Demodulation that accounts for channel estimation error
View Patent ↗A method includes determining a mean square error σ h 2 of an estimate h of a communication channel, and receiving a data symbol y. The received data symbol y corresponds to a data symbol x transmitted over the communication channel. The method also includes determining a likelihood value for a bit in the transmitted data symbol x. Determining the likelihood value for the bit in the transmitted data symbol x includes calculating a quantity according to ⅇ - y - hx 2 σ z 2 + σ h 2 x 2 , where σ z 2 is a noise power associated with the communication channel. The method also includes calculating the likelihood value for the bit in the transmitted data symbol x as a function of the calculated quantity.
1. A method implemented in a communication device configured to receive signals via a communication channel, the method comprising:
determining, at the communication device, a mean square error σ h 2 of an estimate h of the communication channel;
receiving, at the communication device, a data symbol y, wherein the received data symbol y corresponds to a data symbol x transmitted over the communication channel; and
determining, at the communication device, a likelihood value for a bit in the transmitted data symbol x, wherein determining the likelihood value for the bit in the transmitted data symbol x includes
calculating a quantity according to
ⅇ
-
y
-
hx
2
σ
z
2
+
σ
h
2
x
2
,
where σ z 2 is a noise power associated with the communication channel, and
calculating the likelihood value for the bit in the transmitted data symbol x as a function of the calculated quantity.
2. The method of claim 1 , wherein calculating the likelihood value for the bit in the transmitted data symbol x includes calculating a log-likelihood ratio for the bit in the transmitted data symbol x.
3. The method of claim 1 , wherein calculating the likelihood value for the bit in the transmitted data symbol x includes calculating the likelihood value according to
L
(
i
)
=
log
∑
x
∈
S
1
,
i
1
(
σ
z
2
+
σ
h
2
x
2
)
π
ⅇ
-
y
-
hx
2
σ
z
2
+
σ
h
2
x
2
∑
x
∈
S
0
,
i
1
(
σ
z
2
+
σ
h
2
x
2
)
π
ⅇ
-
y
-
hx
2
σ
z
2
+
σ
h
2
x
2
where S 1,i is a set of all possible transmitted data symbols x with bit i equal to 1, and S 0,i is a set of all possible transmitted data symbols x with bit i equal to 0.
4. The method of claim 1 , wherein calculating the likelihood value for the bit in the transmitted data symbol x comprises calculating the likelihood value according to
L
(
i
)
=
max
x
∈
S
1
,
i
log
ⅇ
-
y
-
hx
2
σ
z
2
+
σ
h
2
x
2
(
σ
z
2
+
σ
h
2
x
2
)
π
x
∈
S
1
,
i
max
x
∈
S
0
,
i
log
ⅇ
-
y
-
hx
2
σ
z
2
+
σ
h
2
x
2
(
σ
z
2
+
σ
h
2
x
2
)
π
x
∈
S
0
,
i
where S 1,i is a set of all possible transmitted data symbols x with bit i equal to 1, and S 0,i is a set of all possible transmitted data symbols x with bit i equal to 0.
5. The method of claim 1 , further comprising determining the estimate h of the communication channel.
6. The method of claim 1 , wherein the transmitted data symbol x is modulated using a modulation scheme that generates a plurality of constellation points, and wherein at least two constellation points in the plurality of constellation points have different amplitudes.
7. The method of claim 6 , wherein the modulation scheme is a quadrature amplitude modulation (QAM) having at least 8 constellation points.
8. The method of claim 1 , wherein:
the communication channel includes a plurality of channels corresponding to a plurality of spatial streams; and
receiving a data symbol y includes receiving a data symbol vector that (i) corresponds to a transmitted data symbol vector that includes a plurality of transmitted data symbols, and (ii) includes a plurality of data symbols received in parallel via the plurality of spatial streams.
9. A communication device configured to receive signals via a communication channel, the communication device comprising:
a demodulator configured to
determine a mean square error σ h 2 of an estimate h of the communication channel;
receive a data symbol y, wherein the received data symbol y corresponds to a data symbol x transmitted over the communication channel, and
determine a likelihood value for a bit in the transmitted data symbol x, at least by (i) calculating a quantity according to
ⅇ
-
y
-
hx
2
σ
z
2
+
σ
h
2
x
2
,
where σ z 2 is a noise power associated with the communication channel, and (ii) calculating the likelihood value for the bit in the transmitted data symbol x as a function of the calculated quantity; and
a decoder configured to decode the received data symbol y based at least in part on the calculated likelihood value.
10. The communication device of claim 9 , wherein the demodulator is configured to calculate the likelihood value for the bit in the transmitted data symbol x at least by calculating a log-likelihood ratio for the bit in the transmitted data symbol x.
