Uplink single carrier frequency division multiple access multiple-input multiple-output soft interference cancellation receiver
A system and method are provided for Soft Interference Cancellation (SIC) in receiving Single Carrier Frequency Division Multiple Access (SC-FDMA) Multiple-Input Multiple Output (MIMO) signals. A receiver with Mr antennas accepts multicarrier signals transmitted simultaneously, with N overlapping carrier frequencies. The receiver removes a cyclic prefix (CP), and fast Fourier transforms (FFT) the multicarrier signal from each antenna, supplying Mr number of N-tone signals y. Using either parallel SIC (P-SIC) or successive SIC (S-SIC), interference is canceled in each of the Mr signals, and soft symbols are supplied for each of U layers. Interference is canceled using the P-SIC process by parallel processing the U layers in an i-th iteration, in response to feedback from an (i−1)th iteration. Alternatively, interference is canceled using the S-SIC process by sequentially processing the U layers in an i-th iteration, in the order of u 0 ,u 1 , . . . , u U−1 , using feedback generated from previously processed layers.
1. A method for soft interference cancellation, comprising:
accepting, by a receiver comprising Mr antennas, a plurality of multicarrier signals substantially simultaneously, wherein the plurality of multicarrier signals comprise N overlapping carrier frequencies, and where Mr and N are integers;
removing a cyclic prefix and fast Fourier transforming the plurality of multicarrier signals to yield Mr N-tone signals y; and
canceling interference of respective signals of the Mr N-tone signals using a successive SIC (S-SIC) process, wherein the successive S-SIC process comprises:
re-encoding and re-modulating soft symbols for respective U layers to yield soft symbol feedback from an i-th iteration for layers, of the U layers, already processed in the i-th iteration, and
encoding and re-modulating soft symbols from a (i−1)th iteration for layers, of the U layers, not yet processed in the i-th iteration, where U and i are integers.
2. The method of claim 1 , wherein the S-SIC process further comprises, in an i-th iteration, sequentially processing the U layers in an order of u 0 ,u 1 , . . . , u U−1 using feedback generated from previously processed layers.
3. The method of claim 2 , wherein the S-SIC process further comprises:
performing a discrete Fourier transform (DFT) on the soft symbol feedback from the U layers to yield precoded soft symbol feedback;
weighting the precoded soft symbol feedback from the U layers to yield a weighted feedback sum;
feed-forward weighting the Mr N-tone signals y to yield a feed-forward weighted signal;
subtracting the weighted feedback sum from the feed-forward weighted signal to yield a feedback compensated signal;
performing an inverse discrete Fourier transform and transferring the feedback compensated signal into a time domain to yield a time domain signal;
compensating for bias in the time domain signal; and
demodulating and decoding the bias compensated signal for the U layers to yield soft symbols for the U layers.
4. The method of claim 3 , wherein the Mr N-tone signals y are characterized by
y=H*Γ*s+w,
where
H
=
[
H
0
,
0
…
…
H
0
,
U
-
1
⋮
⋱
⋮
⋮
⋱
⋮
H
M
r
,
0
…
…
H
M
r
,
U
-
1
]
H
m
,
u
=
Diag
[
h
u
,
k
(
m
)
,
(
k
=
0
,
1
,
…
,
N
-
1
)
]
Γ
=
I
U
⊗
F
s
u
=
[
s
0
,
u
,
…
,
s
N
-
1
,
u
]
T
s
=
[
s
0
T
,
…
,
s
u
T
,
…
,
s
U
-
1
T
]
T
w
=
[
w
0
T
,
…
,
w
M
r
-
1
T
]
T
h uk (m) is a channel response from a transmitter sending a uth spatial stream to an mth receive antenna on a kth subcarrier,
F is an N point DFT kernel,
w is a noise vector of length MrN, and
{circle around (x)} is a Kronecker product.
