Compact pulse shaping for QM-MSK and PAM/QAM transmission
View Patent ↗Compact pulse shape partial response (CPS PR) signaling is developed for trellis based signals like QM-MSK, and for PAM/QAM type signals to improve the performance to bandwidth tradeoff. Compact pulse shaped signals are partial response signals that employ a very short pulse shaping filter and use Viterbi decoding to optimally detect the CPS signal in presence of its inherent inter-symbol interference. The CPS filters considered herein have much shorter impulse response than the well-known raised cosine (RC) filter. There is no need to equalize the received signal to eliminate ISI or to allow a fixed amount of ISI between received signal samples as sampled at the symbol rate as is common in partial response maximum likelihood (PRML) systems. Numerical results indicate that CPS QM-MSK and CPS QAM provides between several dB of gain, depending on constellation size, over PR-CPM and RC QAM, when compared at a given value of bandwidth, i.e., B 99 T b .
1. A method for use in a communication transmitter that is adapted to produce a communication signal for transmission of a binary data sequence via a channel to a communication receiver, the method comprising:
generating a first real-valued baseband message signal (m 1 (t) signal) that follows a first trajectory through an amplitude trellis, wherein the binary data sequence is trellis encoded to correspond to the first trajectory, and the first trajectory passes through a first particular sequence of trellis states, Q 0 ,Q 1 . . . Q k , at discrete times, kT, where k is an integer counting variable and T is a symbol interval duration;
transforming the m 1 (t) signal into a first compact pulse shape (CPS) encoded partial response signal (x I (t) signal) wherein
x
I
(
t
)
=
∑
j
=
1
L
+
1
p
Q
(
k
-
j
+
1
)
,
Q
(
k
-
j
+
2
)
(
t
-
k
T
+
j
T
-
T
)
,
for at least a two discrete sample times, t, in each of a plurality of symbol intervals, including a k th symbol interval (kT≦t<(k+1)T), where L is a positive integer and L≦7, p Q (k−j+1), Q (k−j+2) (t)=m Q (k−j+1), Q (k−j+2) (t) h(t) is a compact pulse shape whose length is no longer than (L+1)T, m Q (k−j+1), Q (k−j+2) (t) is a state transition signal of the m 1 (t) signal from a state Q(k−j+1) to a state Q(k−j+2), h(t) is a finite impulse response filter whose impulse response has a length no longer than LT and j is an integer; and
processing the x I (t) signal to generate the communication signal therefrom;
wherein neither h(t) nor the processing, alone or in combination with any subsequent receive equalization, are designed to cause zero intersymbol interference or a fixed relationship of intersymbol interference to exist at discrete sampling points of a received and sampled version of the communication signal ({circumflex over (x)} I (kT+Δ) signal) as observed in the receiver prior to any subsequent trellis decoding, where Δ is an optional receiver variable selectable in the receiver to compensate a time shift introduced between the transmitter and receiver.
2. The method of claim 1 , wherein the m 1 (t) signal corresponds to m 1 (t)=A cos(α 1 (t)), where A is a real number and α 1 (t) is a continuous phase modulation (CPM) phase function.
3. The method of claim 1 , further comprising:
coupling the communication signal onto the channel for transmission to the receiver.
4. The method of claim 1 , wherein the processing further comprises:
amplitude-modulating an in-phase carrier signal with the x I (t) signal to produce an in-phase component signal.
5. The method of claim 4 , further comprising:
coupling the in-phase component signal onto the channel for transmission to the communication receiver.
6. The method of claim 5 , wherein the m 1 (t) signal corresponds to m 1 (t)=A cos(α 1 (t)), where A is a real number and a α 1 (t) is a continuous phase modulation (CPM) phase function.
7. The method of claim 1 , further comprising:
trellis encoding a second binary data sequence to generate a second real-valued baseband message signal, (m 2 (t) signal) that follows a second trajectory through the amplitude trellis, wherein the second trajectory passes through a second particular sequence of trellis states, β 0 ,β 1 , . . . β k , at discrete times, kT, where k is an integer counting variable and T is a symbol interval duration;
transforming the m 2 (t) signal into a second compact pulse shape (CPS) encoded partial response signal (x Q (t) signal) wherein
x
Q
(
t
)
=
∑
j
=
1
L
+
1
p
β
(
k
-
j
+
1
)
,
β
(
k
-
j
+
2
)
(
t
-
k
T
+
j
T
-
T
)
,
for at least the two discrete sample times t in each of the plurality of symbol intervals, kT≦t<(k+1)T, where p β (k−j+1), β (k−j+2) (t)=m β (k−j+1), β (k−j+2) (t) h(t) is a compact pulse shape whose length is no longer than (L+1)T, and m β (k−j+1), β (k−j+2) (t) is a state transition signal of the m 2 (t) signal from a state β(k−j+1) to a state β(k−j+2); and
processing x Q (t−τ) to generate a second communication signal therefrom, where 0≦τ≦T.
8. The method of claim 7 , further comprising:
quadrature multiplexing the first communication signal and the second communication signal onto respective in-phase and quadrature-phase carriers to produce a passband signal; and
coupling the passband signal onto the channel for transmission to the receiver.
