Collaborative Research: Coherent Wideband Processing for Sparse Distributed ELAAs: From Identifiability Theory to ISAC Co-Design

Modern wireless networks, vehicles, and robots increasingly rely on antenna systems whose smaller panels are spread over large physical areas. Such distributed designs can provide finer localization and more reliable communication without requiring one continuous, expensive antenna surface. However, the large gaps between panels can create false target images, or "ghosts," that make a real object difficult to distinguish from many incorrect copies. This project develops the theory, algorithms, and experimental evidence needed to determine when wideband radio signals can resolve these ambiguities and how antenna resources can be shared effectively between sensing and communication. The research supports emerging sixth-generation wireless infrastructure, safer automotive radar, and cooperative sensing for mobile robots. It also provides an open-source research toolkit, reproducible tutorials, and public 77-GHz radar datasets from vehicle and robot experiments, allowing other researchers to validate and extend the results using commercially available hardware. Education and workforce-development activities connect the University of Alabama and the University of California, Irvine through joint student advising, monthly research meetings, and reciprocal short-term graduate research visits. The project also integrates new instructional materials into graduate courses, supports summer and academic-year undergraduate research, broadens participation at an institution in an NSF EPSCoR jurisdiction, and brings live radar and robotics demonstrations to middle-school students through the annual MATHCOUNTS competition in Tuscaloosa, Alabama. The project addresses the unresolved problem of identifiability in sparse distributed extremely large aperture arrays operating with wideband signals in the near field. In these arrays, antenna modules separated by distances far exceeding the signal wavelength produce severe grating-lobe ambiguity under narrowband operation. Coherent wideband processing can suppress angular ghosts, but discrete frequency sampling can introduce periodic range replicas, and existing theory does not explain the transition from an ambiguity-dominated system to a reliably resolvable one. The research comprises three coupled activities. First, it extends the Bessel-Vandermonde harmonic decomposition from single-frequency to multi-frequency operation to derive identifiability conditions, degrees-of-freedom scaling laws, conditioning phase-transition maps, and Cramer-Rao bounds as functions of array geometry, bandwidth, frequency sampling, and target range. Second, it develops joint angle-range recovery and ambiguity-rejection methods that combine randomized stepped-frequency waveforms, Doppler-based kinematic consistency, and motion-assisted synthetic-aperture processing. These methods are validated using two 77-GHz radar modules mounted on an unmanned ground vehicle, together with a phase-calibration and data-integration pipeline for commercial millimeter-wave hardware. Third, it develops an ambiguity-aware integrated sensing and communication framework that allocates usable spatial and spectral resources through antenna geometry, beamforming, waveform design, and communication quality constraints. This framework also incorporates low-dimensional models for extended targets that occupy multiple range and angle resolution cells. The three-year scope centers on two-node distributed configurations as the primary experimentally validated setting across the two collaborating institutions, with multi-node and planar-aperture extensions pursued analytically. Together, these activities establish a rigorous and experimentally grounded foundation for wideband distributed arrays that jointly sense their surroundings and provide wireless communication. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.