Method and apparatus for soft detection of high order QAM symbols in MIMO channels
Methods and apparatus for soft MIMO detection of high order QAM with initial candidate reduction are described. A method includes receiving a plurality of signals including Q-order QAM symbols; determining a reduced candidate set including C potential candidates, where C is less than Q; calculating Euclidean distances (EDs) based on the reduced candidate set; and generating LLR information based on the calculated EDs.
1. A method comprising:
receiving a plurality of signals including Q-order quadrature amplitude modulation (QAM) symbols;
determining a reduced candidate set including C potential candidates, where C is less than Q;
calculating Euclidean distances (EDs) based on the reduced candidate set; and
generating log-likelihood ratio (LLR) information based on the calculated EDs,
wherein determining the reduced candidate set comprises:
determining a linear minimum mean square error (MMSE); and
selecting the reduced candidate set based on the determined linear MMSE, and wherein the linear MMSE is determined using:
x
^
0
=
1
ch
pow
(
(
h
1
2
+
σ
2
)
h
0
H
y
-
h
0
H
h
1
h
1
H
y
)
=
(
(
h
1
2
+
σ
2
)
h
0
2
-
h
0
H
h
1
2
)
x
0
+
σ
2
h
0
H
h
1
2
x
1
+
n
′
ch
pow
where {circumflex over (x)} 0 represents an initial MMSE estimation, y=[y 0 , . . . , y r-1 ] T is an n R ×1 receive signal vector, x=[x 0 , x 1 ] T is a 2×1 transmit signal vector, H=[h 0 , h 1 ] is an n R ×2 channel coefficient matrix, h i =[h i,0 , . . . , h i,n R −1 ] T , h i,j represents a channel between i-th transmit and j-th receive antennas, n is an additive white Gaussian noise vector with covariance E{nn H }=σ 2 I, ch pow =(|h 1 | 2 +σ 2 )(|h 0 | 2 +σ 2 )−|h 0 H h 1 | 2 , and n′=(|h 1 | 2 +σ 2 )h 0 H n−h 0 H h 1 h 1 H n.
2. The method of claim 1 , further comprising providing the generated LLR information to a decoder.
3. The method of claim 1 , wherein Q is 256 and C is 128.
4. The method of claim 1 , wherein the LLR information is generated using:
L
A
(
b
0
,
l
)
≈
log
max
x
0
∈
X
128
(
x
^
0
)
&
b
0
,
l
=
0
max
x
1
ⅇ
-
y
-
Hx
2
σ
2
∏
(
m
,
n
)
≠
(
i
,
l
)
P
(
b
m
,
n
)
max
x
0
∈
X
128
(
x
^
0
)
&
b
0
,
l
=
1
max
x
1
ⅇ
-
y
-
Hx
2
σ
2
∏
(
m
,
n
)
≠
(
i
,
l
)
P
(
b
m
,
n
)
+
L
a
(
b
0
,
l
)
where b 0,l represents an l-th bit of symbol x 0 , L A (b 0,l ) is a posteriori LLR of b 0,l and X 128 ({circumflex over (x)} 0 ) is a set of 128 initial candidates selected using the initial MMSE estimation {circumflex over (x)} 0 .
5. A method comprising:
receiving a plurality of signals including Q-order quadrature amplitude modulation (QAM) symbols;
determining a reduced candidate set including C potential candidates, where C is less than Q;
calculating Euclidean distances (EDs) based on the reduced candidate set; and
generating log-likelihood ratio (LLR) information based on the calculated EDs,
wherein determining the reduced candidate set comprises:
receiving prior information;
determining a linear minimum mean square error (MMSE) soft interference cancellation (MMSE-SIC); and
selecting the reduced candidate set based on the determined linear MMSE-SIC, and wherein the linear MMSE-SIC is determined using:
x
^
0
=
1
ch
pow
(
(
λ
1
2
h
1
2
+
σ
2
)
λ
0
2
h
0
H
y
-
λ
0
2
λ
1
2
h
0
H
h
1
h
1
H
y
-
σ
2
λ
0
2
h
0
H
h
1
μ
1
-
(
(
λ
1
2
h
1
2
+
σ
2
)
λ
0
2
h
0
2
-
λ
0
2
λ
1
2
h
0
H
h
1
2
)
μ
0
)
+
μ
0
=
1
ch
pow
(
(
λ
1
2
h
1
2
+
σ
2
)
λ
0
2
h
0
H
y
-
λ
0
2
λ
1
2
h
0
H
h
1
h
1
H
y
-
σ
2
λ
0
2
h
0
H
h
1
μ
1
+
σ
2
(
λ
1
2
h
1
2
+
σ
2
)
μ
0
)
where y=[y 0 , . . . , y r-1 ] T is an n R ×1 receive signal vector, x=[x 0 , x 1 ] T is a 2×1 transmit signal vector, H=[h 0 , h 1 ] is an n R ×2 channel coefficient matrix, h i =[h i,0 , . . . , h i,n R −1 ] T , h i,j represents a channel between i-th transmit and j-th receive antennas, ch pow =(|h 1 | 2 +σ 2 )(|h 0 | 2 +σ 2 )−|h 0 H h 1 | 2 , μ i =E{x i }, and
E
{
[
x
0
-
μ
0
x
1
-
μ
1
]
[
x
0
*
-
μ
0
*
x
1
*
-
μ
1
*
]
}
=
[
λ
0
2
0
0
λ
1
2
]
.
