Apparatus and method for calculating bit metrics in data receivers
An apparatus and method for calculating bit metrics in data receivers. The apparatus of the invention includes a storage unit and a calculator. The storage unit is configured to store a number of modulation-dependent coefficients; it selects as output one of the coefficients in accordance with a modulation mode being used. The calculator receives the selected coefficient from the storage unit and takes a received signal and a channel response in the frequency domain. According to the selected coefficient, the received signal and the channel response, the calculator generates at least N number of bit metrics for an N-bit codeword in the received signal.
1. An apparatus for calculating bit metrics in data receivers, comprising:
a storage unit for storing a plurality of modulation-dependent coefficients and selecting as output one of the coefficients in accordance with a modulation mode being used; and
a calculator receiving the selected coefficient from the storage unit and taking a received signal and a channel response, for generating at least N number of bit metrics for an N-bit codeword in the received signal based on a function of the selected coefficient, the received signal and the channel response;
wherein the selected coefficient depending on the modulation mode being used is defined by:
C i =2 N/2−i K MOD , for i =1,2 , . . . , N /2−1
where K MOD is a modulation-dependent normalization factor and N is an even integer.
2. The apparatus as recited in claim 1 wherein the N-bit codeword represents a constellation point comprising an I component and a Q component, and the bit metrics in respect of the I component for the N-bit codeword are calculated from:
X
^
(
b
n
i
)
=
{
Re
[
yH
*
]
,
if
i
=
0
-
X
^
(
b
n
i
-
1
)
+
C
i
H
2
,
otherwise
where
subscript n i is an integer and bits (b n 0 b n 1 . . . b n N/2−1 ) encode the I component of the N-bit codeword,
superscript * denotes complex conjugation,
Re denotes the real part of a complex number,
y denotes the received signal,
H denotes the channel response, and
C i denotes the selected coefficient, for i=1, 2, . . . , N/2−1.
3. The apparatus as recited in claim 1 wherein the N-bit codeword represents a constellation point comprising an I component and a Q component, and the bit metrics in respect of the Q component for the N-bit codeword are calculated from:
X
^
(
b
n
i
)
=
{
Im
[
y
H
*
]
,
if
i
=
0
-
X
^
(
b
n
i
-
1
)
+
C
i
H
2
,
otherwise
where
subscript n i is an integer and bits (b n 0 b n 1 . . . b n N/2−1 ) encode the Q component of the N-bit codeword,
superscript * denotes complex conjugation,
Im denotes the imaginary part of a complex number,
y denotes the received signal,
H denotes the channel response, and
C i denotes the selected coefficient, for i=1, 2, . . . , N/2−1.
4. The apparatus as recited in claim 1 wherein the calculator generates the bit metrics for the N-bit codeword in the received signal using the function as follows:
X
^
(
b
i
)
=
{
Re
[
yH
*
]
,
i
=
0
-
X
^
(
b
i
-
1
)
+
C
i
H
2
,
i
=
1
,
2
,
…
,
N
/
2
-
1
for
I
component
X
^
(
b
N
/
2
+
i
)
=
{
Im
[
yH
*
]
,
i
=
0
-
X
^
(
b
N
/
2
+
i
-
1
)
+
C
i
H
2
,
i
=
1
,
2
,
…
,
N
/
2
-
1
for
Q
component
where
bits (b 0 b 1 . . . b N/2−1 ) encode the I component of the N-bit codeword,
bits (b N/2 b N/2+1 . . . b N−1 ) encode the Q component of the N-bit codeword,
superscript * denotes complex conjugation,
Re and Im denote real and imaginary parts of a complex number, respectively,
y denotes the received signal, and
H denotes the channel response.
5. The apparatus as recited in claim 1 wherein the N-bit codeword represents a constellation point comprising an I component and a Q component, and the bit metrics in respect of the I component for the N-bit codeword are calculated from:
X
^
(
b
k
,
n
i
)
=
{
Re
[
y
k
H
k
*
]
,
if
i
=
0
-
X
^
(
b
k
,
n
i
-
1
)
+
C
i
H
k
2
,
otherwise
where
subscript n 1 is an integer and bits (b k,n 0 b k,n 1 . . . b k,n N/2−1 ) encode the I component of the N-bit codeword,
superscript * denotes complex conjugation,
Re denotes the real part of a complex number,
subscript k denotes a subcarrier index,
y k denotes the received signal of subcarrier k,
H k denotes the channel response of subcarrier k, and
C i denotes the selected coefficient, for i=1, 2, . . . , N/2−1.
