Design and analysis of multi-coset arrays

Abstract

An efficient sparse antenna array architecture is developed for coherent imaging of sparse but otherwise unknown scenes. In this architecture, the array elements form a periodic nonuniform pattern. Using analysis that explicitly takes into account the presence of noise, we develop an efficient pattern design procedure based on co-arrays, describe an efficient scene support recovery algorithm as part of image reconstruction in the form of a modification to the MUSIC algorithm, and discuss a failure detection technique based on evaluating "back-projection" error. Since our development exploits a close connection to multi-coset sampling of bandlimited waveforms, our results may in turn may also be useful in the design of those systems.

Compression Limits for Random Vectors with Linearly Parameterized Second-Order Statistics

“…The angular spectrum can be obtained as the coefficients α s in the expansion (12) (see [10]), which correspond to the intensity impinging from 2L−1 looking directions. Recent formulations have also considered circulant subspaces [34], [35]. 4) Sparse Spectrum Estimation: modal analysis can be used to identify the components of a sum of sinusoids in noise (time-domain signals) [36], [37] or to estimate the direction of arrival (DoA) of a number of point sources in the far field (space-domain signals) [12], [20]- [23], [38] using the compressed observations y. Σ is expanded as…”

“…Circular sparse rulers seem to have been introduced in signal/array processing in [47] and used later in [34], [35], [45]. Theorem 6 basically states that a covariance sampler for circulant subspaces is a length-(L − 1) circular sparse ruler, which gives a practical design criterion just for the nonperiodic case.…”

Compressive Periodogram Reconstruction Using Uniform Binning

“…Our work in P1 is motivated in part by [3], which attempts to reconstruct the angular spectrum from spatial-domain samples received by a non-ULA. Comparable works to [3] for P2 are [4] and [5], which focus on the analog signal reconstruction from its sub-Nyquist rate samples.…”

Compressive angular and frequency periodogram reconstruction for multiband signals

“…With respect to P1, our work is inspired by the work of [1], which focuses on the angular spectrum reconstruction from spatial-domain samples received by a non-ULA. However, the intention of [1] to reconstruct the actual angular spectrum instead of its periodogram leads to an underdetermined problem requiring a sparsity constraint on the angular domain to solve it.…”

“…With respect to P1, our work is inspired by the work of [1], which focuses on the angular spectrum reconstruction from spatial-domain samples received by a non-ULA. However, the intention of [1] to reconstruct the actual angular spectrum instead of its periodogram leads to an underdetermined problem requiring a sparsity constraint on the angular domain to solve it. We will show in this paper that by focusing on only the angular periodogram reconstruction, we have an overdetermined problem that is solvable even without a sparsity constraint on the angular domain.…”