MIMO-OQAM/FBMC信道估计：FDM结构前导码优化减小MSE与BER
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本文主要探讨了在多输入多输出（MIMO）系统中，采用基于移位正交幅度调制（OQAM）滤波器银行多载波（FBMC）技术的信道估计中，频率分复用（FDM）结构化前导码的优化方法。发表于2018年12月的《无线通信交易》(IEEE Transactions on Wireless Communications)卷17，第12期，作者为Wenfeng Liu、Da Chen、Kai Luo、Tao Jiang和Daiming Qu。
在MIMO-OQAM/FBMC系统中，前导码的设计对于准确估计信道状态至关重要。信道估计的质量直接影响到系统的性能，如数据传输的可靠性。论文提出了一种优化策略，目标是通过设计周期性的前导码结构，最小化信道估计的均方误差（MSE）。对于两个发射天线的情况，研究者发现了前导码与相邻符号间的固有干扰之间的关系，并推导出了使MSE达到最小的闭式解，这是一项理论上的突破。
当发射天线数量超过两个时，问题变得更复杂，因为优化问题变为非凸形式。作者将其转化为二次约束二次规划（QCQP），并通过放松非凸约束来求得次优解。这种方法展示了在考虑MSE和比特错误率（BER）性能的前提下，如何在实际工程应用中有效地优化FDM结构化前导码。
通过仿真结果，研究者验证了他们的优化方法能够显著改善信道估计的精度以及系统的整体性能。这对于提升多天线系统的效率，特别是在高数据速率和频谱效率要求严格的场景下，具有重要的实践意义。因此，这项工作不仅提供了理论指导，也为MIMO-OQAM/FBMC系统的信道估计技术的发展开辟了新的路径。
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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