A Book of Abstracts for the 2015 Underwater Acoustic Signal Processing

Listings Sparse and Coprime Sampling: Benefits, Challenges and Future Directions Piya Pal University of Maryland, College Park 2305 A V Williams University of Maryland College Park MD 20742 [email protected] Coprime and nested sampling have been recently introduced as powerful sparse deterministic sampling techniques that can exploit statistical properties of signals to sample them at rates significantly lower than the Nyquist limit, without losing the desired information in many applications of practical interest. Coprime and nested samplers, in their original form, were designed for sub-sampling wide-sense stationary (WSS) signals, which commonly arise in a large number of applications such as spectrum estimation, source localization, wireless communication and so forth. Through judicious choice of sampling instants, these samplers can ensure that the autocorrelation of WSS signals get sampled at the Nyquist rate, although the WSS signal itself may be sampled at significantly lower rates. This can have profound impact depending on the application: for instance, in wideband spectrum sensing for cognitive radios, one can monitor a very wide frequency band to look for available spectral holes, without using a power hungry analog-to-digital (A/D) converter. Similarly for source localization in phased antenna arrays, one can identify O(M) sources using only M sensors, thereby significantly saving hardware and real estate. In this talk, I will first review the mathematical principles behind coprime sampling and a related concept of coprime filterbanks for sub-Nyquist sampling of WSS signals. The superior performance of coprime sampling over traditional samplers will be demonstrated with regards to two main applications: wideband spectrum sensing and direction-of-arrival (DOA) estimation. I will show further extensions of these sampling schemes to handle multidimensional signals, as well as those possessing higher order statistics (such as speech). I will also discuss challenges associated with practical implementation of coprime samplers, especially in presence of finite observation length, and under violation of WSS assumptions. These challenges give rise to the possibility of novel extensions, both with regards to sampling geometries, and reconstruction algorithms. I will conclude the talk by discussing some promising future research directions where nested and coprime sampling can be used as generic “data sketching” tools, to compress high dimensional data, and potentially augmenting compressed sensing based techniques, which largely use random sampling.