6. The method of claim 5 , wherein the prior information includes at least one of self-prior information and cross-prior information.
7. An apparatus comprising:
a plurality of antennas; and
a multiple input multiple output (MIMO) detector that receives, via the plurality of antennas, a plurality of signals including Q-order quadrature amplitude modulation (QAM) symbols, determines a reduced candidate set including C potential candidates, where C is less than Q, calculates Euclidean distances (EDs) based on the reduced candidate set, and generates log-likelihood ratio (LLR) information based on the calculated EDs,
wherein the MIMO detector determines the reduced candidate set by:
determining a linear minimum mean square error (MMSE); and
selecting the reduced candidate set based on the determined linear MMSE, and wherein the MIMO detector determines the linear MMSE using:
x
^
0
=
1
ch
pow
(
(
h
1
2
+
σ
2
)
h
0
H
y
-
h
0
H
h
1
h
1
H
y
)
=
(
(
h
1
2
+
σ
2
)
h
0
2
-
h
0
H
h
1
2
)
x
0
+
σ
2
h
0
H
h
1
2
x
1
+
n
′
ch
pow
where {circumflex over (x)} 0 represents an initial MMSE estimation, y=[y 0 , . . . , y r-1 ] T is an n R ×1 receive signal vector, x=[x 0 , x 1 ] T is a 2×1 transmit signal vector, H=[h 0 , h 1 ] is an n R ×2 channel coefficient matrix, h i =[h i,0 , . . . , h i,n R −1 ] T , h i,j represents a channel between i-th transmit and j-th receive antennas, n is an additive white Gaussian noise vector with covariance E{nn H }=σ 2 I, ch pow =(|h 1 | 2 +σ 2 )(|h 0 | 2 +σ 2 )−|h 0 H h 1 | 2 , and n′=(|h 1 | 2 +σ 2 )h 0 H n−h 0 H h 1 h 1 H n.
8. The apparatus of claim 7 , wherein the MIMO detector provides the generated LLR information to a decoder.
9. The apparatus of claim 7 , wherein Q is 256 and C is 128.
10. The apparatus of claim 7 , wherein the MIMO detector generates the LLR information using:
L
A
(
b
0
,
l
)
≈
log
max
x
0
∈
X
128
(
x
^
0
)
&
b
0
,
l
=
0
max
x
1
ⅇ
-
y
-
Hx
2
σ
2
∏
(
m
,
n
)
≠
(
i
,
l
)
P
(
b
m
,
n
)
max
x
0
∈
X
128
(
x
^
0
)
&
b
0
,
l
=
1
max
x
1
ⅇ
-
y
-
Hx
2
σ
2
∏
(
m
,
n
)
≠
(
i
,
l
)
P
(
b
m
,
n
)
+
L
a
(
b
0
,
l
)
where b 0,l represents the l-th bit of symbol x 0 , L A (b 0,l ) is a posteriori LLR of b 0,l and X 128 ({circumflex over (x)} 0 ) is the set of 128 initial candidates selected using the initial MMSE estimation {circumflex over (x)} 0 .
11. An apparatus comprising:
a plurality of antennas; and
a multiple input multiple output (MIMO) detector that receives, via the plurality of antennas, a plurality of signals including Q-order quadrature amplitude modulation (QAM) symbols, determines a reduced candidate set including C potential candidates, where C is less than Q, calculates Euclidean distances (EDs) based on the reduced candidate set, and generates log-likelihood ratio (LLR) information based on the calculated EDs,
wherein the MIMO detector determines the reduced candidate set by:
receiving prior information;
determining a linear minimum mean square error (MMSE) soft interference cancellation (MMSE-SIC); and
selecting the reduced candidate set based on the determined linear MMSE-SIC, and wherein the MIMO detector determines the linear MMSE-SIC using:
x
^
0
=
1
ch
pow
(
(
λ
1
2
h
1
2
+
σ
2
)
λ
0
2
h
0
H
y
-
λ
0
2
λ
1
2
h
0
H
h
1
h
1
H
y
-
σ
2
λ
0
2
h
0
H
h
1
μ
1
-
(
(
λ
1
2
h
1
2
+
σ
2
)
λ
0
2
h
0
2
-
λ
0
2
λ
1
2
h
0
H
h
1
2
)
μ
0
)
+
μ
0
=
1
ch
pow
(
(
λ
1
2
h
1
2
+
σ
2
)
λ
0
2
h
0
H
y
-
λ
0
2
λ
1
2
h
0
H
h
1
h
1
H
y
-
σ
2
λ
0
2
h
0
H
h
1
μ
1
+
σ
2
(
λ
1
2
h
1
2
+
σ
2
)
μ
0
)
where y=[y 0 , . . . , y r-1 ] T is an n R ×1 receive signal vector, x=[x 0 , x 1 ] T is a 2×1 transmit signal vector, H=[h 0 , h 1 ] is an n R ×2 channel coefficient matrix, h i =[h i,0 , . . . , h i,n R −1 ] T , h i,j represents a channel between i-th transmit and j-th receive antennas, ch pow =(|h 1 | 2 +σ 2 )(|h 0 | 2 +σ 2 )−|h 0 H h 1 | 2 , μ i =E{x i }, and
E
{
[
x
0
-
μ
0
x
1
-
μ
1
]
[
x
0
*
-
μ
0
*
x
1
*
-
μ
1
*
]
}
=
[
λ
0
2
0
0
λ
1
2
]
.
