New directions in sparse array signal processing
Abstract
In recent years, sparse arrays such as nested arrays, coprime arrays, and supernested arrays have been of great interest. These arrays admit closed form expressions, and at the same time enjoy good difference coarrays with long ULA (uniform linear array) segments having O(N2) virtual sensors, where N is the number of physical sensors. This has resulted in several advantages of sparse arrays over ULAs in DOA estimation and spectrum sensing, such as the ability to identify O(N2) sources, as well as improved resolvability of closely spaced sources. The proposed project will explore a number of new directions in sparse array signal processing and related areas, including graph signal processing and the identification of hidden periodicities in data. One important problem to be studied is the robustness of sparse arrays to sensor failure. Sensor failure often results in a change in the coarray, especially the ULA part, which degrades the identifiability properties. In this respect sparse arrays are less robust than ULAs — this is the price paid for the O(N2) identifiability. One goal of this project is to undertake a systematic study of robustness of sparse arrays. The tradeoff between robustness and economy will be studied, and the relative importance or “essentialness” of each sensor (from the coarray perspective) and the overall “fragility” of sparse array geometries will be quantified. This is expected to result in new sparse arrays which are more optimized for robustness. Oftentimes, a failed sensor merely results in a punctured coarray where a hole is generated in the central ULA portion of the coarray. The possibility of identifying O(N2) sources from such punctured coarrays will be studied. Another important new direction will be the study of sparse arrays with one-bit quantized outputs. These arrays simplify the electronics a great deal, and have received some attention in the context of DOA estimation and massive MIMO communications. The estimation of DOAs from such quantized information is possible by using some clever connections between covariances of the quantized data and the original data. There is good evidence that this is more successful with sparse arrays than with ULAs. However the method works under restricted assumptions on quantizers and noise statistics, and needs to be generalized. An in depth study will therefore be undertaken. Another important issue in practice is that the DOA changes slowly over time because of moving sources. It is desirable to update DOA estimates in a recursive way, rather than go through the entire computation process from the beginning. Recursive algorithms for updating estimates in the context of sparse arrays with O(N2) sources have received little attention, and this will be explored in detail. Next, the use of machine learning techniques is becoming more widespread in signal processing applications. One of the goals of this project is to study the feasibility of these methods in array processing, especially DOA estimation with sparse arrays. The proposed work will also go deeper into the connection between Ramanujan-periodicity techniques and array processing algorithms such as MUSIC, and put the recently proposed Ramanujan-MUSIC algorithm on a firm footing. Finally the impact of the emerging area of graph signal processing in the field of array processing will be explored.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jul 10, 2018
- Source ID
- N000141812390
Entities
People
- Palghat Vaidyanathan
Organizations
- California Institute of Technology
- Office of Naval Research
- United States Navy