Wireless mobile backhaul networks have been proposed as a substitute in cases in which wired alternatives are not available due to economical or geographical reasons. In this work, we study the location problem of base stations in a given region where mobile terminals are distributed according to a certain probability density function and the base stations communicate through microwave backhaul links. Using results of optimal transport theory, we provide the optimal asymptotic distribution of base stations in the considered setting by minimizing the total power over the whole network.
Within the communication networks community, @cite_9 @cite_11 studied the duopoly situation in the uplink scenario of a cellular network where users are placed on a line segment. Considering the particular cost structure that arises in the cellular context, the authors observe that complex cell shapes are obtained at equilibrium. @cite_2 @cite_6 @cite_1 analyzed the problem of mobile terminals association to base stations using optimal transport theory and considering the data traffic congestion produced by this mobile terminals to base stations association.
@cite_9 @cite_1 @cite_6 @cite_2 @cite_11
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We study the mobile association problem: we determine the cells corresponding to each base station, i.e, the locations at which intelligent mobile terminals prefer to connect to a given base station rather than to others. This paper proposes a new approach based on optimal transport theory to characterize the solution based on previous works on fluid approximations. We characterize the optimal solution from both the global network and the individual user points of view, for the downlink setting. Motivated by the ongoing discussion on coordinated multipoint in wireless cellular standard bodies, this paper considers the problem of base station cooperation in the downlink of heterogeneous cellular networks. The focus of this paper is the joint transmission scenario, where an ideal backhaul network allows a set of randomly located base stations, possibly belonging to different network tiers, to jointly transmit data, to mitigate intercell interference and hence improve coverage and spectral efficiency. Using tools from stochastic geometry, an integral expression for the network coverage probability is derived in the scenario where the typical user located at an arbitrary location, i.e., the general user, receives data from a pool of base stations that are selected based on their average received power levels. An expression for the coverage probability is also derived for the typical user located at the point equidistant from three base stations, which we refer to as the worst case user. In the special case where cooperation is limited to two base stations, numerical evaluations illustrate absolute gains in coverage probability of up to 17 for the general user and 24 for the worst case user compared with the noncooperative case. It is also shown that no diversity gain is achieved using noncoherent joint transmission, whereas full diversity gain can be achieved at the receiver if the transmitting base stations have channel state information. There have been a bulk of analytic results about the performance of cellular networks where base stations are regularly located on a hexagonal or square lattice. This regular model cannot reflect the reality, and tends to overestimate the network performance. Moreover, tractable analysis can be performed only for a fixed location user (e.g., cell center or edge user). In this paper, we use the stochastic geometry approach, where base stations can be modeled as a homogeneous Poisson point process. We also consider the user density, and derive the user outage probability that an arbitrary user is under outage owing to low signal-to-interference-plus-noise ratio or high congestion by multiple users. Using the result, we calculate the density of success transmissions in the downlink cellular network. An interesting observation is that the success transmission density increases with the base station density, but the increasing rate diminishes. This means that the number of base stations installed should be more than @math -times to increase the network capacity by a factor of @math . Our results will provide a framework for performance analysis of the wireless infrastructure with a high density of access points, which will significantly reduce the burden of network-level simulations. The classic optimal transportation problem consists in finding the most cost-effective way of moving masses from one set of locations to another, minimizing its transportation cost. The formulation of this problem and its solution have been useful to understand various mathematical, economical, and control theory phenomena, such as, e.g., Witsenhausen's counterexample in stochastic control theory, the principal-agent problem in microeconomic theory, location and planning problems, etc. In this work, we incorporate the effect of network congestion to the optimal transportation problem and we are able to find a closed form expression for its solution. As an application of our work, we focus on the mobile association problem in cellular networks (the determination of the cells corresponding to each base station). In the continuum setting, this problem corresponds to the determination of the locations at which mobile terminals prefer to connect (by also considering the congestion they generate) to a given base station rather than to other base stations. Two types of problems have been addressed: a global optimization problem for minimizing the total power needed by the mobile terminals over the whole network (global optimum), and a user optimization problem, in which each mobile terminal chooses to which base station to connect in order to minimize its own cost (user equilibrium). This work combines optimal transportation with strategic decision making to characterize both solutions.