5. The method of claim 4 ,
wherein the feed-forward weighting of the Mr N-tone signals comprises using a G u m (i) N×MrN feed-forward matrix in the i-th iteration, for the u m -th layer.
6. The method of claim 5 , wherein the weighting of the soft symbol feedback comprises using a B u m (i) N×UN feed-back matrix in the i-th iteration, for the u m -th layer.
7. The method of claim 6 , wherein the compensating for the bias in the time domain signal comprises using a N×N diagonal matrix D u m (i) to remove the bias in the i-th iteration, for the u m -th layer.
8. The method of claim 7 , wherein using the G u m (i) N×M r N feed-forward matrix in the i-th iteration, for the u m -th layer, comprises minimizing a mean square error (MSE) function per tone, wherein G u m (i) is characterized by:
G u m (i) =[G u m ,0 (i) G u m ,1 (i) . . . G u m ,M r −1 (i) ]
wherein submatrices of G u m (i) are diagonal, and
wherein using the B u m (i) N×UN feed-back matrix in the i-th iteration, for the u m -th layer, comprises minimizing a MSE function per tone, wherein B u m (i) is characterized by:
B u m (i) =[B u m ,0 (i) B u m ,1 (i) . . . B u m ,U−1 (i) ]
wherein submatrices of B u m (i) are diagonal.
9. The method of claim 8 , wherein the MSE function is
J
u
,
k
(
i
)
=
E
[
g
u
m
,
k
(
i
)
H
y
~
k
-
∑
l
=
0
m
-
1
b
u
m
,
u
l
,
k
(
i
)
x
^
k
,
u
l
(
i
)
-
∑
l
=
m
U
-
1
b
u
m
,
u
l
,
k
(
i
)
x
^
k
,
u
l
(
i
-
1
)
-
x
k
,
u
m
2
]
with
constraint
∑
k
=
0
N
-
1
b
u
m
,
u
m
,
k
(
i
)
=
0
where
{tilde over (y)} k =[y k,0 , . . . , y k,M r −1 ] T ,
and
x v =Fs v ,{circumflex over (x)} v =Fŝ v
where
g u m ,k (i) =[G u m ,0 (i) ( k,k ), . . . , G u m ,M r −1 (i) ( k,k )] H
b u m ,u l ,k (i) =B u m ,u l (i) ( k,k )
and wherein a noise and interference covariance matrix R k is assumed to be known by the receiver, and
where
R k ( m,n )= E[w ; m ( k ) w n ( k )*]
wherein B u (i) and G u (i) are computed based upon R k .
10. The method of claim 9 , further comprising determining the feed-forward weighting based on:
g
u
m
,
k
(
i
)
H
=
ρ
u
m
(
i
)
g
~
u
m
,
k
(
i
)
H
g
~
u
m
,
k
(
i
)
H
=
h
u
m
,
k
H
C
u
m
,
k
(
i
)
-
1
ρ
u
m
(
i
)
=
E
ss
1
+
β
u
m
(
i
-
1
)
E
ss
T
u
m
(
i
)
T
u
m
(
i
)
=
1
N
∑
k
=
0
N
-
1
g
~
u
m
,
k
(
i
)
H
h
u
m
,
k
C
u
m
,
k
(
i
)
=
∑
l
=
0
m
-
1
E
ss
(
1
-
β
u
l
(
i
)
)
h
u
l
,
k
h
u
l
,
k
H
+
∑
l
=
m
U
-
1
E
ss
(
1
-
β
u
l
(
i
-
1
)
)
h
u
l
,
k
h
u
l
,
k
H
+
R
k
β
u
(
i
)
=
E
s
s
^
,
u
(
i
)
2
E
s
^
s
^
,
u
(
i
)
E
ss
determining the weighting of the soft symbol feedback based on:
b
u
m
,
u
m
,
k
(
i
)
=
α
u
m
(
i
-
1
)
ρ
u
m
(
i
)
(
g
~
u
m
,
k
(
i
)
H
h
u
m
,
k
-
T
u
m
(
i
)
)
b
u
m
,
u
l
,
k
(
i
)
=
α
u
l
(
i
)
g
u
m
,
k
(
i
)
H
h
u
l
,
k
,
for
l
<
m
b
u
m
,
u
l
,
k
(
i
)
=
α
u
l
(
i
-
1
)
g
u
m
,
k
(
i
)
H
h
u
i
,
k
,
for
l
>
m
α
u
(
i
)
=
E
s
s
^
,
u
(
i
)
E
s
^
s
^
,
u
(
i
)
where T u m (i) , α, and C u m ,k (i) are intermediate terms.
