLUTIONARY TECHNIQUES FOR RESOURCE ALLOCATION IN MU OFDM-BASED CR SYSTEM In a CR system, besides the fading characteristics of wireless communication channels, the available transmission spectrum also changes over time. Resource allocation (RA) algorithms designed for conventional OFDM systems assume that the available spectrum is fixed, which is not the case in CR systems. Thus, in CR systems new RA algorithms are needed that take into account both the fading characteristics of the transmission channel and the timevarying nature of the available spectrum as well as protectively share the spectrum holes without generating undue interference to the PUs. However, the problem of optimal allocation of subcarriers, bits and powers in a multiuser OFDM-based CR system is computationally complex. Therefore, an intelligent approach is used to search for reasonable approximate solution with lesser computational complexity. In literature, Genetic Algorithm (GA) and Swarm Intelligence (SI) have successfully been applied for CR parameter adaptation and to the other combinatorial optimization problems of communication systems [4] [7]. In this work, we formulated resource optimization in OFDM-based CR system as integer programming problem in (4). The main objective of this resource allocation problem is to assign OFDM carriers to users in such a manner that sum rate capacity of the cognitive radio network (CRN) is maximized under the interference and power constraints. An optimal solution to this integer programming problem in (4) is computationally complex thus, not suitable for cognitive radio systems in which channel conditions are constantly changing. Evolutionary techniques proposed for solution of RA optimization problem in multiuser OFDM-based CR system are given below: A. Genetic Algorithm (GA) Genetic algorithms are a class of artificial reasoning whereby the search is performed in a manner similar to genetic evolution. In general, solutions to a problem set are represented by binary strings. These strings then are allowed to act in a manner similar to genetic growth; strings which are considered ‘good’ split and recombine with other good strings to form new solutions, while ‘poorer’ strings are allowed to ‘die’ out of the solution set. This decision is made by the fitness function which inputs the parameters and outputs a score, based on the specific goals of the radio. Strings undergo a process called mutation, that is, a random flipping of bits, to help prevent local minimization from occurring. GAs are typically used as method of problem optimization [13]. Therefore, given its random nature, fast computation time, and ability to spontaneously generate unique solutions, GAs are an appealing candidate for resource allocation in CR systems. Input and output parameters can easily be mapped to a binary form and the size of the genetic population is customizable to space available within any given configuration. GAs are used mainly when the search space is
too large to be simply brute force search to determine the optimal parameter set.
vidt +1 = vidt + c1r1( pidt − xidt ) + c2r2( pgdt − xgdt )
(10)
1 1+
e
(11)
t − vid
The resulting change in position is then defined by the following rule: If r< s (vid ) , then t
vid t
xidt =1; else xidt =0
(12)
The continuous-valued particle swarm algorithm limits by a value Vmax. Whereas, in binary version Vmax is
retained to avoid
s (vidt ) approaching 0 or 1, and a smaller
Vmax allows a higher mutation rate. The fitness function used by BPSO algorithm to converge to optimal solution is (4). BPSO algorithm proceeds as follows: Step 1. Initialize t=0 and randomly generate xid and vid . Step 2. Compute fitness of every particle in the population using fitness function given in (4). Step 3. Update velocity of the particles according to (10). Step 4. Generate random number distributed in [0,1] and update position as per change in position rule described in (12). Step 5. Repeat step 2 and compare particle’s fitness values with its own previous best as well as population’s best and select the greater value. Step 6. Terminate iteration if t= no of predefined iterations; else go to step 3 and repeat. V.
SIMULATION RESULTS AND ANALYSIS
The simulation results present the performance of BPSO and GA algorithms for various scenarios. The number of primary users is set to one. The bands of primary and secondary users are 1MHz each. The channel between BS and secondary users as well as between BS and primary user 40 35
BPSO GA
30 Capacity (b/s/Hz)
B. Binary Particle Swarm Optimization (BPSO) Particle Swarm Optimization (PSO) is population based stochastic optimization technique which is inspired by social behavior of bird flocking or fish school. PSO is distinctly different from other evolutionary-type methods in that it does not use the filtering operation (such as crossover and/or mutation) and the members of the entire population are maintained throughout the search procedure. In PSO algorithm, each member is called “particle” and each particle flies around in the multi-dimensional search space with a velocity, which is constantly updated by the particle’s own experience and the experience of the particle’s neighbors. PSO has a very simple concept, easy to implement and is computationally efficient. Therefore, ever since it is invented by Kennedy [14], it has successfully been applied to a variety of optimization problems [4]. The initially developed continuous PSO was restricted in real number space. However, many real optimization problems which require ordering or rearrange of discrete elements are set in discrete number space e.g. combinatorial problems like scheduling and routing. Therefore, to meet the need Kennedy and Eberhart developed a binary version of PSO, which differs from continuous PSO [15]. In binary space, a particle may be seen to move to nearer and farther corners of the hypercube by flipping various number of bits; thus velocity of the particle overall may be described by number of bits changed per iteration, or hamming distance between particle at time t and at t+1. A particle with zero bits flipped doesn’t move, while it moves the “farthest” by reversing all of its binary coordinates. Using BPSO, potential solution to an optimization problem such as CR parameter optimization is represented as a particle having coordinate xid and rate of change vid in a D-dimensional space. Each particle i maintains a record of its previous best performance in a vector called pid. An iteration comprises evaluation of each particle, then stochastic adjustment of vid in the particle i’s best previous position and the best previous position of any particle in the neighborhood. The variable “g” is assigned the value of the index of the particle with the best performance so far in the neighborhood. The current velocity of the dth bit of the ith particle at a time t+1 is updated as:
s (vidt ) =
25 20 15 10 5
Where, c1 and c2 are acceleration coefficients, and r1and r2 are random numbers uniformly distributed in [0, 1], pid and xid are the integers in {0, 1} and since vid is a probability, it must be constrained to the interval [0.0, 1.0] by using a sigmoid function :
0 -5 10
-4
10
-3
10 Interference Threshold
-2
10
Figure 2. System capacity versus maximum tolerable interference power (Ith Watts), with Pcarrier = 5mW , Ptotal =100 mW, N=16 and K=4.
