no code implementations • 10 Mar 2024 • Yinyan Bu, Robin Rajamäki, Anand Dabak, Rajan Narasimha, Anil Mani, Piya Pal
This paper addresses the problem of single snapshot Direction-of-Arrival (DOA) estimation, which is of great importance in a wide-range of applications including automotive radar.
no code implementations • 13 Jan 2024 • Robin Rajamäki, Piya Pal
In this paper, we show that two array geometries with identical sum co-arrays, and the same number of physical and virtual sensors, need not achieve equal identifiability, regardless of the choice of waveform of a fixed reduced rank.
no code implementations • 12 Jan 2024 • Yinyan Bu, Robin Rajamäki, Pulak Sarangi, Piya Pal
We explore deliberately introducing holes into this virtual array to leverage resolution gains provided by the increased aperture.
no code implementations • 12 Jan 2024 • Robin Rajamäki, Mehmet Can Hücümenoğlu, Pulak Sarangi, Piya Pal
In this paper, we make advances towards solidifying this understanding by revealing the role of the physical beampattern of the sparse array on the performance of low rank matrix completion techniques.
no code implementations • 10 May 2023 • Robin Rajamäki, Piya Pal
We derive necessary and sufficient conditions that the array geometry and transmit waveforms need to satisfy for the Kruskal rank -- and hence identifiability -- to be maximized.
no code implementations • 4 Jan 2023 • Pulak Sarangi, Mehmet Can Hucumenoglu, Robin Rajamaki, Piya Pal
Our results also formally prove the well-known empirical resolution benefits of sparse arrays, by establishing that the minimum separation between sources can be $\Omega(1/P^2)$, as opposed to separation $\Omega(1/P)$ required by a ULA with the same number of sensors.
no code implementations • 4 Jan 2023 • Pulak Sarangi, Ryoma Hattori, Takaki Komiyama, Piya Pal
Distinct from prior works which exploit sparsity in appropriate domains in order to solve the resulting ill-posed problem, this paper explores the role of binary priors in super-resolution, where the spike (or source) amplitudes are assumed to be binary-valued.
no code implementations • 4 May 2016 • Abbas Kazemipour, Sina Miran, Piya Pal, Behtash Babadi, Min Wu
Assuming that the parameters are compressible, we analyze the performance of the $\ell_1$-regularized least squares as well as a greedy estimator of the parameters and characterize the sampling trade-offs required for stable recovery in the non-asymptotic regime.