Gold Sequence Acquisition via Double Iterative Decoding
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Solution Overview
Problem
Current GPS and Galileo system receiver acquisition methods face challenges in achieving low missed detection and false alarm probabilities at low signal-to-noise ratios, particularly with complex serial decoding processes that are time-consuming and computationally intensive.
Innovation Solution
A method involving bipartite graphs and message-passing decoders is employed to acquire Gold sequences, utilizing a first and second M-sequence generator polynomial, with decimation steps to refine estimates and reduce complexity, allowing for shorter acquisition times and lower complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If iterative message passing decoding is used to acquire Gold sequences, then the probability of missed detection and false alarm is reduced, but the decoding complexity and acquisition time increase significantly
Solution Approach 1:
The patent segments the Gold sequence acquisition problem into two separate M-sequence decoding tasks. Instead of directly decoding the full Gold sequence, the method decomposes it into two constituent M-sequences, each decoded independently using simplified message passing on bipartite graphs. This segmentation reduces the overall decoding complexity while maintaining reliability.
Solution Approach 2:
The patent introduces an intermediary element - the bipartite graph structure - as a mediator between the received signal and the final Gold sequence acquisition. By representing the M-sequences as bipartite graphs with variable nodes and check nodes, the decoding process becomes more tractable and less complex while preserving the ability to achieve low error probabilities.
2Reliability
If serial decoding attempts are performed for each satellite signal, then acquisition reliability improves, but the acquisition time exceeds constraints
Solution Approach 1:
The patent performs preliminary action by pre-organizing the decoding structure into bipartite graphs before actual signal acquisition. The graph structures and message passing rules are prepared in advance, allowing rapid decoding when signals are received. This preliminary structuring eliminates the need for time-consuming serial decoding attempts during the critical acquisition phase.
Solution Approach 2:
The patent employs periodic action through iterative message passing, where messages are exchanged periodically between variable nodes and check nodes in the bipartite graph. This iterative periodic process converges quickly to the correct sequence values, achieving reliable acquisition within time constraints unlike sequential decoding methods.
3Productivity
If conventional correlation methods are used for signal acquisition, then the process is simple and fast, but the probability of missed detection and false alarm remains high at low signal-to-noise ratios
Solution Approach 1:
The patent substitutes the conventional mechanical correlation method with a message passing decoding mechanism based on bipartite graphs. Instead of relying on direct signal correlation which fails at low SNR, the method uses algebraic decoding structures that can reliably recover sequences even when signals are buried in noise, while maintaining acceptable acquisition speeds.
Solution Approach 2:
The patent changes the fundamental parameter of the acquisition approach from correlation-based detection to decoding-based detection. By transforming the problem from detecting signal presence through correlation to recovering sequences through message passing on graphs, the system achieves both reliability at low SNR and acceptable speed performance.
Data Source
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AI summary
The invention relates to a method for acquiring a Gold code, obtained as the sum of a first M-sequence (x) and a second M-sequence (yi), the first M-sequence being generated by a first generator polynomial (gx) and the second M-sequence being generated by a second generator polynomial (gy), the weight of the first generator polynomial being less than the weight of the second generator polynomial. The acquisition method employs a first message-passing decoding step along a first bipartite graph (510, 520) whose edges are determined by the coefficients of the first generator polynomial, a decimation step (533) using a predetermined decimation factor, and a second message-passing decoding step along a second bipartite graph (535, 540) whose edges are determined by a third generator polynomial of minimum weight generating a third M-sequence of the same length than that of the second M-sequence.