Reconstructing Spectrum Occupancies for Wideband Cognitive Radio Networks: A Matrix Completion via Belief Propagation

In wideband cognitive radio networks having multiple channels, it improves the efficiency of spectrum access to predict the states of unsensed channels at different locations. On considering the channel states as a matrix, whose rows are the indices of locations and columns are the indices of channels, the prediction of channel states is essentially a matrix completion, i.e. reconstructing the whole matrix by using a few known entries. Due to the challenges of high dimensionality and decentralization, as well as the {\em a priori} information about the similarity between adjacent channels or locations, the traditional matrix completion approaches, like singular value decomposition (SVD) and nuclear norm optimization, are inefficient. In this paper, we propose to apply the framework of Belief Propagation (BP) for the matrix completion. Both centralized and decentralized versions are introduced. Numerical simulation results show that the proposed BP framework can effectively predict the channel states and thus efficiently orient the spectrum sensing of secondary users. Numerical simulations have shown that, for a scenario with 20000 frequency-space pairs, we can achieve a reconstruction error rate less than 20% (5%) with sampling rate 1% (15%). It is also demonstrated that our proposed algorithm significantly outperforms the general-purpose SVD based matrix completion algorithm.