Cognitive Radio (CR) has very promising potential to improve spectrum utilization by allowing unlicensed Secondary Users (SUs) to access the spectrum dynamically without disturbing licensed Primary Users (PUs). Mitigating interference is a fundamental problem in CR scenarios. This is particularly problematic for deploying CR in cellular networks, when users are located at the cell edge, as the intercell interference mitigation and frequency reuse are critical requirements for both PUs and SUs. Further cellular networks require higher cell edge performance, then SUs will meet more challenges than PUs. To solve the performance decrease for SUs at the cell edge, a novel Dynamic Spectrum Allocation (DSA) scheme based on Game Theory is proposed in this paper. Full frequency reuse can be realized as well as intercell interference mitigated according to SUs’ sensing, measurement and interaction in this scheme. A joint power/channel allocation algorithm is proposed to improve both celledge user experience and network performance through distributed pricing calculation and exchange based on game theory. Analytical proof is presented and simulation results show that the proposed scheme achieves high efficiency of spectrum usage and improvement of cell edge SUs’ performance.
1. Introduction
T
oday, spectrum is one of the most valuable natural resource. In order to utilize spectrum fully, Dynamic Spectrum Allocation (DSA) is a promising approach to increase efficiency for wireless networks. The approach has attracted a great deal of attention and has been widely researched
[1]
[2]
. A key technology of the approach is cognitive radio (CR)
[3]
[4]
, which provides unlicensed users capability of sharing the wireless channels with licensed users in an negotiated or opportunistic manner. It is realized by SUs’ sensing the“idle” channels. There are varying sensing methods for SUs such as energy detection and matchedfiltering sensing. After sensing, the data of channels are used for channel selection by SUs. And then, the SUs decide to grant access or not. However, the same channel could be used by a PU or SU simultaneously due to limited range of detection and frequency reuse. As a result, interferences between PUs and SUs might be occurred. An important interference is the intercell interference. In order to mitigate the interference and improve spectrum efficiency, it is necessary to improve the DSA algorithm.
Traditionally, a networkwide spectrum assignment is carried out by a central server. Recently, distributed spectrum allocation approaches have been studied to share spectrum efficiently that is based on solely on local observations. In
[5]
, the research challenges of spectrum management in cognitive radio networks are introduced. In
[6]
[7]
, game theory approaches are presented to deploy DSA. In
[8]
, Markov models are used for DSA. Graph coloring methods are proposed in
[9]
. This work mostly focuses on ad hoc scenarios, but seldom refers to cellular networks.
Because of complex channel characteristics and interference in multiuser cellular networks, DSA is more difficult to design as it is constrained by intercell interference mitigation considerations and frequency reuse requirements. Also, future cellular networks require a higher number of cell edge users throughput
[10]
. In order to improve cell edge performance as well as suppress intercell interference, dynamic frequency allocation schemes have been proposed, such as Soft Frequency Reuse (SFR)
[11]
and Fractional Frequency Reuse (FFR)
[12]
. In these schemes, celledge users can only use part of the total frequency bands, thereby reducing the intercell interference and improving cell edge data rate. However, it comes at a cost of bandwidth reduction.
 1.1 Related works
In this paper, we focus on the scenario where SUs with cognition ability coexist with PUs and SUs share channels in the cell edge, which is shown in
Fig. 1
. The PUs are licensed to access the cellular network, and SUs continuously sense the channels and exploit spectrum “holes” for their transmissions, then access the network as unlicensed users.
System scenarios in Cognitive Radio Networks
There are some previous work address here. The reference
[13]
assumed that SUs’ transmissions do not interfere with each other, i.e., only one SU can operate over a given channel in a given neighborhood. Consequently, there is no spectrum sharing among SUs. Such schemes limit the number of access users, especially when the number of channels is small. Makki and Eriksson introduced the an interference indicator signal, which can get further potential benefits for data transmission of SUs. The ergodic achievable rates of CR based spectrum sharing networks are also researched. And this paper didn’t implement the standard intercell interference avoiding methods, which proposed that the SU’s activity is not restricted within the PU’s inactive periods
[14]
. The reference
[15

16]
researched on the cognitve radio networks with Relay scenario and cooperative communication techniques implemented scenario separately. The spectrum sharing performances are evaluated with different service types. But the interferenceds for SUs at the cell edge are not involved.
