text: A scalable framework is developed to allocate radio resources across a large number of densely deployed small cells with given traffic statistics on a slow timescale. Joint user association and spectrum allocation is first formulated as a convex optimization problem by dividing the spectrum among all possible transmission patterns of active access points (APs). To improve scalability with the number of APs, the problem is reformulated using local patterns of interfering APs. To maintain global consistency among local patterns, inter-cluster interaction is characterized as hyper-edges in a hyper-graph with nodes corresponding to neighborhoods of APs. A scalable solution is obtained by iteratively solving a convex optimization problem for bandwidth allocation with reduced complexity and constructing a global spectrum allocation using hyper-graph coloring. Numerical results demonstrate the proposed solution for a network with 100 APs and several hundred user equipments. For a given quality of service (QoS), the proposed scheme can increase the network capacity several fold compared to assigning each user to the strongest AP with full-spectrum reuse.
  @cite_14: We consider distributed power control in a multicell wireless data system and study the effect of pricing transmit power. Drawing on the earlier work of Goodman and Mandayam (see IEEE Personal Commun. Mag., vol.7, p.48-54, 2000), we formulate the QoS of a data user via a utility function measured in bits per Joule. We consider distributed power control, modeled as a noncooperative game, where users maximize their utilities in a multicell system. Base station assignment based on received signal strength as well as received signal-to-interference ratio (SIR) are considered jointly with power control. Our results indicate that for both assignment schemes, such a procedure results in an inefficient operating point (Nash equilibrium) for the entire system. We introduce pricing of transmit power as a mechanism for influencing data user behavior and our results show that the distributed power control based on maximizing the net utility (utility minus the price) results in improving the Pareto efficiency of the resulting operating point. Variations of pricing based on global and local loading in cells are considered as a means of improving the efficiency of wireless data networks. Finally, we discuss the improvement in utilities through a centralized scheme where each base station (BS) calculates the best SIR to be targeted by the terminals it is assigned.
  @cite_9: In a heterogeneous wireless cellular network, each user may be covered by multiple access points such as macro pico relay femto base stations (BS). An effective approach to maximize the sum utility (e.g., system throughput) in such a network is to jointly optimize users' linear procoders as well as their BS associations. In this paper, we first show that this joint optimization problem is NP-hard and thus is difficult to solve to global optimality. To find a locally optimal solution, we formulate the problem as a noncooperative game in which the users and the BSs both act as players. We introduce a set of new utility functions for the players and show that every Nash equilibrium (NE) of the resulting game is a stationary solution of the original sum utility maximization problem. Moreover, we develop a best-response type algorithm that allows the players to distributedly reach a NE of the game. Simulation results show that the proposed distributed algorithm can effectively relieve local BS congestion and simultaneously achieve high throughput and load balancing in a heterogeneous network.
  @cite_21: In cellular wireless communication systems, transmitted power is regulated to provide each user an acceptable connection while limiting the interference seen by other users. Previous work has focused on maximizing the minimum carrier to interference ratio (CIR) or attaining a common CIR over all radio links. However, previous work has assumed the assignment of mobiles to base stations is known and fixed. In this work, we integrate power control and base station assignment. In the context of a CDMA system, we consider the minimization of the total transmitted uplink power subject to maintaining an individual target CIR for each mobile. This minimization occurs over the set of power vectors and base station assignments. We show that this problem has special structure and identify synchronous and asynchronous distributed algorithms that find the optimal power vector and base station assignment. >
  @cite_6: We consider a multi-cell wireless network with a large number of users. Each user selfishly chooses the Base Station (BS) that gives it the best throughput (utility), and each BS allocates its resource by some simple scheduling policy. First we consider two cases: (1) BS allocates the same time to its users; (2) BS allocates the same throughput to its users. It turns out that, combined with users' selfish behavior, case (1) results in a single Nash Equilibrium (NE), which achieves system-wide Proportional Fairness. On the other hand, case (2) results in many possible Nash Equilibria, some of which are very inefficient. Next, we extend (1) to the case where the users have general concave utility functions. It is shown that the if each BS performs intra- cell optimization, the total utility of all users is maximized at NE. This suggests that under our model, the task of joining the ";correct"; BS can be left to individual users, leading to a distributed solution.
  @cite_0: There is much current interest in spread spectrum wireless mobile communications and in particular the issue of spread spectrum wireless capacity. We characterize spread spectrum cellular capacity and provide a combined power control, cell-site selection algorithm that enables this capacity to be achieved. The algorithm adapts users' transmitter power levels and switches them between cell-sites, and it is shown that the algorithm converges to an allocation of users to cells that is optimal in the sense that interference is minimized. The algorithm is decentralized, and can be considered as a mechanism for cell-site diversity and handover. We provide numerical examples to show how effectively the algorithm relieves local network congestion, by switching users in a heavily congested cell to adjacent, less congested cells. >
  @cite_2: The joint power control and base station assignment for the downlink is considered in this paper. Based on the results and observations of previous work we present an algorithm that finds a feasible joint base assignment and transmission power vector in the downlink. We show that under some conditions the algorithm also minimizes the sum of downlink powers. Interestingly, there is not always a Pareto optimal power vector for the joint problem in the downlink as is the case in the uplink. This fact is demonstrated through a counterexample.
  @cite_15: We study a spectrum sharing problem in an unlicensed band where multiple systems coexist and interfere with each other. Due to asymmetries and selfish system behavior, unfair and inefficient situations may arise. We investigate whether efficiency and fairness can be obtained with self-enforcing spectrum sharing rules. These rules have the advantage of not requiring a central authority that verifies compliance to the protocol. Any self-enforcing protocol must correspond to an equilibrium of a game. We first analyze the possible outcomes of a one shot game, and observe that in many cases an inefficient solution results. However, systems often coexist for long periods and a repeated game is more appropriate to model their interaction. In this repeated game the possibility of building reputations and applying punishments allows for a larger set of self-enforcing outcomes. When this set includes the optimal operating point, efficient, fair, and incentive compatible spectrum sharing becomes possible. We present examples that illustrate that in many cases the performance loss due to selfish behavior is small. We also prove that our results are tight and quantify the best achievable performance in a non-cooperative scenario
summary: User association has been extensively studied for code-division multiple access (CDMA) networks @cite_21 @cite_0 @cite_2 @cite_14 . Results there suggest that joint user association and power control can significantly improve the performance of a CDMA network. Many recent studies focus on system utility maximization in OFDMA HetNets, which often requires solving non-convex integer programs. Game theory has also been used to derive simple distributed scheduling policies (e.g., @cite_6 ). Optimal linear precoder design and base station selection are considered for uplink HetNets in @cite_9 . The authors of @cite_15 studied spectrum sharing by strategic operators in the unlicensed band. While each operator is free to transmit over the entire common spectrum subject to the maximum power constraint, leading to the tragedy of commons, @cite_15 characterized more favorable Nash equilibria of both a one shot game and a repeated game. In contrast to the slow-timescale setting here, the aforementioned studies focus on dynamically updating user and resource allocation on a relatively fast timescale, which depends on the instantaneous channel realizations.