11. The method of claim 10 , wherein the compensating for the bias in the time domain signal comprises calculating
BIAS=ρ u m (i) T u m (i)
MSE= E ss (ρ u m (i) T u m (i) −1) 2 −E ss (1−β u m (i−1) )(ρ u m (i) T u m (i) ) 2 +ρ u m (i) 2 T u m (i)
calculating a bias correction matrix
D
u
m
(
i
)
=
1
BIAS
I
and calculating a symbol-wise signal-to-noise ratio (SNR)
SNR
=
BIAS
2
E
ss
MSE
-
(
BIAS
-
1
)
2
E
ss
=
T
u
m
(
i
)
E
ss
1
-
E
ss
(
1
-
β
u
m
(
i
-
1
)
)
T
u
m
(
i
)
where I is an identity matrix.
12. The method of claim 1 , further comprising generating soft symbols for the respective U layers, comprising:
converting from bit-wise likelihood to symbol-wise likelihood based on:
s
^
k
=
∑
k
=
0
M
-
1
Pr
(
s
k
)
s
k
Pr
(
s
k
)
=
∏
j
=
0
log
2
(
M
)
-
1
Pr
(
b
j
(
s
k
)
)
,
where M is a constellation size; and
where Pr(b j (S k )) is a probability of a j-th bit being fed back from a soft symbol.
13. A system for soft interference cancellation, comprising:
a plurality of antennas configured to accept a plurality of multicarrier signals substantially simultaneously, wherein the plurality of multicarrier signals comprise N overlapping carrier frequencies, where N is an integer;
a plurality of pre-processing modules connected to corresponding antennas of the plurality of antennas, wherein the plurality of pre-processing modules are configured to perform a cyclic prefix removal and a fast Fourier transform for the plurality of multicarrier signals to yield Mr N-tone signals y, where Mr is an integer corresponding to a number of the plurality of antennas;
a plurality of channel estimation modules connected to corresponding outputs of the plurality of pre-processing modules, wherein the plurality of channel estimation modules are configured to provide feed-forward and feedback weighting;
an equalizer comprising a first input connected to the outputs of the plurality of pre-processing modules, a second input configured to accept feed-forward and feedback weighting instructions, a third input configured to accept feedback of previously demodulated soft symbols, and a first output configured to supply bias compensated signals in a time domain;
a demodulator/decoder module comprising a fourth input connected to the equalizer and a second output configured to supply soft symbols; and
a feedback module comprising a fifth input configured to accept soft symbols from the demodulator/decoder module and a second output configured to supply the feedback to the equalizer,
wherein the equalizer is configured to use a successive SIC (S-SIC) process to cancel interference in the Mr N-tone signals, and
the feedback module is configured to, for respective U layers;
re-encode and re-modulate soft symbols to yield soft symbol feedback from an i-th iteration for layers already processed in the i-th iteration, and
re-encode and re-modulate soft symbols from a (i−1)th iteration for layers not yet processed in the i-th iteration, including a u m -th layer, where U and i are integers.
14. The system of claim 13 , wherein the equalizer is further configured to, in the i-th iteration, sequentially process the U layers in an order of u 0 ,u 1 , . . . , u U−1 using feedback generated from previously processed layers of the U layers.
