Compact pulse shaping for QM-MSK and PAM/QAM reception
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 communications receiver that is adapted to process a received communication signal, wherein the received communication signal provides a channel-distorted version of a communication signal that has been encoded in accordance with at least an in-phase component signal (x I (t) signal), wherein
x
I
(
t
)
=
∑
j
=
1
L
+
1
p
Q
(
k
-
j
+
1
)
Q
(
k
-
j
+
2
)
(
t
-
kT
+
jT
-
T
)
,
for at least 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, T is a symbol interval duration, k and j are integer counting variables, 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, h(t) is a finite impulse response filter whose impulse response has a length no longer than LT, m Q (k−j+1), Q (k−j+2) (t) is a state transition signal of a first real-valued baseband message signal (m I (t) signal) from a state Q(k−j+1) to a state Q(k−j+2), the m 1 (t) signal follows a first trajectory through an amplitude trellis in accordance with a binary data sequence that has been trellis encoded therein, and the first trajectory passes through a first particular sequence of trellis states, Q 0 , Q 1 , . . . Q k , at discrete times, kT, the method comprising:
receiving the received communication signal from a channel, extracting at least an in-phase baseband component signal (Z I (t) signal) therefrom, lowpass filtering the Z I (t) signal, and oversampling the output of the lowpass filtering with an analog-to-digital converter (ADC) at an oversampling rate F s =OS/T, where 2≦OS≦8 is an oversampling factor, and the ADC provides OS voltage samples for the k th symbol interval;
computing, for the k th symbol interval, using a k th set of the oversampled data samples that correspond to samples of the Z I (t) signal sampled during the k th symbol interval, a k th set of branch metrics, wherein each branch metric provides a measure of a respective distance between the k th set of the oversampled data samples and a respective one of a set of template state transition signals (x Template (t, S k , S k+1 ) signals) representative of each possible state transition from each possible first state S k =(Q k−1 , Q k−2 , . . . Q k−L ), to each second state S k+1 (Q k , Q k−1 , . . . Q k−L+1 ) for each next permissible state Q k that can be transitioned to from the state Q k−1 ; and
implementing a trellis decoding algorithm using at least the k th set of branch metrics to determine a trellis decoded sequence and deriving an estimate of the binary data sequence based upon the trellis decoded sequence.
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 , wherein the template state transition signal from the first state S k (Q k−1 , Q k−2 , . . . Q k−L ), to each second state S k+1 =(Q k , Q k−1 , . . . Q k−L+1 ), can be written as
x
Template
(
t
,
S
k
,
S
k
+
1
)
=
∑
j
=
1
L
+
1
p
Q
(
k
-
j
+
1
)
,
Q
(
k
-
j
+
2
)
(
t
-
kT
+
jT
-
T
)
,
for at least OS discrete sample times t in the k th symbol interval (kT≦t<(k+1)T).
4. The method of claim 3 , wherein respective ones of the k th set of branch metrics are respective estimates of a respective distance defined by:
B
(
S
k
,
S
k
+
1
)
≅
∫
kT
(
k
+
1
)
T
[
Z
l
(
t
)
-
x
Template
(
t
,
S
k
,
S
k
+
1
)
]
2
ⅆ
t
.
5. The method of claim 3 , further comprising:
computing a set of correlations between the Z I (t) signal and a set of signal segments of the form {p Q (k−j+1), Q (k−j+2) (t−kT+jT−T) for j=1, . . . L+1, and kT≦t<(k+1)T};
wherein the set of correlations are reused multiple times to efficiently compute different ones of the branch metrics in the k th set of branch metrics.
6. The method of claim 1 , wherein the trellis decoding algorithm is a Viterbi algorithm.
7. The method of claim 1 , further comprising:
amplitude demodulating the received communication signal to translate an in-phase carrier component signal to baseband;
wherein the extracting is performed after the amplitude demodulating.
