SPIRAL POLYNOMIAL DIVISION MULTIPLEXING

摘要

A method for communicating using polynomial-based signals. In such a method, a set of basis polynomial functions used to generate waveforms may be identified, wherein each of the basis polynomial functions in the set of basis polynomial functions is orthogonal to each of the other basis polynomial functions in the set of basis polynomial functions in a coordinate space. The set of basis polynomial functions may be combined into a message polynomial. The message polynomial may be convolved with a reference polynomial to produce a transmission polynomial. From the transmission polynomial, a sequence of amplitude values may be generated. Finally, a signal may be transmitted based on the sequence of amplitude values, which may be further modified based on, for example, instantaneous spectral analysis. In some embodiments, orthogonal polynomials may include Chebyshev or Cairns polynomials.

主权项

1. A method for communicating, comprising:
identifying a set of basis polynomial functions used to generate waveforms, wherein each of the basis polynomial functions in the set of basis polynomial functions is orthogonal to each of the other basis polynomial functions in the set of basis polynomial functions in a coordinate space; combining the set of basis polynomial functions into a message polynomial, and generating a transmission polynomial comprising the message polynomial; generating, from the transmission polynomial, a sequence of amplitude values; and transmitting, with a transmitter, a signal based on the sequence of amplitude values.