Modified continuous phase modulation communications system and related methods

1. A communications system comprising:

a first communications device comprising a transmitter and a modulator cooperating therewith and configured to

modulate a coded waveform using a constant phase modulation (CPM) to generate a non-linear CPM waveform,

generate a linear representation of the non-linear CPM waveform, the linear representation comprising a plurality of pulses,

remove all but a first pulse adjacent a first end of the plurality of pulses and a second pulse adjacent a second end of the plurality of pulses to define a modified linear representation of the non-linear CPM waveform, the first and second pulses having at least one pulse therebetween, and

transmit the modified linear representation of the non-linear CPM waveform; and

a second communications device comprising a receiver and a single pulse-matched filter linear demodulator cooperating therewith and configured to demodulate the modified linear representation of the non-linear CPM waveform transmitted from said first communications device.

2. The communications system according to claim 1 , wherein said modulator is configured to modulate the coded waveform using CPM to generate a non-binary M-ary non-linear CPM waveform.

3. The communications system according to claim 1 , wherein said modulator is configured to generate the linear representation of the non-linear CPM waveform based upon a superposition of linearly modulated pulse trains.

4. The communications system according to claim 1 , wherein said modulator is configured to generate the modified linear representation of the CPM waveform to have an envelope within ±20% of a constant value.

5. The communications system according to claim 1 , wherein said single pulse-matched filter linear demodulator is configured to demodulate the modified linear representation of the non-linear CPM waveform based upon a minimum mean square error (MMSE) criterion.

6. The communications system according to claim 1 , wherein said modulator is configured to generate the linear representation of the non-linear CPM waveform based upon a Mengali-Morelli decomposition of the non-linear CPM waveform.

7. A communications device operable for communicating with another communications device comprising a receiver and a single pulse-matched filter linear demodulator cooperating therewith, the communications device comprising:

a transmitter and a modulator cooperating therewith and configured to

modulate a coded waveform using a constant phase modulation (CPM) to generate a non-linear CPM waveform,

generate a linear representation of the non-linear CPM waveform, the linear representation comprising a plurality of pulses,

remove all but a first pulse adjacent a first end of the plurality of pulses and a second pulse adjacent a second end of the plurality of pulses to define a modified linear representation of the non-linear CPM waveform, the first and second pulses having at least one pulse therebetween, and

transmit the modified linear representation of the non-linear CPM waveform.

8. The communications device according to claim 7 , wherein said modulator is configured to modulate the coded waveform using CPM to generate a non-binary M-ary non-linear CPM waveform.

9. The communications device according to claim 7 , wherein said modulator is configured to generate the linear representation of the non-linear CPM waveform based upon a superposition of linearly modulated pulse trains.

10. A communications device operable to communicate with another communications device comprising a transmitter and a modulator cooperating, the communications device comprising:

a receiver configured to receive a linear representation of a non-linear CPM waveform generated by modulating a coded waveform using a constant phase modulation (CPM) to generate the non-linear CPM waveform, the linear representation comprising a plurality of pulses and all but a first pulse adjacent a first end of the plurality of pulses and a second pulse adjacent a second end of the plurality of pulses being removed to define a modified linear representation of the non-linear CPM waveform, the first and second pulses having at least one pulse therebetween; and

a single pulse-matched filter linear demodulator coupled to said receiver and cooperating therewith to demodulate the modified linear representation of the received non-linear CPM waveform.

11. The communications device according to claim 10 , wherein said single pulse-matched filter linear demodulator is configured to demodulate the modified linear representation of the non-linear CPM waveform based upon a minimum mean square error (MMSE) criterion.

12. A communications method comprising:

modulating by a first communications device a coded waveform using a constant phase modulation (CPM) to generate a non-linear CPM waveform;

generating, at the first communications device, a linear representation of the non-linear CPM waveform comprising a plurality of pulses;

removing all but a first pulse adjacent a first end of the plurality of pulses and a second pulse adjacent a second end of the plurality of pulses to define a modified linear representation of the non-linear CPM waveform, the first and second pulses having at least one pulse therebetween; and

transmitting the modified linear representation of the non-linear CPM waveform; and

demodulating the modified linear representation of the non-linear CPM waveform transmitted from the first communications device in a second communications device comprising a single pulse filter linear demodulator.

13. The method according to claim 12 , wherein modulating the coded waveform comprises modulating the coded waveform using CPM to generate a non-binary M-ary non-linear CPM waveform.

14. The method according to claim 12 , wherein generating the linear representations comprises generating the linear representation of the non-linear CPM waveform based upon a superposition of linearly modulated pulse trains.