Multiple gene phylogenetic analysis is of interest since single gene analysis often results in poorly resolved trees. Here the use of spectral techniques for analyzing multi-gene data sets is explored. The protein sequences are treated as categorical time series and a measure of similarity between a pair of sequences, the spectral covariance, is used to build trees. Unlike other methods, the spectral covariance method focuses on the relationship between the sites of genetic sequences. We consider two methods with which to combine the dissimilarity or distance matrices of multiple genes. The first method involves properly scaling the dissimilarity measures derived from different genes between a pair of species and using the mean of these scaled dissimilarity measures as a summary statistic to measure the taxonomic distances across multiple genes. We introduced two criteria for computing scale coefficients which can then be used to combine information across genes, namely the minimum variance (MinVar) criterion and the minimum coefficient of variation squared (MinCV) criterion. The scale coefficients obtained with the MinVar and MinCV criteria can then be used to derive a combined-gene tree from the weighted average of the distance or dissimilarity matrices of multiple genes. The second method is based on the singular value decomposition of a matrix made up of the p-vectors of pairwise distances for k genes. By decomposing such a matrix, we extract the common signal present in multiple genes to obtain a single tree representation of the relationship between a given set of taxa. Influence functions for the components of the singular value decomposition are derived to determine which genes are most influential in determining the combined-gene tree.

Opportunistic spectrum reuse is a promising solution to the two main causes of spectrum scarcity: most of the radio frequency (RF) bands are allocated by static licensing, and many of them are underutilized. Frequency spectrum can be more efficiently utilized by allowing communication systems to find out unoccupied spectrum and to use it harmlessly to the licensed users. Reliable sensing of these spectral opportunities is perhaps the most essential element of this technology. Despite significant work on spectrum sensing, further performance improvement is needed to approach its full potential. In this dissertation, wireless spectrum sensing networks (WSSNs) are investigated for reliable detection of the primary (licensed) users, that enables efficient spectrum utilization and minimal power consumption in communications. Reliable spectrum sensing is studied in depth in two parts: a single sensor algorithm and then cooperative sensing are proposed based on a spectral covariance sensing (SCS). The first novel contribution uses different statistical correlations of the received signal and noise in the frequency domain. This detector is analyzed theoretically and verified through realistic simulations using actual digital television signals captured in the US. The proposed SCS detector achieves significant improvement over the existing solutions in terms of sensitivity and also robustness to noise uncertainty. Second, SCS is extended to a distributed WSSN architecture to allow cooperation between 2 or more sensors. Theoretical limits of cooperative white space sensing under correlated shadowing are investigated. We analyze the probability of a false alarm when each node in the WSSN detects the white space using the SCS detection and the base station combines individual results to make the final decision. The detection performance compared with that of the cooperative energy detector is improved and fewer sensor nodes are needed to achieve the same sensitivity. Third, we propose a low power source coding and modulation scheme for power efficient communication between the sensor nodes in WSSN. Complete analysis shows that the proposed scheme not only minimizes total power consumption in the network but also improves bit error rate (BER). / text