A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless 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 Outline Introduction  Motivations  Related works  Objectives System Model and Problem Formulation Analysis of The Two-tier Game Convergence Algorithm and Simulation Conclusions

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 3 Motivation  The appearance of heterogeneous OFDMA-based wireless access networks, such as WiMAX, LTE, Wi-Fi, etc.  Optimizing the cell selection and resource allocation (CS-RA) processes is an important step towards maximizing the utilization of current and future heterogeneous wireless networks.  Distributed algorithm shows potential ability in CS-RA problem due to the lacking of global central node in wireless networks. An example of a cellular system with 3 heterogeneous base stations and 6 mobile users.

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 4 Related works  The goal of cell selection (CS) procedures is to determine a base user to camp on.  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.  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 achieve this objective.  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 quasi-independence of radio based technology.  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 solution.

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 5 Related works  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 user.  In OFDMA-based system:  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 power.  In [9], Wong et al. investigate margin-adaptive resource allocation problem and propose an iterative subcarrier and power allocation algorithm to minimize total 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 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 Objectives  In this paper, we formulate the CS-RA problem as a two- tier game, namely inter-cell game and intra-cell game, respectively.  In inter-cell game, mobile users select the best cell according to optimal cell selection strategy derived from expected payoff.  In intra-cell game, mobile users choose the proper time-frequency resource in the serving cell to achieve maximum payoff. An illustration of the inter-cell game and intra-cell game. Inter-cell Game Intra-cell Game

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 7 Outline Introduction System Model and Problem Formulation  System Model  Problem Formulation Analysis of The Two-tier Game Convergence Algorithm and Simulation Conclusions

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 8 System Model  A cellular system G = (M, N) with is the set of base stations (BSs) and is the set of mobile users (MSs). Besides, is the set of sub- channels in cell j. 1  Each MS decides which cell it should camp on and which sub-channels (of the serving cell) it should occupy. 1 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. An example of the strategy of MS s 1 -- selecting cell a 2 and sub-channels set {c 1,c 2,c 3,c 4,c 7,c 8 }.

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 9 System Model  We assume that each sub-channel in a cell can be used by multiple MSs without interference by means of orthogonal signals, e.g., separating the MSs in the time-dimension.  We assume that the total available bandwidth on each sub-channel is equally shared among the players selecting this sub-channel. The bandwidth of c 8 is equally shared by s 1 and s 2. Accordingly, the power consumption by s 1 ( or s 2 ) in c 8 reduces to one half if s 1 and s 2 use the time orthogonal signals.

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 10 System Model  Game Model  Players : the MSs set U = {1,2,…,N }.  Strategies (or actions) of player u : (i) selecting a cell, i.e.,, (ii) selecting a set of sub-channels in the serving cell, i.e.,.  Payoff function: defined in latter slide.

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 11 Problem Formulation  Key Notations

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 12 Problem Formulation  The exclusive-payoff of player u in sub-channel c of cell i is defined as following:  As T c players occupying sub-channel c, the bandwidth of c is equally shared by T c players. Accordingly, the power consumption of player u reduce to P u,c /T c. Hence, the achieved payoff of player u in sub-channel c of cell i is :

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 13  The overall-payoff of player u in cell i can be written as: where Problem Formulation

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 14 Problem Formulation  The optimization problem for each player u : where

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 15 Outline Introduction System Model and Problem Formulation Analysis of The Two-tier Game  Optimal Power Allocation  Analysis of Intra-Cell Game  Analysis of Inter-Cell Game Convergence Algorithm and Simulation Conclusions

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 16 Analysis of The Two-tier Game  We decouple the optimization problem as three sub- problems: power optimization problem, intra-cell game and inter-cell game.

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 17 Optimal Power Allocation

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 18 Optimal Power Allocation  Recall the equation of achieved payoff of player u in sub- channel c : The information player u needed for the calculation of optimal power allocation.

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 19 Optimal Power Allocation  Lemma 2 : The optimal power allocation for player u in sub-channel c is: Lagrange Equation

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 20 Optimal Power Allocation  The illustration of optimal power allocation and the optimal absolute payoff in sub-channels. Note that the optimal power is independent to T c from Lemma 2.

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 21 Optimal Power Allocation  The illustration of the optimal achieved payoff in sub- channels.

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 22 Intra-Cell Game

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 23 Analysis of Intra-Cell Game  The optimal sub-channels state vector for player u, i.e.,, can be derived as following : An example of the optimal sub-channels state vector for player u with k u,i =2.

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 24 Analysis of Intra-Cell Game  Lemma 3 : 2 The best response function for player u is: where 2 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 equilibrium state.

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 25 Analysis of Intra-Cell Game  The meaning of Lemma 3 is that each player will choose the sub-channels with least other players occupied. An example of the optimal sub-channels state vector for player u with k u,i =2.

