494 research outputs found
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
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