INTRODUCTION
Spectrum is one of the most valuable resources for wireless communications
while wide spectral ranges are underutilized. Cognitive radio is a promising
technique for improving the spectrum efficiency by dynamically accessing unoccupied
channels licensed to primary users and vacating the channels when the primary
users active. According to the cognitive loop (Mitola, 2006),
secondary users (cognitive users) need to continuously observe the environment,
be oriented by the objectives of the users and decide upon the transmission
parameters (power, frequency, modulation etc.) to improve the overall efficiency
of the radio communications. Though the principal goal of cognitive radio is
to improve spectrum utilization efficiency at first, Quality of Service (QoS)
requirements such as minimizing the BitErrorRate (BER), maximizing the data
throughput, minimizing the power consumption and so on also need to be considered
when the goal of cognitive radio becomes to improve performance optimization.
Therefore, performance optimization of cognitive radio is a multiobjective
optimization problem.
The problem of optimal allocation of subcarriers, bits and transmission powers
in an OFDMbased cognitive radio system is a NPhard problem as its complexity
grows exponentially with respect to the size of the input. Multicarrier techniques,
such as Orthogonal Frequency Division Multiplexing (OFDM), support huge data
rates that are robust to channel impairments. OFDM is a good modulation candidate
for cognitive radio system due to its flexibility in allocating resources among
secondary users (Weiss and Jondral, 2004). Resources
allocation algorithms for OFDM systems have been well studied (Shen
et al., 2003; Jang and Lee, 2003; Wong
et al., 1999). However, most of these algorithms are designed for
OFDM system in which primary user doesn’t exist. Since in cognitive radio
system both secondary users and primary users may exist in side by side band
and their access technologies may be different, the mutual interference is the
limiting factor for performance of both networks (Weiss
et al., 2004). Only a few studies have considered mutual interference
in resources allocation for OFDMbased cognitive radio systems. The mutual interference
in OFDMbased cognitive radio system has been considered when allocating resources
according to single optimizing objective of maximizing the capacity of cognitive
radio system (Zhao et al., 2008; Zhang
and Leung, 2008; Qin and Leung, 2007). But these
resources allocation algorithms have ignored the secondary user’s QoS requirements.
In this study, we focus on the resources allocation to meet the QoS requirement
of OFDMbased cognitive radio system. We suppose a downlink OFDMbased cognitive
radio scenario, in which subcarriers, bits and power are allocated to meet
the secondary user’s requirements with mutual interference considered.
The resources allocation process is accomplished with multiobjective Genetic
Algorithm (GA). GA is well suited to multidimensional optimization due to the
parallel evolution in many dimensions. At the same time, GA also allows easy
implementation of constraints about the problem (Srinivas
and Patnaik, 1994).
SYSTEM MODEL
We consider the scenario that primary user and secondary user coexist which
is depicted in Fig. 1. It is assumed that the primary user
occupies the spectrum in the middle and the spectrum holes can be used for transmission
to secondary user are located on each side of the licensed band 1.

