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... in [13], and power control for multicarrier systems is studied in [14]. The authors in [8] use pricing to obtain a more efficient solution for the power control game. Similar approaches are taken in =-=[9]-=-–[12] for different utility functions. Game-theoretic approaches to power control in delay-constrained networks are proposed in [15], [16]. In this work, we use a game-theoretic approach to study the ...

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...icing function is assumed to be linear in the user’s transmit power. Hence, the net utility for user k is given by where ck is the pricing factor for user k. ũk = ζk log(1 + γk) − ckpk The authors in =-=[12]-=- define the utility function of a user to be a sigmoidal function of the user’s SIR. 2 In this case, the net utility is defined as the difference between the user’s utility function and a (linear) cos...

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...-like, geared toward trying to achieve a target SINR at each user as in [8]. In that case pricing may be used to stabilize power consumption when the SINR targets are close to the non-feasible region =-=[39]-=-. In data-oriented settings, the utility is usually a smoothly increasing function of the SINR. For instance the authors in [24], [40], [41] consider a function giving the amount of information succes...

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...thmic dependency of rates on powers and channel conditions. Note that in general, the the network utility function does not have to be a function of user rates, or a concave function (e.g., [7], [9], =-=[25]),-=- or separable into each individual user’s utility function. B. Problem formulation Consider the single cell downlink case in Figure 1 with M logical users, and assume CDMA transmission with orthogon...

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... networks. However, the main difficulty in solving the problem is that, in general, it cannot be formulated as 2sa convex programming problem, since the utility function may not be concave [9], [10], =-=[11]-=-, [12]. Thus, neither the KKT conditions nor the duality theorem provides a sufficient condition for the optimal solution. In most works on utility and pricing for power control, only Nash equilibria,...

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...roblem: minimize ∑ link(i,j)∈T ∑ k 6=i,j I(βk(i, j)) subject to Pmin ≤ Pt ≤ Pmax. The above problem is an integer program because of the existence of indicator functions. Fortunately, as indicated in =-=[11]-=-, the hard SINR requirement can be “softened” by the sigmoid function. The sigmoid function is a continuous function expressed as sig(x) = 1 1 + e−a(x−b) . (12) When x is greater than the threshold b,...

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...y. The modified hyperbolic tangent function is a type of sigmoid function that can accommodate a large range of performance variations and capture the value of the service to the user quite naturally =-=[74]-=-, [83]. If a solution does not meet the target goal, the utility is decreased sharply. Since solutions that result in excessively high QoS provide little value to the user, the increase of utility is ...