Spectrally-constrained sequences : bounds and constructions

• Main Authors: Liu, Zilong, Guan, Yong Liang, Parampalli, Udaya, Hu, Su
• Other Authors: School of Electrical and Electronic Engineering
• Format: Article
• Language: English
• Published: 2019
• Subjects: Engineering::Electrical and electronic engineering; Cognitive Radio; Spectrally-constrained Sequences (SCS)
• Online Access: https://hdl.handle.net/10356/85248; http://hdl.handle.net/10220/49199
• Institution: Nanyang Technological University

We investigate spectrally-constrained sequences (SCSs), which are applicable to the communication and radar systems operating over non-contiguous carriers or frequency slots. Typical examples of such systems are overlay cognitive radio or cognitive radar networks. First, we derive the periodic- and aperiodic-correlation lower bounds for single-channel SCSs and multi-channel SCSs by convex optimization in the frequency domain. Each of these bounds reduces to a Welch bound when the number of forbidden carriers is set to zero. We then propose systematic constructions of optimal unimodular single-channel SCSs with the aid of cyclic difference sets and the theory of maximal-length shift register sequences.