Repeated FrFT Wiener Filtering for Low-MSE Signal Separation
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Conventional signal separation methods, such as MMSE-FrFT and MMSE-FFT, are inadequate in non-stationary environments for completely separating signal-of-interest (SOI) from interference and noise, as they fail to achieve low mean-square error (MSE) in scenarios with time-varying signals and overlapping frequency domains.
Innovation Solution
Implementing repeated reduced rank minimum mean-square error (MMSE) filtering using a low rank adaptive multistage Wiener filter (MWF) in conjunction with Fractional Fourier Transform (FrFT), which iteratively computes optimal filter coefficients and rotational parameters to achieve MSE below a specified threshold.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional MMSE-FrFT or MMSE-FFT filtering is used, then the filtering process is simple and fast, but the mean-square error (MSE) remains high and signal separation is incomplete in non-stationary environments
Solution Approach 1:
The filtering process is divided into multiple stages, where each stage applies a reduced-rank MMSE filter in the FrFT domain with optimized rotational parameters. This segmentation allows progressive refinement of signal separation, achieving low MSE through iterative filtering rather than a single complex operation.
Solution Approach 2:
The patent transforms the filtering problem from the conventional time or frequency domain to the Fractional Fourier Transform domain, introducing an additional rotational dimension parameter 'a'. This allows signals to be separated along optimized rotational axes in the time-frequency plane, achieving better separation than conventional single-domain filtering.
2Measurement precision
If repeated filtering stages are applied to reduce MSE, then signal separation accuracy improves, but computational complexity and processing time increase
Solution Approach 1:
Instead of applying full-rank filtering at each stage, the patent uses reduced-rank filtering that processes only the most significant signal components. This partial action approach achieves sufficient MSE reduction without the computational burden of complete signal processing at each stage, optimizing the trade-off between accuracy and processing time.
Solution Approach 2:
The patent performs preliminary optimization of rotational parameters and filter ranks before the actual filtering stages. By pre-determining the optimal filtering configuration based on signal characteristics, the subsequent repeated filtering stages can proceed more efficiently with predetermined parameters, reducing real-time processing requirements.
Data Source
AI summary
A signal-of-interest (SOI) may be separated from interference and/or noise using repeated reduced rank minimum mean-square error Fractional Fourier Transform (MMSE-FrFT) filtering and a low rank adaptive multistage Wiener filter (MWF). A number of stages in the MWF, L, may be chosen such that at the Lth stage, the MSE between the SIM estimate and the true SW is less than or equal to an error threshold ∈ (e.g., ∈=0.001). By combining these filtering techniques, significant improvement in reducing the mean-square error (MSE) may be realized over single stage MMSE-FrFT, repeated MMSE-FrFT, and MMSE-FFT algorithms—indeed, by an order of magnitude or more.