Cooperative Precoding/Resource Allocation Games under Spectral Mask and Total Power Constraints

The use of orthogonal signaling schemes such as time-, frequency-, or code-division multiplexing (T-, F-, CDM) in multi-user systems allows for power-efficient simple receivers. It is shown in this paper that by using orthogonal signaling on frequency selective fading channels, the cooperative Nash bargaining (NB)-based precoding games for multi-user systems, which aim at maximizing the information rates of all users, are simplified to the corresponding cooperative resource allocation games. The latter provides additional practically desired simplifications to transmitter design and significantly reduces the overhead during user cooperation. The complexity of the corresponding precoding/resource allocation games, however, depends on the constraints imposed on the users. If only spectral mask constraints are present, the corresponding cooperative NB problem can be formulated as a convex optimization problem and solved efficiently in a distributed manner using dual decomposition based algorithm. However, the NB problem is non-convex if total power constraints are also imposed on the users. In this case, the complexity associate with finding the NB solution is unacceptably high. Therefore, the multi-user systems are categorized into bandwidth- and power-dominant based on a bottleneck resource, and different manners of cooperation are developed for each type of systems for the case of two-users. Such classification guarantees that the solution obtained in each case is Pareto-optimal and actually can be identical to the optimal solution, while the complexity is significantly reduced. Simulation results demonstrate the efficiency of the proposed cooperative precoding/resource allocation strategies and the reduced complexity of the proposed algorithms.Comment: 33 pages, 8 figures, Submitted to the IEEE Trans. Signal Processing in Oct. 200

Cross-layer distributed power control: A repeated games formulation to improve the sum energy-efficiency

The main objective of this work is to improve the energy-efficiency (EE) of a multiple access channel (MAC) system, through power control, in a distributed manner. In contrast with many existing works on energy-efficient power control, which ignore the possible presence of a queue at the transmitter, we consider a new generalized cross-layer EE metric. This approach is relevant when the transmitters have a non-zero energy cost even when the radiated power is zero and takes into account the presence of a finite packet buffer and packet arrival at the transmitter. As the Nash equilibrium (NE) is an energy-inefficient solution, the present work aims at overcoming this deficit by improving the global energy-efficiency. Indeed, as the considered system has multiple agencies each with their own interest, the performance metric reflecting the individual interest of each decision maker is the global energy-efficiency defined then as the sum over individual energy-efficiencies. Repeated games (RG) are investigated through the study of two dynamic games (finite RG and discounted RG), whose equilibrium is defined when introducing a new operating point (OP), Pareto-dominating the NE and relying only on individual channel state information (CSI). Accordingly, closed-form expressions of the minimum number of stages of the game for finite RG (FRG) and the maximum discount factor of the discounted RG (DRG) were established. The cross-layer model in the RG formulation leads to achieving a shorter minimum number of stages in the FRG even for higher number of users. In addition, the social welfare (sum of utilities) in the DRG decreases slightly with the cross-layer model when the number of users increases while it is reduced considerably with the Goodman model. Finally, we show that in real systems with random packet arrivals, the cross-layer power control algorithm outperforms the Goodman algorithm.Comment: 36 pages, single column draft forma

Distributed Multicell Beamforming Design Approaching Pareto Boundary with Max-Min Fairness

This paper addresses coordinated downlink beamforming optimization in multicell time-division duplex (TDD) systems where a small number of parameters are exchanged between cells but with no data sharing. With the goal to reach the point on the Pareto boundary with max-min rate fairness, we first develop a two-step centralized optimization algorithm to design the joint beamforming vectors. This algorithm can achieve a further sum-rate improvement over the max-min optimal performance, and is shown to guarantee max-min Pareto optimality for scenarios with two base stations (BSs) each serving a single user. To realize a distributed solution with limited intercell communication, we then propose an iterative algorithm by exploiting an approximate uplink-downlink duality, in which only a small number of positive scalars are shared between cells in each iteration. Simulation results show that the proposed distributed solution achieves a fairness rate performance close to the centralized algorithm while it has a better sum-rate performance, and demonstrates a better tradeoff between sum-rate and fairness than the Nash Bargaining solution especially at high signal-to-noise ratio.Comment: 8 figures. To Appear in IEEE Trans. Wireless Communications, 201

Game Theory and Microeconomic Theory for Beamforming Design in Multiple-Input Single-Output Interference Channels

