Method and apparatus for generating M-ary CPM waveforms from a superposition of PAM waveforms
View Patent ↗To reflect advantages of a constant phase modulation waveform, the invention provides a pulse amplitude modulated PAM waveform that is a superposition of Q 0 ≦2 L−1 PAM component pulses in each symbol interval such that a significant portion of signal energy over each symbol interval is within the Q 0 PAM component pulses. The present invention distributes most signal energy in one pulse and progressively lower energies in the remaining Q 0 −1 pulses of a symbol interval. The Laurent Decomposition is a special case of the present invention, but the present invention exhibits the energy distribution of the Laurent Decomposition in non-binary CPM waveforms and in multi-h (binary and non-binary) CPM waveforms, where h is a modulating index. All energy is distributed among only Q=2 L−1 pulses in each symbol interval, though only Q 0 <Q pulses may in fact be transmitted in certain embodiments. A method, transmitter, receiver, and computer program are disclosed. Embodiments may exactly duplicate a CPM waveform, or approximate a CPM waveform.
1. An apparatus comprising:
a signal source;
a modulator configured to output a M-ary pulse-amplitude modulated waveform that is a superposition of Q 0 ≦2 L−1 pulse-amplitude modulated component pulses in each symbol interval, where M>2 is a number of allowed discrete amplitude values and L represents a number of symbol intervals;
a multiplier having inputs from the signal source and the modulator; and
a processor configured to drive the modulator to shape the Q 0 pulse-amplitude modulated component pulses in each symbol interval such that at least a significant portion of signal energy for each symbol interval of a transmission burst is carried in that symbol interval's Q 0 pulse-amplitude modulated component pulses.
2. The apparatus of claim 1 , wherein Q 0 =1 and at least a significant portion of signal energy in the one pulse-amplitude modulated component pulse comprises at least 95% of signal energy.
3. The apparatus of claim 1 , wherein Q 0 =2 L−1 and at least a significant portion of signal energy comprises all signal energy.
4. The apparatus of claim 3 , wherein the multiplier operates to multiply the input from the signal source by a truncated input from the modulator, the truncated input characterized by less than all Q 0 =2 L−1 pulse-amplitude modulated component pulses for each symbol interval.
5. The apparatus of claim 1 , wherein the output of the multiplier is represented by:
x
(
t
,
a
,
h
)
=
∑
k
=
0
Q
0
-
1
∑
n
b
k
,
n
g
k
,
n
(
t
-
nT
)
,
1
≤
Q
0
≤
Q
;
(
Q
=
2
L
-
1
)
;
where b k,n represents a pseudo symbol, g k,n (t−nT) represents a function that derives from a phase function of the signal, and T is symbol duration.
6. An apparatus comprising:
a signal source;
a modulator configured to output a binary, multi-h pulse-amplitude modulated waveform that is a superposition of Q 0 ≦2 L−1 pulse-amplitude modulated component pulses in each symbol interval, h>1 is a number of modulating indices, and L represents a number of symbol intervals;
a multiplier having inputs from the signal source and the modulator; and
a processor configured to drive the modulator to shape the Q 0 pulse-amplitude modulated component pulses in each symbol interval such that at least a significant portion of signal energy for each symbol interval of a transmission burst is carried in that symbol interval's Q 0 pulse-amplitude modulated component pulses.
7. The apparatus of claim 6 , wherein Q 0 =1 and at least a significant portion of signal energy in the one pulse-amplitude modulated component pulse comprises at least 95% of signal energy.
8. The apparatus of claim 6 , wherein Q 0 =2 L−1 and at least a significant portion of signal energy comprises all signal energy.
9. The apparatus of claim 8 , wherein the multiplier operates to multiply the input from the signal source by a truncated input from the modulator, the truncated input characterized by less than all Q 0 =2 L−1 pulse-amplitude modulated component pulses for each symbol interval.
10. The apparatus of claim 6 , wherein the output of the multiplier is represented by:
x
(
t
,
a
,
h
)
=
∑
k
=
0
Q
0
-
1
∑
n
b
k
,
n
g
k
,
n
(
t
-
nT
)
,
1
≤
Q
0
≤
Q
;
(
Q
=
2
L
-
1
)
;
where b k,n represents a pseudo symbol, g k,n (t−nT) represents a function that derives from a phase function of the signal, and T is symbol duration.
11. A memory embodying a program of machine-readable instructions, executable by a digital data processor, to perform actions directed toward modulating an input signal, the actions comprising:
determining a M-ary pulse-amplitude modulated waveform that is a superposition of Q 0 ≦2 L−1 pulse-amplitude modulated component pulses in each symbol interval such that at least a significant portion of signal energy over each symbol interval of a burst is within the Q 0 pulse-amplitude modulated component pulses;
combining the M-ary pulse-amplitude modulated waveform with a signal to be transmitted; and
transmitting the modulated signal,
where M>2 is a number of allowed discrete amplitude values and L represents a number of symbol intervals.
12. The memory of claim 11 , wherein Q 0 =1 and at least a significant portion of signal energy in the one pulse-amplitude modulated component pulse comprises at least 95% of signal energy.
