Adaptive Filter Regularization for Stable Convergence
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Solution Overview
Problem
Adaptive filters in communication systems often face instability and non-convergence issues due to regularization terms added to the cost function, leading to performance degradation and potential overflow errors.
Innovation Solution
A method and apparatus for adaptive signal processing that initializes a first vector without regularization, updates it based on an input signal using a regularized cost function, and maintains a second vector to stabilize convergence, minimizing bias and system complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Stability of the object's composition
If regularization terms are added to the cost function, then model capacity is limited and stability is improved, but convergence performance degrades and bias increases
Solution Approach 1:
The patent applies dynamics by making the regularization parameter adaptive rather than fixed. The regularization parameter λ is updated dynamically during the adaptive filtering process based on the current state of the filter coefficients and error signals, allowing the system to transition from strong regularization when needed for stability to weaker regularization when convergence accuracy is prioritized.
Solution Approach 2:
The patent changes the parameter λ (regularization weight) from a static hyperparameter to a dynamic variable that evolves during adaptation. This parameter change enables the system to adjust the trade-off between stability and accuracy in real-time, resolving the contradiction by making the regularization strength adaptive to the current system state.
2Reliability
If regularization is applied to prevent non-convergence, then system reliability improves, but performance degradation occurs due to increased bias
Solution Approach 1:
The patent makes the regularization mechanism dynamic by updating the regularization parameter λ adaptively during the filtering process. This dynamic approach allows the system to maintain reliability when needed while minimizing bias when the filter coefficients are converging, thus resolving the contradiction between reliability and accuracy.
Solution Approach 2:
The patent implements feedback by using the current filter performance and coefficient states to adjust the regularization parameter λ. This feedback mechanism ensures that regularization is applied appropriately - strong enough to prevent non-convergence but weak enough to maintain accuracy - by continuously monitoring system behavior and adjusting accordingly.
3Reliability
If strong regularization is used to stabilize convergence, then overflow errors are prevented, but the filter becomes overly constrained and loses adaptability
Solution Approach 1:
The patent resolves this contradiction by making the regularization strength dynamic. When the filter coefficients approach unstable regions, strong regularization is applied to prevent overflow and ensure reliability. When the system is stable and adapting normally, the regularization is weakened to allow greater adaptability and learning capability.
Solution Approach 2:
The patent changes the regularization parameter λ dynamically based on the current state of the adaptive filter. This parameter modulation allows the system to switch between constrained (high reliability) and flexible (high adaptability) modes, resolving the contradiction by adjusting the parameter according to real-time system needs.
Data Source
AI summary
A method for adaptive signal processing is provided. In the method, a second vector is obtained by initializing a first vector without regularization of a cost function. The cost function is regularized with the first vector and the second vector as variables. The first vector is updated based on an input signal, according to the regularized cost function. Then, an output signal is provided based on the updated first vector. The second vector is updated based on the update of the first vector. An apparatus for adaptive signal processing is provided accordingly. The method and the apparatus are well compatible with existing adaptive signal processing. The convergence coefficients of the adaptive filter system become more stable. Moreover, impact of an extra penalty added to the cost function on a bias can be minimized, and the increased complexity of the system is very limited.