Efficient use of the under-utilized spectrum is primarily dependent upon the accuracy of spectrum sensing in Cognitive Radios (CRs). To this end, wideband spectrum sensing is highly desirable as it increases the probability of detecting unused spectrum but it comes with a challenge of designing very high-speed A/D converters. Further, to achieve high throughput in CRs, primary users (PUs) must be detected within a constrained sensing time and under energy limitations. Here, we develop a reduced complexity compressive sampling cyclostationary detection method which exploits the two dimensional sparsity of the spectral correlation function (SCF). Detection is performed on the reconstructed Nyquist SCF which is obtained directly from the sub-Nyquist samples using a closed-form solution. For a given SCF sparsity, we quantify the bounds on the minimum lossless sampling rates which result in a unique reconstruction. Due to the additional sparsity introduced in the SCF with respect to the power spectral density, the minimum sampling rates for cyclostationary detection are shown to be lower than those required for energy detection.
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