Decision Feedback Equalizer Constrained Tap Weights
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Solution Overview
Problem
Decision feedback equalizers face performance reduction due to error propagation, especially in severe intersymbol interference scenarios, where constraint functions like the 1-norm are not differentiable, making it difficult to calculate optimal tap weights.
Innovation Solution
A method to determine constrained tap weights for decision feedback equalizers using a differentiable tap weight constraint function that approximates non-differentiable functions, such as the 1-norm, to reduce error propagation by limiting feedback tap weights, and an adaptive mechanism to adjust the constraint value based on the mean squared error.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If large feedback tap weights are used in the decision feedback equalizer, then the equalizer can better compensate for severe intersymbol interference, but error propagation is significantly reduced
Solution Approach 1:
The patent changes the parameter of feedback tap weights from large to constrained small values. By imposing a constraint function on the feedback tap weights, the system prevents error propagation while maintaining adequate signal reception quality through optimized feedforward taps that compensate for the reduced feedback capability.
2Reliability
If non-differentiable constraint functions like the 1-norm are used to constrain feedback tap weights, then error propagation is reduced, but the constraint function cannot be used for calculation because it is not differentiable
Solution Approach 1:
The patent introduces a differentiable approximation function as an intermediary between the desired non-differentiable constraint (1-norm) and the calculation process. This approximation function maintains the essential constraint properties while being mathematically differentiable, enabling gradient-based optimization algorithms to compute optimal tap weights efficiently.
Solution Approach 2:
The patent transforms the constraint function from a non-differentiable form (1-norm) to a differentiable approximation form. This parameter change in the mathematical representation of the constraint allows the use of standard optimization techniques while preserving the error propagation mitigation benefit.
3Ease of manufacture
If constrained tap weights are calculated using differentiable approximation functions, then calculation becomes feasible and error propagation is reduced, but the constraint is an approximation rather than the exact 1-norm
Solution Approach 1:
The patent applies partial action by using an approximation that captures the essential properties of the 1-norm constraint without implementing it exactly. The differentiable approximation provides sufficient constraint effectiveness to reduce error propagation while enabling calculation, accepting a small loss in constraint precision for the gain in computational feasibility.
Data Source
AI summary
Constrained tap weights of a decision feedback equalizer are determined according to the channel impulse response of a channel and a constraint function. The constraint function is differentiable and is an approximation of a non-differentiable tap weight constraint function. The tap weight constraint function may have a constraint value M that is a function of a mean squared error of the estimated mean squared error at the output of the decision feedback equalizer.