Eye Diagram Simulation via Fourier Transform
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Solution Overview
Problem
Current methods for computing eye diagrams based on pulse response data are inefficient and slow, especially when simulating large diagrams that capture multiple reflections, due to the need for repeated convolution of voltage cursors, which is impractical for real-world applications.
Innovation Solution
A method and apparatus that utilize a processor and memory to generate an eye diagram probability density function by performing element-wise trigonometric operations on products of input pulse responses and voltage range constraints, followed by an inverse Fourier transform, allowing for efficient computation of eye diagrams.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If repeated convolution of voltage cursors is used to compute eye diagrams, then measurement precision is improved, but productivity deteriorates due to inefficient computation speed
Solution Approach 1:
The patent replaces the traditional mechanical convolution operation with a Fourier transform-based computational approach. By transforming the convolution operation into the frequency domain using Fast Fourier Transform (FFT), the computation is significantly accelerated while maintaining the same mathematical accuracy. This substitution of computational mechanics resolves the contradiction between precise eye diagram measurement and fast computation speed.
Solution Approach 2:
The patent changes the computational parameters by transitioning from time-domain convolution to frequency-domain multiplication. This parameter transformation allows the same computational task to be performed more efficiently, achieving both high precision in eye diagram computation and improved productivity through faster execution times.
2Measurement precision
If large eye diagrams capturing multiple reflections are simulated, then measurement precision is improved, but loss of time increases due to computational complexity
Solution Approach 1:
The patent applies Fourier transform methodology to replace iterative time-domain simulations with a single frequency-domain transformation. This allows large eye diagrams with multiple reflections to be computed accurately without the exponential time increase that would otherwise result from simulating each reflection sequentially.
Solution Approach 2:
The patent performs preliminary Fourier transformation of the pulse response data before computing the eye diagram. This preliminary action prepares the data in a form that enables rapid computation of multiple reflections simultaneously, rather than computing each reflection step-by-step, thereby reducing total simulation time while maintaining precision.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach significantly speeds up the simulation of eye diagrams, making it feasible to compute large diagrams that capture multiple reflections, thereby improving the efficiency and accuracy of signal processing in communication systems.
Implementation Method 1
generating a matrix based at least in part on an element-wise trigonometric-based operation performed on one or more products of each element of the set of input pulse responses and the set of voltage range constraints
Implementation Method 2
generating an eye diagram probability density function based on the matrix... performing an inverse Fourier transform on a columnwise product of the matrix
Data Source
AI summary
Embodiments are disclosed for computing an eye diagram based on input pulse responses. An example method includes receiving a set of input pulse responses in one or more unit interval (UI) spaced samples. The set of input pulse responses is generated based on measuring a signal histogram of a receiver of a pulse amplitude modulation analog signal. The method further includes receiving a set of voltage range constraints and generating a matrix based at least in part on an element-wise trigonometric-based operation performed on one or more products of each element of the set of input pulse responses and the set of voltage range constraints. The method further includes generating an eye diagram probability density function based on the matrix and computing an eye diagram based on the eye diagram probability density function, the voltage range constraints, and time data associated with the one or more unit interval spaced samples.