| Summary: | We study a distributed channel allocation problem of non-cooperative OFDMA femtocells in two-tiered macro-femto networks. The objective is to maximize the total capacity of uplink macro users and femto users. We assume a time-slotted system, a time-invariant channel model (no fading), each user knows the signal-to-interference-plus-noise ratio (SINR) of all channels, and the channel selection happens only at the beginning of each time-slot. We study the performance of a best-response strategy where each user chooses to transmit in the highest-SINR channel. For simplicity, we focus on the homogeneous 3-link, 2-channel case and show that if all users update their actions every time-slot (i.e., all users make simultaneous moves), an oscillation can occur and result in the worst performance. To avoid the oscillation and achieve the highest total capacity, while still assuming no coordination among the users, we propose a stochastic best-response algorithm, where each user updates its channel selection with a selection probability p. We use a Markov chain to analyze the average capacity performance and use simulation results to confirm our analysis and also provide performance of other homogeneous cases with more number of links and channels. It is shown that the highest total capacity can be achieved when the selection probability p is very small. This stochastic best response with small p in effect provides a sequential move mechanism which requires no coordination.
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