13. The memory of claim 11 , wherein Q 0 =2 L− and at least a significant portion of signal energy comprises all signal energy.
14. The memory of claim 11 , wherein determining the M-ary pulse-amplitude modulated waveform comprises:
for each n th symbol of duration T, determining a product of a pseudo symbol b k,n and a function g k,n (t−nT) that derives from a phase function of the signal, and summing the products over Q 0 pulse-amplitude modulated component pulses.
15. The memory of claim 14 , wherein determining further comprises adding the sums of the products over all symbol intervals for all component pulses.
16. The memory of claim 11 , wherein determining the M-ary pulse-amplitude modulated waveform that is a superposition of Q 0 ≦2 L−1 pulse-amplitude modulated component pulses comprises
determining a M-ary pulse-amplitude modulated waveform that is a superposition of Q 0 =2 L−1 pulse-amplitude modulated component pulses in each symbol interval such that all signal energy over each symbol interval of a burst is within the Q 0 pulse-amplitude modulated component pulses, and
truncating to Q 0 <2 L−1 pulse-amplitude modulated component pulses.
17. A memory embodying a program of machine-readable instructions, executable by a digital data processor, to perform actions directed toward modulating an input signal, the actions comprising:
determining a binary multi-h pulse-amplitude modulated waveform that is a superposition of Q 0 ≦2 L−1 pulse-amplitude modulated component pulses in each symbol interval such that at least a significant portion of signal energy over each symbol interval of a burst is within the Q 0 pulse-amplitude modulated component pulses;
combining the binary pulse-amplitude modulated waveform with a signal to be transmitted; and
transmitting the modulated signal,
where h>1 is a number of modulating indices, and L represents a number of symbol intervals.
18. The memory of claim 17 , wherein Q 0 <2 L−1 and at least a significant portion of signal energy in the one pulse-amplitude modulated component pulse comprises at least 95% of signal energy.
19. The memory of claim 17 , wherein Q 0 =2 L−1 and at least a significant portion of signal energy comprises all signal energy.
20. The memory of claim 17 , wherein determining the binary multi-h pulse-amplitude modulated waveform comprises:
for each n th symbol of duration T, determining a product of a pseudo symbol b k,n and a function g k,n (t−nT) that derives from a phase function of the signal, and summing the products over Q 0 pulse-amplitude modulated component pulses.
21. The memory of claim 20 , wherein determining further comprises adding the sums of the products over all symbol intervals for all component pulses.
22. The memory of claim 17 , wherein determining the binary multi-h pulse-amplitude modulated waveform that is a superposition of Q 0 ≦2 L−1 pulse-amplitude modulated component pulses comprises
determining a binary multi-h pulse-amplitude modulated waveform that is a superposition of Q 0 =2 L−1 pulse-amplitude modulated component pulses in each symbol interval such that all signal energy over each symbol interval of a burst is within the Q 0 pulse-amplitude modulated component pulses, and
truncating to Q 0 <2 L−1 pulse-amplitude modulated component pulses.
23. An apparatus comprising:
signal source means; and
modulating means for determining, for each symbol interval of a burst in which symbols are modulated over M>2 discrete amplitudes, a plurality of Q 0 pulses that are shaped such that the pulses are ordered by an amount of signal energy they carry, the modulator means further for superimposing the plurality of Q 0 pulses into a combined waveform with continuous phase that modulates an output of the signal means for transmission;
wherein the modulating means comprises a processor, a memory, a modulator, and a multiplier coupled together.
24. An apparatus comprising:
signal source means;
modulating means for determining, for each symbol interval of a burst in which symbols are modulated over two discrete amplitudes, a plurality of Q 0 pulses modulated with h>1 modulating indices that are shaped such that the pulses are ordered by an amount of signal energy they carry, the modulator means further for superimposing the plurality of Q 0 pulses into a combined waveform with continuous phase that modulates an output of the signal means; and
transmitting means for transmitting the signal modulated on the combined waveform; wherein the modulating means comprises a processor, a memory, a modulator, and a multiplier coupled together.
25. A method comprising:
constructing a function g k,n (t) with a processor of an electronic device to construct a signal x(t, a, h);
the processor shifting the function by nT;
the processor multiplying the shifted function by a pseudo symbol b k,n ;
the processor summing over Q 0 pulses the multiplied and shifted function; and
the processor summing over n symbols the Q 0 pulses;
wherein t is a time index, a={a i } represents a phase of a complex data symbol, h is a modulating index, and T is symbol duration.
26. A method comprising:
determining with a digital processor of an apparatus a M-ary pulse-amplitude modulated waveform that is a superposition of Q 0 =1 pulse-amplitude modulated component pulses in each symbol interval such that at least 95% of signal energy over each symbol interval of a burst is within the Q 0 pulse-amplitude modulated component pulse;
the digital processor combining the M-ary pulse-amplitude modulated waveform with a signal to be transmitted; and
transmitting the modulated signal from a transmitter of the apparatus,
where M>2 is a number of allowed discrete amplitude values.
