Prabhu Babu

This monograph presents a theoretical background and a broad introduction to the Min-Max Framework for Majorization-Minimization (MM4MM), an algorithmic methodology for solving minimization problems by formulating them as min-max problems and then employing majorization-minimization. The monograph lays out the mathematical basis of the approach used to reformulate a minimization problem as a min-max problem. With the prerequisites covered, including multiple illustrations of the formulations for convex and non-convex functions, this work serves as a guide for developing MM4MM-based algorithms for solving non-convex optimization problems in various areas of signal processing. As special cases, the majorization-minimization technique is discussed to solve min-max problems encountered in signal processing applications and min-max problems formulated using the Lagrangian. Detailed examples of using MM4MM in ten signal processing applications such as phase retrieval, source localization, independent vector analysis, beamforming, and optimal sensor placement in wireless sensor networks are presented. The devised MM4MM algorithms are free of hyper-parameters and enjoy the advantages inherited from the use of the majorization-minimization technique such as monotonicity.

This book gives you a comprehensive overview of key optimization tools that can be used to design radar waveforms and adaptive signal processing strategies under practical constraints -- strategies such as power method-like iterations, coordinate descent, and majorization-minimization – that help you to meet the more and more stressing sensing system requirements. The book walks you through how radar waveform synthesis is obtained as the solution to a constrained optimization problem such as finite energy, unimodularity (or being constant-modulus), and finite or discrete-phase (potentially binary) alphabet, which are dictated by the practical limitations of the real systems. Several approaches in each of these broad frameworks are detailed and various applications of these optimization techniques are described. Focusing on a holistic approach rather than a problem-specific approach, the book shows you what you need to effectively formulate waveform design and understand the flexibility of the framework for adapting to your own specific needs. You’ll have full access to the tools and knowledge you need to design waveform with optimized correlation/cross-correlation properties for SISO/SIMO and MIMO radars, taking into account spectral constraints for cognitive rads, as well as coexistence with communications and mitigate possible Doppler and quantization errors, and more. The book also includes representative software codes that further help you generate the described solutions. With its unique style of covering mathematical results along with their applications from diverse areas, this is a much-needed, detailed handbook for industry researchers, scientists and designers including medical, marine, defense, and automotive companies. It is also an excellent resource for advanced courses on radar signal processing.