12. The apparatus of claim 11 , wherein the prior information includes at least one of self-prior information and cross-prior information.
13. A system on chip comprising:
a multiple input multiple output (MIMO) detector that receives a plurality of signals including Q-order QAM symbols, determines a reduced candidate set including C potential candidates, where C is less than Q, calculates Euclidean distances (EDs) based on the reduced candidate set, and generates log-likelihood ratio (LLR) information based on the calculated EDs; and
a decoder that decodes the signals using the LLR information,
wherein the MIMO detector determines the reduced candidate set by:
determining a linear minimum mean square error (MMSE); and
selecting the reduced candidate set based on the determined linear MMSE, and wherein the MIMO detector determines the linear MMSE using:
x
^
0
=
1
ch
pow
(
(
h
1
2
+
σ
2
)
h
0
H
y
-
h
0
H
h
1
h
1
H
y
)
=
(
(
h
1
2
+
σ
2
)
h
0
2
-
h
0
H
h
1
2
)
x
0
+
σ
2
h
0
H
h
1
2
x
1
+
n
′
ch
pow
where {circumflex over (x)} 0 represents an initial MMSE estimation, y=[y 0 , . . . , y r-1 ] T is an n R ×1 receive signal vector, x=[x 0 , x 1 ] T is a 2×1 transmit signal vector, H=[h 0 , h 1 ] is an n R ×2 channel coefficient matrix, h i =[h i,0 , . . . , h i,n R −1 ] T , h i,j represents a channel between i-th transmit and j-th receive antennas, n is an additive white Gaussian noise vector with covariance E{nn H }=σ 2 I, ch pow =(|h 1 | 2 +σ 2 )(|h 0 | 2 +σ 2 )−|h 0 H h 1 | 2 , and n′=(|h 1 | 2 +σ 2 )h 0 H n−h 0 H h 1 h 1 H n.
14. A system on chip comprising:
a multiple input multiple output (MIMO) detector that receives a plurality of signals including Q-order QAM symbols, determines a reduced candidate set including C potential candidates, where C is less than Q, calculates Euclidean distances (EDs) based on the reduced candidate set, and generates log-likelihood ratio (LLR) information based on the calculated EDs; and
a decoder that decodes the signals using the LLR information,
wherein the MIMO detector determines the reduced candidate set by:
receiving prior information;
determining a linear minimum mean square error (MMSE) soft interference cancellation (MMSE-SIC); and
selecting the reduced candidate set based on the determined linear MMSE-SIC, and wherein the MIMO detector determines the linear MMSE-SIC using:
x
^
0
=
1
ch
pow
(
(
λ
1
2
h
1
2
+
σ
2
)
λ
0
2
h
0
H
y
-
λ
0
2
λ
1
2
h
0
H
h
1
h
1
H
y
-
σ
2
λ
0
2
h
0
H
h
1
μ
1
-
(
(
λ
1
2
h
1
2
+
σ
2
)
λ
0
2
h
0
2
-
λ
0
2
λ
1
2
h
0
H
h
1
2
)
μ
0
)
+
μ
0
=
1
ch
pow
(
(
λ
1
2
h
1
2
+
σ
2
)
λ
0
2
h
0
H
y
-
λ
0
2
λ
1
2
h
0
H
h
1
h
1
H
y
-
σ
2
λ
0
2
h
0
H
h
1
μ
1
+
σ
2
(
λ
1
2
h
1
2
+
σ
2
)
μ
0
)
where y=[y 0 , . . . , y r-1 ] T is an n R ×1 receive signal vector, x=[x 0 , x 1 ] T is a 2×1 transmit signal vector, H=[h 0 , h 1 ] is an n R ×2 channel coefficient matrix, h i =[h i,0 , . . . , h i,n R −1 ] T , h i,j represents a channel between i-th transmit and j-th receive antennas, ch pow =(|h 1 | 2 +σ 2 )(|h 0 | 2 +σ 2 )−|h 0 H h 1 | 2 , μ i =E{x i }, and
E
{
[
x
0
-
μ
0
x
1
-
μ
1
]
[
x
0
*
-
μ
0
*
x
1
*
-
μ
1
*
]
}
=
[
λ
0
2
0
0
λ
1
2
]
.