Sparse recovery in MIMO radar - dependence on the support structure

Dorsch, Dominik und Rauhut, Holger (2015): Sparse recovery in MIMO radar - dependence on the support structure. CoSeRa 2015 : 3rd International Workshop on Compressed Sensing Theory and its Applications to Radar, Sonar and Remote Sensing, Pisa, 17-19 June 2015. In: 2015 3rd International Workshop on Compressed Sensing Theory and its Applications to Radar, Sonar and Remote Sensing (CoSeRa), IEEE. S. 56-60

Abstract

We consider a multiple-input-multiple-output (MIMO) radar model and prove recovery results for a compressed sensing (CS) approach. The MIMO radar model is based on random probes emitted by NT transmitters and then, after a linear transformation depending on s targets being present in the angle-range-Doppler domain, are received by NR receivers. Since each receiver takes Nt samples during one time interval, one obtains NtNR measurements overall. We show that the restricted isometry property (RIP) is fulfilled, provided that the number of samples Nt basically grows linearly in the number of targets s (up to some additional logarithmic factors). This result comes somehow surprisingly, considering that only the fraction Nt of the total number of measurements NtNR appears in the condition. However, using general results from CS, we show that our RIP result cannot be improved substantially. Our arguments reveal how the fine structure of the support set comes into play. Indeed, we introduce a deterministic model for the support sets which incorporates a measure on how equally distributed the support set is among certain angle classes. In this way certain “bad” support sets which concentrate on “similar” angles are avoided. As a result we are able to prove a nonuniform recovery result revealing linear dependence of the possible detectable number of targets in the total number of measurements (up to logarithmic factors). We compare our results to a recent analysis by Strohmer & Friedlander in which the support sets are assumed to be random.

• Dokumententyp: Konferenzbeitrag (Paper)
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Lehrstuhl für Mathematik der Informationsverarbeitung
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• Sprache: Englisch