Considering cochannel scenarios in cell edge, we allow multiple SUs in adjacent cell edges to share a particular channel in our work to improve frequency utilization. After sensing a spectrum opportunity, SUs will measure the signaltointerference plus noise ratio (SINR) and then determine whether they are cell edge users according to predefined threshold. If SUs are cell edge users, they need to share channels with other cell edge SUs using the same channels. Interference is measured and interference information is exchanged to mitigate intercell interference and improve spectrum utilization.
 1.2 Contributions
In this article, we propose a game theory based DSA scheme to formulate the interactions and achievable utilities of cell edge SUs. The main contributions of this article are summrized as follows.

1) The proposed utility function is defined to measure the reward SUs received from the network. SUs on the edge of cells cooperatively and competitively share the channels to maximize their own utilities. A userdependent pricing function is presented and SUs exchange their pricings to indicate the “cost” of relative interferences.

2) We also propose a pricebased iterative algorithm, in which we derive the userdependent water filling levels according to the SU’s pricings to achieve locally optimal Nash Equilibrium (NE) and mitigate interference after iterations. Such a pricing function can be determined by allowing each SU to cooperatively acquire its neighborhood information via signaling exchanges with a small group of neighborhood SUs.

3)The SUstoSUs and SUstoPUs interference are treated respectively through setting corresponding protection factors to futher reduce SUstoPUs interference.
Based on the analytical proof and simulation results, the proposed joint power/channel allocation algorithm can effectively improve both celledge user experiences and network performances.
The remainder of the paper is organized as follows: the system model is described in section 2. In section 3, the improved DSA scheme is formulated and analyzed based on the game theroy. Performance evaluation results are provided in section 4. Section 5 concludes the paper.
2. System Model
We assume that a cellular network consists of PUs and SUs. PUs are licensed users, who have priority to access the network. SUs are unlicensed users and work on unutilized spectrum temporally.
In this paper, the total spectrum contains
K
orthogonal frequency subchannels, which are shared by all the users, including the PUs and SUs. In other words, one subchannel cannot be occupied by different users at the same time in the same cell. But for the multicell environments, the adjacent cell users could be allocated with the same subchannels, which may cause the resource collisions and intercell interferences.
N
= {1,2,…,
N
}, K = {1,2,…,
K
} and B = {
B
_{1}
,
B
_{2}
,…,
B_{N}
} denote the sets of SUs, channels and Base Stations (BS), respectively. The main differences of the obtained information for the PUs and SUs come from that PUs have the right for licensed spectrum access and also the channel state information, interference information from neighbor cells on the channels they allocated. The SUs need to carry on the spectrum sensing for available spectrums, which will leads to information loss of above signaling exchanges in the actual network.
For simplify the analytical scenario, we assume that each SU has the ability to sense the spectrum hole exactly and measure interference over all channels.
denotes the total noiseplusinterference level SU
i
measures over channel
k
. This value includes the PUtoSU interference, the SUtoSU interference and the thermal noise.
, which is used by SU
i
to perform channel selection, power control and rate allocation.
We assume that the interferences between cell center SUs can be ignored and no interaction is needed. Because when the users located in the cell center, the interferences actually can be alleviated by two ways, which are the transmission power control/allocation policy and the relatively further distances from adjacent base stations. According to the definition of “cell edge” by the 3GPP, the 5% tile cell throughput CDF will be the cell edge user performance. In this article, the differences of the user received signals strength from the neighboring base stations will be the criteria of cell edge and cell center. If the differences of the user received signal strength are big than the threshold, the user will be regarded as the cell center. And vice versa, the users are regarded as the cell edge users. The criteria are also associated with the frequency reuse strategy.
The transmission power vector of an SU
i
in
B_{i}
over all channels is denoted as
where
is the transmission power of SU
i
over channel
k
. If channel
k
belongs to SU
i
,
> 0 ; otherwise
= 0.
To ensure available spectrum sharing and consider practical deployment, we impose the following constraints:

1) Maximum transmission power constraints: The total transmission power of an SU over all the selected channels should not exceedPmax, i.e.,, where Fidenotes the set of utilized channels of SUi. Here, we assume that the total power constraint is the same for all users. It is easy to extend the treatment to the case wherePmaxis userdependent.

