全双工MIMO系统最大-最小加权下行SINR优化研究
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"这篇研究论文探讨了全双工多用户多输入多输出(MIMO)系统中的最大-最小加权下行信噪比(SINR)问题，其中具有全双工能力的基站(BS)与多个半双工上下行用户在同一系统资源下通信。论文重点关注在满足上行用户特定SINR约束的情况下，最大化下行链路的最小加权SINR的场景。优化过程考虑了BS的发射功率、上行用户的发射功率以及BS的发射和接收波束形成，因此该优化问题受到多个上行SINR约束和多个发射功率约束的影响。"
在这篇发表于《IEEE Transactions on Signal Processing》2017年6月卷的文章中，作者们提出了一种针对全双工MIMO系统的优化策略，旨在解决在上下行链路共存时的信号干扰和噪声问题。全双工通信允许设备同时进行发送和接收，极大地提高了频谱效率，但这也引入了自干扰，尤其是在多天线环境中。
文章的核心问题是最大化下行用户的最小加权SINR，同时保证每个上行用户的SINR达到预设阈值。这是一个非线性优化问题，因为它涉及到多个变量的联合优化：BS的发射功率分配、上行用户的发射功率控制以及BS的发射和接收波束成形设计。这些因素共同影响着系统性能，特别是考虑到自干扰抑制和上下行链路间的干扰管理。
作者们提出的解决方案可能涉及先进的信号处理技术，如干扰消除、预编码和动态功率分配策略，以在保证上行用户服务质量的同时，提升下行用户的整体体验。此外，可能还会涉及对系统资源的智能调度，以平衡上下行链路的性能。
解决这个问题对于全双工MIMO系统的设计和实施至关重要，因为它直接关系到系统容量、覆盖范围以及用户体验。通过这样的优化，可以有效地提高系统的效率，并确保所有用户在全双工模式下都能获得满意的通信质量。
这篇论文为全双工通信环境下的资源管理和干扰控制提供了理论基础，对于未来无线通信网络的开发和改进有着深远的影响。它不仅推动了理论研究的发展，也为实际系统的工程实现提供了有价值的指导。
3280 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 65, NO. 12, JUNE 15, 2017
The SINR of the k-th received stream can hence be expressed
as
SINR
k
(p, W , V )=
p
k
G
kk
l∈K,l= k
p
l
G
kl
+ n
k
, ∀k ∈K
(5)
=
⎧
⎪
⎨
⎪
⎩
p
k
|H
kk
w
k
|
2
(
l ∈K,l= k
p
l
|H
kl
w
l
|
2
)
+n
k
SINR
DL
k
(p, W ) if k ∈K
d
p
k
|v
†
k
H
kk
|
2
(
l ∈K,l= k
p
l
|v
†
k
H
kl
w
l
|
2
)
+n
k
SINR
UL
k
(p, W , V ) if k ∈K
u
.
(6)
Our target is to maximize the minimum weighted SINR of the
downlink (DL) streams when the uplink (UL) streams have to
satisfy certain SINR constraints. We therefore formulate the
problem as
P : max
p,W ,V
min
k
d
∈K
d
SINR
DL
k
d
(p, W )
β
k
d
(7a)
s.t. SINR
UL
k
u
(p, W , V ) ≥ β
k
u
, ∀k
u
∈K
u
(7b)
t
T
i
p ≤ P
i
, p ≥ 0, ∀i =0, 1,...,K
u
(7c)
||w
k
|| =1, ||v
k
|| =1, ∀k ∈K (7d)
where 1/β
k
d
is the weight assigned to the k
d
-th downlink user;
β
k
u
is the pre-assigned SINR constraint for the uplink user
corresponding to k
u
(i.e., the (k
u
− K
d
)-th UL user);
t
0
=[
K
d
1,...,1,
K
u
0,...,0]
T
,
t
i
=[
K
d
0,...,0,
K
u
0,...,0
i−1
, 1, 0,...,0
K
u
−i
]
T
for i =1,...,K
u
; P
0
is the total power constraint at the BS;
P
i
is the individual power constraint of the i-th uplink user
(i =1,...,K
u
); and 0 is an all-zero vector of appropriate size.
