Cubic Exponential Communication Sequences for Doppler Resistance
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Solution Overview
Problem
Existing communication sequences such as the Alltop, ZC, and Zadoff-Chu Cover Alltop sequences suffer from ambiguity issues, limited sequence capacity, and inability to resist Doppler shifts, which affect communication efficiency and reliability.
Innovation Solution
The introduction of a cubic polynomial exponential sequence, where the cubic term coefficient is associated with the quadratic term coefficient, allowing the sequence to resist Doppler shifts with more subcarrier spacings and offering improved sequence capacity, with the sequence capacity positively correlated with the cube of the sequence length.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If Alltop sequence is used, then sequence capacity is improved, but ambiguity function has multiple peak values causing ambiguity
Solution Approach 1:
The patent changes the polynomial degree parameter from quadratic (ZC sequence) or simple cubic (Alltop sequence) to a specific cubic form with constrained coefficients. By setting the cubic coefficient to 1 and constraining the quadratic coefficient to be a multiple of 3, the patent achieves both high sequence capacity and reduced ambiguity function peaks, resolving the contradiction between capacity and ambiguity.
2Ease of manufacture
If ZC sequence is used, then sequence generation is simple, but sequence capacity is limited
Solution Approach 1:
The patent creates a composite sequence structure by combining cubic polynomial phase modulation with constrained quadratic terms. This composite approach generalizes the ZC sequence (quadratic polynomial) to a cubic polynomial with specific coefficient constraints, achieving higher sequence capacity while maintaining generation simplicity through the structured coefficient relationship.
3Quantity of substance
If Zadoff-Chu Cover Alltop sequence is used, then sequence capacity is improved, but ability to resist Doppler shift is lost
Solution Approach 1:
The patent applies local quality by making the cubic coefficient fixed (equal to 1) while allowing the quadratic coefficient to vary based on specific conditions (multiple of 3). This localized constraint on the quadratic term preserves Doppler shift resistance properties while the cubic structure provides high sequence capacity, resolving the contradiction between capacity and reliability.
4Quantity of substance
If sequence length is increased to improve sequence capacity, then capacity increases, but product of maximum round-trip delay and maximum Doppler shift becomes constrained
Solution Approach 1:
The patent transitions from quadratic to cubic polynomial dimensionality, which fundamentally changes the sequence properties. This dimensional change enables sequence capacity to scale with the cube of sequence length while the specific coefficient constraints maintain adaptability in delay-Doppler coverage, resolving the contradiction between capacity and versatility.
Data Source
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AI summary
A communication method and apparatus are disclosed. The method includes: A first apparatus generates a cubic polynomial exponential sequence, where a cubic term coefficient of the cubic polynomial exponential sequence is associated with a quadratic term coefficient of the cubic polynomial exponential sequence; and the first apparatus outputs the cubic polynomial exponential sequence. Compared with existing communication sequences, a sequence capacity of the cubic polynomial exponential sequence is positively correlated with a cube of a sequence length of the cubic polynomial exponential sequence, the cubic polynomial exponential sequence can resist a Doppler shift with more subcarrier spacings, and a product of a maximum round-trip delay and a maximum Doppler shift is not constrained by the sequence length.