A Generic Complementary Sequence Construction and Associated Encoder/Decoder Design

TL;DR

This paper introduces a flexible, recursive construction method for complementary sequences that includes zero-valued elements, enabling efficient OFDM resource allocation and low-PMEPR schemes with improved encoder/decoder design.

Contribution

It extends existing CS constructions by allowing independent control over amplitude and phase, and introduces a systematic method for generating CSs suitable for OFDM and multiple access schemes.

Findings

Supports non-contiguous resource allocations in OFDM

Achieves low PMEPR in uplink multiple access

Demonstrates effective encoder and decoder performance through simulations

Abstract

In this study, we propose a flexible construction of complementary sequences (CSs) that can contain zero-valued elements. To derive the construction, we use Boolean functions to represent a polynomial generated with a recursion. By applying this representation to recursive CS constructions, we show the impact of construction parameters such as sign, amplitude, phase rotation used in the recursion on the elements of the synthesized CS. As a result, we extend Davis and Jedwab's CS construction by obtaining independent functions for the amplitude and phase of each element of the CS, and the seed sequence positions in the CS. The proposed construction shows that a set of distinct CSs compatible with non-contiguous resource allocations for orthogonal frequency-division multiplexing (OFDM) and various constellations can be synthesized systematically. It also leads to a low peak-to-mean-envelope-power ratio (PMEPR) multiple accessing scheme in the uplink and a low-complexity recursive decoder. We demonstrate the performance of the proposed encoder and decoder through comprehensive simulations.