Abstract
We present a general game-theoretical framework for power allocation in the downlink of distributed wireless small-cell networks, where multiple access points (APs) or small base stations send independent coded network information to multiple mobile terminals (MTs) through orthogonal channels. In such a game-theoretical study, a central question is whether a Nash equilibrium (NE) exists, and if so, whether the network operates efficiently at the NE. For independent continuous fading channels, we prove that the probability of a unique NE existing in the game is equal to 1. Furthermore, we show that this power allocation problem can be studied as a potential game, and hence efficiently solved. In order to reach the NE, we propose a distributed waterfilling-based algorithm requiring very limited feedback. The convergence behavior of the proposed algorithm is discussed. Finally, numerical results are provided to investigate the price of anarchy or inefficiency of the NE.
Highlights
There has been an increasing interest for small cell networks, where people can access Internet over many different access points (APs) or small base stations
If users are connected to a single out-door femto-cell, they may suffer from low throughput from time to time due to the limited-backhaul capacity, despite the presence of a high speed wireless link
The issue of load balancing [3] in the wired network, important, is not dealt with in this contribution and we will suppose that perfect load balancing holds
Summary
There has been an increasing interest for small cell networks, where people can access Internet over many different APs or small base stations ( known as out-door femtocells or small cells [1, 2]). We assume that all these femto-cells get independent independent packets (network coding is applied at the source) from the Internet via their backhauls, and send them physically to each MT in a distributed manner In this situation each femto-cell needs to decide how to distribute the total available transmit power over N downlink sub-channels (sub-carriers or clusters of sub-carriers), i.e., should it allocate all its power to a single sub-channel, spread the power over all the sub-channels, or choose some subset of sub-channels on which to transmit?. Non-cooperative games theory [14], borrowed from many economic applications [15] provides an alternative solution by considering every femto-cell as a selfish player who “plays” the game by rationally choosing its transmit power levels In this respect, it is important to study the NE [16] (the solution concept of non-cooperative games) because it represents a predictable outcome for a self-organizing network. N=1 where Pmmax is maximum transmit power of AP m and Pmmax > 0, ∀m
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