Principles of Modern Radar - Volume 2 1891121537

Radar Applications of SparseReconstruction andCompressed SensingJason T. Parker, Matthew A. Ferrara, Lee C. PotterCHAPTER5✬Chapter Outline5.1 Introduction ................................................................... 1475.2 CS Theory ..................................................................... 1505.3 SR Algorithms ................................................................. 1665.4 Sample Radar Applications .................................................... 1835.5 Summary ...................................................................... 1965.6 Further Reading ............................................................... 1965.7 Acknowledgments ............................................................. 1975.8 References ..................................................................... 1975.9 Problems ...................................................................... 207✫✩✪5.1 INTRODUCTIONSparse reconstruction and design through randomization have played significant rolesin the history of radar signal processing. A recent series of theoretical and algorithmicresults known as compressive or compressed sensing (CS) has ignited renewed interest inapplying these ideas to radar problems. A flurry of research has explored the applicationof CS approaches as well as closely related sparse reconstruction (SR) techniques to awide range of radar problems. This chapter will provide some historical context for CS,describe the existing theoretical results and current research directions, highlight severalkey algorithms that have emerged from these investigations, and offer a few examples ofthe application of these ideas to radar.5.1.1 OrganizationThe chapter is organized into three sections. Section 5.2 develops the motivation andtheoretical framework for SR and CS. We attempt to motivate these ideas from a radarperspective while also highlighting intuitions and connections with basic linear algebra andoptimization theory. Section 5.3 explores the myriad of available algorithms for solvingSR problems and the provable performance guarantees associated with these algorithmswhen used in conjunction with measurements which satisfy CS design criteria. Section 5.4concludes with a selection of examples that illustrate how to apply these ideas to radarproblems.147