Generalized Golay Sequences for Spread-Spectrum Modulation
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Solution Overview
Problem
Existing spread spectrum systems face challenges with Golay sequences, including limitations in code lengths, inefficient correlator-matched filters, and suboptimal correlation properties, particularly in multi-code DS-CDMA systems, which suffer from multiple-access interference and inter-symbol interference.
Innovation Solution
The method employs generalized Golay sequences for modulation and demodulation, using a preferred Golay generator to create spreading codes that can be of any length, including odd or even lengths, and combining Golay codes to form generalized Golay codes with improved correlation properties, and utilizes efficient Golay correlators for despreading at the receiver.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional Golay sequences are used for spread spectrum coding, then good autocorrelation properties are achieved, but code lengths are limited and cross-correlation between multiple codes remains high
Solution Approach 1:
The patent segments traditional Golay sequences into component sequences and combines them using direct sum operations to create generalized Golay sequences. This segmentation allows the construction of sequences with arbitrary lengths by combining smaller building blocks, thereby achieving both good autocorrelation properties and flexible code lengths.
Solution Approach 2:
The patent extends the search space from traditional single-dimension Golay sequences to multi-dimensional generalized Golay sequences by incorporating direct sums of component sequences. This dimensional extension enables the construction of sequences with arbitrary lengths while maintaining optimal correlation properties through careful selection of component sequences.
2Quantity of substance
If multiple spreading codes are employed in DS-CDMA systems, then communication capacity is increased, but multiple-access interference and inter-symbol interference increase
Solution Approach 1:
The patent applies local quality by ensuring that each generalized Golay sequence in the code set has optimally low cross-correlation with other sequences in the set. By carefully selecting and constructing sequences with specific local correlation properties, the system can support multiple users while minimizing multiple-access interference and inter-symbol interference.
3Ease of operation
If Budisin's recursive algorithm is used to generate Golay sequences, then efficient correlator-matched filters are obtained, but sequences are limited to power-of-two lengths and may not possess desired correlation properties
Solution Approach 1:
The patent segments the sequence generation process into combining pre-generated component sequences through direct sum operations. This approach allows the construction of generalized Golay sequences with arbitrary lengths by selecting and combining component sequences of appropriate lengths, thereby achieving both filter efficiency and length flexibility.
Solution Approach 2:
The patent extends the sequence generation from single recursive algorithms to multi-dimensional combinations of component sequences. By using direct sums of component sequences generated by various methods, the system achieves arbitrary length capability while maintaining the efficiency benefits of correlator-matched filters through proper construction.
Data Source
AI summary
A method for communicating comprises generating at least one generalized Golay code from a concatenation of constituent Golay codes, and spreading at least a portion of a data stream with the at least one generalized Golay code. Generalized Golay codes comprise pseudo-complementary sequences having code lengths that differ from Golay complementary sequences and are characterized by low autocorrelation sidelobes relative to the autocorrelation peak.