Research On Sub-Nyquist Sampling Models And Its Power Spectrum Estimation

With the rapid development of communication technology,the frequency of signals used to carry information becomes increasingly high,which poses huge challenges to sampling.According to the Shannon sampling theorem,the sampling frequency must be greater than or equal to twice the highest frequency of the analog signal,which is called as the Nyquist rate.Due to the extremely high sampling rate,analog-to-digital converters are hard to be realized.However,it is not necessary to sample at a frequency greater than or equal to the Nyquist rate if the signal is sparse in some domain.Based on the sparsity,the sub-Nyquist sampling system can also capture the complete information carried by the signal even though the sampling frequency is much lower than the Nyquist rate.Then,through specific signal reconstruction algorithms,the original signal can be recovered from the relatively small number of samples captured by the sub-Nyquist system.The subjects of the thesis are three popular sub-Nyquist sampling systems:multiple coset sampling,analog-to-information converter,and coprime sampling.The contents of this thesis includes three aspects: reducing the number of quantization bits of multi-coset sampling to the extreme case,i.e.1-bit sampling,applying analog-to-information converters to power spectrum estimation,and analyzing the recovery failure of coprime sampling.To be specific,the main work includes:1.First,a direct 1-bit sampling model is proposed.Consisting of only one comparator,its hardware structure is extremely simple,which can be equivalent to a special multi-coset sampling system in the stage of data processing.Second,the BIHT algorithm is improved to be applicable for multiple test vectors.Finally,the improved BIHT algorithm is applied to the direct 1-bit sampling model to form a complete sub-Nyquist sampling scheme.2.First,after analyzing the shortcomings of the linear power spectrum of finite-length signals,the circular power spectrum of finite-length signals is proposed,followed by the comparison of the two kinds of power spectrums.Second,a bank of low-pass filters are used to build a sub-Nyquist sampling system based on analog-to-information converters,followed by a detailed comparison between the filter-based sampling system and the integrator-based sampling system.Finally,thesub-Nyquist system based on low-pass filters is used to estimate the circular power spectrum of sparse signals.3.First,the recovery failure of the coprime sampling system is analyzed in details.And the failure cause is defined as rank deficiency.Second,the occurrence conditions of rank deficiency when using two popular signal recovery methods,i.e.direct estimation and multi-coset equivalence,are derived.Finally,a four-channel coprime sampling system is proposed in order to avoid rank deficiency.