Abstract
In this paper, the problem of distributed dynamic frequency allocation is considered for a canonical communication network, which spans several networks such as cognitive radio networks and digital subscriber lines (DSLs). A greedy asynchronous distributed interference avoidance (GADIA) algorithm for horizontal spectrum sharing has been proposed that achieves performance close to that of a centralized optimal algorithm. The convergence of the GADIA algorithm to a near-optimal frequency allocation strategy is proved and several asymptotic performance bounds have been established for various spatial configurations of the network nodes. Furthermore, the near-equilibrium dynamics of the GADIA algorithm has been studied using the Glauber dynamics, by identifying the problem with the antiferromagnetic inhomogeneous long-range Potts model. Using the near-equilibrium dynamics and methods from stochastic analysis, the robustness of the algorithm with respect to time variations in the activity of network nodes is studied. These analytic results along with simulation studies reveal that the performance is close to that of an optimum centralized frequency allocation algorithm. Further simulation studies confirm that our proposed algorithm outperforms the iterative water-filling algorithm in the low signal-to-interference-plus-noise ratio (SINR) regime, in terms of achieved sum rate, complexity, convergence rate, and robustness to time-varying node activities.
Highlights
Dynamic frequency allocation has an important role in improving the performance of communication networks, for it results in less transmission power, which is a crucial objective in system design
There are various proposed methods for decentralized frequency allocation in different contexts (See, for example, [13], [15], [22], [28], [34], [37], [38], [40], [41], [42], [43], [45], [51], [56], [58], and [59]). These include methods based on graph coloring for cognitive networks, greedy interference avoidance techniques, Iterative Water-filling for Digital Subscriber Lines (DSL), game theoretic approaches to dynamics spectrum allocation and methods based on auction theory
We have considered the problem of distributed dynamic frequency allocation in a canonical communication network which spans many networks of interest, such as cognitive/ad hoc networks or Digital Subscriber Lines (DSL)
Summary
Dynamic frequency allocation has an important role in improving the performance of communication networks, for it results in less transmission power, which is a crucial objective in system design. There are various proposed methods for decentralized (distributed) frequency allocation in different contexts (See, for example, [13], [15], [22], [28], [34], [37], [38], [40], [41], [42], [43], [45], [51], [56], [58], and [59]) These include methods based on graph coloring for cognitive networks, greedy interference avoidance techniques, Iterative Water-filling for Digital Subscriber Lines (DSL), game theoretic approaches to dynamics spectrum allocation and methods based on auction theory. A number of achievability and existence results in the context of non-cooperative and cooperative game theory for obtaining efficiency and fairness, as well as a punishment-based mechanism have been established Another approach has been presented by Huang et al [22], where each user in the network announces a price to the other users, so that they can adapt their power allocation . A number of technical lemmas and mathematical derivations are presented in Appendices A and B
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