Fig. 1: 
System model for cognitive radio 
Secondary user employs OFDM modulation scheme and the available frequency
is divided into N subcarriers, N/2 subcarriers on each side. The base station
allocates the transmission power and bits to subcarriers of the secondary user
dynamically. It is assumed that each subcarrier goes under frequency flat fading
and the channel state information is perfectly known at the transmitter.
Multiobjective function: The wireless resources should be allocated according to the objective function. The objectives need to be optimized can be transmission power, bandwidth, BER, throughput, interference etc. These objectives often compete with each other, for example, when maximizing throughput and minimizing power at the same time. Resources allocation optimization requires joint optimization of many objectives. The optimization of the multiple objectives is a Pareto optimal problem. The solutions are tradeoffs between the multiple objectives.
In the user’s QoS requirements, all of above objectives are included.
The relative importance of the objectives depends on the service being used.
For example, service in emergency mode cares most about BER, while service in
multimedia mode cares most about throughput. As a result, BER in emergency mode
service has a bigger weight, while throughput has a bigger weight in multimedia
mode service (Newman et al., 2007) gave the method
using linear weighted sum to represent multiple objectives.
The combination of various kinds of objectives can be used to contribute to different services as below:
in which f_{k} is an objective, the weight of the objective f_{k} is ω_{k}, 0≤ω_{k}≤ω_{k}.
Each objective f_{k} is weighted by its importance and f_{k} is normalized to one. The maximum value of Eq. 1 is 1. According to the user’s QoS requirements, there are several desirable objectives to be achieved. In this study, we mainly consider three objectives: minimizing the power consumed by the system, maximizing the overall data throughput by the radio and minimizing the bit error rate by the radio.
The objective functions are defined as follows (Newman
et al., 2007):
where, P_{n} denotes the transmission power allocated to nth subcarrier, P_{MAX} denotes total secondary user power budget, b_{n} denotes the number of bits allocated to nth subcarrier, M_{MAX} denotes the maximum modulation order, p_{en} denotes the bit error probability in nth subcarrier, is average bit error probability.
From the definition of the objectives we concerned, we can get f_{min_power}≤1, f_{max_throuput}≤1 and f_{min_BER}≤1. The value of these objectives is closer to 1 when the better performance it achieves. We combine the multiple objective functions into a function using the weighted sum approach as below:
subjected to:
in which I_{th} is the primary user’s maximum tolerable interference
power which is given next. According to the multiobjective function in Eq.
7, the resources allocation attempts to meet the user’s QoS requirement
while considering two constraints in Eq. 8 and 9:
(1) a total transmission power constraint for secondary user and (2) a maximum
tolerable interference power which can be tolerated by primary user.
Mutual interference: From the system model depicted above, we assume
that both secondary user and primary user exist in side by side band. There
are interactions between primary user and secondary user due to the nonorthogonality
of their respective signals (Weiss et al., 2004).
Both secondary user and primary user will be influenced by the mutual interference.
The Power Spectral Density (PSD) of the nth subcarrier signal is denoted as:
where, T_{s} is the symbol duration, f_{n} is the intermediate frequency of the nth subcarrier signal.
The interference introduced by nth subcarrier into primary user band is given
as below (Weiss et al., 2004):
where, g_{n} is the nth subcarrier channel gain from base station to the primary user, d_{n} is the spectral distance between the nth subcarrier and the center frequency of the primary user band.
The interference introduced into the nth subcarrier by the signal of primary user is denoted as below:
where, φ_{PU} (e^{jω}) is the PSD of the primary
user signal.
GA BASED RESOURCES ALLOCATION
GA simulates the biology evolution scheme and can be used to solve both constrained
and unconstrained optimization problems (Srinivas and Patnaik,
1994). In GA, basic operations such as encoding, fitness function calculating,
selection, crossover and mutation etc are included.

Fig. 2: 
The
structure of the chromosome 
In encoding, the solutions to a problem are encoded into a chromosome. The
chromosome is represented by binary string. The length of the binary string
is decided by the solutions’ value range and precision needs. A collection
of chromosomes called the population is allowed to act in a manner similar to
genetic growth.
In this study, we generate a population of 100 chromosomes for the experiment. The chromosome is made up of N elements. Each element in the chromosome represents the transmission power and bits allocated to the specific subcarrier, the chromosome can be depicted in Fig. 2.
Fitness function is established based on the specific goals to evaluate the current population and direct the evolution of population. In this study, we use the multiobjective function which is depicted in Eq. 7 as the fitness function in GA. As evaluating the chromosome with the fitness function f, the value of f which is closer to 1 means the allocation is better fulfilling the QoS of the secondary user.
The GA uses three main rules to create a new generation from the current population:
•  Selection:
Select the individual parent chromosomes that have higher scores when
evaluated by fitness function for a new generation 
• 
Crossover: Combine two parent chromosomes to form children 
• 
Mutation: Apply random changes to individual parent chromosomes at random positions
to form children 
This generational cycle repeats until a desired termination criterion is met (For example, a predefined number of generations are processed). The above discussion shows that GA is suitable for the optimization of transmission power and bits allocation in an OFDMbased cognitive radio system. The processing steps are as shown in Fig. 3.
EXPERIMENT RESULTS
Experiment design: In the experiment, we have a primary user and secondary
user with three different services. The band of primary user is 5 MHz and the
bands available for secondary user are on each side of the primary user.

Fig. 3: 
The
block diagram of GA based resources allocation 
Table 1: 
Objective
function weight settings 

The bandwidth of secondary user is also 5 MHz. We divide the secondary user
bands into 16 subcarriers, while each subcarrier takes a bandwidth 312.5 kHz.
The primary user intermediate frequency is 650 MHz and the OFDM symbol duration
is T_{s} = 100 μs. The channel fading is Rayleigh distributed random
with mean of one and the PSD of additive Gaussian noise is 10^{8} W/Hz.
In service 1, power plays an important role, so we set the biggest weight to minimizing power in its objective function. Similarly, we set the biggest weight to the maximizing throughput in its objective function in service 2 in which the throughput is more important. Service 3 belongs to an emergency mode, so we put the biggest weight in minimizing the BER. The weight settings to different services respectively are shown in Table 1.
The number of bits allocated to subcarrier can take 0 bit (no modulation),
2 bits (BPSK), 4 bits (QPSK), 8 bits (8QAM), 16 bits (16QAM), 32 bits (32QAM),
64 bits (64QAM) and 128 bits (128QAM) in this work. The target BER is set to
0.05. We set the GA parameters as follows: crossover parameter is 0.6, mutation
parameter is 0.03, the number of population is 100, the number of generation
is 500. We set the Maximum power transmitted to secondary user is 5 W, the maximum
interference introduced to primary user is 0.01W.