9. The method of claim 8 , wherein the quadrature multiplexing comprises performing digital modulation, and the method further comprising:
analog bandpass filtering the passband signal prior to the coupling.
10. The method of claim 1 , wherein
the m 1 (t) signal corresponds to m 1 (t)=A cos(α 1 (t)), where A is a real number and α 1 (t) is a first continuous phase modulation (CPM) phase function; and
the m 2 (t) signal corresponds to m 2 (t)=A cos(α 2 (t)), where α 2 (t) is a second continuous CPM phase function.
11. The method of claim 1 , wherein the processing further comprises:
passing a set of samples of the x I (t) signal through a digital-to-analog converter (DAC), wherein the DAC is clocked at a clock rate to produce at least two DAC output voltages per symbol interval, kT≦t<(k+1)T; and
passing the output of the DAC through a reconstruction filter to produce the communication signal.
12. The method of claim 11 , wherein the DAC is clocked at an oversampling rate F s =OS/T, where 2≦OS≦8 is an oversampling factor, and the DAC provides OS voltage samples per symbol interval.
13. The method of claim 12 , further comprising:
coupling the communication signal onto the channel for transmission to the communication receiver.
14. The method of claim 12 , further comprising:
amplitude-modulating an in-phase carrier signal with the communication signal to produce an in-phase component signal; and
coupling the in-phase component signal onto the channel for transmission to the communication receiver.
15. The method of claim 12 , further comprising:
trellis encoding a second binary data sequence to generate a second real-valued baseband message signal, (m 2 (t) signal) that follows a second trajectory through the amplitude trellis, wherein the second trajectory passes through a second particular sequence of trellis states, β 0 ,β 1 , . . . β k , at discrete times, kT, where k is an integer counting variable and T is a symbol interval duration;
transforming the m 2 (t) signal into a second compact pulse shape (CPS) encoded partial response signal (x Q (t) signal) wherein
x
Q
(
t
)
=
∑
j
=
1
L
+
1
p
β
(
k
-
j
+
1
)
,
β
(
k
-
j
+
2
)
(
t
-
k
T
+
j
T
-
T
)
,
for at least the two discrete sample times t in each of the plurality of the symbol intervals, where p β (k−j+1), β (k−j+2) (t)=m β (k−j+1), β (k−j+2) (t) h(t) is a compact pulse shape whose length is no longer than (L+1)T, and
m β (k−j+1), β (k−j+2) (t) is a state transition signal of the m 2 (t) signal from a state β(k−j+1) to a state β(k−j+2);
passing a set of samples of x Q (t−τ) through a second DAC, wherein the second DAC is clocked at the clock rate; and where 0≦τ≦T;
passing the output of the second DAC through a second reconstruction filter to produce a second communication signal;
quadrature multiplexing the first communication signal and the second communication signal onto respective in-phase and quadrature-phase carriers to produce a passband signal; and
coupling the passband signal onto the channel for transmission to the receiver.
16. The method of claim 15 , wherein
the m 1 (t) signal corresponds to m 1 (t)=A cos(α 1 (t)), where A is a real number and α 1 (t) is a first continuous phase modulation (CPM) phase function; and
the m 2 (t) signal corresponds to m 2 (t)=A cos(α 2 (t)), where α 2 (t) is a second continuous CPM phase function.
17. The method of claim 1 , wherein L=4.
18. The method of claim 1 , wherein L=3.
19. The method of claim 1 , wherein L=2.
20. The method of claim 1 , wherein L=1.
21. The method of claim 1 , wherein, when a set of real numbers, t 0 , t a , t b and α are defined as t a =αT/2, t b =(LT−t a ), and α=t 0 /T, the h(t) can be written in the form:
h
(
t
)
=
{
1
2
[
1
-
cos
(
π
(
t
-
t
a
)
t
a
)
]
,
0
≤
t
<
t
0
1
,
t
0
≤
t
<
(
L
-
α
)
T
1
2
[
1
+
cos
(
π
(
t
-
t
b
)
t
a
)
]
,
LT
-
t
0
≤
t
<
LT
0
,
otherwise
}
.
22. A method for use in a communication transmitter that is adapted to produce a communication signal for transmission of a binary data sequence via a channel to a communication receiver, the method comprising:
transforming the binary data sequence into a compact pulse shape (CPS) encoded partial response signal, (x I (t) signal) wherein
x
I
(
t
)
=
∑
j
=
1
L
+
1
I
k
-
j
+
1
p
(
t
-
k
T
+
j
T
-
T
)
,
for at least a two discrete sample times t in each of a plurality of symbol intervals, including a k th symbol interval (kT≦t<(k+1)T), where T is a symbol interval duration, k is an integer counting variable, L is a positive integer and L≦7, a k is an M-ary pulse amplitude modulated sequence representative of the binary data sequence, where M≧2, p(t)=z(t) h(t) is a compact pulse shape whose length is no longer than (L+1)T, z(t) is a baseband pulse shape with a pulse width that is no longer than T, and h(t) is a finite impulse response filter whose impulse response has a length no longer than LT;
processing the x I (t) signal to generate the communication signal therefrom; and
wherein neither h(t) nor the processing, alone or in combination with any subsequent receive equalization, are designed to cause zero intersymbol interference or a fixed relationship of intersymbol interference to exist at discrete sampling points of a received and sampled version of the communication signal, {circumflex over (x)} I (kT+Δ), as observed in the receiver prior to any subsequent trellis decoding, where Δ is an optional receiver variable selectable in the receiver to compensate a time shift introduced between the transmitter and receiver.
