PhD Theses

Optical fiber communication systems provide the infrastructure for high-capacity data transfer. The field has shown dramatic increases in transmission capacity, and yet the demand for capacity also grows significantly. We are in a situation in which systems must continually grow in capacity to keep pace with the demand, thereby necessitating continual innovation and technical advances.

Applications of semidefinite optimization in signal processing are often derived from the Kalman-Yakubovich-Popov lemma and its extensions, which give sum-of-squares theorems of nonnegative trigonometric polynomials and generalized polynomials.