  The conventional Cohen's distribution can't meet the requirement of additive
noises jamming signals high-performance denoising under the condition of low
signal-to-noise ratio, it is necessary to integrate the metaplectic transform
for non-stationary signal fractional domain time-frequency analysis. In this
paper, we blend time-frequency operators and coordinate operator
fractionizations to formulate the definition of the metaplectic Wigner
distribution, based on which we integrate the generalized metaplectic
convolution to address the unified representation issue of the convolution type
of metaplectic Cohen's distribution (CMCD), whose special cases and essential
properties are also derived. We blend Wiener filter principle and fractional
domain filter mechanism of the metaplectic transform to design the
least-squares adaptive filter method in the metaplectic Wigner distribution
domain, giving birth to the least-squares adaptive filter-based CMCD whose
kernel function can be adjusted with the input signal automatically to achieve
the minimum mean-square error (MSE) denoising in Wigner distribution domain. We
discuss the optimal symplectic matrices selection strategy of the proposed
adaptive CMCD through the minimum MSE minimization modeling and solving. Some
examples are also carried out to demonstrate that the proposed filtering method
outperforms some state-of-the-arts including Wiener filter and fixed kernel
functions-based or adaptive Cohen's distribution in noise suppression.
