Image formation in synthetic aperture radio telescopes

Next generation radio telescopes will be much larger, more sensitive, have much larger observation bandwidth and will be capable of pointing multiple beams simultaneously. Obtaining the sensitivity, resolution and dynamic range supported by the receivers requires the development of new signal processing techniques for array and atmospheric calibration as well as new imaging techniques that are both more accurate and computationally efficient since data volumes will be much larger. This paper provides a tutorial overview of existing image formation techniques and outlines some of the future directions needed for information extraction from future radio telescopes. We describe the imaging process from measurement equation until deconvolution, both as a Fourier inversion problem and as an array processing estimation problem. The latter formulation enables the development of more advanced techniques based on state of the art array processing. We demonstrate the techniques on simulated and measured radio telescope data.Comment: 12 page

Adaptive beamforming for uniform linear arrays with unknown mutual coupling

This letter proposes a new adaptive beamforming algorithm for uniform linear arrays (ULAs) with unknown mutual coupling. It is based on the fact that the mutual coupling matrix (MCM) of a ULA can be approximated as a banded symmetric Toeplitz matrix as the mutual coupling between two sensor elements is inversely related to their separation, and hence it is negligible when they are separated by a few wavelengths. Taking advantage of this specific structure of the MCM, a new approach to calibrate the signal steering vector is proposed. By incorporating this improved steering vector estimate with a diagonally loaded robust beamformer, a new adaptive beamformer for ULA with unknown mutual coupling is obtained. Simulation results show that the proposed steering vector estimate considerably improves the robustness of the beamformer in the presence of unknown mutual coupling. Moreover, with appropriate diagonal loading, it is found that the proposed beamformer can achieve nearly optimal performance at all signal-to-noise ratio (SNR) levels. © 2002-2011 IEEE.published_or_final_versio

Stochastic Optimization: Theory and Applications

As an important branch of applied mathematics, optimization theory, especially stochastic optimization, becomes an important tool for solving multiobjective decision-making problems in random process recently. Many kinds of industrial, biological, engineering, and economic problems can be viewed as stochastic systems, for example, area of communication, gene, signal processing, geography, civil engineering, aerospace, banking, and so forth. Stochastic optimization is suitable to solve the decision-making problems in these stochastic systems

Model-Switched Beamformer with Large Dynamic Range

The strong desired signal will be mitigated due to "self-nulling" for the adaptive beamformer, even if the array calibration is used. The proposed methodology switches the models between phased array and adaptive array. In general, the system utilizes Frost adaptive beamforming. However, it will be switched to phased array if the "self-nulling" appears. According to the estimation of the array pattern at the direction of desired signal, we can determine if the "self-nulling" happens. The new approach is much easier to implement compared with the various robust beamforming algorithms

Overview of Constrained PARAFAC Models

In this paper, we present an overview of constrained PARAFAC models where the constraints model linear dependencies among columns of the factor matrices of the tensor decomposition, or alternatively, the pattern of interactions between different modes of the tensor which are captured by the equivalent core tensor. Some tensor prerequisites with a particular emphasis on mode combination using Kronecker products of canonical vectors that makes easier matricization operations, are first introduced. This Kronecker product based approach is also formulated in terms of the index notation, which provides an original and concise formalism for both matricizing tensors and writing tensor models. Then, after a brief reminder of PARAFAC and Tucker models, two families of constrained tensor models, the co-called PARALIND/CONFAC and PARATUCK models, are described in a unified framework, for $N^{th}$ order tensors. New tensor models, called nested Tucker models and block PARALIND/CONFAC models, are also introduced. A link between PARATUCK models and constrained PARAFAC models is then established. Finally, new uniqueness properties of PARATUCK models are deduced from sufficient conditions for essential uniqueness of their associated constrained PARAFAC models