80
50 45
BPSO GA
70
BPSO GA
40 60 Capacity (b/s/Hz)
Capacity (b/s/Hz)
35 30 25 20
50 40 30
15 20
10 10
5 0 -5 10
-4
10
-3
10 Interference Threshold
Figure 3. System capacity versus maximum tolerable interference power (Ith Watts), with Pcarrier = 10mW , Ptotal =100 mW, N=16 and K=4. 50 45
0 -5 10
-2
10
-3
10 Interference Threshold
-2
10
Figure 5. System capacity versus maximum tolerable interference power (Ith Watts), with Pcarrier = 5mW , Ptotal =500 mW, N=32 and K=6. 120
BPSO GA
BPSO GA 100
40 35
80 Capacity (b/s/Hz)
Capacity (b/s/Hz)
-4
10
30 25 20 15 10
60
40
20
5
-4
10
-3
10 Interference Threshold
0 -5 10
-2
10
Figure 4. System capacity versus maximum tolerable interference power (Ith Watts), with Pcarrier = 15mW , Ptotal =100 mW, N=16 and K=4.
is assumed to be independent, identically distributed Rayleigh random variables. The value of No, is set 10-3 . The parameters for BPSO are, population size=10, c1=c2=2, Vmax +7 to -7, maximum number of iterations =10. Whereas, for GA the population size is 10 with a crossover rate and mutation probability of 0.9 and 0.1 respectively, the maximum number of generation was set to 10. Figures 2, 3 and 4 present the performance of BPSO and GA for a system with 16 subcarriers, 4 secondary users, and 100mW of total power. The carrier power is set to 5mW, 10mW and 15 mW for figures 2, 3 and 4 respectively. The interference threshold is set to 10uW, 100uW, 1mW and 10 mW. The figures depict that the BPSO-based RA method provides higher average system capacity than GA-based method. It is also observe that the gap between these two algorithms increases with increase in the interference threshold level. The figures 5, 6 and 7 present the performance of BPSO and GA for a system with 32 subcarriers, 6 secondary users, and 500mW of total power. The carrier power is set to 5mW, 15mW and 25 mW for figures 5, 6 and 7 respectively.
-4
10
-3
10 Interference Threshold
-2
10
Figure 6. System capacity versus maximum tolerable interference power (Ith Watts), with Pcarrier = 15mW , Ptotal =500 mW, N=32 and K=6. 140 BPSO GA 120
100 Capacity (b/s/Hz)
0 -5 10
80
60
40
20
0 -5 10
-4
10
-3
10 Interference Threshold
-2
10
Figure 7. System capacity versus maximum tolerable interference power (Ith Watts), with Pcarrier = 25mW , Ptotal =500 mW, N=32 and K=6.
The interference threshold is set to 10uW, 100uW, 1mW and 10 mW. These figures also depict that the BPSO-based RA method provides higher average system capacity than
GA-based method. It is also observe that by increasing the subcarriers a higher average system capacity is achieved. VI.
CONCLUSION
Cognitive radio (CR) technology employing dynamic spectrum access (DSA) improves spectrum utilization by exploiting its unused portions and provides a solution to the apparent spectrum scarcity problem. However, fast and efficient resource allocation (RA) algorithms are required to enable secondary users in a multiuser cognitive radio network (CRN) to adapt their transmission parameters to the rapidly changing environment. We formulated resource optimization in OFDM-based CR system as integer programming problem and applied evolutionary techniques for its solution. Simulations results show that proposed evolutionary techniques, genetic algorithm (GA) and binary particle swarm optimization (BPSO) provide an efficient solution for radio resource management (RRM) in multiuser OFDM-based CR system. They maximize the system capacity while adhering to the interference and power constraints. Moreover, from the simulation results it is also evident that BPSO-based RA algorithm performs better and provides higher average system capacity than GA-based method.
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
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