Devices, systems, and methods employing polynomial symbol waveforms
AssigneeAstrapi Corporation
InventorsJerrold Prothero, James J. Sterling
Life of this patent
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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.
Claims20
A method of designing polynomial symbol waveform (PSW) alphabets for data transmission, comprising:
- providing, to at least one processor, an initial PSW alphabet including at least one PSW, each PSW having polynomial coefficients and polynomial roots, the initial PSW alphabet defining an input PSW alphabet,
- storing, via a memory, the initial PSW alphabet as the input PSW alphabet;
- applying, by at least one of the processors, at least one variation to one of the polynomial coefficients and the polynomial roots of at least one of the PSWs in the input PSW alphabet to produce an edited PSW alphabet;
- calculating, by at least one of the processors, a goodness measure for the initial and edited PSW alphabets;
- comparing, by at least one of the processors, the goodness measure of the input PSW alphabet to the goodness measure of the edited PSW alphabet;
- setting, by at least one of the processors, the input PSW alphabet to be the edited PSW alphabet when the edited PSW alphabet has a higher goodness measure than the input PSW alphabet;
- and
- outputting, by at least one of the processors, one of the input PSW alphabet and the edited PSW alphabet for use in data transmission based on the goodness measure.
A non-transitory computer readable medium storing instructions, the instructions comprising:
- one or more instructions which, when executed by one or more processors, cause the one or more processors to:
- set an initial polynomial symbol waveform (PSW) alphabet to an input PSW alphabet, the input PSW alphabet including at least one PSW, each PSW having polynomial coefficients and polynomial roots,
- apply at least one variation to at least one of the polynomial coefficients and the polynomial roots of at least one PSW of the input PSW alphabet to produce an edited PSW alphabet;
- calculate a goodness measure for the initial and edited PSW alphabets;
- compare the goodness measure of the input PSW alphabet to the goodness measure of the edited PSW alphabet;
- set the input PSW alphabet to be the edited PSW alphabet when the edited PSW alphabet has a higher goodness measure than the input PSW alphabet;
- and
- output one of the input and the edited PSW alphabet for use in data transmission based on the goodness measure.
Dependencies are inferred from the claim text.