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 26  Theorem 1 : A strategy profile is a Nash equilibrium of the intra-cell game (in cell i ) iff the following conditions hold: Analysis of Intra-Cell Game An example of the Nash Equilibrium in a cell with 9 sub-channels.

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 27 Analysis of Intra-Cell Game  Property : all Nash equilibria sub-channel allocations achieve load balancing over the sub-channels in a cell.  The average of the maximal achieved payoff of player u in cell i :

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 28 Inter-Cell Game

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 29 Analysis of Inter-Cell Game  The optimal cell for player u, i.e.,, can be derived as following :

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 30 Analysis of Inter-Cell Game  An example of the optimal cell for player i.

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 31 Analysis of Inter-Cell Game  can be obtained only when the intra-cell game in cell i achieves Nash equilibria, which implies that the player u has connected with cell i. However, the serving cell i is indirectly determined by. This leads to a non-causal problem.  Thus we introduce the mixed strategy of player u as follows: where

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 32 Analysis of Inter-Cell Game  Lemma 4 : The mixed-strategy matrix is a mixed-strategy Nash equilibrium if for each player u, the following conditions hold: where An example of the mixed strategy for 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 all players. The payoff of two players : where Analysis of Inter-Cell Game

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 34 Analysis of Inter-Cell Game  We denote the mixed strategy of players by The expected payoff of player 1 can be written as:  The optimal p 1, p 2 and the mixed-strategy Nash equilibria are shown as following :

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 35 Analysis of Inter-Cell Game  The optimal p 1, p 2, p 3 and the mixed-strategy Nash equilibria for the cellular system with 2 BSs and 3 MSs are shown as following:

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 36 Outline Introduction System Model and Problem Formulation Analysis of The Two-tier Game Convergence Algorithm and Simulation  Convergence algorithm  Simulation Results Conclusions

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 37 Convergence algorithm  To apply the algorithm in practical system, the following three essential assumptions are necessary.  First, we assume that each MS has ability to initiate inter-frequency measurement, from which each MS can measure the average sub- channels gain.  Second, we assume that each cell periodically broadcasts the number of MSs connecting with this cell.  Third, we assume that each cell counts the load on each sub- channel and multicast to all MSs connecting with him.  CS-Algorithm : converge to the inter-cell game Nash equilibrium.  RA-Algorithm : converge to the intra-cell game Nash equilibrium.

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 38  CS-Algorithm  The basic idea of the CS-algorithm :  Problem 1: mixed strategy of one player can not be observed by other players, which makes the calculation of expected payoff impractical.  Problem 2: the mixed strategy z u will degenerate to the pure strategy due to the non-smooth characteristic of best response functions. Convergence algorithm

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 39 Convergence algorithm  Solution of problem 1  Lemma 5 : The expected payoff of player u is equivalent to Qu defining as follows: where

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 40  Solution of problem 2  To overcome the degeneration problem, we introduce the smoothed best response functions : Convergence algorithm The illustration of standard best response and smoothed best response functions.

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 41 Convergence algorithm  The detail pseudo-code of CS-Algorithm

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 42 Convergence algorithm  RA-Algorithm  The basic idea of the RA-algorithm : Greedy occupation  Problem 1: the unstable sub-channel allocations caused by simultaneously moving of different players,  Solution of Problem 1: the technique of backoff mechanism.

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 43 Convergence algorithm  The detail pseudo-code of RA-Algorithm

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 44 Simulation results  The cell selection interval:  The minimal scheduling interval:  The number of cells:  The number of MSs:  The number of sub-channels in each cell i:  Channel model: free-space propagation

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 45 Simulation results  Convergence of RA-algorithm (in a given cell) Variance Ratio always equals to 1 for any Nash Equilibrium

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 46 Simulation results  Expectation of maximum acquired-subchannel-number of players 1 to 15 Red: estimation results according to Eq. (27) Blue: simulation results

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 47 Simulation results  CLPDF learned by player 1 Dash: analytical results Bar: learning results

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 48 Simulation results  Convergence of CS-algorithm

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 49 Simulation results  Impacts of Price and DCR on Mixed-strategy Nash equilibrium in the inter-cell game Fig. 2: Increasing price of BS2  Reduce the load of BS 2 Fig. 3: Increasing bandwidth of BS3  Increase the load of BS 3

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 50 Outline Introduction System Model and Problem Formulation Analysis of The Two-tier Game Convergence Algorithm and Simulation Conclusions  Conclusions

A Game Approach for Cell Selection and Resource Allocation in Heterogeneous Wireless Networks 51 Conclusions  In this paper, We propose a distributed cell selection and resource allocation mechanism, in which the CS-RA processes are performed by the mobile user independently.  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 in details and analyze the existence and property of the Nash equilibria of the proposed games.  We analyze the structure of Nash equilibria and find some interesting properties: load balance, load regulating, connecting directing etc.

Thank you !

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