11. The communication device of claim 9 , wherein the demodulator is configured to calculate the likelihood value for the bit in the transmitted data symbol x at least by calculating the likelihood value according to
L
(
i
)
=
log
∑
x
∈
S
1
,
i
1
(
σ
z
2
+
σ
h
2
x
2
)
π
ⅇ
-
y
-
hx
2
σ
z
2
+
σ
h
2
x
2
∑
x
∈
S
0
,
i
1
(
σ
z
2
+
σ
h
2
x
2
)
π
ⅇ
-
y
-
hx
2
σ
z
2
+
σ
h
2
x
2
where S 1,i is a set of all possible transmitted data symbols x with bit i equal to 1, and S 0,i is a set of all possible transmitted data symbols x with bit i equal to 0.
12. The communication device of claim 9 , wherein the demodulator is configured to calculate the likelihood value for the bit in the transmitted data symbol x at least by calculating the likelihood value according to
L
(
i
)
=
max
x
∈
S
1
,
i
log
ⅇ
-
y
-
hx
2
σ
z
2
+
σ
h
2
x
2
(
σ
z
2
+
σ
h
2
x
2
)
π
x
∈
S
1
,
i
max
x
∈
S
0
,
i
log
ⅇ
-
y
-
hx
2
σ
z
2
+
σ
h
2
x
2
(
σ
z
2
+
σ
h
2
x
2
)
π
x
∈
S
0
,
i
where S 1,i is a set of all possible transmitted data symbols x with bit i equal to 1, and S 0,i is a set of all possible transmitted data symbols x with bit i equal to 0.
13. The communication device of claim 9 , wherein the transmitted data symbol x is modulated using a modulation scheme that generates a plurality of constellation points, and wherein at least two constellation points in the plurality of constellation points have different amplitudes.
14. The communication device of claim 9 , wherein:
the communication channel includes a plurality of channels corresponding to a plurality of spatial streams;
the data symbol y includes a data symbol vector that (i) corresponds to a transmitted data symbol vector that includes a plurality of transmitted data symbols, and (ii) includes a plurality of data symbols received in parallel via the plurality of spatial streams.
15. A tangible, non-transitory computer readable memory storing instructions that, when executed on a processor, cause the processor to:
determine a mean square error σ h 2 of an estimate h of a communication channel via which signals are received by a communication device;
receive a data symbol y, wherein the received data symbol y corresponds to a data symbol x transmitted over the communication channel; and
determine a likelihood value for a bit in the transmitted data symbol x, wherein the instructions cause the processor to determine the likelihood value for the bit in the transmitted data symbol x at least by (i) calculating a quantity according to
ⅇ
-
y
-
hx
2
σ
z
2
+
σ
h
2
x
2
,
where σ z 2 is a noise power associated with the communication channel, and (ii) calculating the likelihood value for the bit in the transmitted data symbol x as a function of the calculated quantity.
16. The tangible, non-transitory computer readable memory of claim 15 , wherein the instructions cause the processor to calculate the likelihood value for the bit in the transmitted data symbol x at least by calculating a log-likelihood ratio for the bit in the transmitted data symbol x.
17. The tangible, non-transitory computer readable memory of claim 15 , wherein the instructions cause the processor to calculate the likelihood value for the bit in the transmitted data symbol x at least by calculating the likelihood value according to
L
(
i
)
=
log
∑
x
∈
S
1
,
i
1
(
σ
z
2
+
σ
h
2
x
2
)
π
ⅇ
-
y
-
hx
2
σ
z
2
+
σ
h
2
x
2
∑
x
∈
S
0
,
i
1
(
σ
z
2
+
σ
h
2
x
2
)
π
ⅇ
-
y
-
hx
2
σ
z
2
+
σ
h
2
x
2
where S 1,i is a set of all possible transmitted data symbols x with bit i equal to 1, and S 0,i is a set of all possible transmitted data symbols x with bit i equal to 0.
18. The tangible, non-transitory computer readable memory of claim 15 , wherein the instructions cause the processor to calculate the likelihood value for the bit in the transmitted data symbol x at least by calculating the likelihood value according to
L
(
i
)
=
max
x
∈
S
1
,
i
log
ⅇ
-
y
-
hx
2
σ
z
2
+
σ
h
2
x
2
(
σ
z
2
+
σ
h
2
x
2
)
π
x
∈
S
1
,
i
max
x
∈
S
0
,
i
log
ⅇ
-
y
-
hx
2
σ
z
2
+
σ
h
2
x
2
(
σ
z
2
+
σ
h
2
x
2
)
π
x
∈
S
0
,
i
where S 1,i is a set of all possible transmitted data symbols x with bit i equal to 1, and S 0,i is a set of all possible transmitted data symbols x with bit i equal to 0.
19. The tangible, non-transitory computer readable memory of claim 15 , wherein the instructions further cause the processor to determine the estimate h of the communication channel.
20. The tangible, non-transitory computer readable memory of claim 15 , wherein:
the communication channel includes a plurality of channels corresponding to a plurality of spatial streams; and
the data symbol y includes a data symbol vector that (i) corresponds to a transmitted data symbol vector that includes a plurality of transmitted data symbols, and (ii) includes a plurality of data symbols received in parallel via the plurality of spatial streams.