Fig. 4: 
Resources
allocation of service 1 based on GA 
Experiment results: Multiobjective function depicted in Eq.
7 is employed as the fitness function when we allocate resources based on
GA. The fitness functions are different in different services due to different
weight settings which have been described in section 4.1. In the experiment,
resources including transmission power and bits have been allocated for three
kinds of services considering two constraints: total transmission power of secondary
user and maximum tolerable interference power of primary user. Two groups of
figures have been shown.
Figure 46 show the transmission power
and bits allocation of different services based on GA. There are 4 subfigures
in all figures from Fig. 46. The first
subfigure shows the GA converging situation according to the fitness function.
The process for GA converging is an optimization process for transmission parameters
(power and bits) allocation. The convergence happens at about the 200th generation
which shows that GA could quickly find a good solution. It is especially crucial
for a timevariant wireless environment. The fourth subfigure shows the interferences
introduced to the subcarriers by primary user. The second and third subfigure
shows the transmission power and bits allocation at the final generation. Mutual
interference between primary user and secondary user has been considered. From
the figures, we can tell that the interference introduced by primary user influences
the transmission power and bits allocation.

Fig. 5: 
Resources
allocation of service 2 based on GA 

Fig. 6: 
Resources
allocation of service 3 based on GA 
Transmission power and bits allocated to the subcarriers with bigger interference
are smaller. In Fig. 4, we can get that all transmission powers
on the subcarriers are below 0.2 W which means that the requirement of minimizing
transmission power has been met in service 1. Similarly, Fig.
5 and 6 show that the objective of maximizing the throughput
and the objective of minimizing the BER have also been met. The fitness function
directs the evolution of the GA to optimize the given objectives for each service.

Fig. 7: 
Comparison
of the throughput in different services 

Fig. 8: 
Comparison
of total power in different services 

Fig. 9: 
Comparison
of average bit error rate in different services 
Figure 7 shows the comparison of throughput in different
services. The throughputs of different services change as generation grows in
different directions. The throughput of service 2 becomes larger and converges
to a specific high value, while the throughputs of service 1 and service 3 become
smaller and converge to low values. In service 2, the weight of maximizing throughput
in fitness function is much bigger than the weight of minimizing power and the
weight of minimizing BER which means that the primary objective of the service
2 is maximizing the throughput with sacrificing the power and BER. In service
1 and service 3, the weight of maximizing throughput is much smaller that maximizing
throughput is not the most important objective and we can sacrifice it for other
more important objectives. Figure 8 and 9
can give us the similarly situation. We can get the conclusion that the resources
allocation based on GA with multiobjective fitness function can meet the user’s
QoS requirements.
DISCUSSION
The first group of figures shows the resources allocation of different services based on GA. The second group of figures shows the comparison of allocation results in different services.
These experiments on different services prove that GA can be used to optimize the constrained allocation problem and promptly converge to find a good solution. GA based optimization algorithm is competent for cognitive radio system which is a timevariant wireless environment.
The mutual interference influences the resources allocation. More resources (power and bits) are allocated to channels with better channel state in which less mutual interference is introduced by primary user. Mutual interference can not be ignored in OFDMbased cognitive radio system.
Fitness function with a weighted sum of multiple objectives can orient the direction of the evolution of the GA to optimize the resources allocation for each service. After resources allocation with different weighted in multiple objectives, service 1 which is in multimedia mode gains large throughput, service 2 which is in energy shortage mode gains small consuming power and service 3 which is in emergency mode gains small bit error rate. Resources allocation based on GA with multiobjective fitness function can meet the user’s QoS requirements.
CONCLUSION
We have presented the transmission power and bits allocation for OFDMbased cognitive radio system. The allocation of transmission power and bits is restricted to the maximum transmission power and interference tolerance of primary user. Mutual interference between primary user and secondary user influences the transmission power and bits allocation. When the channel state is good, an appropriate power could be loaded to get a good SNR and high order modulation is adopted to reach a big bit rate and vice versa low order modulation is to guarantee the reliability of system if the channel state is bad. Resources allocation algorithm based on GA converges fast enough to adapt to the dynamic wireless environment. The fitness function used to direct the evolution of the GA makes the resources allocation successfully fulfill the QoS requirement of user.
ACKNOWLEDGMENTS
This research was supported by the National Basic Research Program (973 Program) under Grant No. 2009CB320400. The author would like to thank Mr. W. Lin for his assistance in this research.