In this interview, we talk to Greg and Jon authors of the book Optimal-Peak-Sidelobe Polyphase Codes. We discuss the motivation behind writing the book, the target audience, the most useful aspects of the book, the challenges of writing the book, and advice for other engineers who are considering writing a book.
1.Could you summarize the main content of your book? What are the key topics addressed?
The book’s central focus is the pursuit of the lowest achievable autocorrelation peak sidelobe level (PSL) of polyphase codes for code lengths of interest, and the codes that achieve them. This pursuit has challenged engineers and mathematicians for nearly 80 years. It relates to, and draws from, fields as diverse as Combinatorics, Design Theory, Discrete Optimization, Fourier Theory, and Real Analysis. In connection with, and at time in addition to, this central focus, the book develops approaches, algorithms, and mathematics essential to signal processing, optimization or search.
The benefit of this knowledge and these codes is the ability to enhance detection performance for radar and communications, for targets or transmitters of interest. While the application that serves as the motivation for this work, the material also has applications in communications system, LIDAR, ultrasound, remote sensing, and centering control systems.
This book gives history and background, then theoretical foundations, before addressing search approaches and results to date. It provides analytical tools for pursuing the best codes of given lengths. This particular endeavor is known to be computationally demanding, and is suspected to be NP-Hard, hence requiring resources that grow exponentially with the code length. Still, the book is intended to show that the chase can at times yield excellent codes, and that there are useful methods and fascinating mathematics that can help along the way.
2.What is the primary purpose of your book? How do you envision it helping readers in their work or studies?
The book is intended for students or practitioners of waveform design for radar and communications, but should also be useful in applications including LIDAR, ultrasound, remote sensing, and centering control systems.
Waveform design is a creative and challenging endeavor that involves trade-offs, something it has in common with the larger endeavor of radar and communication systems design. A practitioner needs a toolbox of methods for the job. Our book provides one class of tools for that toolbox, specifically, those for finding or constructing the optimal-sidelobe codes for different lengths.
This is meant to be both a starting point for aspiring waveform designers, and a resource for experienced practitioners, enabling them to develop sets of optimal-sidelobe codes. We provide some of the background and history before moving on to the theoretical foundations, ultimately arriving at search methods and results achieved to this point in time. The final chapter looks ahead to some of the promising computational developments that may change, and hopefully even revolutionize, the search for optimal codes.
3.What sets your book apart from other works in the same field? Are there any innovative concepts, methodologies, or insights that make it stand out?
Although there are a number of books on radar and communications waveforms, few, if any, focus squarely on the search for binary or polyphase codes with optimal sidelobes for aperiodic autocorrelation (which is most likely the best model for most radar systems). For example, an existing book that would seem to be similar in focus is Signal Design for Good Correlation by Solomon Golomb and Guang Gong (Cambridge University, 2005). However, the reader of Golomb and Gong must wait until Chapter 12 (and only Chapter 12) to find material relevant for the aperiodic model. Another is Radar Signals (Wiley, 1005) by Nadav Levanon and Eli Mozeson, which is broader in scope, while our book delves more deeply into challenges and methods for finding optimal peak sidelobe codes. Our book benefits from twenty years of searching, analyzing and publishing results in this special area of waveform design for radar and communications.
The book provides working Python code for some of the searches described. The book provides working Python code illustrating how to efficiently navigate complex search space, modulate realizable signals, and analyze their properties. It also identifies approaches that have worked the best for us in our twenty years and more of pursuing optimal codes. Despite the well-known computational challenges, and cases where optimal codes occur more often than expected, there exist methods for constructing sets of optimal codes. The hope is to hand off to new practitioners these insights and lessons learned.
The initial chapters also provide some of the history of radar pulses and pulse compression that first spawned interest in low-sidelobe codes. The story highlights a number of figures whose names are not necessarily well-known, but who contributed to pre-World-War-II radar development, to the Mercury program and to radio-astronomy, in other words, some of the greatest stories of the twentieth century.
4.Who is the intended readership of this book? Are there specific industries, professionals, or fields of study that would benefit most from this content?
There are really two sets of intended readers. One set are colleagues working in waveform design for radar, communications and related applications. The hope is to provide them with tools and inspiration that will lead to new designs of waveforms employing optimal-sidelobe codes.
Another set are mathematicians looking for interesting practical applications of Mathematics. It has been a pleasant discovery for me (the first author), as a former Mathematics graduate student, to find that the pursuit of optimal-PSL polyphase codes calls for concepts and methods from Group Theory, Combinatorics, Matrix Theory, Complexity Theory, and other areas.
5.What are the most important lessons or insights you want readers to take away from this book?
I hope that readers come away with a sense that the book is a labor of love. We have enjoyed collecting and putting in writing what we have learned from working on these problems for the past twenty years. These lessons have enriched our lives, but have, by no means, been gained easily
In addition, we hope that other investigators take advantage of the computer code provided in this book, and help advance the frontier of optimal peak sidelobe levels and codes.
6.Does your book include any original research, cases studies or data? If so, could you highlight some of the most significant findings?
The book includes a number of results that were original at the time they were generated and published, most of them in IEEE journals, primarily Transactions on Aerospace and Electronic Systems. This book should be a good resource for those in certain applications, because it brings these results together for easy access.
The book includes a number of results that were original at the time they were generated and published, most of them in IEEE journals, primarily Transactions on Aerospace and Electronic Systems. This book should be a good resource for those in certain applications, because it brings these results together for easy access.
