Non-linear Channel Response Extraction via Symmetric Decomposition
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Solution Overview
Problem
Determining the characteristic response of non-linear transmit channels is challenging due to their non-linear characteristics, which complicate the prediction of signal integrity and bit error rate, especially since many non-linear devices require a warming-up period and do not allow repeated logical inputs.
Innovation Solution
The method involves identifying a first and second input sequence, determining their complements, generating input and response matrices, and iteratively solving systems of equations to extract symmetrical and asymmetrical response components, allowing for the determination of the channel's characteristic response without directly applying the isolated input to the channel.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If direct measurement of channel response to isolated input is performed, then measurement precision is improved, but device complexity increases due to warming-up requirements and restricted input patterns
Solution Approach 1:
The patent creates virtual copies of the channel response by measuring the channel's response to known training sequences and mathematically deriving the impulse response. Instead of directly measuring the response to an isolated impulse (which requires complex setup), the system measures responses to practical training sequences and uses deconvolution algorithms to compute the equivalent impulse response, thereby obtaining precise channel characteristics without the complexity of direct measurement
Solution Approach 2:
The patent applies preliminary action by first transmitting known training sequences through the channel before attempting to determine channel characteristics. The channel is pre-loaded with training data that allows subsequent mathematical extraction of the impulse response, avoiding the need for complex direct measurement setups and warming-up periods
2Measurement precision
If isolated impulse input is applied to determine Dirac response, then measurement accuracy is improved, but ease of operation deteriorates due to warming-up period requirements
Solution Approach 1:
The system creates a mathematical copy of the Dirac response by measuring the channel's response to practical training sequences and using deconvolution to compute the equivalent impulse response. This approach achieves accurate channel characterization without requiring the complex operational conditions needed for direct Dirac response measurement
Solution Approach 2:
Instead of directly applying an isolated impulse and measuring the response (the conventional approach), the patent inverts the process by applying known training sequences and mathematically inverting the relationship through deconvolution to extract the impulse response. This reversal simplifies the operational requirements while maintaining measurement accuracy
3Productivity
If repeated logical inputs are used for measurement, then productivity is improved, but measurement precision deteriorates due to non-linear device characteristics
Solution Approach 1:
The patent uses partial action by transmitting only the necessary portions of training sequences that are sufficient to determine channel characteristics, rather than requiring exhaustive testing. The training sequences are designed to provide just enough information for accurate impulse response extraction through deconvolution, achieving both speed and accuracy by avoiding unnecessary measurements that would trigger non-linear effects
Data Source
AI summary
Techniques for extracting the characteristic response of a non-linear channel are presented. In various implementations of the invention, a channel's characteristic response may be determined by identifying a first input sequence, determining the ones compliment of the first input sequence and then determining the response of the channel to these two input sequences. Subsequently, two input matrices and two response matrices may be generated based upon the two input sequences and their corresponding responses. Given these four matrices, a symmetrical response component may be determined by iteratively solving a system of equations formed from the columns of each matrix. Subsequently, given the symmetric component and these four matrices, an asymmetrical response component may be determined by again iteratively solving the system of equations for the columns of each matrix.