15. The system of claim 14 ,
wherein the equalizer further comprises:
a discrete Fourier transform (DFT) module connected to the feedback module and configured to perform a discrete Fourier transform on the soft symbol feedback to yield precoded soft symbol feedback;
a feedback weighting module connected to the DFT module and configured to weight the precoded soft symbol feedback to yield a weighted feedback signal;
a feed-forward weighting module connected to the plurality of pre-processing modules and configured to weight the N-tone signals y to yield weighted feed-forward signals;
a summing module configured to subtract the weighted feedback signals from the feed-forward weighted signals to yield feedback compensated signals; and
an inverse discrete Fourier transform (IDFT) module configured to transfer the feedback compensated signals into the time domain to yield time domain signals,
wherein the demodulator/decoder is further configured to demodulate and decode the bias compensated signals for the U layers.
16. The system of claim 15 , wherein the N-tone signals y as are characterized by:
y=H*Γ*s+w,
where
H
=
[
H
0
,
0
…
…
H
0
,
U
-
1
⋮
⋱
⋮
⋮
⋱
⋮
H
M
r
,
0
…
…
H
M
r
,
U
-
1
]
H
m
,
u
=
Diag
[
h
u
,
k
(
m
)
,
(
k
=
0
,
1
,
…
,
N
-
1
)
]
Γ
=
I
U
⊗
F
s
u
=
[
s
0
,
u
,
…
,
s
N
-
1
,
u
]
T
s
=
[
s
0
T
,
…
,
s
u
T
,
…
,
s
U
-
1
T
]
T
w
=
[
w
0
T
,
…
,
w
M
r
-
1
T
]
T
h u,k (m) is a channel response from a transmitter sending a uth spatial stream to an mth receive antenna on a kth subcarrier
F is a N point DFT kernel,
w is a noise vector of length MrN, and
{circle around (x)} is a Kronecker product.
17. The system of claim 16 , wherein the equalizer is configured to feed-forward weight the Mr N-tone signals using a G u m (i) N×M r N feed-forward matrix in the i-th iteration, for the u m -th layer, weight the soft symbol feedback from U layers using a B u m (i) N×UN feed-back matrix in the i-th iteration, for the u m -th layer, and compensate for bias in the time domain signal using a N×N diagonal matrix D u m (i) to remove bias in the i-th iteration for the u m -th layer.
18. The system of claim 17 , wherein the equalizer is configured to use the G u m (i) N×MrN feed-forward matrix to minimize a mean square error (MSE) function per tone, wherein G u m (i) is characterized by:
G u m (i) =[G u m ,0 (i) G u m ,1 (i) . . . G u m ,M r −1 (i) ]
wherein submatrices of G u m (i) are diagonal
B u m (i) =[B u m ,0 (i) B u m ,1 (i) . . . B u m ,U−1 (i) ]
19. The system of claim 18 , wherein using the B u m (i) N×UN feed-back matrix comprises minimizing a MSE function per tone, wherein B u m (i) is characterized by:
B u m (i) =[B i m ,0 (i) B u m ,1 (i) . . . B u m ,U−1 (i) ]
wherein submatrices of B u m (i) are diagonal.
20. The system of claim 19 , wherein the equalizer minimizes the MSE function based on:
J
u
,
k
(
i
)
=
E
[
g
u
m
,
k
(
i
)
H
y
~
k
-
∑
l
=
0
m
-
1
b
u
m
,
u
l
,
k
(
i
)
x
^
k
,
u
l
(
i
)
-
∑
l
=
m
U
-
1
b
u
m
,
u
l
,
k
(
i
)
x
^
k
,
u
l
(
i
-
1
)
-
x
k
,
u
m
2
]
with
constraint
∑
k
=
0
N
-
1
b
u
m
,
u
m
,
k
(
i
)
=
0
where
{tilde over (y)} k =[y k,0 , . . . , y k,M r −1 ] T ,
and
x v =Fs v ,{circumflex over (x)} v =Fŝ v
where
g u m ,k (i) =[G u m ,0 (i) ( k,k ), . . . , G u m ,M r −1 (i) ( k,k )] H
b u m ,u l ,k (i) =B u m ,u l (i) ( k,k )
and wherein a noise and interference covariance matrix R k is assumed to be known by the receiver, and
where
R k ( m,n )= E[w m ;( k ) w n ( k )*]
wherein B u (i) and G u (i) are computed based upon R k .