8. The method of claim 1 , further comprising:
quadrature demodulating the received communication signal to translate both an in-phase carrier component signal and a quadrature-phase carrier signal to baseband, wherein the extracting of the Z I (t) signal occurs after the quadrature demodulating; and
extracting at least a quadrature-phase baseband component signal (Z Q (t) signal) to after the quadrature demodulating, lowpass filtering the Z Q (t) signal, and oversampling the output of the lowpass filtering with a second ADC at the oversampling rate F s to provide OS voltage samples of the Z Q (t) signal for the k th symbol interval, wherein the Z Q (t) signal is a received version of an x Q (t) that has been encoded similarly to the x I (t) signal, but based upon a second real-valued baseband message signal (m 2 (t) signal) follows a second trajectory through the amplitude trellis that is determined in accordance with a second binary data sequence.
9. The method of claim 8 , further comprising:
computing, for the k th symbol interval, using a k th set of the oversampled data samples that correspond to samples of the Z Q (t) signal sampled during the k th symbol interval, a second k th set of branch metrics which measure a respective distance between the k th set of the oversampled data samples of the Z Q (t) signal and each of the set of template state transition signals; and
implementing a trellis decoding algorithm using at least the second k th set of branch metrics to determine a trellis decoded data sequence, and deriving an estimate of the second binary data sequence therefrom.
10. The method of claim 9 , wherein:
the template state transition signal from the first state the template state transition signal from the first state S k (Q k−1 , Q k−2 , . . . Q k−L ), to each second state S k+1 =(Q k , Q k−1 , . . . Q k−L+1 ), can be written as
x
Template
(
t
,
S
k
,
S
k
+
1
)
=
∑
j
=
1
L
+
1
p
Q
(
k
-
j
+
1
)
,
Q
(
k
-
j
+
2
)
(
t
-
kT
+
jT
-
T
)
,
for at least OS discrete sample times t in the k th symbol interval (kT≦t<(k+1)T).
11. The method of claim 1 , wherein L=4.
12. The method of claim 1 , wherein L=3.
13. The method of claim 1 , wherein L=2.
14. The method of claim 1 , wherein L=1.
15. 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
}
.
16. A method for use in a communications receiver that is adapted to process a received communication signal, wherein the received communication signal provides a channel-distorted version of a communication signal that has been encoded in accordance with at least an in-phase component signal (x I (t) signal), wherein
x
I
(
t
)
=
∑
j
=
1
L
+
1
a
k
-
j
+
1
p
(
t
-
kT
+
jT
-
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 that has been generated in accordance with a 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, the method comprising:
receiving the received communication signal from a channel, extracting at least an in-phase baseband component signal (Z I (t) signal) therefrom, lowpass filtering the Z I (t) signal, and oversampling the output of the lowpass filtering with an analog-to-digital converter (ADC) at an oversampling rate F s =OS/T, where 2≦OS≦8 is an oversampling factor, and the ADC provides OS voltage samples for the k th symbol interval;
computing, for the k th symbol interval, using a k th set of the oversampled data samples that correspond to samples of the Z I (t) signal sampled during the k th symbol interval, a k th set of branch metrics, wherein each branch metric provides a measure of a respective distance between the k th set of the oversampled data samples and a respective one of a set of template state transition signals (x Template (t, S k , S k+1 ) signals) representative of each possible state transition from each possible first state S k =(a k−1 , a k−2 , . . . a k−L ), to each second state S k+1 =(a k , a k−1 , . . . a k−L+1 ), for each next permissible pulse amplitude modulated symbol, a k ; and
implementing a trellis decoding algorithm using at least the k th set of branch metrics to determine a trellis decoded sequence and deriving an estimate of the binary data sequence based upon the trellis decoded sequence.
