Evolutionary Schemes for Cognitive Radio Adaptation

Muhammad Waheed, Anni Cai Multimedia Communication Center

Beijing University of Posts and Telecommunications Beijing, People Republic of China

rmwaheed@gmail.com

Abstract—Radio parameter adaptation in multicarrier cognitive radio system is a challenging task. The computational complexity of parameter adaptation increases with the number of carriers, power levels and constellation size. In this paper we apply different evolutionary algorithms for cognitive radio parameter adaptation. The effectiveness of the proposed algorithms is evaluated through simulations under different environmental scenarios. Simulations results reveal that swarm family of algorithms outperform genetic algorithm-based adaptation method, towards rapid convergence of multicarrier fitness functions, provide high converged fitness values and can trade off multiple objectives more efficiently.

Keywords- Cognitive radio; multiobjective optimization; evolutionary algorithms.

I. INTRODUCTION In recent years Cognitive Radios (CR) have been proposed

as an approach to alleviate the apparent scarcity of available radio spectrum [1-4]. Since, most of the radio frequency spectrums are inefficiently utilized [3], CR while offering a solution to this scarcity problem, follows dynamic spectrum access policies to make efficient use of radio spectrum and to better accommodate the increasing wireless bandwidth demands. It can intelligently detect whether any portion of the spectrum is in use or not and can temporarily latch into or out of it without interfering with the transmissions of other users and confirming to FCC rules. A high level controller is the central part of such a cognitive radio system that drives its sensing, learning and adaptation process. These three tasks however are both computationally expensive and resource intensive and it is therefore in the cognitive radio’s best interest to minimize the time spent to sense, learn and adapt to its surroundings while still meeting its operational targets.

Hence, cognitive radios are motivated by complexity, heterogeneity and reliability requirements of tomorrow’s networks, which are increasingly expected to be self-organized to meet users and application objectives. Thus, there are several desirable objectives that the cognitive radio system wants to achieve. In Section II, we have focused on cognitive radio adaptation problems and defined three such objectives for multicarrier fitness function. The simple weight vector is used to represent the relative importance of the objective functions in the decision making process. In this framework, CR adaptation process becomes a multiobjective optimization problem so, to simplify the problem, we transform the multiple objective functions into a single multiobjective function. But, real world optimization problems are often so complex and

having huge search space that finding the best solution becomes computationally infeasible. Therefore, an intelligent approach is often used to search for reasonable approximate solution with lesser computational complexity. Many techniques that imitate nature’s own ingenious ways to explore optimal solution for both single and multiobjective optimization problems have been proposed.

In this paper we also apply different evolutionary algorithms for CR parameter adaptation and perform their comparative evaluation to frame a better heuristic solution for CR adaptation problem. We utilize different evolutionary methods to optimize multiple CR objectives for four different modes and plot average fitness function as well as their sample adaptation results, to observe the transmission parameters on which they converge. Simulations results reveal that swarm algorithms outperform genetic algorithm (GA) based adaptation method, towards rapid convergence of multicarrier fitness functions, provide high converged fitness values and can trade off multiple objectives more efficiently. Moreover, binary particle swarm optimization (BPSO) performs even better than binary ant colony (BACO) based adaptation method. It is simple to implement and has smooth convergence.

The remainder of the paper is organized as follows. CR fitness objectives and multiobjective fitness function are given in section II. Section III gives CR parameter adaptation using swarm algorithms. Simulation setup for multicarrier cognitive radio system, its analysis and results are discussed in Section IV. Section V finally concludes the paper.

II. COGNITIVE RADIO A primary feature of Cognitive Radio (CR) is the ability to

adapt to the surrounding environment. CR should not only be capable of adapting to the frequency spectrum being used around it, but also the channel conditions that could possibly prevent it from effectively communicating in the available bandwidth. This paper focuses on the technical issues that exist, once multiple radios are communicating simultaneously and channel problems become the source of communication errors, that is after spectrum assignments have been determined. We have focused on adaptation of radio parameters to the prevailing channel conditions for multicarrier system. Cognitive radio adjustable parameters are denoted as a= [a1, a2,………,an], where n is the number of parameters. Examples of radio adjustable parameters are power, center frequency, modulation type, symbol rate etc.

