安全多载波FD中继系统的QoS驱动功率优化

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本文主要探讨了在安全多载波全双工（Full-Duplex, FD）中继通信系统中，利用服务质量（Quality of Service, QoS）驱动的功率分配策略。随着无线通信对数据传输效率和安全性需求的提升，全双工技术作为一种同时进行收发的先进技术，对于提高频谱利用率和系统性能具有重要意义。然而，全双工通信引入了自干扰问题，这使得传统的功率分配方法面临挑战。针对这一问题，研究者提出了一种基于QoS的鲁棒功率分配策略，特别关注的是在存在信道不确定性的情况下，如何最大化系统的安全有效容量（Secure Effective Capacity, SEC）。安全有效容量是衡量在保证信息传输安全的前提下，系统能够提供的最大信息传输速率，它结合了传输效率与信息安全的要求。在设计策略时，文章考虑了两个关键约束：总系统功率的限制和残留环路回波功率（residual loopback power），这是全双工系统特有的问题，需要在确保自干扰抑制的同时，合理分配各载波的功率，以满足实时应用所需的统计延迟QoS。为了实现这一目标，研究者采用优化方法，可能包括动态调整各个子载波的发射功率，通过估计和建模信道条件，以及考虑到无线环境的不确定性，找到一个能够在满足QoS要求下的最优功率分配方案。这个策略旨在平衡信号强度、抗干扰能力以及系统整体的能效。论文还提到了引用信息，表明该成果已被IEEE Transactions on Wireless Communications接受发表，但可能存在未公开的最终编辑内容。读者可以通过DOI 10.1109/TWC.2019.2950009访问这篇论文，以获取更深入的技术细节和详细的算法描述。这篇研究论文为安全多载波全双工中继系统提供了一个重要的理论支持，展示了如何通过有效的QoS驱动功率分配策略，提升系统的可靠性和安全性，这对于未来的无线通信网络设计具有实际应用价值。

1536-1276 (c) 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TWC.2019.2950009, IEEE

Transactions on Wireless Communications

IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. XX, NO. YY, MONTH 2019 3

We assume that the wireless channels of the system undergo

independent identically distributed (i.i.d.) fading, where the

channels keep invariant within a frame duration T

and vary

between frames independently. Furthermore, the multicarri-

er transmission has been adopted to overcome the channel

frequency selective fading in the wireless environment and

we divide the whole system bandwidth B into N orthogonal

subcarriers.

For the kth subcarrier, h

(k)

, h

(k)

, h

(k)

, and h

(k)

respec-

tively represent the corresponding channel coefﬁcients of the

source-relay (SR) link, the relay-destination (RD) channel, the

relay-eavesdropper (RE) link, and the LI channel. x

(k)

with

E[|x

(k)

] = p

(k)

and x

(k)

with E[|x

(k)

] = p

(k)

are the

transmitted signals from S and R over the kth subcarrier,

respectively, where E[·] is the expectation operator. p

(k)

and

(k)

respectively represent the transmit power of S and R

over the kth subcarrier [1]. Considering that nodes S, D, E

are all the legitimate network nodes, we premise that h

(k)

, h

(k)

, ∀k, can be estimated via training pilot sequences

exchanged between the transmitter and receiver. Hence, the

perfect CSI about h

(k)

, h

(k)

, and h

(k)

is available during the

information transmission.

In the FD mode, over the kth subcarrier, the received signals

at R, D, and E are expressed respectively as y

(k)

, y

(k)

, and

(k)

. We have

(k)

= h

(k)

+ h

(k)

+ n

(k)

, (1)

(k)

= h

(k)

+ n

(k)

, (2)

(k)

= h

(k)

+ n

(k)

, (3)

where n

(k)

, n

(k)

, and n

(k)

are the corresponding complex

additive white Gaussian noises (AWGNs) with the distribution

(k)

∼ CN (0, σ

), i ∈ {R, D, E} and σ

is the variance of

the complex AWGN. The two items, h

(k)

and h

(k)

(1), are the desired signal and the LI, respectively. In practice,

for the FD relay, its LI is much larger than the desired signal

sometimes. The LI cancelation becomes necessary, but it is

hard to completely remove the LI due to the imperfect channel

estimation. Considering the above non-ideal LI cancelation,

the practical received signal at R is written as

˜y

(k)

= h

(k)

+ n

(k)

, (4)

where

(k)

is the estimated channel coefﬁcient of the residual

LI link and

(k)

is the practical residual LI.

The instantaneous signal-to-noise ratios (SNRs) correspond-

ing to the above four transmission channels can be deﬁned

as γ

(k)

(σ

(k)

)

, γ

(k)

(σ

(k)

)

, γ

(k)

(σ

(k)

)

, and

(k)

(σ

(k)

)

, respectively. Then, the instantaneous signal-

to-interference-and-noise ratios (SINRs) of R, D, and E

over the kth subcarrier are obtained as γ

(k)

1+p

(k)

= p

(k)

, and γ

(k)

= p

(k)

, respectively.

Based on the achievable secrecy rate of the HD relaying

system [25] and the SINRs of the relay and the eavesdropper

[1], we obtain the achievable secrecy rate of the kth subcarrier

in the secure FD relay system as

(k)

sec

log

1 + min{γ

(k)

, γ

(k)

}

1 + γ

(k)

, (5)

where [x]

means the maximum value selection for a real

random variable x, also expressed as max{x, 0}.

From (5), it is noted that min

(k)

, γ

(k)

≤ γ

(k)

if γ

(k)

≤

(k)

, which means that the achievable secrecy rate R

(k)

sec

the kth subcarrier becomes zero. In other words, no transmit

power should be assigned to the kth subcarrier in this case.

Therefore, the system would interrupt the transmission from

R to D at the moment. Thus, the secrecy rate is non-negative

and γ

(k)

> γ

(k)

should always be satisﬁed.

The achievable system secrecy rate is the sum of the

achievable secrecy rate over all the subcarriers, which is

expressed as

sec

k=1

(k)

sec

. (6)

B. Secure Effective Capacity

The effective capacity is a powerful tool to address the

issue of statistical QoS guarantees, in terms of queue-length-

bound/delay-bound violation probability. In particular, for

a discrete-time stable queue with inﬁnite buffer size, let

a[τ], (τ = 1, 2, ...), denote a discrete-time stationary and

ergodic service process, and A(t) ,

τ =1

a[τ] be the partial

sum of the service process. Supposing that G¨artner-Ellis limit

of A(t) exits, we can express it as

(θ) = lim

t→∞

log E[e

θA(t)

]= lim

t→∞

log E[e

τ =1

a[τ ]

], (7)

where θ denotes a delay QoS exponent. It is a convex function

differentiable for all θ ≥ 0 [26].

Then, the effective capacity of this service process can be

formulated as [16]

sec

(θ) = −

(−θ)

. (8)

If the service process is uncorrelated, then we have

sec

(θ) = −

log(E

−θa[τ ]

]). (9)

According to the deﬁnition of the effective capacity [16], [26],

[27], the SEC essentially deﬁne the maximum secrecy rate

at a given delay QoS requirement [14]. Accordingly, for the

stochastic process which provides the secrecy service rate, we

formulate the SEC as

sec

(θ) = −

log





−θT

sec



, (10)

where the delay QoS exponent θ is a crucial parameter to

characterize the exponential decay rate of the delay viola-

tion probability, B denotes the system bandwidth, and E

means a mathematical expectation operation on the channel

state information. It is noticed that the SEC is a monotonic

decreasing function of the delay QoS exponent θ. Given θ, the

secure effective capacity E

sec

(θ) can be calculated. Moreover,

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