Compressive Power Spectrum Estimation

Abstract

In the recent development of wireless communication several applications, such as spectrum sensing for cognitive radio are only interested in the power spectrum. These applications do not require the reconstruction of the original analog signal. According to the Whittaker-Kotelnikov-Shannon-Nyquist theorem, the sampling rate must be at least twice the maximum frequency present in the signal if we want to recover the signal from its samples. If we estimate the power spectrum directly by using a high-rate analog-to-digital converter, we will find that such high-rate ADCs consume a large amount of power because of its high sampling rate. To reduce the burden on the ADCs, we investigate compressive power spectrum sensing. Since the power spectrum is calculated based on the autocorrelations of the signal, we do not need to recover the signals. This allows a reduction of the sampling rate compared with the Nyquist rate while maintaining perfect power spectrum reconstruction. In this thesis, we study power spectrum estimation of a wide-sense stationary signal. In general, the signal, whose power spectrum is to be estimated, is sampled by multi-coset sampling. The parametric method to estimate the power spectrum of the signal is also evaluated and the study of the performance of non-uniform sampling is explored as well.