Compressed sensing radar imaging of polar mesospheric summer echoes using tracking and MIMO approaches (CS-PMSE-MIMO)

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The basic physics behind the existence of polar mesospheric summer echoes (PMSE) is nowadays well understood, where atmospheric turbulence, charged ice particles and electrons play significant roles. Given this basic understanding, PMSE are being used as tracers to study the complicated atmospheric dynamics at polar mesospheric altitudes. PMSE observations with typical atmospheric radars are difficult to interpret, since temporal and spatial features can not be separated. In order to resolve these temporal and spatial ambiguities, atmospheric radar imaging (ARI) has been applied with different degrees of success, due to the systems used (beam widths, limited number of receivers, etc.), and due to the nature of the echoes. In general the echoes present relatively long correlations times (few hundreds of milliseconds to seconds) while they are horizontally drifting. Such drifting does not allow us to reduce the uncertainties on the obtained spatial correlations used in traditional methods. Usually, beamforming type algorithms, some of them including some type of regularization, are used for image formation. Unfortunately, this leads to artifacts in the image. A possible solution to this challenge is the exploitation of a priori knowledge about the image. Typically, the image is sparse and only changes slowly over time. The application of compressed sensing (CS) techniques in ARI has been proposed by other research groups but needs further investigation and implementation. We have recently applied coherent MIMO techniques in ARI to study ionospheric irregularities. This was the first time MIMO was used in atmospheric radars. Combining MIMO with CS rises many challenging research questions as the sensing matrix is highly structured. Furthermore, the combination of CS and tracking opens a new field of research in ARI. First theoretical challenges and opportunities arise from the fact that the number of measurements may not be large enough so that existing results and algorithms for large problems can not be applied. Special challenges arise from the fact that we have to characterize the sparsity, i.e., the domain in which it holds, and the time dynamics without having a reliable reference. A possible solution to this problem might be the use of recovery and tracking algorithms which do not focus on making a best effort in image reconstruction alone but also yield some information on the trustworthiness of the result. Besides simulations, we will exploit existing radar experiments to create physically motivated models for the sparsity and the time dynamics, and conduct new experiments to test and improve our proposed methods. The inclusion of MIMO, besides helping in the inversion, might serve also as test scenario to evaluate the performance of the proposed methods in systems not able to use MIMO.