Golay Complementary Sequence Generation Using Algebraic Structures

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Solution Overview

Problem

Existing methods for constructing Golay complementary sequences are limited to lengths that are powers of two, leading to restricted application ranges and increased hardware costs due to memory requirements for non-power-of-two lengths.

Innovation Solution

An algebraic structure is used to generate Golay complementary sets with flexible lengths, allowing for the construction of sequences that are not limited to powers of two, utilizing a generalized Boolean function and specific conditions to define the sequence arrangement.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Adaptability or versatility

If computer exhaustion method is used to construct Golay complementary sequences with non-power-of-two lengths, then feasible lengths can be found, but memory space is required to record the sequences, increasing hardware costs

Engineering Contradiction:

Improvesequence length flexibilityVSAvoidhardware cost

Core Design Contradiction:

Adaptability or versatilityVSDevice complexity

Solution Approach 1:

The patent uses algebraic structures (generalized Boolean functions) to enable self-generation of Golay complementary sequences with any desired length. The system serves itself by computing sequences on-demand through mathematical formulas rather than storing pre-computed sequences in memory, eliminating the need for additional hardware storage resources.

Inventive Principle:

Principle #25Self-service

Solution Approach 2:

The patent replaces the mechanical/memory-based approach (storing sequences in memory) with an algebraic/computational approach (generating sequences via generalized Boolean functions). This substitution eliminates the need for physical memory storage by using mathematical generation methods.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

2Reliability

If Golay complementary sequences are constructed based on Boolean functions, then good aperiodic autocorrelation properties are achieved, but the length is limited to powers of two, restricting application range

Engineering Contradiction:

Improveautocorrelation propertyVSAvoidsequence length flexibility

Core Design Contradiction:

ReliabilityVSAdaptability or versatility

Solution Approach 1:

The patent generalizes the traditional Boolean function construction by introducing new parameters and variables in the algebraic structure. The generalized Boolean function includes additional terms and flexibility in parameter selection, allowing the sequence length to be any positive integer while preserving the good autocorrelation properties through careful parameter choice.

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent creates a universal construction method that works for both power-of-two lengths (maintaining compatibility with existing systems) and non-power-of-two lengths (enabling new applications). The generalized Boolean function serves multiple purposes: it maintains good autocorrelation properties while adapting to any desired sequence length requirement.

Inventive Principle:

Principle #6Universality (Multi-functionality)

Data Source

PatentUS10862608B2Communication device and communication method

Publication Date: 2020.12.08 NAT CHENG KUNG UNIV

AI summary

A communication device and a communication method are provided. The communication device includes: a processor configured to generate a Golay complementary set, and a modulator configured to modulate the Golay complementary set to a carrier. Herein, the generated Golay complementary set is generated by using an algebraic structure and has an elastic length, and is adapted to communication application such as channel estimation or signal synchronization.