Super-Resolution with Phased-Array Digital Signal Processing for Weather Radars

Phased-array technology has long been applied to atmospheric radars to measure upper-air motions in troposphere—mesosphere [1] and is emerging for weather radars to rapidly observe tropospheric precipitation [2] [3]. It is necessary for phased-array signal processing (methodologies to digitally process snap-shot signal values received in element antennas of which a phased-array antenna consists) of these radars to accomplish highly flexible sidelobe controls since these radars have to receive signals from enormous numbers of small targets distributed in wide regions of angles.

The atmospheric radars have used a method based on Capon’s proposal [4]. It is known that the Capon method accomplishes very good sidelobe controls with a large number of snap shots which can be obtained in the atmospheric radars. Meanwhile, (phased-array) weather radars offer only several snap shots to perform rapid scan, for which a type of minimum mean square error (MMSE) methods was proposed. The MMSE method can be interpreted as a modification of the Capon method, which is to include an approximation to work with a small number of snap shots [5].

To additionally achieve super-resolution, sparse estimation methods such as ones including L1 regularization have been proposed and their good performances have been shown [6] [7] [8]. However, from a perspective of atmospheric and weather radars to those sparse estimators (for example, LASSO [9]), two problems can be pointed out. One is that their solutions can be biased by the regularization which is not derived from probabilistic properties of received signals but added intentionally to force solutions to be sparse vectors. The other is that they have a hyper parameter on the regularization term, which requires us to develop an extension method to tune it properly.

This work proposes a phased-array signal processing method to achieve both super-resolution and unbiased features. The method is completely based on probabilistic properties of received signals of these radars and maximizes a marginal likelihood derived by Bayes’ theorem. The method does not have any intentional additions such as the L1 regularization term to give biases onto its solutions and hyper-parameters which need to be tuned. Furthermore, it is known that an iterative process to maximize the marginal likelihood tends to converge to sparse solutions [10]. The proposed method is evaluated in qualitative and quantitative manners in comparison with existing methods. The evaluations are performed by simulations assuming weather targets whose angular distributions are created by real radar data obtained by the CSU-CHILL radar. Also, simulations assuming some solid targets are carried out to apparently show performances of its super-resolution.

The proposed method can contribute to get more details of weather system. For example, it would enable us to precisely reveal on-RHI melting layer with constant angular resolution (not affected by changes of angular resolution depending on range). Furthermore, the proposed method can be applied to various signal processing in atmospheric and weather radars. Furthermore, it can be expected to work in weather radar Doppler spectral processing with almost the same performances since governing equations of Doppler spectral and phased-array signal processing are approximately equivalent as indicated in [11]. Also, it is worth applying for ranging as in [12].

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