Research On MWC-based Sub-nyquistsampling Technology Of Sparse Wideband Signals

With the constant rise of signal bandwidth in the areas of radio communication etc, sampling has been becoming a bottleneck blocking the development of signal processing system. Especially for many practical applications, the frequencies of carriers are unknown, or changing with time, which calls for the information to be acquired through sampling the wideband signal directly. This situation makes the traditional sampling method that follows Nyquist theory become a great challenge in terms of sampling rate. The newly proposed sub-Nyquist sampling method named Modulated Wideband Converter (MWC) can perform sampling and compressing in one step for wideband signals with sparse structure, which draws much attention from scholars. Currently the research of MWC sampling technology is still at the preliminary stage, there still exists several problems to be further studied in depth, in terms of recovery algorithm, recovery condition, implementation technology and so on.Aiming at the problems in MWC such as poor performance of recovery algorithm and severe condition for recovery, this paper proposes new recovery algorithms and full-blind sub-Nyquist sampling method which can relax the recovery condition, and further explores the theoretical and practical issues involved in the implementation of MWC sampling system. The research of this paper can provide a low-rate receiving method of information for the communication domain, and can provide an effective solution for wideband spectrum sensing in cognitive radio, suggesting a good application prospect. Moreover, this research has important theoretical significance for enriching and developing sub-Nyquist sampling technology. The main research content of this paper is as follows:1. The recovery performance of the Multiple Measurement Vector (MMV) problem in existing recovery algorithm for MWC is not high in terms of recovery success rate, maximal sparsity of recoverable signals and minimal number of measurements. Aiming at this problem, a recovery algorithm framework adopting random projection method is proposed from the perspective of general MMV problem. This algorithm framework transforms the recovery problem into several lower-dimensional MMV problems to solve tentatively by projecting the sampling value matrix to lower-dimensional vector spaces. To take full advantage of the performance benefits of the framework, a support set identification strategy which makes full use of the joint sparse property in the preliminary solution is presented. Experiments show that the proposed algorithm can improve recovery success rate, increase maximal recoverable sparsity of signals, and decrease the number of measurements required.2. Aiming at the problem that the recovery performance of existing algorithm is poor in the presence of noise, the paper brings multiple signal classification (MUSIC) method into the MWC recovery algorithm to perform support recovery. To satisfy the recovery condition and decrease the recovery complexity, the singular value decomposition method is adopted to reduce dimension of the sampling value matrix and depress noise on the premise of not changing support set of the unknown matrix. Experiments show that, under conditions of signal-to-noise ratios (SNR) great than10dB, the proposed approach can improve recovery success rate, reduce the requirement for number of channels and sampling rate for recovering with high probability.3. Aiming at the problem that the recovery performance of a single MWC is unsatisfactory under low signal-to-noise ratio, and some applications need sampling in a distributed manner, a distributed sub-Nyquist sampling mode and especially a joint recovery algorithm are presented. The algorithm based on MUSIC is generalized through exploring the joint sparse structure between different signals. As a result, a joint recovery algorithm for distributed sub-Nyquist sampling is presented. Experiments show that, compared to the recovery using a single MWC, the joint recovery enhances the success rate for the support recovery, especially under low SNRs.4. Aiming at the problem that the existing recovery condition for MWC is severe, combining the background of wideband spectrum sensing for cognitive radio, a full-blind sub-Nyquist sampling method is proposed, which does not require the maximal bandwidth and the exact number of bands as a priori. In sampling theory, combining the channel band model for radio transmission and the multiband signal model, the signal model suitable for MWC is redefined. On this basis, an improved sufficient condition of recovery is proposed. In recovery algorithm, the sparsity adaptive matching pursuit algorithm for the single-measurement-vector problem is generalized to the multiple-measurement-vector problem, and applied to the process of MWC recovery, which eliminates the dependence on the number of frequency bands. Experiments show that the performance of this algorithm under the condition without knowing the number of frequency bands is comparable to that of traditional algorithm under the condition knowing the exact sparsity level, and the full-blind sampling and recovery perform well.5. The implementation technology of MWC-based sub-Nyquist sampling is investigated in this paper, and the realization method of MWC using hardware is discussed in depth. A complete sub-Nyquist sampling verification system is designed and realized. Aiming at the problem of the large difference between the exact sampling matrix corresponding to the hardware circuit and the result achieved theoretically, an experimental construction method based on sinusoidal response is proposed. This method can sequentially obtain each column vector of the sampling matrix through exerting a series of sinusoidal excitations of different frequencies. Experimental results verify the effectiveness of the achieved MWC sampling system, the proposed construction method of sampling matrix, and the proposed recovery algorithms.