a game approach for cell selection and resource allocation in heterogeneous wireless networks lin...
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A Game Approach for Cell Selection and A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Resource Allocation in Heterogeneous
Wireless NetworksWireless Networks
Lin Gao, Xinbing Wang
Institute of Wireless Communication Technology (IWCT)
Shanghai Jiao Tong University
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 2
OutlineOutline IntroductionIntroduction
MotivationsMotivations Related worksRelated works ObjectivesObjectives
System Model and Problem FormulationSystem Model and Problem Formulation
Analysis of The Two-tier GameAnalysis of The Two-tier Game
Convergence Algorithm and SimulationConvergence Algorithm and Simulation
ConclusionsConclusions
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 3
MotivationMotivation
The appearance of heterogeneous OFDMA-based wireless access The appearance of heterogeneous OFDMA-based wireless access networks, such as WiMAX, LTE, Wi-Fi, etc.networks, such as WiMAX, LTE, Wi-Fi, etc.
Optimizing the cell selection and resource allocation (CS-RA) Optimizing the cell selection and resource allocation (CS-RA) processes is an important step towards maximizing the utilization of processes is an important step towards maximizing the utilization of current and future heterogeneous wireless networks.current and future heterogeneous wireless networks.
Distributed algorithm shows potential ability in CS-RA problem due to Distributed algorithm shows potential ability in CS-RA problem due to the lacking of global central node in wireless networks.the lacking of global central node in wireless networks.
An example of a An example of a cellular system with cellular system with 3 heterogeneous 3 heterogeneous base stations and 6 base stations and 6 mobile users.mobile users.
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 4
Related works Related works
The goal of cell selection (CS) procedures is to determine a base user to camp The goal of cell selection (CS) procedures is to determine a base user to camp on.on. In [5], Hanly et al. propose a cell selection algorithm to determine power allocation among In [5], Hanly et al. propose a cell selection algorithm to determine power allocation among
different users so as to satisfy per-user SINR constraints.different users so as to satisfy per-user SINR constraints. In [6], Wang et al. study an HSPA based handoff/cell-site selection technique to maximize In [6], Wang et al. study an HSPA based handoff/cell-site selection technique to maximize
the number of connected mobile stations, and propose a new scheduling algorithm to the number of connected mobile stations, and propose a new scheduling algorithm to achieve this objective.achieve this objective.
In [7], Mathar et al. provide an integrated design of optimal cell-site selection and frequency In [7], Mathar et al. provide an integrated design of optimal cell-site selection and frequency allocation, which maximizes the number of connected MSs and meanwhile maintains allocation, which maximizes the number of connected MSs and meanwhile maintains quasi-independence of radio based technology.quasi-independence of radio based technology.
In [8], Amzallag et al. formulate cell selection as an optimization problem called all-or-In [8], Amzallag et al. formulate cell selection as an optimization problem called all-or-nothing demand maximization, and propose two algorithms to achieve approximate optimal nothing demand maximization, and propose two algorithms to achieve approximate optimal solution.solution.
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 5
Related works Related works
The goal of resource allocation (RA) is to determine the radio resource The goal of resource allocation (RA) is to determine the radio resource (including time, frequency and power etc) in a particular cell to a mobile (including time, frequency and power etc) in a particular cell to a mobile user. user.
In OFDMA-based system: In OFDMA-based system: Subchannel-and-power allocation algorithms for multiuser OFDM have been Subchannel-and-power allocation algorithms for multiuser OFDM have been
investigated in [9]-[10] to maximize the overall data rate or minimize the total transmit investigated in [9]-[10] to maximize the overall data rate or minimize the total transmit power.power.
In [9], Wong et al. investigate margin-adaptive resource allocation problem and In [9], Wong et al. investigate margin-adaptive resource allocation problem and propose an iterative subcarrier and power allocation algorithm to minimize total propose an iterative subcarrier and power allocation algorithm to minimize total transmit power given fixed data rates and bit error rate (BER)..transmit power given fixed data rates and bit error rate (BER)..
In [10], Jang et al. investigate rate-adaptive problem and propose a mechanism to In [10], Jang et al. investigate rate-adaptive problem and propose a mechanism to maximize total data rate over all users subjected to power and BER constraints.maximize total data rate over all users subjected to power and BER constraints.