978-1-4244-3693-4/09/$25.00 ©2009 IEEE

A. Fitness Objectives In order to communicate successfully, CR must balance

multiple objectives and constraints to fit in the specific channel conditions while meeting the user needs as well obeying regulatory requirements [4]. In a wireless communication system there are several desirable objectives that a radio system may want to achieve. This work focuses on three such objectives for the fitness functions, in order to lead the CR system to an optimal state. We denote objective functions which a CR needs to optimize as f = [f1, f2,……..,fm], where m is the number of objective functions. The objective functions are designed to reflect the current link quality [5], examples of which are minimizing transmitting power (power consumption), minimizing bit error rate (BER) and maximizing through put (data rate). Several approaches exist for determining the preference information for a set of objectives [6]. We have used weight vector aggregate sum approach where each objective receives a weight w = [w1, w2,…….,wm], to represent the relative importance of the objective function in the decision making process, where wi denotes the importance of the ith objective function. In this framework, CR adaptation process becomes a multiobjective optimization problem that is how to adjust radio parameters to optimize multiobjective function given the weight vector.

B. Multiobjective Fitness Function The weighted sum approach allows us to develop a single

objective function for each objective and then combine them to create a multiobjective function. Suppose all the objective functions in f = [f1,f2,……..,fm], have been normalized to the range [0,1] then the multiple objective functions can be transformed into a single multiobjective function as:

1

m

i ii

f w f=

= ∑ (1)

Where, iw ≥ 0 (1≤i≤ m) and 11

m

ii

w =

=∑

The simple weighted sum approach differs from the method of the other CR work because we restrict our weight sum to 1. This normalization makes the weighting of the objective more intuitive for both human and cognitive system. Moreover, when using a normalized system there is no ambiguity about how much importance is given to an objective. For a multicarrier system with N subcarriers, the objective functions are given as:

1minmax

1N

iipower

Pf

N p=

− = −×∑ (2)

10min

10

log (0.5)1log ( )

berbe

fp

− = − (3)

2

max2 max

log ( )log ( )

idata rate

MfM

− − = (4)

Where, Pi is the transmit power over subcarrier i, Pmax is the maximum available transmitting power, p be is the average probability of bit error rate (BER) for a given modulation scheme and given channels, Mi the modulation order used in the ith channel and Mmax is the maximum modulation order. Using a gray-code bit assignment and assuming an AWGN channel model, BER of the BPSK and QAM signal constellations can be computed using equations as in reference [7]. And using weighted sum approach the three objective functions are combined into a single multiobjective function as follows:

min min m1 2 3power ber ax dataratef w f w f w f− − −+ += (5)

Hence, the CR adaptation mechanism needs to adjust the parameters to maximize Equation (5).

III. CR ADAPTATION AND SWARM ALGORITHMS There are two popular swarm-inspired methods in

computational intelligence; Ant Colony Optimization (ACO) which is inspired by behavior of ants and Particle Swarm Optimization (PSO).

A. Particle Swarm Optimization (PSO) 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 [8], it has successfully been applied to a variety of optimization problems [9].

B. Binary Particle Swarm Optimization (BPSO) 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 [10]. 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:

11 1 2 2( ) ( )t t t t t t

id id id id gd gdv v c r p x c r p x+ = + − + − (6)

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 :

1

1( )t

tid vids v

e−+

= (7)

The resulting change in position is then defined by the

following rule: If r< ( )t

ids v , then t

idx =1; else t

idx =0. (8)

The continuous-valued particle swarm algorithm limits t

idv by a value Vmax. Whereas, in binary version Vmax is retained to avoid ( )t

ids v 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 equation (5). 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 equation (5) Step 3. Update velocity of the particles according to eqn. (6). Step 4. Generate random number distributed in [0,1] and update position as per change in position rule described in (8). 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.

