Research On Compressive Sampling Of Sparse Multiband Signals

Radio frequency technology enables the modulation of narrowband signals by high carrier frequencies. Those manmade signals are commonly sparse. That is, they consist of a relatively small number of narrowband transmissions across a wide spectrum range. Due to the wideband nature of those radio signals, the corresponding Nyquist frequency is so high rendering heavy burden on the ADC. Meanwhile, the consequent large volumes of data challenges the process of storage and transmission. Fortunately, the sparse signal sampling based on the emerging compressive sampling enables the sampling of those radio signals at sub-Nyquist frequency, of which the most famous work is Modulated Wideband Converter(MWC). Through in-depth research on the MWC, a series of research work has been carried out and the main body is organized from the following aspects, the way to simplify the measurement matrix, the alternative algorithm to improve the signal recovery performance and the possibility to further reduce the sampling frequency. The main research work is as follows.For the problem of high degree of the measurement matrix of MWC, the toeplitz matrix is exploited, based on which the compressive circulant matrix based analog to information conversion(CCM-AIC) is proposed. CCM-AIC reuses the architecture of MWC, however, the measurement matrix is constructed by cyclic shift of a single random sequence. Compared to MWC, the degree of freedom of the measurement matrix is significantly reduced. Fortunately, this reduction does not affect the system performance. CCM-AIC even outperforms MWC and behaves more robust when measurements are highly contaminated by white noise.The problem of signal recovery which lies at the heart of a compressive sampling system is investigated. Signal recovery of compressive sampling is essentially searching for the sparsest solution subject to underdetermined linear constrains, which is commonly regarded as a NP-hard problem. Alternative strategies have been exploited. l1-norm minimization is a popular strategy, the solution of which is proved to be sparsest with certain constrains and also global optimal, however, algorithms are commonly of high computational complexity. Greedy algorithms which turns out to be of computational efficiency are sub-optimal. The emerging concept called smoothed l0-norm which exploits some smooth function to mimic the non-smooth l0-norm is adapted to solve the signal recovery in the framework of MWC. The global solution is reached by use of steepest ascent methods with comparable computational complexiy. The paramters of the adapted algorithm is analyzed separately. The optimal configuration is derived to guarantee signal recovery.The way of further sampling frequency reduction is investigated and a modified framework named information bandwidth based MWC(IBbMWC) is established by exploiting the separate bandwidths. The sampling frequency of the MWC grows linearly with the product of number of bands and the maxmum bandwidth, which is proved to be ineffective when the bandwidth distinct from each other. This inefficiency becomes more sharp with enlarged difference of the bandwidth. By exploiting the bandwidth, the relationship between the sampling frequency and the information bandwidth(the summed up bandwidth of active bands) is established. The sampling frequency is proved to be reduced significantly when the bandwidth show large difference. Meanwhile, the sufficient condition for multipe signal classification algrithm is adapted to solve signal recovey in the framework of IBbMWC is derived. The relationship between the reduction of sampling frequency and the increase of number of channels is analyzed. The optimal condition is reached. IBbMWC is some kind of extension of MWC. MWC is showed to be a special case of IBbMWC. IBbMWC fufills the demand of sampling frequency reduction and thus mitigates the increasing demand of high-performance ADCs.