27. A method comprising:
determining with a digital processor of an apparatus a M-ary pulse-amplitude modulated waveform that is a superposition of Q 0≦ 2 L−1 pulse-amplitude modulated component pulses in each symbol interval such that at least a significant portion of signal energy of signal energy over each symbol interval of a burst is within the Q 0 pulse-amplitude modulated component pulses;
the digital processor combining the M-ary pulse-amplitude modulated waveform with a signal to be transmitted; and
transmitting the modulated signal from a transmitter of the apparatus,
where M>2 is a number of allowed discrete amplitude values and L represents a number of symbol intervals;
wherein determining with the digital processor of the apparatus the M-ary pulse-amplitude modulated waveform comprises:
for each n th symbol of duration T, determining with the digital processor a product of a pseudo symbol b k,n and a function g k,n (t−nT) that derives from a phase function of the signal, and the digital processor summing the products over Q 0 pulse-amplitude modulated component pulses.
28. The method of claim 27 , wherein determining with the digital processor of the apparatus the M-ary pulse-amplitude modulated waveform further comprises the digital processor adding the sums of the products over all symbol intervals for all component pulses.
29. A method comprising:
determining with a digital processor of an apparatus a M-ary pulse-amplitude modulated waveform that is a superposition of Q 0 ≦2 L−1 pulse-amplitude modulated component pulses in each symbol interval such that at least a significant portion of signal energy of signal energy over each symbol interval of a burst is within the Q 0 pulse-amplitude modulated component pulses;
the digital processor combining the M-ary pulse-amplitude modulated waveform with a signal to be transmitted; and
transmitting the modulated signal from a transmitter of the apparatus,
where M>2 is a number of allowed discrete amplitude values and L represents a number of symbol intervals;
wherein determining with the digital processor of the apparatus the M-ary pulse-amplitude modulated waveform that is a superposition of Q 0 ≦2 L−1 pulse-amplitude modulated component pulses comprises:
determining with the digital processor a M-ary pulse-amplitude modulated waveform that is a superposition of Q 0 =2 L−1 pulse-amplitude modulated component pulses in each symbol interval such that all signal energy over each symbol interval of a burst is within the Q 0 pulse-amplitude modulated component pulses, and
the digital processor truncating to Q 0 <2 L−1 pulse-amplitude modulated component pulses.
30. A method comprising: determining with a digital processor of an apparatus a binary multi-h pulse-amplitude modulated waveform that is a superposition of Q 0 <2 L−1 pulse-amplitude modulated component pulses in each symbol interval such that at least 95% of signal energy over each symbol interval of a burst is within the Q 0 pulse-amplitude modulated component pulses;
the digital processor combining the binary pulse-amplitude modulated waveform with a signal to be transmitted; and
transmitting the modulated signal from a transmitter of the apparatus,
where h>1 is a number of modulating indices, and L represents a number of symbol intervals.
31. A method comprising:
determining with a digital processor of an apparatus a binary multi-h pulse-amplitude modulated waveform that is a superposition of Q 0 ≦2 L−1 pulse-amplitude modulated component pulses in each symbol interval such that at least a significant portion of signal energy over each symbol interval of a burst is within the Q 0 pulse-amplitude modulated component pulses;
the digital processor combining the binary pulse-amplitude modulated waveform with a signal to be transmitted; and
transmitting the modulated signal from a transmitter of the apparatus,
where h>1 is a number of modulating indices, and L represents a number of symbol intervals;
and wherein determining with the digital processor the binary multi-h pulse-amplitude modulated waveform comprises:
for each n th symbol of duration T, determining with the digital processor a product of a pseudo symbol b k,n and a function g k,n (t−nT) that derives from a phase function of the signal, and the digital processor summing the products over Q 0 pulse-amplitude modulated component pulses.
32. The method of claim 31 , wherein determining further comprises the digital processor adding the sums of the products over all symbol intervals for all component pulses.
33. A method comprising:
determining with a digital processor of an apparatus a binary multi-h pulse-amplitude modulated waveform that is a superposition of Q 0 ≦2 L−1 pulse-amplitude modulated component pulses in each symbol interval such that at least a significant portion of signal energy over each symbol interval of a burst is within the Q 0 pulse-amplitude modulated component pulses;
the digital processor combining the binary pulse-amplitude modulated waveform with a signal to be transmitted; and
transmitting the modulated signal from a transmitter of the apparatus,
where h>1 is a number of modulating indices, and L represents a number of symbol intervals;
and wherein determining with the digital processor the binary multi-h pulse-amplitude modulated waveform that is a superposition of Q 0 ≦2 L−1 pulse-amplitude modulated component pulses comprises:
determining with the digital processor a binary multi-h pulse-amplitude modulated waveform that is a superposition Q 0 =2 L−1 pulse-amplitude modulated component pulses in each symbol interval such that all signal energy over each symbol interval of a burst is within the Q 0 pulse-amplitude modulated component pulses, and
the digital processor truncating to Q 0 <2 L−1 pulse-amplitude modulated component pulses.