0 50 100 150 200 250 300 350 400 450 5000.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

Iterations

Avera

ge F

itness F

uncti

on

BPSO

BACO

GA

(a)

0 50 100 150 200 250 300 350 400 450 5000.83

0.84

0.85

0.86

0.87

0.88

0.89

0.9

0.91

0.92

Iterations

Ave

rag

e F

itn

es

s F

un

cti

on

BPSO

BACO

GA

(b)

0 50 100 150 200 250 300 350 400 450 5000.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

Iterations

Avera

ge

Fit

ne

ss

Fu

ncti

on

BPSO

BACO

GA

(c)

0 50 100 150 200 250 300 350 400 450 5000.65

0.7

0.75

0.8

0.85

0.9

0.95

1

Iterations

Av

era

ge F

itness F

uncti

on

BPSO

BACO

GA

(d)

Figure 1. Performance comparison of: BPSO, BACO and GA (a) Mode 1 (b) Mode 2 (c) Mode 3 and (d) Mode 4

IV. SIMULATION ANALYSIS

A. Multicarrier System Design We simulated a multicarrier system with 128 carriers. Each

subcarrier was assigned a random attenuation value which ranges form 0 to 1 to simulate a dynamic channel. Hence, the SNR varied for each channel, inducing a need for adaptation for each individual channel. The modulation types considered in the simulation are BPSK, QPSK, 16QAM and 64QAM. The transmitting power ranges from 0.25mW to 5mW with an increment of 75μW. The noise floor is assumed to be 1μW. So, with 64 possible values for the transmit power and four possible modulation indexes, this gives 256 possible values for each subcarrier. In this case of 128 subcarrier system, it gives a total search space of 21024 , that requires 1024 bits to represent a potential solution.

B. Simulation Results BPSO, BACO and GA were compared by simulation,

targeted to determine the convergence time as well as converged fitness values, using fitness function of equation (5). The parameters for BPSO were: population size=40, c1=c2=2, no of iterations =500. Whereas, parameters for BACO were: cf: [0.3000 0.3500 0.4000 0.6000 0.9900], 0τ = 0.5 (at start),

Hτ = 0.99 Lτ = 0.01, evaporation rate=0.95 i.e. 0.95 0ρ ρ= , where 0 0.5ρ = and the iteration would be terminated after 500 runs. The GA used a 40 chromosome population with a crossover and mutation rate of 0.99 and maximum generation was set to 500. Four different weight settings given in the Table I, were used to test the effectiveness of the proposed methods. Each mode emphasizes different objectives and is appropriate for different situations and applications. Mode 1 emphasizes on minimizing power and it is for applications like text messaging. Mode 2 is for emergency applications like ECG data and Mode 3 is for applications requiring high throughput like broadband video, while Mode 4 has no preference to any specific objective.

TABLE I. WEIGHT SETTINGS

Weights Mode 1 Mode 2 Mode 3 Mode 4

W1 0.80 0.05 0.05 1/3W2 0.15 0.80 0.15 1/3W3 0.05 0.15 0.80 1/3

Ten independent experiments were conducted for each mode using BPSO, BACO and GA respectively. The objective function value of the particle, ant or individual which has the highest fitness value at each iteration was recorded and the resulting average objective function values over 10 simulation runs are shown in Figure 1. These average fitness function plots for four modes are drawn under different weight settings assigned as per Table I. Each scenario consisted of a primary goal with 80 percent weight and two secondary goals with much smaller weight settings. For Mode 1 we have assigned maximum weight of 0.80 to 1w i.e. the weight vector for minimizing power function. High fitness values and convergence of average fitness function shown in Figure 1(a) indicate that the main goal of Mode 1 which is minimizing power is achieved. The other two goals still have an impact on

the optimal parameter set inspite of their small weights. Figures 1(b) and 1(c) show similar information for Mode 2 and Mode 3 where a maximum weight assignment of 80 percent to

2w yields a low average BER while keeping small balance on the objectives of minimizing power and maximizing data rate. Similarly a maximum weight assignment to 3w provides maximum possible data rate to achieve the main goal of Mode 3 i.e. maximum throughput. Although Mode 4 has no preference to any specific objective, the algorithms tend to minimize transmitting power and maximize data rate rather than minimize BER, because the particle, ant or individual, which minimizes transmitting power and maximizes data rate has far higher fitness than the one which only minimizes BER.