2) Power mask constraints: The transmission power of SUion channelkshould fulfill≤, whereis the power mask on channelk. The power mask is often specified by a radio management agent, e.g., the Federal Communications Commission (FCC). However, because the number of SUs that share a given channel varies in time and space, it is impractical to define an independent power mask. We use the vectorto denote the power mask on all channels.
SUs are assumed to be either static or be moving slowly compared to the convergence time of the resource assignment algorithm. In addition, SUs are homogeneous, meaning that they follow the same operation rules and have the same system constraints.
3. DSA Scheme Simulation
In a CR network, each SU is interested in maximizing its own achievable rate. Such selfserving behavior can be modeled using game theory. Game theory analyzes the interactions of players in decisionmaking processes. Based on the aforementioned system model, a game can be formulated as follows: The players in this game are the SUs
N
= {1,2,⋯,
N
}, the strategy of each player is the transmission power vector , i.e., the strategy of SU
i
is denoted by
. The payoff of SU
i
is the utility function
U_{i}^{Bi}
, which depends on the strategies of all players. The solution of the game is the NE.
 3.1 Utility Function
In this game, the utility function of SU
^{i}
can be defined as the reward received by this SU from the network. This reward should depend on this SU’s action
P
_{i}^{Bi}
and the set of all other SUs’ action
. The basic principle of defining a utility function is to characterize and resolve practical problems. A natural selection of the utility function of an SU
i
is its transmission rate, which is taken as the channel capacity. SUs select their transmission powers to maximize their own utility functions, and under certain conditions, they eventually reach an NE after several iterations. Because of the noncooperative nature of the game, each SU behaves selfishly. Thus the resulting NE may be far from the Pareto optimum
[17]
. To drive the NE towards the Pareto optimum boundary, we exploit a pricing function to coerce SUs into working in a cooperative manner. The utility function is shown as follows:
Where
denotes the channel gain between SU
i
and BS
B_{i}
over channel
k
,
N_{i,k}
is the background noise over channel
k
,
I_{k}^{PR}
denotes the PUtoSU interference, while
η
is a protection factor, given as:
It has the implication that the PUtoSU interference and SUtoPU interference are relevant (e.g., in a Time Division Duplex (TDD) system, they can be considered the same),
η
gives the PU priority to avoid being severely interfered with by SUs, where
B_{i}^{Adjacent}
is
B_{i}
's adjacent BSs.
denotes the pricing factor of an SU
i
on channel
k
. In this paper, we define userdependent pricing corresponding to different interference degrees and driving SUs to converge to efficient NE. In addition, this utility function is specialized for the uplink, When used in the downlink the interfering SUs’ channel gain
should be transformed to
, which denotes the channel gain between interference BS to SU
i
. The same is with other terms in the discussion.
Considering the priority of different SUs may be different, we define a weighted sum of all utilities for all SUs, shown as follows:
s.t.
where
ω_{i}
denotes the weight assigned to SU
i
, which can be explained in different ways (e.g., priority of SU
i
). Based on the above utility definition and optimization objectives with corresponding constraints, the QoS of SUs will be guaranteed.
 3.2 Pricing function
Pricing is an idea originating from economic, and always used to improve the efficiency of a NE
[18]
as well as mitigate interference
[19]
. Although an “optimal” pricing function may exist that allows the NE to converge to a Paretooptimum solution, the search for such a pricing function generally requires global information and is difficult to implement. In this paper, we propose a userdependent pricing function, which requires neighborhood interference information. Through pricing calculation and interaction, it can improve the NE and suppress interference among SUs.
We derive a linear pricing function by introducing the Lagrangian function for (3) satisfying KarushKuhnTucker (KKT) necessary conditions
[6]
[19]
. The pricing factor of SU
i
is shown as follows:
From the above pricing function, we can conclude that a higher pricing factor
will prevent an SU
i
from using a large transmission power on channel
k
. In order to get an optimal pricing function, an SU
i
should obtain the transmission power
, the measured interference plus noise
and the channel gain
of its neighbor
j
on channel
k
, so cooperation is required between SUs. The information can be exchanged through control signaling in a broadcast.
