Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học được đăng trên tạp chí toán học quốc tế đề tài: Probabilistic framework for opportunistic spectrum management in cognitive ad hoc networks | Khattab et al. EURASIP Journal on Wireless Communications and Networking 2011 2011 188 EURASIP Journal on . http content 2011 1 i88 Wireless Communications and Networking a SpringerOpen Journal RESEARCH Open Access Probabilistic framework for opportunistic spectrum management in cognitive ad hoc networks Ahmed Khattab Dmitri Perkins and Magdy A Bayoumi Abstract Existing distributed opportunistic spectrum management schemes do not consider the inability of today s cognitive transceivers to measure interference at the primary receivers. Consequently optimizing the constrained cognitive radio network performance based only on the local interference measurements at the cognitive senders does not lead to truly optimal performance due to the existence of hidden or exposed primary senders. In this paper we present a probabilistic framework for opportunistic spectrum management in cognitive ad hoc networks that optimizes the constrained cognitive user goodput while taking the unavoidable inaccuracy of spectrum sensing into account. The proposed framework i randomly explores individual spectrum bands as local interference measurements lead to inaccurate spectrum access decisions and ii adopts a non-greedy probabilistic spectrum access policy that prevents a single cognitive transmission from monopolizing an available spectral opportunity. In contrast to existing techniques our approach allows multiple cognitive flows to fairly share the available opportunities without explicit inter-flow coordination. We analytically formulate the cognitive user performance optimization problem as a mixed-integer non-linear programming to derive the optimal parameter values. We use packet-level simulations to show that our approach achieves up to 138 higher goodput with significantly better fairness characteristics compared to greedy approaches. Keywords Cognitive radio networks Opportunistic spectrum management Medium access control 1. Introduction The .