The Welch Bounds
DateThursday, February 7, 2019 - 12:30pm
AbstractThe Welch bounds provide important design criteria for sequences in telecommunications and sensing applications. This talk will describe how the bounds, and useful characterizations of sequences that satisfy them with equality, can be obtained from a geometric perspective. This viewpoint unifies a number of observations that have been made regarding tightness of the bounds and their connections to symmetric tensors, tight frames, homogeneous polynomials, and t-designs. (Joint work with Somantika Datta and Steve Howard)
Fundamental Limits of Low Probability of Detection/Intercept Communications: Core Results and Future Directions
DateThursday, February 14, 2019 - 12:30pm
AbstractHiding transmitted signals is of paramount importance in many communication settings. While traditional security (e.g., encryption) prevents unauthorized access to message content, detection of the mere presence of a message by the adversary can have significant negative impact. This necessitates the use of low probability of detection/interception (LPD/LPI) communication, which not only protects the information contained in a transmission from unauthorized decoding, but also prevents the detection of a transmission in the first place. In this talk, I will present the fundamental classical and quantum limits of LPD/LPI communication, and overview future research directions.
Inverse source problem in a forced network
DateThursday, February 21, 2019 - 12:30pm
AbstractWe address the nonlinear inverse source problem of identifying a time- dependent source occurring in one node of a network governed by a wave equation. This is an important problem for applications like monitoring the electrical grid or testing a network of acoustic pipes. We prove that time records of the associated state taken at a strategic set of two nodes yield uniqueness of the two unknown elements: the source position and the emitted signal. Using graph theory, we discuss the number and location of the observation nodes. A non-iterative identification method that localizes the source node by solving a set of well posed linear systems is developped. Once the source node is localized, the emitted signal is identified using a deconvolution problem or a Fourier expansion. Numerical experiments on a five node graph confirm the feasability of the approach.