In this thesis, advanced techniques for spectrum sensing in cognitive radio are addressed. The problem of small sample size in spectrum sensing is considered, and resampling-based methods are developed for local and collaborative spectrum sensing. A method to deal with unknown parameters in sequential testing for spectrum sensing is proposed. Moreover, techniques are developed for multiband sensing, spectrum sensing in low signal to noise ratio, and two-bits hard decision combining for collaborative spectrum sensing.
The assumption of using large sample size in spectrum sensing often raises a problem when the devised test statistic is implemented with a small sample size. This is because, for small sample sizes, the asymptotic approximation for the distribution of the test statistic under the null hypothesis fails to model the true distribution.
Therefore, the probability of false alarm or miss detection of the test statistic is poor. In this respect, we propose to use bootstrap methods, where the distribution of the test statistic is estimated by resampling the observed data. For local spectrum sensing, we propose the null-resampling bootstrap test which exhibits better performances than the pivot bootstrap test and the asymptotic test, as common approaches. For collaborative spectrum sensing, a resampling-based Chair-Varshney fusion rule is developed. At the cognitive radio user,
a combination of independent resampling and moving-block resampling is proposed to estimate the local probability of detection. At the fusion center, the parametric bootstrap is applied
when the number of cognitive radio users is large.
The sequential probability ratio test (SPRT) is designed to test a simple hypothesis against a simple alternative hypothesis.
However, the more realistic scenario in spectrum sensing is to deal with composite hypotheses, where the parameters are not uniquely defined. In this thesis, we generalize the sequential probability ratio test to cope with composite hypotheses, wherein the thresholds are updated in an adaptive manner, using the parametric bootstrap.
The resulting test avoids the asymptotic assumption made in earlier works. The proposed bootstrap based sequential probability ratio test minimizes decision errors due to errors induced by employing maximum likelihood estimators in the generalized sequential probability ratio test. Hence, the proposed method achieves the sensing objective. The average sample number (ASN) of the proposed method is better than that of the conventional method which uses the asymptotic assumption. Furthermore, we propose a mechanism to reduce the computational cost incurred by the bootstrap, using a convex combination of the latest K bootstrap distributions. The reduction in the computational cost does not impose a significant increase on the ASN, while the protection against decision errors is even better. This work is motivated by the fact that the sequential probability ratio test produces a smaller sensing time than its counterpart of fixed sample size test. A smaller sensing time is preferable to improve the throughput of the cognitive radio network.
Moreover, multiband spectrum sensing is addressed, more precisely by using multiple testing procedures. In a context of a fixed sample size, an adaptive Benjamini-Hochberg procedure is suggested to be used, since it produces a better balance between the familywise error rate and the familywise miss detection, than the conventional Benjamini-Hochberg. For the sequential probability ratio test, we devise a method based on ordered stopping times. The results show that our method has smaller ASNs than the Bonferroni procedure.
Another issue in spectrum sensing is to detect a signal when the signal to noise ratio is very low. In this case, we derive a locally optimum detector that is based on the assumption that the underlying noise is Student's t-distributed. The resulting scheme outperforms the energy detector in all scenarios. Last but not least, we extend the hard decision combining in collaborative spectrum sensing to include a quality information bit. In this case, the multiple thresholds are determined by a distance measure criterion. The hard decision combining with quality information performs better than the conventional hard decision combining
