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A stackelberg game approach to distributed spectrum management

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Abstract

We consider a cognitive radio system with one primary (licensed) user and multiple secondary (unlicensed) users. Given the interference temperature constraint, the secondary users compete for the available spectrum to fulfill their own communication need. Borrowing the concept of price from market theory, we develop a decentralized Stackelberg game formulation for power allocation. In this scheme, the primary user (leader) announces prices for the available tones such that a system utility is maximized. Using the announced prices, secondary users (followers) compete for the available bandwidth to maximize their own utilities. We show that this Stackelberg game is polynomial time solvable under certain channel conditions. When the individual power constraints of secondary users are inactive (due to strict interference temperature constraint), the proposed distributed power control method is decomposable across the tones and unlike normal water-filling it respects the interference temperature constraints of the primary user. When individual power constraints are active, we propose a distributed approach that solves the problem under an aggregate interference temperature constraint. Moreover, we propose a dual decomposition based power control method and show that it solves the Stackelberg game asymptotically when the number of tones becomes large.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Minnesota, 200 Union Street SE, Minneapolis, MN, 55455, USA

    Meisam Razaviyayn & Zhi-Quan Luo

  2. Department of Mathematics, University of Washington, Seattle, WA, 98195-4350, USA

    Paul Tseng

  3. Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, 61822, USA

    Jong-Shi Pang

Authors
  1. Meisam Razaviyayn
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  2. Zhi-Quan Luo
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  3. Paul Tseng
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  4. Jong-Shi Pang
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Corresponding author

Correspondence to Meisam Razaviyayn.

Additional information

It is with deep sorrow that we completed this paper on behalf of our esteemed colleague and dear friend, Professor Paul Tseng, who was missing on a kayak trip in Yunnan, China in August 2009. Paul embarked upon this joint research during a visit to Minnesota shortly before his fateful kayak trip, and we are very sad that he could not see its completion. He would have been able to make many more contributions to this research topic, as he did with so many others before. The work of the first two authors are supported in part by the Air Force Office of Scientific Research, Grant No. 00008547, and by National Science Foundation, grant number CMMI-0726336. The work of the fourth author is based on research supported by the U.S.A. National Science Foundation grants CMMI 0969600 and by the Air Force Office of Sponsored Research award No. FA9550-09-10329.

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Razaviyayn, M., Luo, ZQ., Tseng, P. et al. A stackelberg game approach to distributed spectrum management. Math. Program. 129, 197–224 (2011). https://doi.org/10.1007/s10107-011-0469-8

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  • DOI: https://doi.org/10.1007/s10107-011-0469-8

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