Signal Time-Alignment Using Complex Conjugate Functions
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Quadrature amplitude modulation introduces errors that make it challenging to time-align input signals and amplified signals, especially when the time-shift difference is unknown and quadrature modulation errors are present, such as during radio transmitter initialization.
Innovation Solution
A method to estimate the time-difference between input and amplified signals by comparing them across a range of time-shifts using a function that includes the amplified signal, its complex conjugate, and a constant, calculating an error statistic that is insensitive to quadrature modulation errors, allowing for accurate time-alignment independent of quadrature modulation errors.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If quadrature amplitude modulation is used to transmit data signals, then data transmission capability is improved, but time-alignment accuracy deteriorates due to introduced quadrature errors
Solution Approach 1:
The patent introduces an intermediary function that combines the amplified signal with its complex conjugate and a constant term. This intermediary construction serves as a mediator that eliminates quadrature errors from the time-alignment measurement process, allowing accurate time-difference estimation despite the presence of quadrature modulation errors
Solution Approach 2:
The patent converts the harmful quadrature modulation errors into a beneficial situation by using the complex conjugate operation. The errors that would normally degrade time-alignment accuracy are transformed through the conjugate and function combination into a form that cancels out, enabling accurate measurement despite the errors
2Device complexity
If traditional time-alignment methods are used with quadrature modulation, then implementation simplicity is maintained, but measurement precision deteriorates due to sensitivity to quadrature errors
Solution Approach 1:
The patent changes the mathematical parameters of the signal processing by introducing the complex conjugate operation and a specific function form. This parameter change transforms the time-alignment measurement to be insensitive to quadrature errors while maintaining reasonable implementation complexity through standard signal processing operations
3Measurement precision
If signal comparison is performed across multiple time-shifts to estimate time-difference, then time-alignment accuracy is improved, but computational complexity increases
Solution Approach 1:
The patent uses a copying technique by creating a function of the amplified signal that includes its complex conjugate. This copied version allows the system to compare signals across multiple time-shifts more efficiently, reducing the computational burden while maintaining accurate time-difference estimation through the minimized error statistic approach
Data Source
AI summary
Data is received characterizing a first signal and a second signal. The first signal and a function of the second signal is compared at a plurality of time-shifts to estimate a time-difference between the first signal and the second signal. The function of the second signal includes the second signal, a complex conjugate of the second signal, and a constant. The comparison is provided. At least one of receiving, comparing, and providing is performed by at least one processor of at least one computing system.