To send content items to your account,
please confirm that you agree to abide by our usage policies.
If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.
Find out more about sending content to .
To send content items to your Kindle, first ensure email@example.com
is added to your Approved Personal Document E-mail List under your Personal Document Settings
on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part
of your Kindle email address below.
Find out more about sending to your Kindle.
Note you can select to send to either the @free.kindle.com or @kindle.com variations.
‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi.
‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Learn about the most recent theoretical and practical advances in radar signal processing using tools and techniques from compressive sensing. Providing a broad perspective that fully demonstrates the impact of these tools, the accessible and tutorial-like chapters cover topics such as clutter rejection, CFAR detection, adaptive beamforming, random arrays for radar, space-time adaptive processing, and MIMO radar. Each chapter includes coverage of theoretical principles, a detailed review of current knowledge, and discussion of key applications, and also highlights the potential benefits of using compressed sensing algorithms. A unified notation and numerous cross-references between chapters make it easy to explore different topics side by side. Written by leading experts from both academia and industry, this is the ideal text for researchers, graduate students and industry professionals working in signal processing and radar.
In this chapter, we study specific rank-1 decomposition techniques for Hermitian positive semidefinite matrices. Based on the semidefinite programming relaxation method and the decomposition techniques, we identify several classes of quadratically constrained quadratic programming problems that are polynomially solvable. Typically, such problems do not have too many constraints. As an example, we demonstrate how to apply the new techniques to solve an optimal code design problem arising from radar signal processing.
Introduction and notation
Semidefinite programming (SDP) is a relatively new subject of research in optimization. Its success has caused major excitement in the field. One is referred to Boyd and Vandenberghe  for an excellent introduction to SDP and its applications. In this chapter, we shall elaborate on a special application of SDP for solving quadratically constrained quadratic programming (QCQP) problems. The techniques we shall introduce are related to how a positive semidefinite matrix can be decomposed into a sum of rank-1 positive semidefinite matrices, in a specific way that helps to solve nonconvex quadratic optimization with quadratic constraints. The advantage of the method is that the convexity of the original quadratic optimization problem becomes irrelevant; only the number of constraints is important for the method to be effective. We further present a study on how this method helps to solve a radar code design problem. Through this investigation, we aim to make a case that solving nonconvex quadratic optimization by SDP is a viable approach.
Email your librarian or administrator to recommend adding this to your organisation's collection.