Recursive Least Squares Equalization Using Approximate Covariance
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Solution Overview
Problem
Communication networks, particularly optical communication channels, face signal degradation due to polarization mode dispersion, polarization dependent loss, state of polarization rotation, amplified spontaneous emission, and chromatic dispersion, which existing equalization methods struggle to compensate for effectively, especially when channel conditions change rapidly.
Innovation Solution
A receiver device employs an adaptive filter with coefficients calculated using error estimates and an approximate covariance matrix, which is recursively updated and expressed in the frequency domain, allowing for efficient compensation of channel impairments and polarization effects, even in rapidly changing conditions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If conventional equalization methods are used to compensate for channel degradations, then signal quality may be maintained under stable conditions, but the methods struggle to compensate effectively when channel conditions change rapidly
Solution Approach 1:
The patent implements a dynamic equalization approach where the filter coefficients are continuously updated using an adaptive filter. The system transitions from static equalization to dynamic adaptation by calculating updated coefficients based on incoming signal blocks and error estimates, allowing the equalizer to track and compensate for rapidly changing channel conditions in real-time
Solution Approach 2:
The patent employs feedback mechanisms where error estimates are calculated from previously filtered blocks and fed back into the coefficient calculation process. This feedback loop enables the system to learn from past performance and continuously refine its equalization parameters, improving adaptability to changing channel conditions while maintaining reliable signal quality
2Measurement precision
If full covariance matrix inversion is performed for adaptive filter coefficient calculation, then equalization accuracy is improved, but computational complexity increases significantly
Solution Approach 1:
The patent segments the full covariance matrix into smaller sub-matrices corresponding to different frequency bins. Instead of inverting one large matrix, the system divides the problem into multiple smaller inversion tasks that can be performed independently and more efficiently, reducing overall computational complexity while maintaining equalization accuracy
Solution Approach 2:
The patent applies approximate covariance matrix inversion where only the necessary portions of the full matrix are inverted. By using approximations and focusing computational effort on the most critical frequency components, the system achieves sufficient equalization accuracy without the excessive computational burden of complete matrix inversion
Data Source
AI summary
A receiver is configured to detect, at a communication interface, a received signal that suffers from degradations incurred over a communication channel. The receiver applies an adaptive filter to a series of received blocks of a digital representation of the received signal, thereby generating respective filtered blocks, where each received block represents 2N frequency bins, and where N is a positive integer. The receiver calculates coefficients for use by the adaptive filter on a jth received block as a function of (i) error estimates associated with an (j−D−1)th filtered block, where D is a positive integer representing a number of blocks, and where j is a positive integer greater than (D−1); and (ii) an inverse of an approximate covariance matrix associated with the (j−D−1)th received block, where the approximate covariance matrix is a diagonal matrix of size L×L, and where L is a positive integer lower than 2N.