23. The method of claim 22 , further comprising:
coupling the communication signal onto the channel for transmission to the receiver.
24. The method of claim 22 , wherein the transforming further comprises:
pulse amplitude modulating the binary data sequence by mapping respective sets of one or more bits of the binary data sequence onto respective ones of the M-ary pulse amplitude modulated sequence values, a k .
25. The method of claim 24 , wherein the transforming further comprises:
generating a pulse amplitude modulated signal,
a
(
t
)
=
∑
k
a
k
z
(
t
-
kT
)
;
convolving the pulse amplitude modulated signal with h(t) to produce the x I (t) signal.
26. The method of claim 25 , wherein
z
(
t
)
=
A
T
rect
(
t
/
T
)
.
27. The method of claim 22 , wherein the processing further comprises:
amplitude-modulating an in-phase carrier signal with the x I (t) signal to produce an in-phase component signal.
28. The method of claim 27 , further comprising:
coupling the in-phase component signal onto the channel for transmission to the communication receiver.
29. The method of claim 27 , further comprising:
transforming a second binary data sequence into a second CPS encoded partial response signal, (x Q (t) signal) wherein
x
Q
(
t
)
=
∑
j
=
1
L
+
1
b
k
-
j
+
1
p
(
t
-
k
T
+
j
T
-
T
)
,
for at least a two discrete sample times t in the symbol interval (kT≦t<(k+1)T), and b k is a second M-ary pulse amplitude modulated sequence derived from the second binary data sequence; and
processing the x Q (t) signal to generate a second communication signal therefrom.
30. The method of claim 29 , further comprising:
quadrature multiplexing the first communication signal and the second communication signal onto respective in-phase and quadrature-phase carriers to produce a passband signal; and
coupling the passband signal onto the channel for transmission to the receiver.
31. The method of claim 30 , wherein the quadrature multiplexing comprises performing digital modulation, the method further comprising:
analog bandpass filtering the passband signal prior to the coupling.
32. The method of claim 22 , wherein the processing further comprises:
passing a set of samples of the x I (t) signal through a digital-to-analog converter (DAC), wherein the DAC is clocked at a clock rate to produce at least two DAC output voltages per symbol interval (kT≦t<(k+1)T); and
passing the output of the DAC through a reconstruction filter to produce the communication signal.
33. The method of claim 32 , wherein the DAC is clocked at an oversampling rate F s =OS/T, where 2≦OS≦8 is an oversampling factor, and the DAC provides OS voltage samples per symbol interval.
34. The method of claim 33 , further comprising:
coupling the communication signal onto the channel for transmission to the communication receiver.
35. The method of claim 33 , further comprising:
amplitude-modulating an in-phase carrier signal with the communication signal to produce an in-phase component signal;
coupling the in-phase component signal onto the channel for transmission to the communication receiver.
36. The method of claim 33 , further comprising:
transforming a second binary data sequence onto a second CPS encoded partial response signal (x Q (t) signal) wherein
x
Q
(
t
)
=
∑
j
=
1
L
+
1
b
k
-
j
+
1
p
(
t
-
k
T
+
j
T
-
T
)
,
for at least a two discrete sample times t in the range kT≦t<(k+1)T, where b k is a second M-ary pulse amplitude modulated sequence derived from the second binary data sequence;
passing a set of samples of the x Q (t) signal through a second DAC, wherein the second DAC is clocked at the clock rate;
passing the output of the second DAC through a second reconstruction filter to produce a second communication signal;
quadrature multiplexing the first communication signal and the second communication signal onto respective in-phase and quadrature-phase carriers to produce a passband signal; and
coupling the passband signal onto the channel for transmission to the receiver.
37. The method of claim 22 , wherein L=4.
38. The method of claim 22 , wherein L=3.
39. The method of claim 22 , wherein L=2.
40. The method of claim 22 , wherein L=1.
41. The method of claim 22 , wherein, when a set of real numbers, t 0 , t a , t b and α are defined as t a =αT/2, t b =(LT−t a ), and α=t 0 /T, the h(t) can be written in the form:
h
(
t
)
=
{
1
2
[
1
-
cos
(
π
(
t
-
t
a
)
t
a
)
]
,
0
≤
t
<
t
0
1
,
t
0
≤
t
<
(
L
-
α
)
T
1
2
[
1
+
cos
(
π
(
t
-
t
b
)
t
a
)
]
,
LT
-
t
0
≤
t
<
LT
0
,
otherwise
}
.