21. The system of claim 20 , wherein the equalizer is configured to optimize the feed-forward weighting according to:
g
u
m
,
k
(
i
)
H
=
ρ
u
m
(
i
)
g
~
u
m
,
k
(
i
)
H
g
~
u
m
,
k
(
i
)
H
=
h
u
m
,
k
H
C
u
m
,
k
(
i
)
-
1
ρ
u
m
(
i
)
=
E
ss
1
+
β
u
m
(
i
-
1
)
E
ss
T
u
m
(
i
)
T
u
m
(
i
)
=
1
N
∑
k
=
0
N
-
1
g
~
u
m
,
k
(
i
)
H
h
u
m
,
k
C
u
m
,
k
(
i
)
=
∑
l
=
0
m
-
1
E
ss
(
1
-
β
u
l
(
i
)
)
h
u
l
,
k
h
u
l
,
k
H
+
∑
l
=
m
U
-
1
E
ss
(
1
-
β
u
l
(
i
-
1
)
)
h
u
l
,
k
h
u
l
,
k
H
+
R
k
β
u
(
i
)
=
E
s
s
^
,
u
(
i
)
2
E
s
^
s
^
,
u
(
i
)
E
ss
wherein weighting of soft symbol feedback from the U layers is optimized according to:
b
u
m
,
u
m
,
k
(
i
)
=
α
u
m
(
i
-
1
)
ρ
u
m
(
i
)
(
g
~
u
m
,
k
(
i
)
H
h
u
m
,
k
-
T
u
m
(
i
)
)
b
u
m
,
u
l
,
k
(
i
)
=
α
u
l
(
i
)
g
u
m
,
k
(
i
)
H
h
u
l
,
k
,
for
l
<
m
b
u
m
,
u
l
,
k
(
i
)
=
α
u
l
(
i
-
1
)
g
u
m
,
k
(
i
)
H
h
u
i
,
k
,
for
l
>
m
α
u
(
i
)
=
E
s
s
^
,
u
(
i
)
E
s
^
s
^
,
u
(
i
)
where
T
u
(
i
)
,
α
,
and
C
u
m
,
k
(
i
)
are
intermediate
terms
.
22. The system of claim 21 , wherein the compensation module is configured to compensate for bias in the time domain signal by calculating
BIAS=ρ u m (i) T u m (i)
MSE= E ss (ρ u m (i) T u m (i) −1) 2 −E ss (1−β u m (i−1) )(ρ u m (i) T u m (i) ) 2 +ρ u m (i) 2 T u m (i)
calculating a bias correction matrix
D
u
m
(
i
)
=
1
BIAS
I
and calculating a symbol-wise signal-to-noise ratio (SNR)
SNR
=
BIAS
2
E
ss
MSE
-
(
BIAS
-
1
)
2
E
ss
=
T
u
m
(
i
)
E
ss
1
-
E
ss
(
1
-
β
u
m
(
i
-
1
)
)
T
u
m
(
i
)
where I is an identity matrix.
23. The system of claim 13 , wherein the demodulator/decoder is configured to supply soft symbols for the respective U layers by converting from bit-wise likelihood to symbol-wise likelihood according to:
s
^
k
=
∑
k
=
0
M
-
1
Pr
(
s
k
)
s
k
Pr
(
s
k
)
=
∏
j
=
0
log
2
(
M
)
-
1
Pr
(
b
j
(
s
k
)
)
,
where M is a constellation size; and
where Pr(b j (S k )) is a probability of a j-th bit being fed back from a soft symbol.