Compensation Coefficient Calculation for Optical Communication
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Solution Overview
Problem
In coherent optical communication, determining the tap coefficient for adaptive equalization is challenging due to potential divergence when calculating the inverse matrix, especially near the Nyquist condition, leading to decreased equalization accuracy and unnecessary high-frequency component amplification.
Innovation Solution
A compensation coefficient calculation method that involves extracting a known signal, adding pseudo-random numbers to it, and calculating the compensation coefficient by comparing the modified signal with a reference signal using a minimal mean square error method to prevent divergence and improve accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the inverse matrix is calculated to determine the tap coefficient for adaptive equalization, then the equalization can be performed, but the calculation may diverge especially near the Nyquist condition, leading to decreased equalization accuracy
Solution Approach 1:
A regularization term (lambda * I) is introduced as an intermediary between the correlation matrix and the inverse calculation. This mediator prevents direct inversion of potentially singular or ill-conditioned matrices, ensuring convergence while maintaining calculation accuracy through the modified normal equation: Rxx * w + lambda * w = rxd
Solution Approach 2:
The mathematical parameter of the inversion process is changed by adding a regularization parameter (lambda) to the diagonal elements of the correlation matrix. This parameter modification transforms the potentially divergent inverse matrix calculation into a stable pseudo-inverse calculation, ensuring convergence near the Nyquist condition while preserving equalization accuracy
2Measurement precision
If the tap coefficient is determined by minimizing the mean square error using the inverse matrix method, then the theoretical optimal solution is obtained, but unnecessary high-frequency components are raised in the FIR filter
Solution Approach 1:
The regularization parameter (lambda) is used to modify the frequency response characteristics of the filter. By adding lambda to the diagonal of the correlation matrix, the solution naturally suppresses high-frequency components that would otherwise be amplified, while still providing accurate tap coefficients for the important frequency ranges
Data Source
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AI summary
In a method in which a compensation coefficient calculating portion (6) calculates a compensation coefficient of a compensation portion (5) which compensates transmission characteristics of a signal, a known signal is extracted from the signal. Next, a pseudo-random number is added to the extracted known signal. Next, the compensation coefficient is calculated by comparing a true value of the known signal with the known signal to which the pseudo-random number is added.