Joint MLD and MMSE-SIC over spatially correlated MIMO systems L. Fan
et al.
3.1. Review of minimum-mean-square error
with successive interference canceler
Minimum-mean-square error with SIC is a popular subop-
timal MIMO detection algorithm, which outperforms con-
siderably ZF and MMSE at the expense of a mild increase
in the computational complexity [8,9]. The procedure of
MMSE-SIC algorithm is provided as follows.
Initialization:
(
A D;
Q
HŒ1 D H
Main program:
for q D 1;:::;L
T
PŒq D
Q
H
Œq
Q
HŒq C
2
n
I
L
T qC1
1
SINR
q;l
D
1
2
n
.PŒq/
l;l
1
l
q
D arg max
l2Œ1;L
T
;l62A
SINR
q;l
AŒq D l
q
O
b
l
q
D Dec
PŒq
Q
H
Œqy
l
q
y
y H
l
q
O
b
l
q
Q
HŒq C 1
Q
HŒq without the l
q
th column
end
In there,
Q
HŒq 2 C
L
R
.L
T
qC1/
represents the chan-
nel of the residual data streams at the qth step, and A
denotes the set of transmit antennas with the largest signal-
to-interference-plus-noise ratios (SINRs). Specifically, at
the qth step, there are .q 1/ data streams to be canceled in
the previous steps. In addition, MMSE-SIC detects the data
stream of the maximum SINR and subtracts a replica sig-
nal of the detected symbol from the received signal. This
process is repeated until the last transmitted data stream is
detected.
3.2. Noise enhancement in
minimum-mean-square error with
successive interference canceler
Let us denote R
n
Œq 2 C
.L
T
qC1/.L
T
qC1/
as the
covariance matrix of the noise component at the qth step.
Then, we have
R
n
Œq D
2
n
PŒq
Q
H
Œq
Q
HŒqPŒq D
2
n
V
Œq
Q
D
1
ŒqVŒq
(5)
where
Q
DŒq D diag
Q
1
Œq;
Q
2
Œq;:::;
Q
L
T
qC1
Œq
(6)
Q
l
Œq D
l
Œq C
2
n
2
l
Œq
(7)
with
Q
l
Œq satisfying
Q
1
Œq
Q
2
Œq
Q
L
T
qC1
Œq (8)
and VŒq 2 C
.L
T
qC1/.L
T
qC1/
is the unitary matrix
that diagonalizes
Q
H
Œq
Q
HŒq. Moreover,
l
Œq in Equation
(7) denotes an eigenvalue of
Q
H
Œq
Q
HŒq. The number of
negligible f
Q
l
Œqg represents the number of noise enhance-
ment directions. For small
, the correlation of
Q
HŒ1
between the receive antenna elements becomes high. In
this case, the number of negligible eigenvalues is generally
more than one. In other words, there are possibly more than
one directions of noise enhancement. In fact, for highly
correlated channels, existing suboptimal algorithms, such
as conventional joint CS [12–14], GBS [15,16], and SP
[17], all exhibit inferior BER performances because they
all assume that there exists only one negligible eigenvalue.
3.3. Proposed scheme
To cope with the noise enhancement problem in highly
correlated channels, we propose a novel joint CS that
adaptively controls the number of streams, denoted by
l
w
0 l
w
l
max
w
, to be detected by MLD, where l
max
w
is a predetermined threshold that can be linked with a spe-
cific BER requirement. Specifically, the proposed joint CS
is first initialized by l
w
D 0 and checks whether a sat-
isfied BER performance is obtained. If not, l
w
will be
increased by one to achieve a more reliable detection until
the required performance or l
w
D l
max
w
is reached. In the
following, the proposed CS is described in detail.
3.3.1. Extension of conventional joint CS.
In the conventional joint CS algorithm [12–14], only one
data stream (i.e., l
w
D 1) is detected by MLD, which gives
rise to the performance loss especially for highly corre-
lated channels. To describe the proposed algorithm, note
that first, b and H can be decomposed into two blocks as
follows:
b D
b
s
b
w
; and H D ŒH
s
H
w
(9)
where b
s
2 C
.L
T
l
w
/1
and b
w
2 C
l
w
1
represent,
respectively, the streams to be detected by MMSE-SIC and
MLD. Likewise, H
s
2 C
L
R
.L
T
l
w
/
and H
w
2 C
L
R
l
w
denote the channel matrices associated with the signals of
b
s
and b
w
, respectively. Apparently, the selection of b
w
associated with H
w
depends on SINR
q;l
of MMSE-SIC.
In particular, at each step of MMSE-SIC, the data stream
associated with the minimum SINR
q;l
is selected. Further,
define
y
s
, y H
w
b
w
D H
s
b
s
C n (10)
y
w
, y H
s
b
s
D H
w
b
w
C n (11)
1194
Wirel. Commun. Mob. Comput.
2013; 13:1192–1204 © 2012 John Wiley & Sons, Ltd.
DOI: 10.1002/wcm