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We consider a spectrum sharing problem in which each wireless transmitter can select a single channel from a set of available channels, along with the transmission power. An asynchronous distributed pricing (ADP) scheme is proposed, in which users exchange "price" signals that indicate the negative effect of interference at the receivers. Given this set of prices, each transmitter chooses a channel and power level to maximize its net benefit (utility minus cost). We show that a sequential version of this single-channel (SC)-ADP algorithm converges with two users and an arbitrary number of channels, and observe via simulation that it exhibits rapid convergence with more users in the network. The pricing algorithm always outperforms the heuristic algorithm in which each user picks the best channel without exchanging interference prices. In a dense network with heavy interference, the SC-ADP algorithm can also perform better than the iterative water-filling algorithm where each user transmits over multiple channels but the users do not exchange any information. The performance of the SC-ADP algorithm is also compared with a multi-channel (MC)-ADP algorithm in which users can transmit over multiple channels and exchange interference prices over each channel
Huang et al. (Sat,) studied this question.