2246 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 58, NO. 4, APRIL 2010 Decentralized Dynamic Spectrum Allocation Based on Adaptive Antenna Array Interference Mitigation Diversity Alexandr M. Kuzminskiy, Member, IEEE, and Yuri I. Abramovich, Fellow, IEEE Abstract—A new class of decentralized dynamic spectrum allo- cation (DSA) algorithms that exploit adaptive antenna array in- terference mitigation (IM) diversity at the receiver, is proposed for interference-limited environments with high level of frequency reuse. The system model consists of base stations (BS) that can optimize uplink frequency allocation to their subscriber stations (SS) to achieve the least impact of IM on the useful signal, as- suming no control over band allocation of other BSs sharing the same bands. It is demonstrated that when the number of SSs that share the same frequency approaches the number of antenna ele- ments at a BS, the potential performance gain is most significant for the IM-based DSA compared to the random frequency alloca- tion. A “good neighbor” decentralized DSA strategy is introduced. The convergence and convergence rate of IM-based DSA are inves- tigated by means of the theory of absorbing Markov chains and sta- tistical simulations. It is shown that the “good neighbor” strategy leads to much better convergence properties of the entire system compared with the conventional “selfish” approach. This suggests that the “good neighbor” IM-based DSA techniques may have a practical perspective even in the scenarios, where global conver- gence with probability one cannot be established. Index Terms—Absorbing Markov chain, decentralized dynamic spectrum allocation, interference mitigation, “selfish” and “good neighbor” strategies. I. INTRODUCTION D YNAMIC SPECTRUM ALLOCATION (DSA) is effec- tive way to increase the spectral efficiency of wireless communications systems [1], [2], including cellular [3], WLAN [4], WIMAX [5] and ad hoc [6]–[8] networks. DSA can be im- plemented using explicit coordination between access nodes, which is mostly suitable for cellular systems [3] in a licensed spectrum. However, in an unlicensed spectrum [9] or in cogni- tive radio systems with primary and secondary users [10], fre- quency band allocation has to be performed by each (secondary) provider in a decentralized autonomous way [5], [11]. If the number of available frequency bands exceeds the total number of subscriber stations (SSs), a DSA strategy may be Manuscript received March 25, 2009; accepted December 21, 2009. First published January 19, 2010; current version published March 10, 2010. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Amir Leshem. Part of this work has been performed with financial support from the IST FP7 PHYDYAS project. A. M. Kuzminskiy is with Alcatel-Lucent, The Quadrant, Stonehill Green, Westlea, Swindon SN5 7DJ, U.K. (e-mail: Alexandr.Kuzminskiy@alcatel-lu- cent.com). Y. I. Abramovich is with the Intelligence, Surveillance and Reconnaissance Division, Defence Science and Technology Organisation (DSTO), Edinburg SA 5111, Australia (e-mail: Yuri.Abramovich@dsto.defence.gov.au). Digital Object Identifier 10.1109/TSP.2010.2040688 focused on the maximal interference avoidance. For example, in [5], a multichannel version of the carrier sense multiple ac- cess/collision avoidance (CSMA/CA) algorithm operates by se- lectively activating or deactivating groups of OFDM subcarriers separated by the guard bands in the WIMAX system [12]. In the more challenging interference-limited scenario, where the total number of SSs that belong to different closely located sub- systems exceeds the number of available bands, joint DSA and multiple-antenna interference suppression is required. A gen- eral theoretic formulation of the spectrum sharing problem in multiple input multiple output (MIMO) systems is studied in [13]–[18]. Based on game theory methodology, in [14] and [16], it is proven that under a number of assumptions and constraints, there exists a strategy that converges to the Nash equilibrium (NE) from which every user is not willing to unilaterally move. Furthermore, the conditions that allow to prove uniqueness of the NE are specified in [13], [15] in the spectrum sharing game. In [19], it is demonstrated that the most obvious unre- stricted local “selfish” (greedy) algorithm, where each player is searching for the maximum data rates, does not necessarily converge to NE. In [8], simulations showed promising results for a network based on the “selfish” DSA and MIMO beam- forming [20], though convergence of this algorithm could not be proven. For this reason, an algorithm whose convergence could not be guaranteed is treated as “useless from a practical perspective” in [21]. One way to overcome this difficulty could be some coopera- tion in band allocation. Theoretically, the convergence solution can always be established in this case. In [21], a band selection algorithm is developed under the assumption that not only in- terference at the receiver node is known, but the impact of the interference created by the transmitter node on receivers of all other nodes is known as well. To provide nodes with such an information, an explicit MAC layer cooperation between nodes is required that significantly complicates practical implementa- tion of such networks. In this paper, we propose a different approach to decentral- ized DSA that may be treated as practically useful, despite the fact that convergence with probability one to certain stationary (equilibrium) points cannot be guarantied. Indeed, if we are able to introduce a rule regulated [22] ap- proach, whereby all nodes are still not explicitly cooperating with each other, but follow certain rules, such that • an overwhelming majority of stationary points with suf- ficiently high steady-state performance exists with only a few inappropriate ones, and 1053-587X/$26.00 © 2010 IEEE