## 1 Introduction  
Nowadays, with the advancement of modern communication technology, the demand for spectrum resources is growing heavily. Authorized users are suffering from heavy interference caused by other users sharing the same spectrum. Cognitive radio (CR) is regarded as a promising technology which can fully use the spectrum by dynamically accessing the currently unused licensed spectrum [1]. In this technology, obviously, spectrum sensing is a crucial task, which requires not only high reliability and short sensing time but also the ability to sense a wide bandwidth. Customarily, there are three common spectrum sensing techniques [2; 3; 4]. The first approach is called matched filter which requires a prior knowledge of the primary users signaling features such as bandwidth, operating frequency, modulation type, pulse shaping and so on. However, these are usually infeasible to acquire in practice. The second is energy detector, it is the most common way of spectrum sensing owing to its low computation and implementation complexities. However, its sensing accuracy is highly susceptible to noise uncertainty and becomes unacceptable when the signal-to-noise-ratio (SNR) is pretty low. The third one is cyclostationary feature detector. Although this way is quite robust to both noise uncertainty and strong noise, it still takes a long time due to high computational complexities. Besides, all the approaches mentioned above apply to the narrow band signals or low frequency field. When it comes to wideband spectrum, in [5], two possible ways are discussed. One is to divide the whole wideband spectrum into lots of narrow band channels and then we can carry out the above sensing approaches channel-by-channel. Similarly, this approach introduces a big time delay and a significant amount of bandpass filters because of its serial process. Another approach is to directly sample the entire wideband spectrum using a high-rate analog-to-digital converter (ADC). However, under Nyquist sampling framework, such high sampling rate may exceed today's best ADCs performance. What is more, this will generate a large number of samples to process, affecting speed and power consumption. Many studies have been performed to overcome this bottleneck. In [6], [PERSON] developed a minimal sampling rate requirement that allows perfect reconstruction as early as 1967. Unfortunately, the article did not point out a feasible method of implementation when the carrier frequencies are unknown. The recent theory of compressed sensing (CS) [7; 8], indicates that if the signal has a sparse representation in some space, we can linearly transform the signal to a lower-dimension space from which the signals can be recovered without any distortion. In this strategy, the sampling rate is no longer determined by the highest frequency of the signal, but decided by its valid information. Based on this, a number of CS structures have been proposed for sub-Nyquist sampling of continuous-time signals in recent years. Such as random demodulation (RD), Multi-coset sampling, modulated wideband converter (MWC) and so on [9; 10; 11; 12]. However, the RD system can only treat the multi-tone signal model. In reality, the analog signals require a extremely large number of harmonics to approximate them well within the discrete model, which may cause the reconstruction computationally infeasible. Multi-coset sampling system has a good performance of the multiband signal. However, this scheme is fairly hard to implement because maintaining accurate time shifts, on the order of the Nyquist interval, is extremely difficult to design and realize. Lately, [PERSON] et al. proposed MWC sampling structure. Through a series of processing steps on a special analog front-end, the signal can be reconstructed from low rate samples, using the known relation between samples and the original signal. It is the most striking structure and can be realized by commercial components. Whereas, the amount of sampling channels can become very large when the sparsity is great [13].