6. The apparatus as recited in claim 1 wherein the N-bit codeword represents a constellation point comprising an I component and a Q component, and the bit metrics in respect of the Q component for the N-bit codeword are calculated from:
X
^
(
b
k
,
n
i
)
=
{
Im
[
y
k
H
k
*
]
,
if
i
=
0
-
X
^
(
b
k
,
n
i
-
1
)
+
C
i
H
k
2
,
otherwise
where
subscript n i is an integer and bits (b k,n 0 b k,n 1 . . . b k,n N/2−1 ) encode the Q component of the N-bit codeword,
superscript * denotes complex conjugation,
Im denotes the imaginary part of a complex number,
subscript k denotes a subcarrier index,
y k denotes the received signal of subcarrier k,
H k denotes the channel response of subcarrier k, and
C i denotes the selected coefficient, for i=1, 2, . . . , N/2−1.
7. The apparatus as recited in claim 1 wherein the calculator generates the bit metrics for the N-bit codeword in the received signal using the function as follows:
X
^
(
b
k
,
i
)
=
{
Re
[
y
k
H
k
*
]
,
i
=
0
-
X
^
(
b
k
,
i
-
1
)
+
C
i
H
k
2
,
i
=
1
,
2
,
…
,
N
/
2
-
1
for
I
component
X
^
(
b
k
,
N
/
2
+
i
)
=
{
Im
[
y
k
H
k
*
]
,
i
=
0
-
X
^
(
b
k
,
N
/
2
+
i
-
1
)
+
C
i
H
k
2
,
i
=
1
,
2
,
…
,
N
/
2
-
1
for
Q
component
where
bits (b 0 b 1 . . . b N/2−1 ) encode the I component of the N-bit codeword,
bits (b N/2 b N/2+1 . . . b N−1 ) encode the Q component of the N-bit codeword,
superscript * denotes complex conjugation,
Re and Im denote real and imaginary parts of a complex number, respectively,
subscript k denotes a subcarrier index,
y k denotes the received signal of subcarrier k, and
H k denotes the channel response of subcarrier k.
8. The apparatus as recited in claim 1 wherein each bit metric can further be multiplied by 1/α k , where α k is a noise normalization factor of subcarrier k.
9. A method for calculating bit metrics in data receivers, comprising the steps of:
selecting one of a plurality of modulation-dependent coefficients in accordance with a modulation mode being used;
taking a received signal and a channel response in a frequency domain; and
calculating at least N number of bit metrics for an N-bit codeword in the received signal based on the selected coefficient, the received signal and the channel response;
wherein the selected coefficient depending on the modulation mode being used is defined by:
i C i =2 N/2−i K MOD , for i =1, 2, . . . , N/2−1
where K MOD is a modulation-dependent normalization factor and N is an even integer.
10. The method as recited in claim 9 wherein the N-bit codeword represents a constellation point having an I component and a Q component, and the calculating step further comprises the steps of:
computing a multiplication product of the received signal and the complex conjugate of the channel response; and
computing each of the bit metrics in respect of the I component for the N-bit codeword based on the selected coefficient along with a related piecewise linear function of the multiplication product's real part.
11. The method as recited in claim 9 wherein the N-bit codeword represents a constellation point having an I component and a Q component, and the calculating step further comprises the steps of:
computing a multiplication product of the received signal and the complex conjugate of the channel response; and
computing each of the bit metrics in respect of the Q component for the N-bit codeword based on the selected coefficient along with a related piecewise linear function of the multiplication product's imaginary part.
12. The method as recited in claim 9 wherein the N-bit codeword represents a constellation point comprising an I component and a Q component, and the calculating step generates the bit metrics in respect of the I component for the N-bit codeword by:
X
^
(
b
n
i
)
=
{
Re
[
yH
*
]
,
if
i
=
0
-
X
^
(
b
n
i
-
1
)
+
C
i
H
2
,
otherwise
where
subscript n i is an integer and bits (b n 0 b n 1 . . . b n N/2−1 ) encode the I component of the N-bit codeword,
superscript * denotes complex conjugation,
Re denotes the real part of a complex number,
y denotes the received signal,
H denotes the channel response, and
C i denotes the selected coefficient, for i=1, 2, . . . , N/2−1.