20 40 60 80 100 1200

0.5

1

Carrier Index

Att

enuati

on

20 40 60 80 100 1200

5

10

Carrier Index

Num

ber of bit

s

20 40 60 80 100 1200

5

Carrier IndexPow

er Level m

W

Figure 2. BPSO, Transmission parameters for max. throughput mode

20 40 60 80 100 1200

0.5

1

Carrier Index

Att

enuation

20 40 60 80 100 1200

5

10

Carrier Index

Num

ber of

bit

s

20 40 60 80 100 1200

5

Carrier IndexPow

er Level m

W

Figure 3. BACO, Transmission parameters for max. throughput mode

20 40 60 80 100 1200

0.5

1

Carrier Index

Att

enuatio

n

20 40 60 80 100 1200

5

10

Carrier Index

Num

ber o

f bits

20 40 60 80 100 1200

5

Carrier Index

Pow

er L

evel m

W

Figure 4. GA, Transmission parameters for max. throughput mode

Another, important result is the transmission parameter values to which all algorithms converge. We have also plotted snapshots of final decisions after 500 iterations, for aforementioned four different modes and for all the three algorithms we applied. Due to space limitations we present only final decisions plot for maximum throughput mode i.e. Mode 3. The middle window of all the Figures 2, 3 and 4 show bits per symbol for BPSO, BACO and GA respectively. All modulation types in aforementioned figures are optimized to the maximum modulation index used in our simulations i.e. 64QAM, to provide the maximum possible data rate which is 6Mbps, to achieve the main goal of Mode 3. In a similar manner, from the final decision plots for the remaining Modes 1, 2 and 4, we also observed that objectives of respective modes are achieved.

Thus, simulation results for all the modes verify that the fitness functions steer the evolution of the all optimization methods in the correct direction to optimize the given objective for each scenario. Moreover, from the average fitness function and sample adaptation plots of different modes, it is also evident that both swarm algorithms BPSO and BACO outperform GA-based adaptation method in terms of convergence speed and converged fitness values, as well trade off multiple CR objectives more efficiently. Moreover, it is also apparent that binary particle swarm optimization (BPSO) performs even better than ant colony-based adaptation method. It is simple to implement, has more smooth convergence and yields higher fitness values.

V. CONCLUSION In this paper, we applied BPSO, BACO and GA for

parameter adaptation in cognitive radio (CR). We presented cognitive radio adaptation problem in multicarrier system under different environmental conditions and performed computer simulations to evaluate different evolutionary schemes, in order to frame a better heuristic solution for cognitive radio adaptation problem. Simulations results reveal that swarm algorithms outperform genetic algorithm (GA)-

based adaptation method in terms of rapid convergence of multicarrier fitness functions and provide higher converged fitness values. From the fitness function plots it is also evident that binary particle swarm optimization (BPSO) has better performance and smooth convergence than binary ant colony optimization (BACO) and GA. Moreover, BPSO is simple to implement and robust to environmental changes.

REFERENCES [1] Joint Tactical Radio Systems, “Software communications architecture

specification,” November 2002. [2] C.J. Rieser, “Biologically inspired cognitive radio engine model utilizing

distributed genetic algorithms for secure and robust wireless communications and networking,”PhD. Dissertation, April 2004, [Online] Available: http://scholar.lib.vt.edu/theses/available/etd- 10142004-023653/unrestricted/CJRieserVTPhDEEDissertation 101804.pdf [May, 17 2009]

[3] R. Etkin , A. Parekh and D. Tse, “ Spectrum sharing for unlicensed bands,” in IEEE International Symposium on New Frontiers in Dynamic Spectrum Access, 2005, pp. 251–258.

[4] Spectrum Policy Task Force, “Report of the spectrum policy workgroup,” November 2002, [Online] Available: http://hraunfoss.fcc.gov/edocs_public/attachmatch/DOC-228542A1.pdf [May, 19 2009]

[5] T. W. Rondeau, C. J. Rieser and C.W. Bostian, “Cognitive radios with genetic algorithms: intelligent control of software defined radios,” Software Defined Radio Forum Technical Conference, 2004, pp. C3–C8.

[6] C.M. Fonseca and P.J. Fleming, “An overview of evolutionary algorithms in multiobjective optimization,” Evolutionary Computation, 1995, 3(1) 1-16.

[7] J. G. Proakis, Digital Communications (4th edition), McGraw-Hill: New York, 2000.

[8] J. Kennedy and R. C. Eberhart, “Particle swarm optimization,” in Proceedings of IEEE International Conference on Neural Networks, 1995, pp. 1942–1948.

[9] M. F. Taşgetiren and Yun-Chia Liang, “A Binary Particle Swarm Optimization Algorithm for Lot Sizing Problem,” Journal of Economic and Social Research, 5 (2), 1-20.

[10] 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.