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The authors study distributed algorithms for allocating powers and/or adjusting beamforming vectors in a peer-to-peer wireless network which may have Multiple-Input-Single-Output (MISO) links. The objective is to maximize the total utility summed over all users, where each user's utility is a function of the received Signal-to-Interference-plus-Noise Ratio (SINR). Each user (receiver) announces an interference price, representing the marginal cost of interference from other users. A particular user (transmitter) then updates its power and beamforming vector to maximize its utility minus the interference cost to other users, which is determined from their announced interference prices. They show that if each transmitter update is based on a current set of interference prices and the utility functions satisfy certain concavity conditions, then the total utility is non-decreasing with each update.
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