 3.3 Game analysis and algorithm
From the aforementioned propositions, the players, strategy and playoffs are all specifically defined. By definition, the NE of a game is a strategy profile with the property that no player can increase his payoff by choosing a different action, given other players’ actions. In this case, the NE is obtained by using the best response function which is the most advantageous strategy of player given others’ strategies. The best response function of SU
i
is given as:
The set
denotes the NE of this game on power if and only if
, where
denotes the set of the best response of player
j
for
j
≠
i
.
In view of the above, it is indicative that this is a strictly convex optimization problem with bounds on individual variables. The optimal solution
can be derived by the method of Lagrange multipliers, for solving the problem of conditional extreme values. Specifically, without considering the priority of different SUs, this sequential algorithm is described as follows:
maximize
s.t.
If there’s a solution to the game, it would be one that will achieve the NE. The following proposition shows that an NE solution always exists for the above game.
Proposition: For any given and values, there is at least one NE solution for (6).
Proof: The game in our setup can be shown to be a concave game if the following two properties are satisfied:

1) the action space is a closed and bounded convex set;

2) the utility function is concave over its strategy set.
It is straightforward to show that the two properties are satisfied by the game. Because a concave game always admits at least one NE
[20]
, the proposition follows immediately.
Thus, (6) is a convex problem and it can be solved by the way of Lagrange multipliers. Then the Lagrangian of (6) is given by
where
. Accordingly,
are the Lagrange multipliers,
y_{i}
and
γ_{i}
are nonnegative real numbers, and
z
is real number.
In order to solve the optimization problem and obtain the NE, we have to solve the following set of equations
∂L
/
∂x_{i}
for all SUs mathematically. This is depicted as follows:
Substituting Eq. (7) into (8), we get
In addition, for the optimum solution of
u_{i}^{Bi}
(
x_{i}
), we have to determine the value of those Lagrange multipliers. They are depicted as follows:
Using Eqs. (7), (10), (11) and (12), we get the value of
and
z
. Substituting Eq. (1) and these values into Eq. (9), then
where
, and
x_{i}^{*}
is just the NE of the game.
Furthermore, substituting Eq. (13) into (1), we get the maximum value of
for SU
i
on the channel
k
, which is the optimum solution of the problem. That is,
Finally, substituting Eq. (14) into (5), we arrive at the best response function of SU
i
on the channel
k
, referring to Eq. (15).
According to real scenarios, by treating other SUs’ transmission as interference, the best response of SU
i
on channel
k
is given as follows:
where
, with
b
>
a
, denotes the Euclidean projection of
x
in the interval [
a
,
b
], i.e.,
=
a
if
x
>
a
,
=
x
if
a
<
x
<
b
, and
=
b
if
x
>
b
.
λ
denotes the fixed water level, which is constrained by the total transmission power.
contributes a userdependent water level, which is ultimately determined by the interference SU
i
and its neighbors measured together. This userdependent variable water level improves the efficiency of power allocation and spectrum utilization.
We exploit a classical iterative algorithm to reach the NE. It can be generalized as follows:
The convergence condition can be predefined as the maximum circle time
Loop
_{max}
or the terminating criteria (
P
_{i}^{Bi(j)}

P
_{i}
^{Bi(j1)}
/
P
_{i}
^{Bi(j1)}
) ≤
ε
, where
ε
is a small value(e.g., 5%).
4. Performance Evaluation
 4.1 Parameter Setting
In this section, we evaluate the performance of the proposed DSA scheme. We simulate this scheme in a multiuser cellular network with the specific parameter settings list as
Table 1
. There are 27 cells depolyed with Hexagonal grid. The parameters are in line with LTE requirement. Path loss and shadowing are both taken into account. Because the time scale of resource allocation is longer than that of fast fading, so it is reasonable to average the effect of fast fading. The interference model is mainly based on the LTE multicell scenario with homogeneous network deployment. The schemes compared are the SFR and FFR schemes introduced in the introduction and related works.
Simulation Parameters and Setting
Simulation Parameters and Setting
 4.2 Simulation Results
The simulation results are shown with the
Fig. 2
to
Fig. 5
.
