LIU et al.: FDM-STRUCTURED PREAMBLE OPTIMIZATION FOR CHANNEL ESTIMATION IN MIMO-OQAM/FBMC SYSTEMS 8435
Fig. 1. The MIMO-OQAM/FBMC system model.
with ja
(i)
m,n
being the intrinsic imaginary interference from the
neighboring frequency-time (FT) points. With a well localized
pulse g[k] in time and frequency, it can be assumed that the
intrinsic imaginary interference mostly originates from the
first-order neighboring FT points [34]. Let us denote
ζ
p,q
m,n
=
∞
k=−∞
g
m,n
[k]g
∗
p,q
[k]. (3)
Then, the imaginary interference term ja
(i)
m,n
can be approxi-
mated as
ja
(i)
m,n
≈
(p
0
,q
0
)∈Ω
1
a
m+p
0
,n+q
0
ζ
m,n
m+p
0
,n+q
0
, (4)
where the neighborhood Ω
1
= {(p
0
,q
0
)| p
0
, q
0
∈{−1,
0, 1} and (p
0
,q
0
) =(0, 0)} and ζ
m,n
m+p
0
,n+q
0
represents the
contribution of a
m+p
0
,n+q
0
to the imaginary interference
ja
(i)
m,n
. It is noteworthy that for a well-designed prototype filter
g[k], ζ
m,n
m+p
0
,n+q
0
is pure imaginary for any (p
0
,q
0
) =(0, 0)
and ζ
m,n
m+p
0
,n+q
0
=1for (p
0
,q
0
)=(0, 0). Thus, for (p
0
,q
0
) =
(0, 0), in the remainder of this paper, we refer to the terms
ζ
m,n
m+p
0
,n+q
0
as the imaginary interference coefficients.
Note that, the intrinsic imaginary interference could be
removed by taking the real part after channel equalization.
In this paper, since we mainly focus on the preamble design
issues, the equalization and operation of taking real part are
not discussed.
B. MIMO-OQAM/FBMC System Model
The MIMO-OQAM/FBMC system model is depicted
in Fig. 1, where the transmitter and the receiver are equipped
with N
t
and N
r
antennas, respectively. Since the channel esti-
mation performance of MIMO-OQAM/FBMC systems would
not differ in the case of channel coding, we only consider the
uncoded scenario below.
At the transmitter side, the symbols spatially multiplexed
on the mth subcarrier at the nth time index are denoted by
a
m,n
=
a
1
m,n
,a
2
m,n
, ··· ,a
N
t
m,n
T
, each element of which
is transmitted at different antennas after the corresponding
OQAM/FBMC modulation. At the receiver side, the link
of each transmit and receive antenna pair is degraded by
multipath fading and contaminated with AWGN. For each
given FT position (m, n),letH
r,t
m
be the frequency response
of the channel between the tth transmit antenna and the rth
receive antenna and η
r
m,n
be the noise component at the
rth receive antenna. By assuming perfect time and frequency
synchronization, the demodulated symbol of the rth receive
antenna can be obtained by extending (2) to the MIMO case
as [16], [20]
y
r
m,n
=
N
t
t=1
H
r,t
m
c
t
m,n
+ η
r
m,n
, 1 ≤ r ≤ N
r
, (5)
where c
t
m,n
represents the corresponding virtually transmitted
symbol at the tth transmit antenna. According to (4), c
t
m,n
can
be written as
c
t
m,n
= a
t
m,n
+
(p
0
,q
0
)∈Ω
1
a
t
m+p
0
,n+q
0
ζ
m,n
m+p
0
,n+q
0
, 1 ≤ t ≤ N
t
.
(6)
We denote the demodulated symbol vector by y
m,n
=
y
1
m,n
,y
2
m,n
, ··· ,y
N
r
m,n
T
, the virtually transmitted vector by
c
m,n
=
c
1
m,n
,c
2
m,n
, ··· ,c
N
t
m,n
T
and the additive noise vector
by η
m,n
=
η
1
m,n
,η
2
m,n
, ··· ,η
N
r
m,n
T
. Thus, the equation (5)
can be expressed as
y
m,n
= H
m
c
m,n
+ η
m,n
, (7)
where
H
m
=
⎡
⎢
⎢
⎢
⎣
H
1,1
m
H
1,2
m
··· H
1,N
t
m
H
2,1
m
H
2,2
m
··· H
2,N
t
m
.
.
.
.
.
.
.
.
.
.
.
.
H
N
r
,1
m
H
N
r
,2
m
··· H
N
r
,N
t
m
⎤
⎥
⎥
⎥
⎦
(8)
is the MIMO channel frequency response (CFR) at that FT
point.
III. T
HE CONVENTIONAL PREAMBLE DESIGN METHODS
IN
MIMO-OQAM/FBMC SYSTEMS
Since the orthogonality condition of the OQAM/FBMC
system only holds in the real field, which causes intrinsic
imaginary interference to preamble symbols at the receiver,
preamble design in the OQAM/FBMC system is more difficult
than that in OFDM. Worse is that there also exists multi-
antenna interference when OQAM/FBMC is extended to the
MIMO case. In this section, we tackle the preamble design
problem in MIMO-OQAM/FBMC systems and give a brief
review of the conventional preamble design methods.
A. IAM Method
IAM preamble design method has drawn much attention
due to its simplicity and efficiency [20]. The IAM family
that includes IAM-R, IAM-imaginary (IAM-I), IAM-C, and
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