Cognitive radio is a promising technology that improves the spectral utilisation by allowing
unlicensed secondary users to access underutilised frequency bands in an opportunistic manner.
This task can be carried out through spectrum sensing: the secondary user monitors the
presence of primary users over the radio spectrum periodically to avoid harmful interference to
the licensed service.
Traditional energy based sensing methods assume the value of noise power as prior knowledge.
They suffer from the noise uncertainty problem as even a mild noise level mismatch will lead
to significant performance loss. Hence, developing an efficient robust detection method is
important. In this thesis, a novel sensing technique using the F-test is proposed. By assuming
a multiple antenna assisted receiver, this detector uses the F-statistic as the test statistic which
offers absolute robustness against the noise variance uncertainty. In addition, since the channel
state information (CSI) is required to be known, the impact of CSI uncertainty is also discussed.
Results show the F-test based sensing method performs better than the energy detector and has
a constant false alarm probability, independent of the accuracy of the CSI estimate.
Another main topic of this thesis is to address the sensing problem for non-Gaussian noise.
Most of the current sensing techniques consider Gaussian noise as implied by the central limit
theorem (CLT) and it offers mathematical tractability. However, it sometimes fails to model the
noise in practical wireless communication systems, which often shows a non-Gaussian heavy-tailed
behaviour.
In this thesis, several sensing algorithms are proposed for non-Gaussian noise. Firstly, a non-parametric
eigenvalue based detector is developed by exploiting the eigenstructure of the sample
covariance matrix. This detector is blind as no information about the noise, signal and
channel is required. In addition, the conventional energy detector and the aforementioned F-test
based detector are generalised to non-Gaussian noise, which require the noise power and
CSI to be known, respectively. A major concern of these detection methods is to control the
false alarm probability. Although the test statistics are easy to evaluate, the corresponding null
distributions are difficult to obtain as they depend on the noise type which may be unknown and
non-Gaussian. In this thesis, we apply the powerful bootstrap technique to overcome this difficulty.
The key idea is to reuse the data through resampling instead of repeating the experiment
a large number of times. By using the nonparametric bootstrap approach to estimate the null
distribution of the test statistic, the assumptions on the data model are minimised and no large
sample assumption is invoked. In addition, for the F-statistic based method, we also propose
a degrees-of-freedom modification approach for null distribution approximation. This method
assumes a known noise kurtosis and yields closed form solutions. Simulation results show that
in non-Gaussian noise, all the three detectors maintain the desired false alarm probability by
using the proposed algorithms. The F-statistic based detector performs the best, e.g., to obtain
a 90% detection probability in Laplacian noise, it provides a 2.5 dB and 4 dB signal-to-noise
ratio (SNR) gain compared with the eigenvalue based detector and the energy based detector,
respectively
