Devices, Systems, And Methods Employing Polynomial Symbol Waveforms

Abstract

Systems, devices, and methods of the present invention enhance data transmission through the use of polynomial symbol waveforms (PSW) and sets of PSWs corresponding to a symbol alphabet is here termed a PSW alphabet. Methods introduced here are based on modifying polynomial alphabet by changing the polynomial coefficients or roots of PSWs and/or shaping of the polynomial alphabet, such as by polynomial convolution, to produce a designed PSW alphabet including waveforms with improved characteristics for data transmission. In various embodiments, transmitter and receivers utilize symbol waveforms based on a PSW alphabet designed using methods that may include specifying the location of particular polynomial roots, such as placing roots at the symbol time boundaries with amplitude zero, to minimize symbol boundary discontinuities, translating the nearest polynomial root to a particular point in the complex plane, directly editing the location of one or more polynomial roots, adjusting the complex conjugate of an edited PSW root in order to keep the PSW real-valued, and shaping one of more PSWs using polynomial convolution with polynomial versions of the raised cosine, root raised cosine, Gaussian, or other band-limiting filters. Stochastic methods for PSW optimization are also introduced.

Dependencies are inferred from the claim text.