A Radix-M Construction for Complementary Sets

TL;DR

This paper introduces a new Radix-M generator for constructing complementary sets and complete complementary codes, extending paraunitary theory and providing efficient correlation methods for various sequence types.

Contribution

It proposes a novel Radix-M construction extending paraunitary theory to generate complementary sets and codes, with detailed analysis and practical correlator design.

Findings

Radix-M generator generalizes Boolean generator for complementary pairs

Efficient correlator for standard complementary sets and CCCs

Examples include polyphase, QAM, and hexagonal PU sets

Abstract

We extend the paraunitary (PU) theory for complementary pairs to comple- mentary sets and complete complementary codes (CCC) by proposing a new PU construction. A special, but very important case of complementary sets (and CC- C), based on standard delays, is analyzed in details and a new 'Radix-M generator' (RM-G) is presented. The RM-G can be viewed as a generalization of the Boolean generator for complementary pairs. An efficient correlator for standard complemen- tary sets and CCC is also presented. Finally, examples of polyphase, QAM and hexagonal PU sets of three sequences are given.