Frequency Hopping Sequence Generation Using Cyclotomic Classes
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Solution Overview
Problem
Low-power wireless devices face challenges in generating frequency hopping sequences (FHS) with long lengths, which are necessary for reducing interference and packet retransmissions, due to high processing and memory requirements, especially when channel blacklisting occurs, exceeding the capabilities of resource-constrained devices.
Innovation Solution
The generation of FHS using cyclotomic classes in a field of an odd prime number, employing algorithms that reduce processing complexity and memory requirements, such as the baby-step giant-step algorithm, to facilitate efficient sequence generation and lookup, allowing devices to operate with reduced power consumption and interference.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If long FHS lengths are used to reduce interference probability, then reliability is improved, but device complexity increases
Solution Approach 1:
The patent changes the parameter of FHS generation by using cyclotomic classes with primitive roots in finite fields, transforming the generation process into a mathematical structure that achieves long sequence lengths with reduced computational complexity compared to conventional methods
Solution Approach 2:
The patent replaces complex iterative FHS generation algorithms with a closed-form mathematical solution based on cyclotomic classes, substituting computational mechanics with mathematical theory to reduce processing burden while maintaining long sequence lengths
2Reliability
If long FHS lengths are used to reduce packet retransmissions, then reliability is improved, but use of energy increases
Solution Approach 1:
The patent modifies the energy consumption parameter by implementing an efficient FHS generation method using cyclotomic classes that requires fewer computational operations, directly reducing the power consumption of resource-constrained wireless devices while maintaining long FHS lengths for reliability
3Reliability
If long FHS lengths are used to ensure randomness, then reliability is improved, but loss of time increases
Solution Approach 1:
The patent applies preliminary action by pre-defining the mathematical structure of cyclotomic classes and their properties, allowing devices to quickly generate FHS sequences without extensive real-time computation, thus reducing generation time while maintaining randomness quality through the inherent mathematical properties
4Reliability
If channel blacklisting is implemented to reduce interference, then reliability is improved, but device complexity increases
Solution Approach 1:
The patent changes the memory utilization parameter by optimizing the FHS generation algorithm to work efficiently with channel blacklisting, using mathematical properties of cyclotomic classes to reduce the memory footprint required for tracking and avoiding blacklisted channels
Data Source
AI summary
Disclosed examples include methods and network devices for communicating in a wireless network, in which the device generates frequency hopping sequence y(j) having a prime number sequence length p, using cyclotomic classes in a field of p or using a baby-step giant-step algorithm, where y(0)=p−1 and the remaining sequence values y(j)=logα(j) mod (p−1). In certain examples, α=2 and the sequence is generated without solving logarithms using one or more algorithms to conserve memory and processing complexity for low power wireless sensors or other IEEE 802.15.4e based networks using Time-Slotted Channel Hopping (TSCH) communications.