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 6
ObjectivesObjectives
In this paper, we formulate the CS-RA problem as a two-tier In this paper, we formulate the CS-RA problem as a two-tier game, namely inter-cell game and intra-cell game, game, namely inter-cell game and intra-cell game, respectively.respectively. In In inter-cell gameinter-cell game, mobile users select the best cell according to , mobile users select the best cell according to
optimal cell selection strategy derived from expected payoff.optimal cell selection strategy derived from expected payoff. In In intra-cell gameintra-cell game, mobile users choose the proper time-frequency , mobile users choose the proper time-frequency
resource in the serving cell to achieve maximum payoff.resource in the serving cell to achieve maximum payoff.
An illustration of the An illustration of the inter-cell game and inter-cell game and intra-cell game.intra-cell game.
Inter-cell GameInter-cell Game
Intra-cell Intra-cell GameGame
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 7
OutlineOutline IntroductionIntroduction
System Model and Problem FormulationSystem Model and Problem Formulation System ModelSystem Model Problem FormulationProblem Formulation
Analysis of The Two-tier GameAnalysis of The Two-tier Game
Convergence Algorithm and SimulationConvergence Algorithm and Simulation
ConclusionsConclusions
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 8
System Model System Model
A cellular system A cellular system G = (M, N)G = (M, N) with with is the set of is the set of base stations (BSs) and base stations (BSs) and is the set of mobile is the set of mobile users (MSs). Besides, users (MSs). Besides, is the set of sub- is the set of sub-channels in cell channels in cell jj. . 11
Each MS decides which cell it should camp on and which Each MS decides which cell it should camp on and which sub-channels (of the serving cell) it should occupy.sub-channels (of the serving cell) it should occupy.
11 Note : we assume that the cell number in each BS is 1 and thus the meaning of cell is Note : we assume that the cell number in each BS is 1 and thus the meaning of cell is equivalent to BS in this paper.equivalent to BS in this paper.
s2
Sub-channels
s2 s2 s2 s1 s1 s1 s1
8c
s1 s1 s4 s4
7c 6c 5c 4c 3c 2c 1c
a1 a2
s3
s2
s1s4
An example of the An example of the strategy of MS strategy of MS ss11 -- --
selecting cell selecting cell aa22 and and
sub-channels set sub-channels set {{cc1 1 ,c,c2 2 ,c,c3 3 ,c,c4 4 ,c,c7 7 ,c,c88}}..
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 9
System Model System Model
We assume that each sub-channel in a cell can be used by We assume that each sub-channel in a cell can be used by multiple MSs multiple MSs without interferencewithout interference by means of orthogonal by means of orthogonal signals, e.g., separating the MSs in the time-dimension.signals, e.g., separating the MSs in the time-dimension.
We assume that the total available bandwidth on each We assume that the total available bandwidth on each sub-channel is sub-channel is equallyequally shared among the players selecting shared among the players selecting this sub-channel.this sub-channel.
The bandwidth of The bandwidth of cc88 is is
equally shared by equally shared by ss11 and and ss22. .
Accordingly, the power Accordingly, the power consumption by consumption by ss11 ( or ( or ss2 2 ) )
in in cc88 reduces to one half if reduces to one half if
ss11 and and ss22 use the time use the time
orthogonal signals.orthogonal signals.
s2
Sub-channels
s2 s2 s2 s1 s1 s1 s1
8c
s1 s1 s4 s4
7c 6c 5c 4c 3c 2c 1c
a1 a2
s3
s2
s1s4
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 10
System Model System Model
s2
Sub-channels
s2 s2 s2 s1 s1 s1 s1
8c
s1 s1 s4 s4
7c 6c 5c 4c 3c 2c 1c
a1 a2
s3
s2
s1s4
Game ModelGame Model PlayersPlayers : the MSs set : the MSs set U U = {= {1,2,…,N1,2,…,N }.}.
StrategiesStrategies (or actions) of player (or actions) of player u u : (i) selecting a cell, i.e., , (ii) : (i) selecting a cell, i.e., , (ii) selecting a set of sub-channels in the serving cell, i.e., selecting a set of sub-channels in the serving cell, i.e., . .
PayoffPayoff function: defined in latter slide. function: defined in latter slide.