13. The method as recited in claim 9 wherein the N-bit codeword represents a constellation point comprising an I component and a Q component, and the calculating step generates the bit metrics in respect of the Q component for the N-bit codeword by:
X
^
(
b
n
i
)
=
{
Im
[
yH
*
]
,
if
i
=
0
-
X
^
(
b
n
i
-
1
)
+
C
i
H
2
,
otherwise
where
subscript n i is an integer and bits (b n 0 b n 1 . . . b n N/2−1 ) encode the Q component of the N-bit codeword,
superscript * denotes complex conjugation,
Im denotes the imaginary part of a complex number,
y denotes the received signal,
H denotes the channel response, and
C i denotes the selected coefficient, for i=1, 2, . . . , N/2−1.
14. The method as recited in claim 9 wherein the calculating step generates the bit metrics for the N-bit codeword in the received signal using the following function:
X
^
(
b
i
)
=
{
Re
[
yH
*
]
,
i
=
0
-
X
^
(
b
i
-
1
)
+
C
i
H
2
,
i
=
1
,
2
,
…
,
N
/
2
-
1
for
I
component
X
^
(
b
N
/
2
+
i
)
=
{
Im
[
yH
*
]
,
i
=
0
-
X
^
(
b
N
/
2
+
i
-
1
)
+
C
i
H
2
,
i
=
1
,
2
,
…
,
N
/
2
-
1
for
Q
component
where
bits (b 0 b 1 . . . b N/2−1 ) encode the I component of the N-bit codeword,
bits (b N/2 b N/2+1 . . . b N−1 ) encode the Q component of the N-bit codeword,
superscript * denotes complex conjugation,
Re and Im denote real and imaginary parts of a complex number, respectively,
y denotes the received signal, and
H denotes the channel response.
15. The method as recited in claim 9 wherein the N-bit codeword represents a constellation point comprising an I component and a Q component, and the calculating step generates the bit metrics in respect of the I component for the N-bit codeword by:
X
^
(
b
k
,
n
i
)
=
{
Re
[
y
k
H
k
*
]
,
if
i
=
0
-
X
^
(
b
k
,
n
i
-
1
)
+
C
i
H
k
2
,
otherwise
where
subscript n i is an integer and bits (b k,n 0 b k,n 1 . . . b k,n N/2−1 ) encode the I component of the N-bit codeword,
superscript * denotes complex conjugation,
Re denotes the real part of a complex number,
subscript k denotes a subcarrier index,
y k denotes the received signal of subcarrier k,
H k denotes the channel response of subcarrier k, and
C i denotes the selected coefficient, for i=1, 2, . . . , N/2−1.
16. The method as recited in claim 9 wherein the N-bit codeword represents a constellation point comprising an I component and a Q component, and the calculating step generates the bit metrics in respect of the Q component for the N-bit codeword by:
X
^
(
b
k
,
n
i
)
=
{
Im
[
y
k
H
k
*
]
,
if
i
=
0
-
X
^
(
b
k
,
n
i
-
1
)
+
C
i
H
k
2
,
otherwise
where
subscript n i is an integer and bits (b k,n 0 b k,n 1 . . . b k,n N/2−1 ) encode the Q component of the N-bit codeword,
superscript * denotes complex conjugation,
Im denotes the imaginary part of a complex number,
subscript k denotes a subcarrier index,
y k denotes the received signal of subcarrier k,
H k denotes the channel response of subcarrier k, and
C i denotes the selected coefficient, for i=1, 2, . . . , N/2−1.
17. The method as recited in claim 9 wherein the calculating step generates the bit metrics for the N-bit codeword in the received signal using the following function:
X
^
(
b
k
,
i
)
=
{
Re
[
y
k
H
k
*
]
,
i
=
0
-
X
^
(
b
k
,
i
-
1
)
+
i
=
1
,
2
,
…
,
C
i
H
k
2
,
N
/
2
-
1
for
I
component
X
^
(
b
k
,
N
/
2
+
i
)
=
{
Im
[
y
k
H
k
*
]
,
i
=
0
-
X
^
(
b
k
,
N
/
2
+
i
-
1
)
+
i
=
1
,
2
,
…
,
C
i
H
k
2
,
N
/
2
-
1
for
Q
component
where
bits (b 0 b 1 . . . b N/ 2−1 ) encode the I component of the N-bit codeword,
bits (b N/2 b N/2+1 . . . b N−1 ) encode the Q component of the N-bit codeword,
superscript * denotes complex conjugation,
Re and Im denote real and imaginary parts of a complex number, respectively,
subscript k denotes a subcarrier index,
y k denotes the received signal of subcarrier k, and
H k denotes the channel response of subcarrier k.
18. The method as recited in claim 9 further comprising the step of multiplying each bit metric by 1/α k , where α k is a noise normalization factor of subcarrier k.