The following are two examples of interesting recent results discussed in the book:
(a) Complementary Code Sets are fascinating sets of polyphase codes whose autocorrelations sum to give zero sidelobes for every delay. It might also be desired to have codes that can be swapped in and out of the set, and replaced, in such a way that complementarity is preserved. A useful property of these sets is that what these codes bring to the set is their autocorrelation. So, if it is desired to replace one code with another while preserving complementarity, it is enough to find other codes having the same autocorrelation as that code. Despite decades of work of study on autocorrelation properties of binary and polyphase codes, it has only been in recent years (since about 2005) that the properties of codes sharing the same autocorrelation has been determined. Another nice aspect of this is that it suggests another waveform property to investigate – predictability. In the cat-and-mouse games of today’s electronic battlespaces, reduced predictability can be as important as optimally low sidelobes.
(b) Generalized Barker Sequence generalize to polyphase codes of the well-known (binary) Barker Codes. The binary Barker Codes are famously few in number (assuming the Barker Conjecture holds). We experimented in departing from the usual process of fixing the number of phases and then seeking the longest code length for which the best peak sidelobe can be found. Instead, we tried fixing code lengths and determining the lowest achievable peak sidelobe level for each setting of number of phases.
In the process, we found that Generalized Barker Sequences are not as rare as might be expected.
7. Does your book address any new or emerging trends in the field? How does it prepare readers for future developments?
The final chapter, Chapter 9, is focused on promising new developments that may change the game of optimal-PSL code searches. One of these is quantum computing, for which the jury is still mostly out regarding its revolutionary possibilities. Others include evolutionary methods, parallel computing, optical computing, and the use of Graphical Processing Units (GPUs) and Tensor Processing Units (TPUs).
Another development of a more engineering nature that is mentioned in the book is the prospect of lower-cost amplifiers of certain classes. Someday, it will be possible to loosen or remove the current constant-amplitude requirement, making possible a wider class of optimization approaches.
8.What personal experiences, if any, have shaped your perspective or approach to the topics discussed in your book?
I (the first author) have had several personal experiences that helped lead to the material in this book. One was my PhD research at the University of Wisconsin, that involved determining the computational complexity of certain robust stability problems. After that experience, I was more than ready to work on something for which computer methods could yield results. Optimal-PSL code searches gave me that something. While admittedly the problems are computationally complex (and likely NP-Hard), I learned that it was possible to run computer code and find results for some cases, even for some cases requiring daunting computational requirements. The searches also led me to work with remarkable people, including Charlie Hughes, Carroll Nunn, Bill Haloupek, Hieu Duc Nguyen, Angeline Luther, Dennis Spellman, Bill Correll, Chris Swanson, and, of course, my co-author Jon Russo. I am extremely grateful for these collaborations, which have enriched my life greatly, and for the results they made possible.
Several years ago when my colleague Charles (“Chuck’’) Quintero left the company where I was working, to pursue other challenges, he left me a task to complete. It involved analyzing a set of binary codes provided to my organization by another organization. The codes had been found and collected without restricting the codes to have the balance property (defined in the book). The task I inherited was to determine how far from balance the codes could be before breaking the system (in the sense of causing false detections). When I graphed the results from my computer program, they showed something remarkable and unexpected, in a clear and fascinating way. That experience led me to explore further, and in particular, to try and find all optimal-peak-sidelobe binary codes of lower code lengths (that is, lengths for which searches were practical, using the computers I had at my disposal). I was hoping that my results would help extrapolate trends to optimal codes of greater lengths, where, for me at the time, were out of reach. The Haitians have a saying: “beyond mountains, there are mountains”. This expression captures what I have experienced after that first experience – that each discovery leaves me with new questions. Once these were answered (and sometimes not), new questions arise. It has been an adventure.
For several years, I focused on single codes, even when colleagues would tell me about fascinating code sets they had heard about that yielded all zero autocorrelation sidelobes. I stubbornly resisted following up on those discussions because, for me, the challenge of finding optimal-PSL codes was enough. Then one summer in 2008, I participated in a Mathematical Problems in Industry (MPI) Workshop at Worcester Polytechnic Institute (WPI); it was a wild, stressful, ultimately life-altering week. The experience left me fired up with new questions. I spent the rest of the summer pursuing one compelling question after another. At the end of that summer, I was captivated by those sets of codes yielding zero sidelobes, the so-called complementary code sets. Chapters 7 and 8 in the book summarize some of the many results related to binary and polyphase complementary code sets.
About the Authors:
Gregory E. Coxson has been teaching electrical engineering courses and developing a course in Principles of Radar at the United States Naval Academy (USNA) in Annapolis Maryland. Prior to joining USNA, he worked as a radar systems engineer at Hughes Radar in El Segundo, California, Lockheed Martin MS2 in Moorestown, New Jersey, Technology Service Corporation in Silver Spring, Maryland, and the Radar Division at the Naval Research Laboratories (NRL) in Washington DC. He has bachelor’s degrees in Physics and Mathematics from the University of Virginia, a master’s degree in Mathematics from the University of Wisconsin, and a Ph.D. in electrical engineering from the University of Wisconsin.
Jon Russo completed Bachelor’s and Master’s degrees in electrical engineering at Cornell University, where he was a teaching assistant and helped with the summer college program. In 1992 he joined the research group at Lockheed Martin Advanced Technology Laboratories working in communications, radar, hardware design, reconfigurable computing, cognitive radio, and quantum sensing. He writes papers in areas of high performance computing, waveform design, and machine learning and has several U.S. patents. His research includes combinatorics, quantum sensing, cognitive architectures, and interference mitigation in sensor systems.
Learn more about the book on our websites:
ARTECH HOUSE USA : Optimal-Peak-Sidelobe Polyphase Codes
ARTECH HOUSE U.K.: Optimal-Peak-Sidelobe Polyphase Codes
More Radar content here: Radar – Artech House Insider