1 1 1
2 2 1
3
4 4 1
1 1 ,
2 1 ,
3 2
4 1 ,
: , = 1,1,1,1,0,0,1,1 ;
: , = 0,0,0,0,1,1,1,1 ;
: ;
: , = 0,0,1,1,0,0,0,0 ;
s s a
s s a
s
s s a
s x a y
s x a y
s x a
s x a y
1 2, , , ,= , ,...,
iu i u c u c u cy Y Y Y
ux
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 11
Problem Formulation Problem Formulation
Key NotationsKey Notations
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 12
Problem Formulation Problem Formulation
The The exclusive-payoffexclusive-payoff of player of player uu in sub-channel in sub-channel cc of cell of cell ii is defined is defined as following:as following:
As As TTcc players occupying sub-channel players occupying sub-channel cc, the bandwidth of , the bandwidth of cc is is
equallyequally shared by shared by TTcc players. Accordingly, the power consumption players. Accordingly, the power consumption
of player of player uu reduce to reduce to PPu,cu,c//TTcc . Hence, the . Hence, the achievedachieved payoffpayoff of player of player uu
in sub-channel in sub-channel cc of cell of cell ii is :is :
,u c
c
U
T
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 13
The The overall-payoffoverall-payoff of player of player uu in cell in cell i i can be written as:can be written as:
wherewhere
Problem Formulation Problem Formulation
, ,1 means player occupying and 0 otherwise.u c u cY u c Y
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 14
Problem Formulation Problem Formulation
, ,
,
,
: Indication of the cell player selected.
: State of player in sub-channel , 1 means player
occupying and 0 otherwise.
: The power of player in sub-channel
u c k u c
u c
u c
i u
Y u c Y u
c Y
P u
.c
The The optimization problemoptimization problem for each player for each player uu ::
wherewhere
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 15
OutlineOutline IntroductionIntroduction
System Model and Problem FormulationSystem Model and Problem Formulation
Analysis of The Two-tier GameAnalysis of The Two-tier Game Optimal Power Allocation Optimal Power Allocation Analysis of Intra-Cell GameAnalysis of Intra-Cell Game Analysis of Inter-Cell GameAnalysis of Inter-Cell Game
Convergence Algorithm and SimulationConvergence Algorithm and Simulation
ConclusionsConclusions
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 16
Analysis of The Two-tier GameAnalysis of The Two-tier Game
We decouple the optimization problem as three sub-We decouple the optimization problem as three sub-problems: power optimization problem, intra-cell game and problems: power optimization problem, intra-cell game and inter-cell game.inter-cell game.
Select cell 1
Player u
The intra-cell game in 1
… …
Find the optimal sub-channel state vector in cell 1
Select cell 2
Find the optimal sub-channel state vector in cell 2
Select cell M
Find the optimal sub-channel state vector in cell M
The inter-cell game
Calculate the optimal power allocation vector Pu,1 Pu,2 …
in all cells
The intra-cell game in 2 The intra-cell game in M
Optimal power allocation
Payoff: Uu,1 Payoff: Uu,2 Payoff: Uu,M
… …
… …
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 17
Optimal Power AllocationOptimal Power Allocation
Optimal Power AllocationOptimal Power Allocation
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 18
Optimal Power Allocation Optimal Power Allocation
s1a3
a2
a1
Channels Gain Channels Gain Channels Gain
Sub-channels Sub-channels Sub-channels
a1 a2 a3
Recall the equation of achieved payoff of player Recall the equation of achieved payoff of player uu in sub- in sub-channel channel cc ::
The information The information player player uu needed for needed for the calculation of the calculation of optimal power optimal power allocation. allocation.
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 19
Optimal Power Allocation Optimal Power Allocation
Lemma 2Lemma 2 : The optimal power allocation for player : The optimal power allocation for player uu in sub- in sub-channel channel cc is: is:
Lagrange EquationLagrange Equation
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 20
Optimal Power Allocation Optimal Power Allocation
The illustration of optimal power allocation and the optimal The illustration of optimal power allocation and the optimal absolute payoff in sub-channels. Note that the optimal absolute payoff in sub-channels. Note that the optimal power is power is independentindependent to to TTcc from Lemma 2. from Lemma 2.
c1 channels
Channels Gain
c2 c3 c4 c5 c6 c7 c8 c9
c1 channels
Optimal Power
c2 c3 c4 c5 c6 c7 c8 c9
Pt
0 c1 channels
Optimal Absolute Payoff
c2 c3 c4 c5 c6 c7 c8 c9
*,u cU
*,u cP
,u ch
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 21
Optimal Power Allocation Optimal Power Allocation
c1 channels
Optimal Absolute Payoff
c2 c3 c4 c5 c6 c7 c8 c9
*,u cU
c1 channels
Player Number
c2 c3 c4 c5 c6 c7 c8 c9
cT
1
23
c1 channels
Optimal Absolute Payoff
c2 c3 c4 c5 c6 c7 c8 c9
Optimal Achieved Payoff*,u cU
The illustration of the optimal achieved payoff in sub-The illustration of the optimal achieved payoff in sub-channels. channels.
