In cognitive radio (CR), the problem of spectrum hole detection has been extensively studied in single dimension, such as frequency domain, spatial domain, and so on. Recently, a class of two dimension spectrum hole detection methods, named as joint angle-frequency estimation (JAFE), has attracted much attention. Nevertheless, most of the existing approaches are only suitable for the scenario with matching frequency-angle pairs, rather than the non-matching scenario between the two parameters, like space division multiple access (SDMA) or frequency division multiplexing access (FDMA) communication mode which allows the same frequency band (or angle) to be reused in different angles (or frequencies). For the above two cases, including matching and non-matching scenarios, this paper develops an effective frequency-angle spectrum hole detection algorithm with Taylor expansion based focusing transformation (TFT-FASHD), on the basis of signal sparse representation by extending the array manifold from angle domain to frequency-angle domain. In the proposed method, for Fourier transform representation of the sparse model, a focusing transformation based on Taylor expansion is first performed to focus the signal subspaces at different frequencies to a single frequency, so as to carry out dimension reduction of dictionary in angular domain. TFT is derived by decomposing the array manifold with Taylor expansion, and further the optimum focusing frequency of focusing transform is discussed theoretically. Second, atoms with high representative performance are chosen by the presented TFT and compressed sensing (CS). Third, according to the low dimension dictionary, the TFT-FASHD is implemented by CS under multiple measurement vector (MMV) circumstances. The accuracy of the algorithm in non-matching scenario is verified by simulation results. For the matching scenario, compared with the related JAFE methods, the proposed algorithm has a lower computational complexity, smaller detection error, and higher energy efficiency, which are validated through simulation.

In most of compressed sensing (CS) contributions, the sparsity of interesting signals is usually assumed to be prior. It may incur performance degradation of CS in such environments, where the sparsity order of channel occupancy changes dynamically. Therefore, sparsity order estimation (SOE) is vital, so that the sampling rate can be adjusted adaptively to exploit fully CS techniques. This paper studies the SOE problem for wideband cognitive radio. To investigate this issue, at first, the theoretical expression of sparsity order of the considered signals is derived via random matrix theory. The theoretical analysis shows that the sparsity order can be expressed with the ratio, which consists of the trace of measured signals' covariance matrix, compression sampling ratio, signal-to-noise ratio, and so on. And then, according to the theoretical expressions, a novel SOE approach is presented. In the proposed method, the trace of measured signals' covariance matrix is first calculated, and second, the sparsity order is estimated based on the trace. Compared with the previous work, the proposed algorithm, besides the lower computational complexity, has some superior performance, such as better robustness, smaller SOE error, and so on. Theoretical analysis and simulation results demonstrate the performance of the proposed approach.