Fig. 2
shows that the cell throughput of the DSA scheme is always larger than SFR and FFR schemes with different Frequency Reuse Factor (FRF). That is because the full frequency reuse leads to a more accessible frequency in cell edge under interference and total power constraints.
Fig. 2
also shows that the improvement of a DSA scheme is relatively large when the user number is moderate, while it is relatively small when the user number is very small or large. The reason is that the celledge accessible frequency is sufficient with a small user number in SFR and FFR schemes, producing slight interference and leading to a high transmission rate. While, when the user number is large, the interference is severe, limiting the performance of the DSA scheme. This takes into account the mutual interference of SUs as pricings. Comparing these following simulation results, it’s obviously that the cell throughput decreases along with FRF. It results from the higher FRF, and means more available frequency in the cell center, which has a better channel quality and can produce higher throughput.
Cell Throughput with different FRF
Fig. 3
shows that the celledge average transmission rate of a DSA scheme is always better than SFR and FFR schemes with different FRF, because of the full frequency reuse and the interference information interactions of SUs in cell edge.
Fig. 3
also shows that the improvement decreases as the user number increases, due to the interference worsening with more access users. Obviously, the average data bits increase as FRF decreases. Because smaller FRF leads to more available frequency in the cell edge.
Celledge Average transmission rate with different FRF
Fig. 4
shows the CDF curves of users’ throughput of the three schemes with FRF=8/9. We can see that the DSA scheme is always better than SFR and FFR schemes, because the object of the proposed DSA scheme is to maximize the throughput of each SU in a cell edge.With the enhancement of the performance of the edge users, the whole network is encouraged.
CDF of users’ throughput with FRF=8/9
Fig. 5
shows the outage of users of a DSA scheme is always larger than SFR and FFR schemes with FRF=8/9, because the object of the DSA scheme is to maximize the utility of SUs. By the way of userdependent water filling, users with better performance will be allocated higher power. As a result, the outage is higher than SFR and FFR schemes.
Fig. 5
also shows that the outage of a DSA scheme increases at first but then decreases. This is consequent to the feature of the water filling algorithm, which is stated above.
Outage of users with FRF=8/9
5. Conclusion
In this paper, a game theory based DSA scheme specialized for cellular network cell edge SUs is proposed, in which full frequency reuse is realized and intercell interference is mitigated according to SUs’ sensing, measurement and interaction. We define a utility function to maximize the transmission rate under the interference and total power constraints. A userdependent pricing function is designed. We also propose a joint power/channel allocation algorithm that improves celledge user experience and network performance through setting userdependent water filling levels relevant to userdependent pricings. We compare it with SFR and FFR schemes. Simulation results show that the proposed scheme outperforms existing SFR and FFR schemes on cell throughput and celledge average data bits. The DSA scheme obviously improves celledge performance, spectrum utilization and spectrum efficiency.
BIO
SungJin JANG is a Ph.D., Faculty of Department of Electronic Communication in the Daelim University College, Gyeonggido Korea. His research interests focus on Delay Tolerant Network, Performance Analysis of SCTP Protocol, Cognitive Radio Network, Ubiquitous Tagging.
Jongbae Kim is a Ph.D., professor in the Graduate School of Software, Soongsil University, Seoul, Korea. His research interests focus on Software Engineering, and Open Source Software.
Jungwon Byun is a Ph.D. from Soongsil University, Seoul, Korea. His research interests focus on Software Engineering, Requirements Engineering, Usability Analysis, and Open Source Software.
Yongtae Shin is a Ph.D., professor in the School of Computer Science and Engineering, Soongsil University, Seoul, Korea. His research interests focus on Multicast, IoT, Information Security, Content Security, Mobile Internet, Next Generation Internet.
Hooli K.
2005
“D6.3 WINNER Spectrum Aspects: Assessment Report”
IST WINNER
IST2003507581 WINNER
Article (CrossRef Link)
2003
DARPA XG WG, The XG Architectural Framework V1.0
Article (CrossRef Link)
Mitola J.
,
Maguire G.Q.
1999
“Cognitive radio: making software radios more personal”
IEEE Personal Commun
Article (CrossRef Link)
6
(4)
13 
18
DOI : 10.1109/98.788210
Hykin Simon
2005
“Cognitive radio brainempowered wireless communications”
IEEE J. Sel. Areas Commun.
