2604 Kong et al.: Differencing Multiuser Detection using error feedback filter for MIMO DS-UWB system
( ) ( ) ( ) ( )
,
1
( ) ( ) ( ) ( )
T
k k k k k
k
M
k k k k
n m n m n
m
r t x t h t z t
=
= ⊗ +
∑
(6)
where
⊗
denotes linear convolution and
( )
( )
k
k
n
z t
is zero-mean additive white Gaussian noise.
3. MIC DFE-EFF （COA）with DA
The DFE which is considered as an effective equalization technique has been widely
employed in the modern wideband communications during this decade
[12][13][14][15][16]
[18][19]
.
In this work, we focus on the MIC DFE-EFF (COA) with DA to assist MUD for MIMO
DS-UWB system. The proposed MIC DFE-EFF (COA) with DA consists of three aspects—
MIC DFE-EFF
[15], COA and DA, which will be discussed in the following.
3.1 MMSE performance of MIC DFE-EFF
The investigation of MMSE performance of MIC DFE-EFF should be based on the DFE and
DFE-EFF. The block diagram of the DFE-EFF is shown in
Fig. 1. The FFF coefficients W
f
, the
FBF coefficients W
b
and the EFF coefficients W
e
for K users can be defined as,
(1) (2) ( ) ( ) ( ) ( ) ( )
,1 ,2 ,
[ , ,..., ] ; [ , ,..., ]
f
K k k k k
T T
f f f f f f f f N
w w w= =W w w w w
(7)
(1) ( 2) ( ) ( ) ( ) ( ) ( )
,1 ,2 ,
[ , ,..., ] ; [ , ,..., ]
b
K k k k k
T T
b b b b b b b b N
w w w= =W w w w w
(8)
( ) ( ) ( )
(1) (2) ( ) ( )
,1 ,2 ,
[ , ,..., ] ; [ , ,..., ]
e
k k k
K T k T
e e e e e e e e N
w w w= =W w w w w
(9)
( )
k
n
y
( )
1
k
n
y
−
( )
2
k
n
y
−
( )
3
k
n
y
−
( )
,1
k
f
w
( )
,2
k
f
w
( )
,3
k
f
w
( )
,4
k
f
w
( )
,1
k
e
w
( )
,2
k
e
w
( )
2
k
n
e
−
( )
1
k
n
e
−
( )
k
n
e
( )
,3
k
b
w
( )
,2
k
b
w
( )
,1
k
b
w
( )
3
ˆ
k
n
I
−
( )
2
ˆ
k
n
I
−
( )
1
ˆ
k
n
I
−
( )
ˆ
k
n
I
( )
k
n
I
%
Fig. 1. Schematic of the DFE-EFF
where N
f,
, N
b
and N
e
are the number of forward, feedback and error taps, respectively. The
superscript (k) in (7)-(9) is used to indicate the kth user for the purpose of MUD, k = 1,...,K.
The inputs of forward, feedback and error filters with time index n are given, respectively, as
follows,
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