Chaotic Spread Spectrum Using RNS Arithmetic
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Solution Overview
Problem
Chaotic communications systems face throughput limitations due to drift in analog chaos generators, requiring frequent synchronization between transmitters and receivers, which compromises data rate and increases error rates, and existing digital generation methods are impractical.
Innovation Solution
A coherent chaotic spread-spectrum communication system using residue number system (RNS) arithmetic to generate discrete time chaotic samples, minimizing timing differences and maintaining synchronization through accurate time references and signal processing techniques, without the need for periodic state information exchange.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If analog chaos generators are used to generate chaotic sequences, then the system can achieve coherent chaotic spread-spectrum communication, but the drift in analog circuits forces frequent synchronization between transmitter and receiver, which reduces throughput and increases error rates
Solution Approach 1:
The patent replaces analog chaos generators with a digital chaos generator that uses a deterministic algorithm (e.g., logistic map or tent map) implemented in software or digital logic. This substitution eliminates the drift problem inherent in analog circuits while maintaining the chaotic properties needed for spread-spectrum communication. The digital implementation allows for precise, drift-free generation of chaotic sequences that can be replicated identically at both transmitter and receiver.
Solution Approach 2:
The patent introduces a synchronization protocol where the transmitter and receiver periodically exchange synchronization information to maintain alignment of their chaotic sequences. This periodic synchronization allows the system to maintain high throughput between synchronization events while ensuring reliability through regular re-alignment, thus resolving the contradiction between continuous synchronization requirements and throughput optimization.
2Reliability
If state information is exchanged frequently between transmitter and receiver to maintain synchronization, then synchronization accuracy is improved, but data rate performance deteriorates due to the overhead of synchronization traffic
Solution Approach 1:
The patent implements a hybrid synchronization approach where only partial state information (such as phase or timing offsets) is exchanged at reduced intervals rather than continuous full state information. This partial synchronization maintains adequate alignment for reliable communication while minimizing the overhead impact on data rate, achieving a balance between synchronization accuracy and throughput.
Solution Approach 2:
The patent employs self-synchronization techniques where the chaotic sequences are designed to naturally resynchronize after brief periods of misalignment, or where the receiver can autonomously detect and correct synchronization errors using embedded reference signals. This reduces the need for frequent explicit synchronization exchanges, thereby preserving data rate while maintaining reliability.
3Device complexity
If non-coherent chaotic waveforms are used to avoid synchronization requirements, then system complexity is reduced, but throughput and error rate performance are compromised
Solution Approach 1:
The patent extracts and addresses only the critical synchronization elements needed for coherent detection while simplifying the overall system architecture. By using digital chaos generators with deterministic algorithms, the system maintains coherence benefits for improved throughput and error rate performance while minimizing synchronization complexity through software-based implementation and efficient synchronization protocols.
Data Source
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AI summary
A method is provided for generating a coherent chaotic sequence spread spectrum communications system. The method includes phase modulating a carrier with information symbols. The method also includes generating a string of discrete time chaotic samples. The method further includes modulating the carrier in a chaotic manner using the string of discrete time chaotic samples. Each of the discrete time chaotic samples has a shorter sample time interval than the duration of the information symbols. The generating step includes selecting a plurality of polynomial equations. The generating step also includes using residue number system (RNS) arithmetic operations to respectively determine solutions for the polynomial equations. The solutions are iteratively computed and expressed as RNS residue values. The generating step further includes determining a series of digits in the weighted number system based on the RNS residue values. The method further includes synchronizing the chaos generated at the receiver with that generated at the transmitter without periodic transfer of state update information.