Spectrum occupancy reconstruction is an important issue often encountered in collaborative spectrum sensing in distributed cognitive radio networks (CRNs). This issue arises when the spectrum sensing data that are collaborated by secondary users have gaps of missing entries. Many data imputation techniques, such as matrix completion techniques, have shown great promise in dealing with missing spectrum sensing observations by reconstructing the spectrum occupancy data matrix. However, matrix completion approaches achieve lower reconstruction resolution due to the use of standard singular value decomposition (SVD), which is designed for more general matrices. In this paper, we consider the problem of spectrum occupancy reconstruction where the spectrum sensing results across the CRN are represented as a plenary grid on a Markov random field. We formulate the problem as a magnetic excitation state recovery problem, and the stochastic gradient descent (SGD) method is applied to solve the matrix factorization. SGD is able to learn and impute the missing values with a low reconstruction error compared with SVD. The graphical and numerical results show that the SGD algorithm competes favorably SVD in the matrix factorization by taking advantage of correlations in multiple dimensions. INDEX TERMS Cognitive radio networks, Ising model, matrix factorization, Metropolis-Hastings algorithm, missing values, stochastic gradient descent.

To make best use of the various radio resources in the heterogeneous network enabled by the software defined network or cognitive radio (CR) technology, a resource allocation framework with flexibility and quick reconfigurability in the network control layer is an important issue. In this paper, the authors propose a channel allocation framework with configurable objectives and high computing efficiency in the complicated context of a multiuser multi-channel CR network cell. First, a channel allocation protocol named the distribution probability matrix (DPM) is applied to model the channel allocation scenarios quantitatively. Then, a queueing analytical framework using DPM is built to model the CR system and comprehensive performance evaluations of every individual secondary user are obtained separately. An overall performance evaluation of the CR system is carried out using the concept of weighted throughput, which is introduced to represent the importance of the users and the feature to distinguish different types of users. Then, a parameter named overtime probability (OP) is introduced to describe the measure of delay approximately with high computing efficiency. Thereby, an optimization of the system is formulated to maximize the overall weighted throughput under delay constraints represented by OP and a hill climbing algorithm is developed to find the solution in terms of DPM. The numerical results reveal how to allocate the resources to achieve the optimization objective under various system settings and prove the computing efficiency of the framework.