FrFT Adaptive Filtering for Non-Stationary Signal Separation
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Solution Overview
Problem
Conventional signal separation methods, such as MMSE-FrFT and MMSE-FFT, are inadequate in non-stationary environments for effectively separating signal-of-interest (SOI) from interference and noise, as they fail to achieve low mean-square error (MSE) in dynamic conditions.
Innovation Solution
Implementing repeated reduced rank minimum mean-square error (MMSE) filtering using a low rank adaptive multistage Wiener filter (MWF) in the Fractional Fourier Transform (FrFT) domain, which iteratively computes optimal filter coefficients and rotational parameters to minimize MSE, thereby improving signal separation.
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 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 improvement rather than a single complex operation.
Solution Approach 2:
The filter adapts dynamically by adjusting the rotational parameter a in each FrFT stage based on the non-stationary characteristics of the signal. This dynamic adaptation allows the filter to track time-varying signal properties, maintaining high separation accuracy in changing environments.
2Measurement precision
If single-stage filtering is used, then the computational complexity is low, but the MSE reduction is insufficient
Solution Approach 1:
The signal is pre-transformed into the FrFT domain with optimized rotational parameters before filtering. This preliminary transformation aligns the signal components in a way that facilitates more effective separation in subsequent filtering stages, reducing the computational burden required to achieve a given MSE level.
Solution Approach 2:
The filtering operation is extended from the traditional time or frequency domain to the fractional Fourier transform domain, introducing an additional dimensional perspective. This dimensional change enables better separation of non-stationary signal components that are inseparable in conventional domains.
3Measurement precision
If repeated MMSE-FrFT filtering is applied, then the MSE is reduced compared to single-stage filtering, but the performance is still insufficient in low Eb/N0 and CIR scenarios
Solution Approach 1:
The filter employs feedback mechanisms where the output of each stage is fed back as input to the next stage, with parameters optimized based on performance metrics from previous stages. This feedback loop enables progressive MSE reduction even in challenging low Eb/N0 and CIR conditions.
Solution Approach 2:
The filter dynamically changes parameters such as the rotational parameter a and filter coefficients across multiple stages based on the statistical properties of the signal and interference. These parameter adaptations enable the filter to maintain effectiveness under varying signal conditions.
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 SOI estimate and the true SOI is less than or equal to an error threshold ϵ (e.g., ϵ=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.