Appendix 2.A Assumptions for Stochastic Approximation
6.4 Game-theoretic Model
6.6.2 Capacity performance
Capacity under unilateral deviation
In Fig. 6.5 we have shown that unilateral deviation leads to decreased utility. While the altruistic utility function design reduces the mutual interference, we are also interest
1 2 3 4 5 6 7 8 9 10
Figure 6.8: Test of unilateral deviation from the resulting strategy profile of each of the 10 players.
in the performance of Nash equilibrium strategy in terms of the throughput of each cluster as well as the whole system. Therefore, in Fig. 6.8 we test the change on capacity under unilateral deviation from the NE strategy for all players. As depicted in Fig. 6.8(a), there is no significant change on the average capacity per sensor link when only one player unilaterally deviates from its NE strategy. From Fig. 6.8(b) we observe that for all players, deviation from NE strategy decreases their own capacity.
Comparison with Other Methods
We further compare the performance of the proposed channel selection scheme with two other approaches, namely, random allocation and exhaustive search, described as follows:
• In the random allocation scheme, each cluster head randomly selects a channel for its sensor node in each frame. Neither learning algorithm nor centralized controller is implemented.
Table 6.4: Comparison of the capacity and fairness for different channel assignment schemes
Number of SUs Proposed Exhaustive Random active ratio = 25%, Ravg 6.0426 6.2433 4.7912 active ratio = 25%, J 0.9370 0.8512 0.9516 active ratio = 50%, Ravg 4.8375 4.9454 4.0955 active ratio = 50%, J 0.8855 0.8235 0.9056
• In the exhaustive search scheme, it is assumed that there exists a centralized con-troller which knows all system information including the channel gains, the channel availability statistics, and the number of clusters. The channel assignment profile is determined by maximizing the expected sum capacity (i.e., solving (6.8)).
The performance of different channel selection schemes are evaluated by the average capacity per sensor node, Ravg = N1 ∑N
i=1Ri and the fairness among sensor nodes. In the literature, fairness of resource allocation is usually quantified by the Jain’s fairness index (JFI) [45], which is defined as
J = (∑N
i=1Ri)2 N∑N
i=1R2i. (6.17)
The value of JFI falls in the interval of [1/N, 1], and a higher JFI value indicates better fairness.
The simulation results of average capacity and JFI for different active ratios are sum-marized in Table 6.4. We observe that the exhaustive search method results in the best average capacity with worst fairness. The random selection scheme, in contrast, has the lowest average capacity but good fairness due to its randomness nature. The proposed method performs well balanced in terms of both average capacity and fairness. The res-ults show the advantages of the proposed method: through the learning procedure toward equilibrium, the capacity of each player is considered and fewer players are sacrificed.
If we examine the final channel selection profile, it is observed that in the progress of convergence toward the NE point, the proposed learning algorithm allocates the mutually interfered users on different channels.
6.7 Concluding Remarks
In this work, we studied the problem of self-organized channel assignment in dis-tributed two-tier networks with unknown channel and unknown number of clusters. We presented a game-theoretic approach to distributively manage interference and enable the coexistence of sensor and macrocell operations in a scenario where secondary nodes oper-ate in the same spectrum as a cellular system. We modeled channel assignment problem by means of an ordinal potential game. A decentralized stochastic learning algorithm has been proposed. Simulation results have demonstrated the convergence of the algorithm toward a pure strategy Nash equilibrium with sufficiently small learning rates. The pro-posed method outperforms the random selection scheme in terms of average capacity, while the performance loss compared to the exhaustive search is limited. In addition, its fairness level is comparable to that of the random selection, and surpasses the exhaustive search scheme.
Chapter 7
Distributed Channel Allocation in Network MIMO
The cooperative frequency reuse among base stations (BSs) can improve the system spectral efficiency by reducing the intercell interference (ICI) through channel selection and precoding. This chapter presents a game-theoretic study of channel selection for realizing network multiple-input multiple-output (MIMO) operation under time-varying wireless channel. We propose a new joint precoding scheme that carries enhanced inter-ference mitigation and capacity improvement abilities for network MIMO systems. We formulate the channel selection problem as a non-cooperative game with BSs as the play-ers, and show that our game is an exact potential game (EPG) given the proposed utility function. A decentralized, stochastic learning-based algorithm is proposed where each BS progressively moves toward the Nash equilibrium (NE) strategy based on its action-reward history and not actions taken by others. The convergence properties of the proposed learn-ing algorithm toward a pure-strategy NE point are theoretically shown and numerically verified for different network topologies. The proposed learning algorithm also demon-strates a fine capacity and fairness performance as compared to other schemes through extensive link-level simulations.
7.1 Introduction
U
niversal frequency reuse is a key technique to improve the throughput of broad-band wireless networks. However, frequency reuse among neighboring cells in-evitably results in intercell interference (ICI) and degrades the achievable throughput performance. To overcome this problem, ICI management techniques such as ICI co-ordination (ICIC) and base-station cooperation (BSC) have been proposed [65, 66]. BSC, also known as network multiple-input multiple-output (MIMO), is a multi-antenna signal processing technique that enables several nearby BSs to jointly serve multiple mobile sta-tions (MSs). The implementation of network MIMO may require a partial or full sharing of channel state information (CSI) and data among the BSs.Much of the research on network MIMO and multicell cooperation has focused on sig-nal processing techniques in an orthogosig-nal frequency-division multiple access (OFDMA) system. The channel assignment for each MS is generally assumed determined or treated separately from the network MIMO mechanism. Efficient channel allocation (particularly in a distributed manner) for network MIMO in a multi-antenna multicell environment has not yet been extensively studied. The aim of this work is therefore to study the distrib-uted channel allocation problem in network MIMO systems. We adopt a game-theoretic approach and incorporate reinforcement learning procedures into the proposed channel selection game where each player (i.e., the BS) can act (i.e., perform channel selection) without explicitly knowing other players’ actions and the forms of utility functions. The main contributions of this work are as follows:
• We propose a novel joint processing scheme where an MS is jointly served by a set of selected BSs. The capacity advantages of the proposed scheme over conventional precoding methods are numerically demonstrated.
• We formulate the channel allocation problem as a non-cooperative game and show the existence of Nash equilibrium (NE). A stochastic learning (SL)-based algorithm is developed to achieve self-organized channel allocation. The convergence
beha-viors of the proposed algorithm toward an NE point are theoretically proven and numerically verified for different network topologies.
The rest of the chapter is organized as follows. In Section 7.2, we review related works on precoding in multicell multi-antenna networks as well as those on distributed resource allocation. In Section 7.3, the system model and the proposed joint processing are described. The game-theoretic formulation of the channel allocation problem is presented in Section 7.4 and the SL-based solutions are presented in Section 7.5. Numerical results are provided in Section 7.6. Conclusion is given in Section 7.7.