Demodulation that accounts for channel estimation error
View Patent ↗Methods and apparatus for demodulating data symbols received over a communication channel. One method includes receiving a data symbol y over a communication channel h, where the received data symbol y corresponds to a transmitted data symbol x. The method further includes determining an estimate of the communication channel h. The method further includes determining a measure of a channel estimation error corresponding to the estimate of the communication channel h. The method further includes determining a likelihood value for a bit in the transmitted data symbol y based at least in part on the measure of the channel estimation error.
1. A method comprising:
receiving a data symbol y over a communication channel, wherein the received data symbol y corresponds to a transmitted data symbol x;
processing the data symbol y according to a model y=(h+Δh) x+z, where h is an estimate of the communication channel, Δh is a channel estimation error corresponding to the estimate h of the communication channel, and z is noise corresponding to the communication channel, and wherein processing the data symbol y comprises
determining, with a hardware device, the estimate h of the communication channel,
determining, with the hardware device, a mean square error σ h 2 corresponding to the channel estimation error Δh, and
determining, with the hardware device, a likelihood value for a bit in the transmitted data symbol x at least in part by
calculating a first quantity equal to σ z 2 +σ h 2 |x| 2 , where σ z 2 is the noise power of the communication channel,
calculating a second quantity equal to
e
-
y
-
hx
2
σ
z
2
+
σ
h
2
x
2
,
and
calculating the likelihood value for the bit using at least (i) the first quantity and (ii) the second quantity.
2. The method of claim 1 , wherein determining the likelihood value for the bit in the transmitted data symbol x comprises calculating a log-likelihood ratio for the bit.
3. The method of claim 1 , wherein determining the likelihood value for the bit comprises calculating
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 comprises calculating
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
)
x
∈
S
1
,
i
π
-
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 , wherein the transmitted data symbol x is modulated using a modulation scheme that generates a plurality of constellation points, wherein at least two constellation points in the plurality of constellation points have different amplitudes.
6. The method of claim 5 , wherein the modulation scheme is a quadrature amplitude modulation (QAM) having at least 8 constellation points.
7. The method of claim 6 , wherein the modulation scheme is one of 16-QAM and 64-QAM.
8. The method of claim 1 , wherein the communication channel comprises a plurality of spatial streams, and wherein receiving the data symbol y comprises receiving a data symbol vector, the data symbol vector comprising a plurality of data symbols that are received in parallel via the plurality of spatial streams, wherein the data symbol vector corresponds to a transmitted data symbol vector comprising a plurality of transmitted data symbols.
9. The method of claim 1 , wherein the noise power of the communication channel is a scaled noise power.
10. An apparatus comprising:
a demodulator configured to:
receive a data symbol y over a communication channel, wherein the received data symbol y corresponds to a transmitted data symbol x;
process the data symbol y according to a model y=(h+Δh) x+z, where h is an estimate of the communication channel, Δh is a channel estimation error corresponding to the estimate h of the communication channel, and z is noise corresponding to the communication channel, and wherein the demodulator is configured to process the data symbol y at least in part by
determining the estimate h of the communication channel,
determining a mean square error σ h 2 corresponding to the channel estimation error Δh, and
determining a likelihood value for a bit in the transmitted data symbol x at least in part by
calculating a first quantity equal to σ z 2 +σ h 2 |x| 2 , where σ z 2 is the noise power of the communication channel,
calculating a second quantity equal to
e
-
y
-
hx
2
σ
z
2
+
σ
h
2
x
2
,
and
calculating the likelihood value for the bit using at least (i) the first quantity and (ii) the second quantity; and
a decoder configured to decode the data symbol y based at least in part on the calculated likelihood value.
11. The apparatus of claim 10 , wherein the demodulator is configured to determine the likelihood value for the bit in the transmitted data symbol x by calculating a log-likelihood ratio for the bit.
12. The apparatus of claim 10 , wherein the demodulator is configured to determine the likelihood value for the bit by calculating
L
(
i
)
=
log
∑
w
∈
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.
13. The apparatus of claim 10 , wherein the demodulator is configured to determine the likelihood value for the bit by calculating
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
)
x
∈
S
1
,
i
π
-
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.
14. The apparatus of claim 10 , wherein the transmitted data symbol is modulated using a modulation scheme that generates a plurality of constellation points, wherein at least two constellation points in the plurality of constellation points have different amplitudes.
15. The apparatus of claim 10 wherein the noise power of the communication channel is a scaled noise power.