*,*
,
u c
u cc
UU
T
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 22
Intra-Cell GameIntra-Cell Game
Intra-Cell GameIntra-Cell Game
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 23
Analysis of Intra-Cell Game Analysis of Intra-Cell Game
The optimal sub-channels state vector for player The optimal sub-channels state vector for player uu, i.e., , i.e., , can be derived as following : , can be derived as following :*
,yu i
An example of the An example of the optimal sub-channels optimal sub-channels state vector for player u state vector for player u with with kku,i u,i =2.=2.
c1 channelsc2 c3 c4 c5 c6 c7 c8 c9
*,u cU
Player u
*,y (0,0,0,0,0,0,1,0,1)u i
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 24
Analysis of Intra-Cell Game Analysis of Intra-Cell Game
Lemma 3Lemma 3 ::22 The best response function for player The best response function for player uu is: is:
wherewhere
,
1 2
: the required subchannel number of player in cell .
{ , ,..., }: permutation of sub-channels according to the
ascending order of .
: the number of players
i
u c
uc
uc
k k u i
T
T
excluding player in sub-channel .u c22 Note : we assume that the average channel gains of different sub-channels are Note : we assume that the average channel gains of different sub-channels are approximately the same. We use this assumption to facilitate the description of Nash approximately the same. We use this assumption to facilitate the description of Nash equilibrium state.equilibrium state.
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 25
Analysis of Intra-Cell Game Analysis of Intra-Cell Game
The meaning of Lemma 3 is thatThe meaning of Lemma 3 is that each player will choose each player will choose
the sub-channels with the sub-channels with leastleast other players occupied.other players occupied.
An example of the An example of the optimal sub-channels optimal sub-channels state vector for player state vector for player uu with with kku,i u,i =2.=2.
c1 channelsc2 c3 c4 c5 c6 c7 c8 c9
1
23
ucT
Number of Players except u
Player u
*,( ) (0,0,0,0,1,0,1,0,0)u iy
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 26
Theorem 1Theorem 1 : A strategy profile: A strategy profile is a is a Nash equilibrium of the intra-cell game (in cell Nash equilibrium of the intra-cell game (in cell ii) iff the ) iff the following conditions hold:following conditions hold:
Analysis of Intra-Cell Game Analysis of Intra-Cell Game
* * * *1, 2, ,{ , ,..., }i i i Ni iy y yY
An example of the Nash An example of the Nash Equilibrium in a cell with Equilibrium in a cell with 9 sub-channels.9 sub-channels.c1 channels
c2 c3 c4 c5 c6 c7 c8 c9
1
23
cT Number of Players
Nash Equilibrium
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 27
Analysis of Intra-Cell Game Analysis of Intra-Cell Game
Property Property : all Nash equilibria sub-channel allocations : all Nash equilibria sub-channel allocations achieve achieve load balancingload balancing over the sub-channels in a cell. over the sub-channels in a cell.
The average of the maximal achieved payoff of player The average of the maximal achieved payoff of player uu in in cell cell ii : :
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 28
Inter-Cell GameInter-Cell Game
Inter-Cell GameInter-Cell Game
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 29
Analysis of Inter-Cell Game Analysis of Inter-Cell Game
The optimal cell for player The optimal cell for player uu, i.e., , can be derived as , i.e., , can be derived as following :following :
*i
*
,
* *, , ,* arg max ,
u i
u i u i u ii
U
i U P y
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 30
Analysis of Inter-Cell Game Analysis of Inter-Cell Game
An example of the optimal cell for player An example of the optimal cell for player ii..
c1 channelsc2 c3 c4 c5 c6 c7 c8 c9
*,1uU
Player u
Optimal payoff in cell 1
c1 channelsc2 c3 c4 c5 c6 c7 c8 c9
Player u
Optimal payoff in cell 2
Cell Index (i)1 2
*,u iU
Player u
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 31
Analysis of Inter-Cell Game Analysis of Inter-Cell Game
can be obtained only when the intra-cell game in cellcan be obtained only when the intra-cell game in cell ii achieves Nash achieves Nash equilibria, which implies that the player equilibria, which implies that the player uu has connected with cell has connected with cell ii. However, the . However, the serving cell serving cell ii is is indirectlyindirectly determined by . This leads to a determined by . This leads to a non-causalnon-causal problem. problem.
