Given a set of wireless links, a fundamental problem is to find the largest subset that can transmit simultaneously, within the SINR model of interference. Significant progress on this problem has been made in recent years. In this note, we study the problem in the setting where we are given a fixed set of arbitrary powers each sender must use, and an arbitrary gain matrix defining how signals fade. This variation of the problem appears immune to most algorithmic approaches studied in the literature. Indeed it is very hard to approximate since it generalizes the max independent set problem. Here, we propose a simple semi-definite programming approach to the problem that yields constant factor approximation, if the optimal solution is strictly larger than half of the input size.
Kesselheim obtained a @math -approximation algorithm for the capacity problem with power control for doubling metrics @cite_22 . Around the same time, the first constant factor algorithm for all sub-linear, length monotone power assignments was achieved on general metrics @cite_6 . Other recent studies in the SINR model include work on topological maps @cite_14 , distributed algorithms for scheduling @cite_24 , distributed power control @cite_9 and auction based spectrum allocation @cite_3 .
@cite_14 @cite_22 @cite_9 @cite_6 @cite_3 @cite_24
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We give algorithms with constant-factor performance guarantees for several capacity and throughput problems in the SINR model. The algorithms are all based on a novel LP formulation for capacity problems. First, we give a new constant-factor approximation algorithm for selecting the maximum subset of links that can be scheduled simultaneously, under any non-decreasing and sublinear power assignment. For the case of uniform power, we extend this to the case of variable QoS requirements and link-dependent noise terms. Second, we approximate a problem related to cognitive radio: find a maximum set of links that can be simultaneously scheduled without affecting a given set of previously assigned links. Finally, we obtain constant-factor approximation of weighted capacity under linear power assignment. In this paper, we propose a joint subchannel and power allocation algorithm for the downlink of an orthogonal frequency-division multiple access (OFDMA) mixed femtocell macrocell network deployment. Specifically, the total throughput of all femtocell user equipments (FUEs) is maximized while the network capacity of an existing macrocell is always protected. Towards this end, we employ an iterative approach in which OFDM subchannels and transmit powers of base stations (BS) are alternatively assigned and optimized at every step. For a fixed power allocation, we prove that the optimal policy in each cell is to give each subchannel to the user with the highest signal-to-interference-plus-noise ratio (SINR) on that subchannel. For a given subchannel assignment, we adopt the successive convex approximation (SCA) approach and transform the highly nonconvex power allocation problem into a sequence of convex subproblems. In the arithmetic-geometric mean (AGM) approximation, we apply geometric programming to find optimal solutions after condensing a posynomial into a monomial. On the other hand, logarithmic and d ifference-of-two- c oncave-functions (D.C.) approximations lead us to solving a series of convex relaxation programs. With the three proposed SCA-based power optimization solutions, we show that the overall joint subchannel and power allocation algorithm converges to some local maximum of the original design problem. While a central processing unit is required to implement the AGM approximation-based solution, each BS locally computes the optimal subchannel and power allocation for its own servicing cell in the logarithmic and D.C. approximation-based solutions. Numerical examples confirm the merits of the proposed algorithm. In this paper the problem of wireless transmissions scheduling in the path-loss SINR model is considered for different fixed power schemes. The lower bounds for the optimum schedule length proven by Kesselheim and Voecking are considered. It is shown that the lower bound for the linear power scheme is tight, by presenting a constant-factor approximation algorithm. On the other hand, it is shown that the lower bounds proven for many other interesting power schemes can be essentially far from the optima. In this paper, we study resource allocation for a multicarrier-based cognitive radio (CR) network. More specifically, we investigate the problem of secondary users’ energy-efficiency (EE) maximization problem under secondary total power and primary interference constraints. First, assuming cooperation among the secondary base stations (BSs), a centralized approach is considered to solve the EE optimization problem for the CR network where the primary and secondary users are using either orthogonal frequency-division multiplexing (OFDM) or filter bank based multicarrier (FBMC) modulations. We propose an alternating-based approach to solve the joint power-subcarrier allocation problem. More importantly, in the first place, subcarriers are allocated using a heuristic method for a given feasible power allocation. Then, we conservatively approximate the nonconvex power control problem and propose a joint successive convex approximation-Dinkelbach algorithm (SCADA) to efficiently obtain a solution to the nonconvex power control problem. The proposed algorithm is shown to converge to a solution that coincides with the stationary point of the original nonconvex power control subproblem. Moreover, we propose a dual decomposition-based decentralized version of the SCADA. Second, under the assumption of no cooperation among the secondary BSs, we propose a fully distributed power control algorithm from the perspective of game theory. The proposed algorithm is shown to converge to a Nash-equilibrium (NE) point. Moreover, we propose a sufficient condition that guarantees the uniqueness of the achieved NE. Extensive simulation analyses are further provided to highlight the advantages and demonstrate the efficiency of our proposed schemes.