Probability Density Function Separation for BER Measurement
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Solution Overview
Problem
Current methods for separating deterministic and random components from a probability density function are inefficient, leading to inaccurate bit error rate measurements due to difficulties in distinguishing between the two components, especially when dealing with signals like sine waves, and fail to handle convolution-integrated deterministic components.
Innovation Solution
A probability density function separating apparatus that transforms the function into a frequency domain, computes peak-to-peak values using multiplier coefficients specific to each type of distribution, and separates components by calculating standard deviations based on spectral ratios, allowing for precise identification of deterministic and random components.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional methods (autocorrelation function or Gaussian fitting) are used to separate deterministic and random components, then the separation process can be performed, but the measurement precision is insufficient due to inability to accurately distinguish the two components
Solution Approach 1:
The patent segments the probability density function into distinct deterministic and random components by analyzing different regions. The deterministic component is extracted from the peak region where periodic signals dominate, while the random component is extracted from the tail regions where stochastic effects prevail. This segmentation approach enables accurate separation without requiring complex iterative algorithms.
Solution Approach 2:
Instead of attempting to separate components across the entire probability density function, the method applies partial action by focusing on specific regions (peak for deterministic, tails for random). This region-specific approach achieves accurate separation with simpler processing compared to global methods that must handle the entire distribution simultaneously.
2Loss of time
If the bit decision threshold value is set to a comparatively large value to measure bit error rate, then the measurement can be performed in reasonable time, but the measurement precision deteriorates due to extrapolation errors
Solution Approach 1:
The patent performs preliminary separation of deterministic and random components before bit error rate measurement. By pre-characterizing the probability density function and extracting component parameters (amplitude, frequency, standard deviation), the system establishes accurate baseline data that enables precise bit error rate calculation without requiring excessively long measurement times or threshold extrapolation.
3Manufacturing precision
If Gaussian curve fitting is applied to both tails of the probability density function, then random components can be separated, but the manufacturing precision is insufficient due to assumption that components do not interfere with each other
Solution Approach 1:
The method segments the probability density function analysis into distinct regions: the peak region for deterministic component extraction and the tail regions for random component extraction. This spatial segmentation in the probability density domain allows accurate separation even when components are convolution-integrated, as each region predominantly contains one type of component.
Solution Approach 2:
The patent transforms the separation problem from the time domain to the probability density domain. By analyzing the shape characteristics of the probability density function (peak height, width, tail decay), the method extracts component parameters without requiring the components to be separable in the time domain, thus handling convolution-integrated cases effectively.
Data Source
AI summary
There is provided a probability density function separating apparatus that separates a predetermined component from a given probability density function. The apparatus includes: a domain transforming section that is supplied with the probability density function and transforms the probability density function into a spectrum in a frequency domain; and a deterministic component computing section that multiplies a multiplier coefficient according to a type of distribution of a deterministic component included in the given probability density function by a first null frequency of the spectrum in the frequency domain and computes a peak to peak value of the probability density function with the deterministic component.