17. The method of claim 16 , wherein the template state transition signal from the first state S k =(a k−1 , a k−2 , . . . a k−L ) to the second state S k+1 =(a k , a k−1 , . . . a k−L+1 ) can be written as
x
Template
(
t
,
S
k
,
S
k
+
1
)
=
∑
j
=
1
L
+
1
a
k
-
j
+
1
p
(
t
-
kT
+
jT
-
T
)
,
for at least OS discrete sample times t in the k th symbol interval (kT≦t<(k+1)T).
18. The method of claim 17 , wherein the respective branch metrics are respective estimates of the respective distance defined by:
B
(
S
k
,
S
k
+
1
)
≅
∫
kT
(
k
+
1
)
T
[
Z
l
(
t
)
-
x
Template
(
t
,
S
k
,
S
k
+
1
)
]
2
ⅆ
t
.
19. The method of claim 17 , further comprising:
computing a set of correlations between the Z I (t) signal and a set of signal segments of the form {p(t−kT+jT−T) for j=1, . . . L+1, and kT≦t<(k+1)T};
wherein the set of correlations are reused multiple times to efficiently compute different ones of the branch metrics in the k th set of branch metrics.
20. The method of claim 16 , wherein the trellis decoding algorithm is a Viterbi algorithm.
21. The method of claim 16 , further comprising:
amplitude demodulating the received communication signal to translate an in-phase carrier component signal to baseband;
wherein the extracting is performed after the amplitude demodulating.
22. The method of claim 16 , further comprising:
quadrature demodulating the received communication signal to translate both an in-phase carrier component signal and a quadrature-phase carrier signal to baseband, wherein the extracting of the Z I (t) signal occurs after the quadrature demodulating; and
extracting at least a quadrature-phase baseband component signal (Z Q (t) signal) after the quadrature demodulating, lowpass filtering the Z Q (t) signal, and oversampling the output of the lowpass filtering with a second ADC at the oversampling rate F s to provide OS voltage samples of the Z Q (t) signal for the k th symbol interval, wherein the Z Q (t) signal is a received version of an x Q (t) that has been encoded according to
x
Q
(
t
)
=
∑
j
=
1
L
+
1
b
k
-
j
+
1
p
(
t
-
kT
+
jT
-
T
)
,
where {b k } is a second M-ary pulse amplitude modulated sequence that has been generated in accordance with a second binary data sequence.
23. The method of claim 22 , further comprising:
computing, for the k th symbol interval, using a second k th set of the oversampled data samples that correspond to samples of the Z Q (t) signal sampled during the k th symbol interval, a second k th set of branch metrics which measure a respective distance between the second k th set of the oversampled data samples and each of the set of template state transition signals; and
implementing the trellis decoding algorithm using at least the second k th set of branch metrics to determine a second trellis decoded sequence and deriving an estimate of the second binary data sequence based upon the second trellis decoded sequence.
24. The method of claim 23 , wherein:
the template state transition signal from the first state S k =(a k−1 , a k−2 , . . . a k−L ) to the second state S k+1 =(a k , a k−1 , . . . a k−L+1 ) can be written as
x
Template
(
t
,
S
k
,
S
k
+
1
)
=
∑
j
=
1
L
+
1
a
k
-
j
+
1
p
(
t
-
kT
+
jT
-
T
)
,
for at least OS discrete sample times t in the k th symbol interval (kT≦t<(k+1)T); and
the template state transition signal from a first state β k =(b k−1 , b k−2 , . . . b k−L ), to a second state β k+1 =(b k , b k−1 , . . . b k−L+1 ) can be written as
x
Template
(
t
,
β
k
,
β
k
+
1
)
=
∑
j
=
1
L
+
1
b
k
-
j
+
1
p
(
t
-
kT
+
jT
-
T
)
,
for at least OS discrete sample times t in the k th symbol interval (kT≦t<(k+1)T).
25. The method of claim 16 , wherein L=4.
26. The method of claim 16 , wherein L=3.
27. The method of claim 16 , wherein L=2.
28. The method of claim 16 , wherein L=1.
29. The method of claim 16 , 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
}
.