Compressive power spectral density estimation with non-uniform sampling

Wireless communications have experienced a fast growth over the last two decades, which is still going on nowadays. This fact, together with the current static spectrum allocation, has made spectral resources scarce and has left very few bandwidth to new applications. However, actual measurements of spectrum utilization show that many assigned bands are not being used at every location and time. A solution that allows secondary users to transmit information using available spectrum is cognitive radio. A cognitive radio transceiver performs spectrum sensing, that is, it estimates the power spectral density of the received signal and then reliably detects whether unused spectrum is available or not. The estimation has to be done over a wide frequency range in order to increase the probability of finding available spectrum. With uniform sampling, the scheme considered in classical sampling theory, estimation over a wide frequency band requires very high sampling rates, which for current analog-to-digital conversion technology means a high power consumption. In this thesis, we study several methods for estimation of the power spectral density. They use non-uniform sampling schemes which allow reductions in the sampling rate, hence the word "compressive". These methods are least squares with hard limiting, maximum likelihood and a correlogram approach. The first two strategies use compressive sampling, while the last one employs random sampling. The performance of each method is studied by means of computer simulations. Besides, we have attempted to find new sampling matrices that guarantee the statistical identifiability of the power spectral density when compressive sampling is employed.