Devices and methods for multicarrier modulation schemes

A receiver device, comprising:

• a processor;
• and
• a non-transitory memory, storing executable program code for execution the processor, the program code including instructions for:
• determining a plurality of signature roots (ρk), wherein each signature root of the plurality of signature roots (ρk) is a nonzero complex point;
• constructing one of a Lagrange matrix or a Vandermonde matrix from the plurality of signature roots (ρk) and according to a gradient descent algorithm;
• and
• performing demodulation of a multicarrier modulated signal based on the Lagrange matrix or the Vandermonde matrix.

A method, comprising:

• obtaining, by a transmitter device, a plurality of signature roots (ρk) based on a feedback message received from a receiver device, wherein each signature root of the plurality of signature roots is a nonzero complex point;
• constructing one of a Lagrange matrix or a Vandermonde matrix from the plurality of signature roots (ρk) and according to a gradient descent algorithm;
• and
• generating a multicarrier modulated signal based on the Lagrange matrix or the Vandermonde matrix.

A method, comprising:

• determining, by a receiver device, a plurality of signature roots (ρk), wherein each signature root of the plurality of signature roots is a nonzero complex point;
• constructing a Lagrange matrix or a Vandermonde matrix from the plurality of signature roots (ρk) and according to a gradient descent algorithm;
• and
• performing a demodulation of a multicarrier modulated signal based on the Lagrange matrix or the Vandermonde matrix.

A non-transitory memory, storing executable program code for execution by a processor, the program code including instructions for:

• obtaining a plurality of signature roots (ρk) based on receiving a feedback message from a receiver device, wherein each signature root of the plurality of signature roots is a nonzero complex point;
• constructing one of a Lagrange matrix or a Vandermonde matrix from the plurality of signature roots (ρk) and according to a gradient descent algorithm;
• and
• generating a multicarrier modulated signal based on the Lagrange matrix or the Vandermonde matrix.

A non-transitory memory, storing executable program code for execution by a processor, the program code including instructions for:

• determining a plurality of signature roots (ρk), wherein each signature root of the plurality of signature roots is a nonzero complex point;
• constructing one of a Lagrange matrix or a Vandermonde matrix from the plurality of signature roots (ρk) and according to a gradient descent algorithm;
• and
• performing a demodulation of a multicarrier modulated signal based on the Lagrange matrix or the Vandermonde matrix.