Zadoff-Chu Sequence Generation via Modular Arithmetic
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Solution Overview
Problem
Existing methods for generating Zadoff-Chu sequences in mobile communication systems require significant computational complexity due to the need for multiple multiplications in calculating exponents, especially for long sequences used in uplink synchronization and reference signal generation.
Innovation Solution
An iterative procedure based on modulo N arithmetic is employed to calculate the exponents of Zadoff-Chu sequences, reducing the need for multiplications and simplifying the sequence generation process.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional methods are used to calculate exponents in Zadoff-Chu sequences, then accurate sequence generation is achieved, but computational complexity is high due to multiple multiplications
Solution Approach 1:
The patent changes the calculation parameters by expressing the exponent calculation in terms of modular arithmetic operations (addition, subtraction, multiplication by pre-calculated inverses) instead of direct division operations. This parameter transformation maintains mathematical equivalence while reducing computational complexity, as modular operations can be pre-computed and stored in lookup tables.
Solution Approach 2:
The patent performs preliminary calculations by pre-computing the modular inverse of 2 modulo N and storing it in a lookup table. This preliminary action eliminates the need for complex division operations during runtime sequence generation, reducing computational complexity while maintaining accuracy.
2Measurement precision
If long Zadoff-Chu sequences are generated for uplink synchronization, then better time estimates are achieved, but computational complexity increases significantly
Solution Approach 1:
The patent transforms the exponent calculation parameters to use modular arithmetic with pre-computed inverses, allowing long sequences to be generated efficiently. The key parameter change is replacing division operations with multiplication by pre-stored modular inverses, which maintains precision for long sequences while dramatically improving generation efficiency.
Solution Approach 2:
The patent substitutes complex arithmetic operations (division and multiple multiplications) with simpler operations (addition, subtraction, and multiplication by pre-computed values). This substitution reduces the computational burden for generating long sequences, improving productivity while maintaining the accuracy needed for reliable time estimates.
Data Source
AI summary
The present application discloses methods and apparatus for generating a Zadoff-Chu sequence for use by a mobile station. One embodiment discloses generating exponents oof elements of a Zadoff-Chu sequence representing a preamble for uplink synchronization of a mobile station or a mobile station reference signal by first obtaining a preamble index defining the Zadoff-Chu sequence. Then an initial exponent of the first element in the Zadoff-Chu sequence and an initial first difference between exponents of consecutive elements of the Zadoff-Chu sequence are determined. Finally the embodiment discloses determining exponents of the remaining elements in the Zadoff-Chu sequence from the initial first difference and the initial exponent in an iterative procedure that avoids multiplication operations.