High spectral efficiency data communications system

A method of recovering input digital data encoded into successive symbol waveforms of a plurality of symbol waveforms wherein each symbol waveform of the plurality of symbol waveforms represents bits of the input digital data and wherein each of the successive symbol waveforms occupies one period of a composite encoded waveform, each symbol waveform of the plurality of symbol waveforms being of an identical period T and being divided into two segments separated by a zero crossing wherein the two segments correspond to a first segment and a second segment of substantially equal energy wherein a zero crossing from the first segment to the second segment is different for each symbol waveform of the plurality of symbol waveforms, the method including:

• receiving an encoded analog waveform generated using the symbol waveforms;
• generating digital symbol samples representing the symbol waveforms;
• identifying a first sample of the digital symbol samples corresponding to a transition in polarity of the digital symbol samples from a first polarity to a second polarity;
• determining a second sample of the digital signal samples corresponding to a transition from ones of the digital signal samples of the second polarity to ones of the digital signal samples of the first polarity, the second sample of the digital samples defining a transition from the first segment of one of the symbol waveforms to the second segment of the one of the symbol waveforms;
• and
• estimating the input digital data based upon the first sample and the second sample.

A system, comprising:

• an input buffer configured to store input digital data;
• a time domain modulator for encoding, using a plurality of symbol waveforms, the input digital data into successive symbol waveforms of the plurality of symbol waveforms wherein each symbol waveform of the plurality of symbol waveforms represents bits of the input digital data, is of an identical period T, and is divided into two parts consisting of one positive segment and one negative segment and wherein each of the successive symbol waveforms occupies one period of a composite encoded waveform;
• wherein the time domain modulator defines each symbol waveform so that (i) a zero crossing from the one positive segment to the one negative segment of the symbol waveform is different for each of the plurality of symbol waveforms, and (ii) an energy of the positive segment of the symbol waveform is substantially equal to an energy of the negative segment of the symbol waveform;
• one or more digital-to-analog converters for generating an encoded analog waveform from a digital representation of the composite encoded waveform.

A system, comprising:

• an input buffer configured to store input digital data;
• a time domain modulator for encoding the input digital data using a plurality of symbol waveforms wherein each of the plurality of symbol waveforms occupies a period of a composite encoded waveform and represents bits of the input digital data, each symbol waveform of the plurality of symbol waveforms having a positive segment and a negative segment wherein the positive segment and the negative segment for each of the plurality of symbol waveforms are elliptical in shape;
• wherein the time domain modulator defines each symbol waveform so that (i) a zero crossing from the positive segment to the negative segment of the symbol waveform is different for each of the plurality of symbol waveforms, and (ii) an energy of the positive segment of the symbol waveform is substantially equal to an energy of the negative segment of the symbol waveform;
• one or more digital-to-analog converters for generating an encoded analog waveform from a digital representation of the composite encoded waveform.

A data communication method, the method comprising:

• receiving input digital data;
• encoding the input digital data using a plurality of symbol waveforms wherein each of the plurality of symbol waveforms represents bits of the input digital data and wherein each period of a composite encoded waveform is occupied by one symbol waveform of the plurality of symbol waveforms, each symbol waveform of the plurality of symbol waveforms being of an identical period T and being divided into two parts consisting of one positive segment and one negative segment;
• wherein each symbol waveform is defined so that (i) a zero crossing from the positive segment to the negative segment of the symbol waveform is different for each of the plurality of symbol waveforms, and (ii) an energy of the positive segment of the symbol waveform is substantially equal to an energy of the negative segment of the symbol waveform;
• generating an encoded analog waveform from a representation of the composite encoded waveform.

A method of recovering input digital data encoded by a plurality of symbol waveforms wherein each symbol waveform of the plurality of symbol waveforms is of an identical period T and is divided into two segments separated by a zero crossing wherein the two segments correspond to a positive segment and a negative segment of substantially equal energy and wherein a zero crossing within each symbol waveform of the plurality of symbol waveforms is different for each symbol waveform, the method including:

• receiving an encoded analog waveform generated using the symbol waveforms;
• generating digital symbol samples representing the symbol waveforms;
• identifying a first sample of the digital symbol samples corresponding to a transition from ones of the digital signal samples having negative values to ones of the digital signal samples having positive values;
• determining a second sample of the digital signal samples corresponding to a transition from other ones of the digital signal samples having positive values to other ones of the digital signal samples having negative values, the second sample of the digital samples defining a transition from the positive elliptical segment of one of the symbol waveforms to the negative segment of the one of the symbol waveforms;
• and
• estimating the input digital data based upon the first sample and the second sample.