Chaotic Spreading Codes Generation Using Tent Maps
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Conventional spreading codes used in satellite navigation systems, such as those for the Galileo system, face issues with truncation leading to sub-optimum autocorrelation and cross-correlation performance, particularly due to their periodic nature and difficulty in generating codes of arbitrary length, which affects their reliability and interference resistance.
Innovation Solution
A method is developed to generate chaotic spreading codes using iterative chaotic maps, specifically the tent map, to produce codes with delta-peak-like autocorrelation and low cross-correlation properties, allowing for arbitrary code lengths without truncation, by selecting and modifying seed codes based on binary operations such as shifting and flipping.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If conventional m-sequences are used for spreading codes, then they are easy to generate and possess perfect autocorrelation behaviour, but the truncation process required to ensure desired code length destroys the perfect autocorrelation behaviour and has adverse effect on performance
Solution Approach 1:
The patent changes the fundamental parameter of code generation from linear feedback shift registers (LFSR) to chaotic maps. This allows codes to be generated with arbitrary lengths without truncation, preserving the desired autocorrelation properties while maintaining ease of generation through simple iterative calculations.
Solution Approach 2:
Instead of truncating maximal length sequences to achieve desired code lengths (which destroys autocorrelation properties), the patent inverts the approach by generating chaotic sequences of the exact desired length from the beginning using chaotic maps, thus avoiding truncation entirely while maintaining perfect autocorrelation behaviour.
2Ease of manufacture
If m-sequences are used for spreading codes, then they are easy to generate, but they have moderate cross-correlation performance and suffer from periodic nature
Solution Approach 1:
The patent changes the generation mechanism from periodic LFSR-based m-sequences to aperiodic chaotic map-based sequences. This fundamental parameter change eliminates the periodic nature of m-sequences and improves cross-correlation performance while maintaining simplicity of generation through iterative chaotic map calculations.
Solution Approach 2:
The patent uses chaotic maps to generate sequences that copy the desirable properties of m-sequences (simplicity of generation) while eliminating their drawbacks (periodicity and moderate cross-correlation). The chaotic sequences are generated using simple iterative formulas similar in complexity to LFSR but with superior performance characteristics.
3Ease of operation
If chaotic codes are used for spreading codes, then they offer simple implementation and non-periodicity, but conventional chaotic sets have unacceptably weak cross-correlation performance
Solution Approach 1:
The patent applies local quality by carefully selecting specific parameters and configurations for the chaotic map (such as particular tent map parameters) and applying local transformations (shifting, flipping) to individual code sequences. This localized optimization improves cross-correlation performance while maintaining the overall simplicity of chaotic map implementation.
Solution Approach 2:
The patent performs preliminary actions by selecting and modifying seed codes before generating the full spreading code set. Specific transformations (shifting, flipping) are applied to seed codes to ensure that the resulting chaotic sequences have improved cross-correlation properties, preventing poor performance before it occurs.
4Adaptability or versatility
If spreading codes of arbitrary length are required, then conventional m-sequences require truncation which destroys autocorrelation behaviour, but chaotic codes can be generated of arbitrary length without truncation
Solution Approach 1:
The patent changes the generation approach from fixed-length maximal sequences requiring truncation to flexible-length chaotic sequences generated directly at the desired length. The chaotic map iteration count is simply adjusted to produce codes of any required length, maintaining perfect autocorrelation properties throughout.
Solution Approach 2:
The patent introduces dynamics by allowing the code length to be freely adjustable without compromising performance. The chaotic map can be iterated for any number of steps to generate codes of arbitrary length, making the system adaptable to different application requirements while maintaining optimal autocorrelation characteristics.
Data Source
Figure 1
Figure 2
Figure 3
AI summary
Generation of a set of spreading codes starts with determining first and second chaotic pseudo-random noise codes having delta-peak-like autocorrelation functions and a low cross-correlation function. Further codes are obtained by the steps: (a) generating a further pseudo-random noise code by computing Dk = F(C1) + TkC2 +F(C2), where k represents a positive integral index, Dk the generated pseudo-random noise code, C1 the first code, C2 the second code, F a binary function based on basic binary operations and Tk the operator cyclically shifting a code by k chip positions; (b) adding code Dk to the set of already determined pseudo-random noise codes if it has a delta-peak-like autocorrelation and low cross-correlation functions with the pseudo-random noise codes already determined; (c) discarding code Dk if the conditions of step (b) are not satisfied; (d) modifying index k and repeating steps (a)-(d) until the cardinal number of the set of determined pseudo-random noise codes reaches the cardinal number of the set of spreading codes to be generated.