Article (CrossRef Link)
23
(2)
201 
220
DOI : 10.1109/JSAC.2004.839380
Akyildiz I.F.
,
Lee WonYeol
,
Vuran M.C.
,
Mohanty S.
2008
“A survey on spectrum management in cognitive radio networks”
IEEE Commun. Magazine
Article (CrossRef Link)
46
(4)
40 
48
DOI : 10.1109/MCOM.2008.4481339
Wang Fan
,
Krunz M.
,
Cui Shuguang
2008
“PriceBased Spectrum Management in Cognitive Radio Networks”
IEEE J. Sel. Topics Sig. Proc.
Article (CrossRef Link)
2
(1)
74 
87
DOI : 10.1109/JSTSP.2007.914877
Niyato D.
,
Hossain E.
2007
“A GameTheoretic Approach to Competitive Spectrum Sharing in Cognitive Radio Networks”
IEEE WCNC
March
Article (CrossRef Link)
16 
20
Xing Yiping
,
Chandramouli R.
2006
“Dynamic spectrum access in open spectrum wireless networks”
IEEE J. Sel. Areas Commun
Article (CrossRef Link)
24
(3)
626 
637
DOI : 10.1109/JSAC.2005.862415
Wang Wei
,
Liu Xin
2005
“Listcoloring based channel allocation for openspectrum wireless networks”
VTC 2005 Fall
Sept.
Vol. 1, Article (CrossRef Link)
690 
694
2008
3GPP TR 36.913, Requirements for Further Advancements for EUTRA
Article (CrossRef Link)
3GPP R1050507, Soft Frequency Reuse Scheme for UTRAN LTE, Huawei
Article (CrossRef Link)
3GPP R1050896, Description and simulations of interference management technique for OFDMA based EUTRA downlink evaluation
QUALCOMM Europe
Article (CrossRef Link)
Shu T.
,
Cui S.
,
Krunz M.
2006
“Medium access control for multichannel parallel transmission in cognitive radio networks”
IEEE GLOBECOM
Nov.
Article (CrossRef Link)
Makki B.
,
Eriksson T.
2012
“On the Ergodic Achievable Rates of Spectrum Sharing Networks with Finite Backlogged Primary Users and an Interference Indicator Signal”
IEEE Trans. on Wireless Commun.
Article (CrossRef Link)
11
(9)
3079 
3089
DOI : 10.1109/TWC.2012.071612.110447
Chen D.
,
Ji H.
,
Leung V. C. M.
2012
“Distributed BestRelay Selection for Improving TCP Performance Over Cognitive Radio Networks: A CrossLayer Design Approach”
IEEE J. on Sel. Areas in Commun.
Article (CrossRef Link)
30
(2)
315 
322
DOI : 10.1109/JSAC.2012.120210
Si P.
,
Yu F. R.
,
Ji H.
,
Leung V. C. M.
2010
“Optimal Cooperative Internetwork Spectrum Sharing for Cognitive Radio Systems with Spectrum Pooling”
IEEE Trans. on Veh. Tech.
Article (CrossRef Link)
59
(4)
1760 
1768
DOI : 10.1109/TVT.2010.2041941
Fudenberg D.
,
Tirole J.
1991
Game Theory
The MIT Press
Cambridge, Massachusetts
Article (CrossRef Link)
Ji Zhu
,
Liu K.J.R
2008
“MultiStage Pricing Game for CollusionResistant Dynamic Spectrum Allocation”
IEEE J. Sel. Areas Commun
Article (CrossRef Link)
26
(1)
182 
191
DOI : 10.1109/JSAC.2008.080116
Huang Jianwei
,
Berry R.A.
,
Honig M.L.
2006
“Distributed interference compensation for wireless networks”
IEEE J. Sel. Areas Commun
Article (CrossRef Link)
24
(5)
1074 
1084
DOI : 10.1109/JSAC.2006.872889
Rosen J. B.
1965
“Existence and uniqueness of equilibrium points for concave Nperson games”
Econometrica
Article (CrossRef Link)
33
(3)
520 
534
DOI : 10.2307/1911749