Subspace-constrained partial update method for high-dimensional adaptive processing systems

A method for implementing partial-update methods (PUMs) in any adaptive processor that adjusts weights to optimize an adaptation criterion using any of a signal estimation and a parameter estimation algorithm in digital signal processing (wherein ‘digital’ refers to the nature of the computational processing and ‘signal’ refers analog electromagnetic waveforms) when said adaptive processor employs large numbers of adaptation weights for any adaptation criterion of the set of signal estimation, parameter estimation, measured quality, and any combination thereof for “adapt-path” operations used to tune the adaptive processor, not “data-path” operations used by the adaptive processor during and after tuning, said method comprising:

• for each adaptation event comprising a partial-update effected by the adaptive processor for an adapt path operation having M-dimensions, performing a dimensionality reduction comprising a linear transformation of the processor parameters being adapted from M-dimensions to (M1+L)-dimensions in said partial update, said linear transformation further comprising:
• adapting M1 weights without constraints;
• and,
• adapting M0=M−M1 weights subjected to L soft constraints forcing them into an L-dimensional subspace spanned by the those weights;
• applying the same dimensionality reduction to input data using the same linear transformation;
• and,
• adapting the reduced-dimensionality weights using the same optimization strategy employed by the adaptive processor, except with the input data to which the same dimensionality reduction has been applied.

A method for digital signal processing (wherein ‘digital’ refers to the nature of the computational processing and ‘signal’ refers to analog electromagnetic waveforms) on devices employing at least one adaptive processor that employs large numbers of adaptation weights for any adaptation criterion of the set of signal estimation, parameter estimation, measured quality, and any combination thereof for “adapt-path” operations used to tune the adaptive processor, not “data-path” operations used by the adaptive processor during and after tuning, said method comprising:

• for each adaptation event having M-dimensions, performing a dimensionality reduction comprising a linear transformation of the processor parameters being adapted from M-dimensions to (M1+L)-dimensions in each adaptation event, said linear transformation further comprising:
• adapting M1 weights without constraints;
• and,
• adapting M0=M−M1 weights subjected to L soft constraints forcing them into an L-dimensional subspace spanned by the those weights;
• applying the same dimensionality reduction to input data using the same linear transformation;
• and,
• adapting the reduced-dimensionality weights using substantively the same optimization strategy employed by the adaptive processor for the input data to which the same dimensionality reduction has been applied.