Thus we introduce the Thus we introduce the mixed strategymixed strategy of player of player uu as follows: as follows:
wherewhere
*,u iU
*,u iU
1: the probability of player selecting cell , 1.
Mi iu ui
p u i p
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 32
Analysis of Inter-Cell Game Analysis of Inter-Cell Game
1 2 3 4 5 Cells Index (i)
*,u iU
player u
1up
2up
3up
4up
5up
Lemma 4Lemma 4 : The mixed-strategy matrix is a : The mixed-strategy matrix is a mixed-strategy Nash equilibrium if for each player mixed-strategy Nash equilibrium if for each player uu, the , the following conditions hold:following conditions hold:
wherewhere
An example of the An example of the mixed strategy for mixed strategy for player u.player u.
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 33
For simplicity, we consider an example with 2 BSs and 2 MSs. We assume that for For simplicity, we consider an example with 2 BSs and 2 MSs. We assume that for all players. The payoff of two players : all players. The payoff of two players :
wherewhere
Analysis of Inter-Cell Game Analysis of Inter-Cell Game
strategy of player 2
stra
tegy
of
1 ,u i ik
*,, = : The maximum exclusive-payoff of player in cell u iu i iF U u i
MS2
BS2BS1
MS1
F2,2
F1,1
F2,1
F1,2
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 34
Analysis of Inter-Cell Game Analysis of Inter-Cell Game
We denote the mixed strategy of players by The expected We denote the mixed strategy of players by The expected payoff of player payoff of player 11 can be written as: can be written as:
The optimal The optimal pp11, , pp22 and the mixed-strategy Nash equilibria are shown as and the mixed-strategy Nash equilibria are shown as
following :following :
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 35
Analysis of Inter-Cell Game Analysis of Inter-Cell Game
The optimal The optimal pp11, , pp2 2 , , pp33 and the mixed-strategy Nash and the mixed-strategy Nash
equilibria for the cellular system with 2 BSs and 3 MSs are equilibria for the cellular system with 2 BSs and 3 MSs are shown as following:shown as following:
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 36
OutlineOutline IntroductionIntroduction
System Model and Problem FormulationSystem Model and Problem Formulation
Analysis of The Two-tier GameAnalysis of The Two-tier Game
Convergence Algorithm and SimulationConvergence Algorithm and Simulation Convergence algorithmConvergence algorithm Simulation Results Simulation Results
ConclusionsConclusions
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 37
Convergence algorithm Convergence algorithm
To apply the algorithm in practical system, the following To apply the algorithm in practical system, the following three essential assumptions are necessary.three essential assumptions are necessary. First, we assume that each MS has ability to initiate inter-frequency First, we assume that each MS has ability to initiate inter-frequency
measurement, from which each MS can measure the average sub-measurement, from which each MS can measure the average sub-channels gain.channels gain.
Second, we assume that each cell periodically broadcasts the Second, we assume that each cell periodically broadcasts the number of MSs connecting with this cell.number of MSs connecting with this cell.
Third, we assume that each cell counts the load on each sub-Third, we assume that each cell counts the load on each sub-channel and multicast to all MSs connecting with him.channel and multicast to all MSs connecting with him.
CS-Algorithm CS-Algorithm : converge to the inter-cell game Nash : converge to the inter-cell game Nash equilibrium.equilibrium.
RA-Algorithm RA-Algorithm : converge to the intra-cell game Nash : converge to the intra-cell game Nash equilibrium.equilibrium.
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 38
CS-AlgorithmCS-Algorithm The basic idea of the CS-algorithm :The basic idea of the CS-algorithm :
Problem 1Problem 1: mixed strategy of one player can : mixed strategy of one player can notnot be observed by other players, which makes the calculation of expected be observed by other players, which makes the calculation of expected payoff impractical.payoff impractical.
Problem 2Problem 2: the mixed strategy : the mixed strategy zzuu will will degeneratedegenerate to the pure strategy due to the to the pure strategy due to the non-smoothnon-smooth characteristic of best response characteristic of best response
functions.functions.
Convergence algorithm Convergence algorithm
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 39
Convergence algorithm Convergence algorithm
Solution of problem 1Solution of problem 1 Lemma 5Lemma 5 : The expected payoff of player : The expected payoff of player uu is equivalent to is equivalent to Qu Qu defining as defining as
follows:follows:
wherewhere
,
*,
: The probability of players (excluding player itself) in cell .
