Optimal Sensor Placement for Calibration-Involved Radio Astronomy Imaging Applications

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Abstract

In radio astronomy (RA), one of the key tasks is the estimation of the celestial source powers, i.e. imaging. To maximize the performance, it is crucial to optimize the receiver locations before the construction of a telescope array. However, although system calibration is an integral and crucial process of imaging, it has rarely been addressed for RA sensor placement problems previously. This motivates us to investigate whether incorporating calibration can result in better array designs. In this thesis, we focus on the calibration of the sensors’ complex-scalar gains in particular, which are treated as nuisance parameters for the image estimation. The associated Cramer-Rao bound (CRB) is derived and employed as the design criterion. The nonlinear CRB-based sensor placement problem is cast as an NP-hard combinatorial optimization problem, and we adopt two approaches to solve such by approximation: (i) greedy algorithm and (ii) convex optimization with semidefinite relaxation. The former is chosen for simulations due to its good performance and lower computational complexity. Extensive simulations shows that compared to the calibration-excluded design, the proposed one only provides slight improvements to the imaging quality. However, the proposed array demonstrates the potential of accelerating the convergence of the gain estimation procedures. Through further investigation, we conclude that the lack of imaging quality improvident can be a consequence of the gain and image being near-orthogonal parameters.