In interference-limited wireless networks, interference management techniques are important in order to improve the performance of the systems. Given that spectrum and energy are scarce resources in these networks, techniques that exploit the resources efficiently are desired. We consider a set of base stations operating concurrently in the same spectral band. Each base station is equipped with multiple antennas and transmits data to a single-antenna mobile user. This setting corresponds to the multiple-input single-output (MISO) interference channel (IFC). The receivers are assumed to treat interference signals as noise. Moreover, each transmitter is assumed to know the channels between itself and all receivers perfectly. We study the conflict between the transmitter-receiver pairs (links) using models from game theory and microeconomic theory. These models provide solutions to resource allocation problems which in our case correspond to the joint beamforming design at the transmitters. Our interest lies in solutions that are Pareto optimal. Pareto optimality ensures that it is not further possible to improve the performance of any link without reducing the performance of another link. Strategic games in game theory determine the noncooperative choice of strategies of the players. The outcome of a strategic game is a Nash equilibrium. While the Nash equilibrium in the MISO IFC is generally not efficient, we characterize the necessary null-shaping constraints on the strategy space of each transmitter such that the Nash equilibrium outcome is Pareto optimal. An arbitrator is involved in this setting which dictates the constraints at each transmitter. In contrast to strategic games, coalitional games provide cooperative solutions between the players. We study cooperation between the links via coalitional games without transferable utility. Cooperative beamforming schemes considered are either zero forcing transmission or Wiener filter precoding. We characterize the necessary and sufficient conditions under which the core of the coalitional game with zero forcing transmission is not empty. The core solution concept specifies the strategies with which all players have the incentive to cooperate jointly in a grand coalition. While the core only considers the formation of the grand coalition, coalition formation games study coalition dynamics. We utilize a coalition formation algorithm, called merge-and-split, to determine stable link grouping. Numerical results show that while in the low signal-to-noise ratio (SNR) regime noncooperation between the links is efficient, at high SNR all links benefit in forming a grand coalition. Coalition formation shows its significance in the mid SNR regime where subset link cooperation provides joint performance gains. We use the models of exchange and competitive market from microeconomic theory to determine Pareto optimal equilibria in the two-user MISO IFC. In the exchange model, the links are represented as consumers that can trade goods within themselves. The goods in our setting correspond to the parameters of the beamforming vectors necessary to achieve all Pareto optimal points in the utility region. We utilize the conflict representation of the consumers in the Edgeworth box, a graphical tool that depicts the allocation of the goods for the two consumers, to provide closed-form solution to all Pareto optimal outcomes. The exchange equilibria are a subset of the points on the Pareto boundary at which both consumers achieve larger utility then at the Nash equilibrium. We propose a decentralized bargaining process between the consumers which starts at the Nash equilibrium and ends at an outcome arbitrarily close to an exchange equilibrium. The design of the bargaining process relies on a systematic study of the allocations in the Edgeworth box. In comparison to the exchange model, a competitive market additionally defines prices for the goods. The equilibrium in this economy is called Walrasian and corresponds to the prices that equate the demand to the supply of goods. We calculate the unique Walrasian equilibrium and propose a coordination process that is realized by the arbitrator which distributes the Walrasian prices to the consumers. The consumers then calculate in a decentralized manner their optimal demand corresponding to beamforming vectors that achieve the Walrasian equilibrium. This outcome is Pareto optimal and lies in the set of exchange equilibria. In this thesis, based on the game theoretic and microeconomic models, efficient beamforming strategies are proposed that jointly improve the performance of the systems. The gained results are applicable in interference-limited wireless networks requiring either coordination from the arbitrator or direct cooperation between the transmitters

A Game-Theoretic View of the Interference Channel: Impact of Coordination and Bargaining

This work considers coordination and bargaining between two selfish users over a Gaussian interference channel. The usual information theoretic approach assumes full cooperation among users for codebook and rate selection. In the scenario investigated here, each user is willing to coordinate its actions only when an incentive exists and benefits of cooperation are fairly allocated. The users are first allowed to negotiate for the use of a simple Han-Kobayashi type scheme with fixed power split. Conditions for which users have incentives to cooperate are identified. Then, two different approaches are used to solve the associated bargaining problem. First, the Nash Bargaining Solution (NBS) is used as a tool to get fair information rates and the operating point is obtained as a result of an optimization problem. Next, a dynamic alternating-offer bargaining game (AOBG) from bargaining theory is introduced to model the bargaining process and the rates resulting from negotiation are characterized. The relationship between the NBS and the equilibrium outcome of the AOBG is studied and factors that may affect the bargaining outcome are discussed. Finally, under certain high signal-to-noise ratio regimes, the bargaining problem for the generalized degrees of freedom is studied.Comment: 43 pages, 11 figures, to appear on Special Issue of the IEEE Transactions on Information Theory on Interference Networks, 201