( 1) : The average of the maximal achieved payoff of player
in cell if there exists
i r
u i
r u i
U r u
i
E
other players in cell .r i
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 40
Solution of problem 2Solution of problem 2 To overcome the degeneration problem, we introduce the To overcome the degeneration problem, we introduce the
smoothedsmoothed best response functions : best response functions :
Convergence algorithm Convergence algorithm
1 2( , ,..., )Mu u u uz p p p
The illustration of The illustration of standard best response standard best response and smoothed best and smoothed best response functions.response functions.1
2p
1
0
1p Standard Best Response
Smoothed Best Response with small
Smoothed Best Response with large
2p
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 41
Convergence algorithm Convergence algorithm
The detail pseudo-code ofThe detail pseudo-code of CS-Algorithm CS-Algorithm
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 42
Convergence algorithm Convergence algorithm
RA-AlgorithmRA-Algorithm
The basic idea of the RA-algorithm : The basic idea of the RA-algorithm : Greedy occupationGreedy occupation
Problem 1Problem 1: the unstable sub-channel allocations caused by simultaneously moving of : the unstable sub-channel allocations caused by simultaneously moving of different players,different players,
Solution of Problem 1Solution of Problem 1: the technique of : the technique of backoffbackoff mechanism. mechanism.
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 43
Convergence algorithm Convergence algorithm
The detail pseudo-code ofThe detail pseudo-code of RA-Algorithm RA-Algorithm
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 44
Simulation results Simulation results
The cell selection interval: The cell selection interval: The minimal scheduling interval:The minimal scheduling interval: The number of cells: The number of cells: The number of MSs: The number of MSs: The number of sub-channels in each cell The number of sub-channels in each cell ii:: Channel model: free-space propagation Channel model: free-space propagation
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 45
Simulation results Simulation results
Convergence of RA-algorithm (in a given cell)Convergence of RA-algorithm (in a given cell)
Variance Ratio always Variance Ratio always equals to 1 for any Nash equals to 1 for any Nash EquilibriumEquilibrium
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 46
Simulation results Simulation results
Expectation of maximum acquired-subchannel-number of Expectation of maximum acquired-subchannel-number of players 1 to 15players 1 to 15
Red: estimation results Red: estimation results according to Eq. (27)according to Eq. (27)
Blue: simulation resultsBlue: simulation results
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 47
Simulation results Simulation results
CLPDF learned by player 1CLPDF learned by player 1
Dash: analytical resultsDash: analytical results
Bar: learning resultsBar: learning results
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 48
Simulation results Simulation results
Convergence of CS-algorithm Convergence of CS-algorithm
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 49
Simulation results Simulation results
Impacts of Price and DCR on Mixed-strategy Nash Impacts of Price and DCR on Mixed-strategy Nash equilibrium in the inter-cell gameequilibrium in the inter-cell game
Fig. 2: Increasing price of BS2 Fig. 2: Increasing price of BS2 Reduce the load of BS 2Reduce the load of BS 2
Fig. 3: Increasing bandwidth of BS3 Fig. 3: Increasing bandwidth of BS3 Increase the load of BS 3 Increase the load of BS 3
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 50
OutlineOutline IntroductionIntroduction
System Model and Problem FormulationSystem Model and Problem Formulation
Analysis of The Two-tier GameAnalysis of The Two-tier Game
Convergence Algorithm and SimulationConvergence Algorithm and Simulation
ConclusionsConclusions ConclusionsConclusions
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 51
ConclusionsConclusions In this paper, We propose a distributed cell selection and resource In this paper, We propose a distributed cell selection and resource
allocation mechanism, in which the CS-RA processes are performed allocation mechanism, in which the CS-RA processes are performed by the mobile user independently.by the mobile user independently.
We formulate the problem as a two-tier game named as inter-cell We formulate the problem as a two-tier game named as inter-cell game and intra-cell game, respectively. We study the two-tier game game and intra-cell game, respectively. We study the two-tier game in details and analyze the existence and property of the Nash in details and analyze the existence and property of the Nash equilibria of the proposed games.equilibria of the proposed games.
We analyze the structure of Nash equilibria and find some We analyze the structure of Nash equilibria and find some interesting properties: interesting properties: load balance, load regulating, connecting load balance, load regulating, connecting directingdirecting etc. etc.
Thank you !Thank you !
A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 53
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