Unimodular Perfect and Nearly Perfect Sequences: A Variation of Björck’s Scheme
Constant Amplitude (CA), Zero Auto Correlation (ZAC) sequences (or CAZAC sequences, aka perfect sequences) have numerous applications. We generalize the CAZAC notion to what we term as CASAC by permitting small autocorrelations (SAC). We extend Björck’s classification result of two-valued CAZAC sequences by providing a complete classification of all almost 2-valued (i.e., two-valued except for the first position which uses a third value) CASAC sequences.
While Björck’s original work dealt only with primes p, we extend his ideas to any abelian group of order v≡1(mod4) , as opposed to restricting just to the prime fields GF(p). Björck sequences have better ambiguity function than Zadoff-Chu sequences, making them suitable for radar and communications applications in the presence of high Doppler shifts. In fact, the discrete narrow band ambiguity function has an optimal bound in case of Björck sequences (as opposed to Gauss sequences). A one-parameter infinite family of CASAC we construct would have applications in Multiple-Input Multiple-Output (MIMO) areas. Toward MIMO applications, we introduce a performance measure we term as cross merit factor to study cross correlation behavior, generalizing the well-known notion of Golay Merit Factor (GMF).
- Year: 2022
- Category: Secure & Resilient Systems
- Category: Radar Systems
- Tag: Autocorrelation, Radar applications, Doppler radar, Behavioral sciences, Wireless communication, Multiaccess communication, Long Term Evolution
- Author: K. T. Arasu, Michael R. Clark, Jeffrey R. Hollon
- Released: IEEE Transactions on Information Theory
Featured Riverside Research Author(s)
K. T. Arasu
K. T. Arasu (Member, IEEE) is a senior research scientist at Riverside Research in the Engineering and Support Solutions Group. He received the B.S. and M.S. degrees in
mathematics from Panjab University, India, and the Ph.D. degree from The
Ohio State University. Prior to joining
Riverside Research, he was a Professor with the Department of Mathematics
and Statistics, Wright State University, for 35 years. He investigates novel
techniques on error correcting codes, cryptography, data security and privacy,
as well as topics at the intersection of machine learning, security, and
information theory. He has published over 110 research papers. During
his time as a professor at Wright State University, he was presented the
Teaching Excellence Award from the College of Science and Mathematics, the
Presidential Research Excellence Award, and the Trustees' Award for Faculty
Excellence. He serves on the editorial board of several technical international
journal publications.
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Michael R. Clark
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The above listed authors are current or former employees of Riverside Research. Authors affiliated with other institutions are listed on the full paper. It is the responsibility of the author to list material disclosures in each paper, where applicable – they are not listed here. This academic papers directory is published in accordance with federal guidance to make public and available academic research funded by the federal government.