Non-uniform sampling and reconstruction of multi-band signals and its application in wideband spectrum sensing of cognitive radio

Abstract

Sampling theories lie at the heart of signal processing devices and communication systems. To accommodate high operating rates while retaining low computational cost, efficient analog-to digital (ADC) converters must be developed. Many of limitations encountered in current converters are due to a traditional assumption that the sampling state needs to acquire the data at the Nyquist rate, corresponding to twice the signal bandwidth. In this thesis a method of sampling far below the Nyquist rate for sparse spectrum multiband signals is investigated. The method is called periodic non-uniform sampling, and it is useful in a variety of applications such as data converters, sensor array imaging and image compression. Firstly, a model for the sampling system in the frequency domain is prepared. It relates the Fourier transform of observed compressed samples with the unknown spectrum of the signal. Next, the reconstruction process based on the topic of compressed sensing is provided. We show that the sampling parameters play an important role on the average sample ratio and the quality of the reconstructed signal. The concept of condition number and its effect on the reconstructed signal in the presence of noise is introduced, and a feasible approach for choosing a sample pattern with a low condition number is given. We distinguish between the cases of known spectrum and unknown spectrum signals respectively. One of the model parameters is determined by the signal band locations that in case of unknown spectrum signals should be estimated from sampled data. Therefore, we applied both subspace methods and non-linear least square methods for estimation of this parameter. We also used the information theoretic criteria (Akaike and MDL) and the exponential fitting test techniques for model order selection in this case