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The spectrum allocation for cognitive radio networks (CRNs) has received considerable studies under the assumption that the bandwidth of spectrum holes is static. However, in practice, the bandwidth of spectrum holes is time-varied due to primary user/secondary user (PU/SU) activity and mobility, which result in non-determinacy. This paper studies the spectrum allocation for CRNs with non-deterministic bandwidth of spectrum holes. We present a novel probability density function (PDF) model through order statistic to describe the non-deterministic bandwidth of spectrum holes and provide a bound to approximate it. After that, a statistical spectrum allocation model based on stochastic multiple knapsack problem (MKP) is established for spectrum allocation with non-deterministic bandwidth of spectrum holes. To reduce the computational complexity, we transform this stochastic programming probleminto a constant MKP though exploiting the properties of cumulative distribution function (CDF), which can be solved via MTHG algorithm by using auxiliary variable. Simulation results illustrate that the proposed statistical spectrum allocation algorithm can achieve better performances compared to the existing algorithms when the bandwidth of spectrum holes istime-varied

Spectrum Assignment with Non-Deterministic Bandwidth of Spectrum Holein Cognitive Radio Networks