Moreover, P
0
and P
i
(i =1,...,K
u
) are finite. We also define
β =[β
1
,...,β
K
] in which the k-th element is related to the
weight or constraint assigned to the SINR of the k-th stream.
P is a joint power and beamforming optimization prob-
lem with multiple power and multiple SINR constraints. In
Section III, we firstly investigate the multiple-power-and-
multiple-SINR (MP-MSINR) constraint optimization prob-
lem with fixed beamforming. We prove that the MP-MSINR
constraint problem can be decoupled into single-power-and-
multiple-SINR (SP-MSINR) constraint sub-problems which
can further solved by the subgradient projection-based method
jointly. Then, in Section IV, under a SP-MSINR constraint sce-
nario, we derive the network duality of the optimization problem
P. Thus, by using network duality, minimum-mean-squared-
error (MMSE) criterion and the solution for power optimization
problem with fixed beamforming, the j oint power and trans-
mit/receive beamforming solution can be iteratively derived ac-
cordingly.
III. P
OWER OPTIMIZATION WITH FIXED BEAMFORMING
In this section, we fix the transmit and receive beamforming
vectors and aim to optimize the power vector p. The problem
T , under the problem P with fixed beamforming vectors, is
defined as
T : max
p
min
k
d
∈K
d
SINR
DL
k
d
(p)
β
k
d
(8a)
s.t. SINR
UL
k
u
(p) ≥ β
k
u
, ∀k
u
∈K
u
(8b)
t
T
i
p ≤ P
i
, p ≥ 0, ∀i =0, 1,...,K
u
(8c)
where SINR
k
(p)=SINR
k
(p, W , V ) with fixed W and V .
It can be seen that T is a max-min power optimiza-
tion problem (refer to (8a)) with multiple power constraints
(P
0
,P
1
,...,P
K
u
in (8c)) and multiple SINR constraints
(β
K
d
+1
,β
K
d
+2
,...,β
K
d
+K
u
in (8b)). Next, we consider T un-
der a certain i and formulate the new SP-MSINR constraint
problem as
T
i
: max
τ
i
,p
τ
i
(9a)
s.t. τ
i
≤
SINR
DL
k
d
(p)
β
k
d
, ∀k
d
∈K
d
(9b)
SINR
UL
k
u
(p) ≥ β
k
u
, ∀k
u
∈K
u
(9c)
t
T
i
p ≤ P
i
, p ≥ 0 (9d)
where τ
i
is simply an auxiliary variable.
Lemma 1: Under the optimal solutions of T
i
, the constraints
in (9b), (9c) and (9d) must be satisfied with equality for all
k
d
∈K
d
and k
u
∈K
u
. That is to say,
ˆτ
i
=
SINR
DL
k
d
(
ˆ
p
i
)
β
k
d
, ∀k
d
∈K
d
(10a)
SINR
UL
k
u
(
ˆ
p
i
)=β
k
u
, ∀k
u
∈K
u
(10b)
t
T
i
ˆ
p
i
= P
i
,
ˆ
p
i
≥ 0 (10c)
where ˆτ
i
and
ˆ
p
i
are the optimal solutions.
Proof: Refer to Appendix A.
Theorem 1: Let
ˆ
p
i
denote the unique solution and ˆτ
i
be the
optimal value of T
i
. Also, let s = arg min
i=0,...,K
u
ˆτ
i
. Then
the optimal value and unique solution of the original problem
T are given by ˆτ =ˆτ
s
and
ˆ
p =
ˆ
p
s
, respectively.
Proof: Refer to Appendix B.
Corollary 1: We define a function T (θ) as
T (θ) : max
p
min
k
d
∈K
d
SINR
DL
k
d
(p)
β
k
d
(11a)
s.t. SINR
UL
k
u
(p) ≥ β
k
u
, ∀k
u
∈K
u
(11b)
i
θ
i
t
T
i
p ≤
i
θ
i
P
i
, p ≥ 0. (11c)
Then, the optimal solution ˆτ of T is equal to
ˆτ = min{T (θ):θ ≥ 0}. (12)
Proof: Refer to Appendix C.
Corollary 2: T (θ) is a quasi-convex function with respect
to (w.r.t.) θ.
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