New Mathematical Theory Could Address Cell Communication Breakdown

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Full patent pending on American University math professor Stephen Casey’s “projection method.”

Using projection method, communications would be transmitted in a hierarchy from most simplistic to most complex (text first, then voice, and lastly video or social media).

Projection method is not a device, but a mathematical theory of a device.

It is an experience that has frustrated many: an emergency situation occurs, such as the recent Boston Marathon attacks or the tornadoes in Oklahoma, and people try to use their cell phones to get in touch with loved ones in the affected area, but can't get through. At a time when the need to get through is paramount.

American University mathematics professor Stephen Casey thinks he has found a way to solve this problem. He calls it “projection method.” It is so promising that Casey already has two provisional patents for it, plus, the method is under review for a full patent.

“Projection method is not a device, but a mathematical theory of a device,” Casey said.

Projection method grew out of Casey’s research project funded by a $145,537 grant from the Air Force Office of Scientific Research called “New Techniques in Time Frequency Analysis: Adaptive Band, Ultra Band, and Multi-Rate Signal Processing.”

First awarded to Casey September 2012, the grant supports his research during the next three years.

Casey says projection method would distribute our communications in a hierarchy, pushing through the most simplistic forms of first, followed by increasingly complex forms—text messages would be first, then voice messages, and lastly, video uploads or social media statuses. So, in an emergency situation, the lower level communications would get through.

Casey realized this potential application during the August 2011 earthquake that rocked much of the east coast, including Washington, D.C.

“As we all made texts and calls, I noted that early texts made it through, and then the system collapsed,” Casey said. “I thought, ‘Projection can fix this— to a degree.’”

How It Would Work

Casey says projection method would require a different approach to signal processing, or how cell service carriers handle various communications—phone calls/voice mails, text messages, emails, social media statuses—the original “signals.”

The current, general signal processing architecture for cell phones is “sample and hold”—an analog circuit used in linear systems, or systems in which data is conveyed in a specific sequence (much like a line with a definite beginning point and a definite end point). Digital systems, on the other hand, are based on discontinuous data or events—things that don’t have to be handled in any particular order but come together to form a final, definite product (ex: a sound or an image)—much like a jigsaw puzzle.

But wait? Aren’t cell phones digital? Not exactly. Most cell phones are actually analog to digital devices—they take the analog signal (a person's voice or the text or images someone wishes to send) and convert it to a digital one so that the digital networks cell phones use can process it. On the receiving end, the digital signal is converted back to an analog one so the person receiving the communication can hear the other person's voice, read a text, or see sent images.

Those digital networks rely on wireless technologies that are represented by an alphabet soup of acronyms: GSM, CDMA, and LTE. But there is one wireless technology that has great potential in that it is more powerful (capable of sending vast amounts of data) but uses less energy: Ultra Wide Band (UWB).

UWB is not new. The U.S. military and Department of Defense have used it since the1960s—among other uses, UWB applications involving radar can detect objects concealed by walls and other coverings. Even so, it was not until 2002 that the Federal Communications Commission authorized UWB’s commercial use. Since then, for a variety of reasons, the consumer market has been slow to adopt UWB, despite its obvious advantages. Technology to use it broadly and efficiently in cell phone communication has not been developed. Casey’s projection method could help change that.

“I was looking to develop an efficient method to analyze a signal so that we allow for changing and/or ultra-wide frequency bands—something conventional analog-to-digital devices don’t do,” Casey said, who aside from being a mathematics and statistics professor at AU, is a self-trained electrical engineer and sits on the boards of two international signal processing journals. “Projection is a clear advancement in that it is far more energy efficient and far more computationally sound. We look at the signal's location in both time and frequency simultaneously, and window adaptively.”

Parallel Computing

Casey says looking at a signal’s location in time and frequency all at once would be accomplished through parallel computing, a form of computation in which tasks are addressed at the same time by multiple, but linked, computer processors. High performance computers use parallel computing to analyze “big data” at extremely high speeds. How much data, how fast, depends on the system.

By “window adaptively,” Casey means that once a signal’s time and frequency information are analyzed simultaneously via parallel computing, the signal would be transmitted in a manner “customized” to the signal’s needs and parameters. This is why communications would be distributed in a hierarchy from most simplistic to most complex. Text messages are the most simplistic and would go first because they require the smallest “window” and the least energy to get through.

“The simplicity of a text vs. a Facebook post allows us to process so much more efficiently,” Casey said. “I am in the process of exploring these ideas. There will be no ‘perfect solution,’ as there is no ‘perfect’ way to measure simultaneously in both time and frequency, but this will be a huge step in the right direction.”

Next Steps

How projection method could improve cell phone communication is just one potential application of Casey’s research funded by the Air Force Office of Scientific Research.

“In theory, projection method can be used by chip designers and hardware engineers,” Casey said. “But overall, this is a HUGE area of research.”

This summer, Casey will finish a scholarly paper that he coauthored with two engineers. The engineers’ part of the paper will discuss projection method and chip design. The paper is for the Proceedings of the IEEE, the peer-reviewed, monthly scientific journal of the Institute of Electrical and Electronics Engineers.

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Maggie Barrett
American University Communications
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