保密通信中同相和正交通道失衡对干扰抑制性能的影响^*

宋长庆^1,2

机构：

1. 电子科技大学通信抗干扰全国重点实验室, 四川成都 611731
2. 电磁空间认知与智能控制技术国家级重点实验室, 北京 100089

×
，陈雯雯^1,2

机构：

1. 电子科技大学通信抗干扰全国重点实验室, 四川成都 611731
2. 电磁空间认知与智能控制技术国家级重点实验室, 北京 100089

×
，赵宏志^1,2

机构：

1. 电子科技大学通信抗干扰全国重点实验室, 四川成都 611731
2. 电磁空间认知与智能控制技术国家级重点实验室, 北京 100089

×
，邵士海^1,2

机构：

1. 电子科技大学通信抗干扰全国重点实验室, 四川成都 611731
2. 电磁空间认知与智能控制技术国家级重点实验室, 北京 100089

×
，唐友喜^1,2

机构：

1. 电子科技大学通信抗干扰全国重点实验室, 四川成都 611731
2. 电磁空间认知与智能控制技术国家级重点实验室, 北京 100089

×

1. 电子科技大学通信抗干扰全国重点实验室, 四川成都 611731；
2. 电磁空间认知与智能控制技术国家级重点实验室, 北京 100089；

Impact of transceiver IQ imbalances on cooperative jamming suppression in confidential communications

SONG Changqing^1,2

Affiliation：

1. National Key Laboratory of Wireless Communications, University of Electronic Science and Technology of China, Chengdu 611731 , China
2. Laboratory of Electromagnetic Space Cognition and Intelligent Control, Beijing 100089 , China

×
，CHEN Wenwen^1,2

Affiliation：

1. National Key Laboratory of Wireless Communications, University of Electronic Science and Technology of China, Chengdu 611731 , China
2. Laboratory of Electromagnetic Space Cognition and Intelligent Control, Beijing 100089 , China

×
，ZHAO Hongzhi^1,2

Affiliation：

1. National Key Laboratory of Wireless Communications, University of Electronic Science and Technology of China, Chengdu 611731 , China
2. Laboratory of Electromagnetic Space Cognition and Intelligent Control, Beijing 100089 , China

×
，SHAO Shihai^1,2

Affiliation：

1. National Key Laboratory of Wireless Communications, University of Electronic Science and Technology of China, Chengdu 611731 , China
2. Laboratory of Electromagnetic Space Cognition and Intelligent Control, Beijing 100089 , China

×
，TANG Youxi^1,2

Affiliation：

1. National Key Laboratory of Wireless Communications, University of Electronic Science and Technology of China, Chengdu 611731 , China
2. Laboratory of Electromagnetic Space Cognition and Intelligent Control, Beijing 100089 , China

×

1. National Key Laboratory of Wireless Communications, University of Electronic Science and Technology of China, Chengdu 611731 , China；
2. Laboratory of Electromagnetic Space Cognition and Intelligent Control, Beijing 100089 , China；

作者简介:

宋长庆（1996—），男，江苏徐州人，博士研究生，E-mail：202011220616@std.uestc.edu.cn；

赵宏志，男，河北栾城人，教授，博士，博士生导师，E-mail：lyn@uestc.edu.cn

通讯作者:

赵宏志，男，河北栾城人，教授，博士，博士生导师，E-mail：lyn@uestc.edu.cn

中图分类号:TN975

文献标识码:A

文章编号:1001-2486(2023)06-064-07

DOI:10.11887/j.cn.202306009

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目录contents

摘要 Abstract
关键词 Keywords
1 系统模型
1.1 跳频发射机
1.2 接收机
1.2.1 IQ混频
1.2.2 协作干扰抑制
2 IQ通道失衡下系统性能分析
2.1 接收信号成分分析
2.2 协作干扰抑制性能
3 系统仿真与性能分析
4 结论
参考文献

摘要

针对同时存在恶意干扰与非法窃听的通信环境，提出一种协作干扰(cooperative jamming, CJ)掩护的保密通信架构，收发信机之间采用跳频技术躲避恶意干扰，并采用协作干扰技术阻塞非法窃听。但该架构的通信带宽较大，会在收发频率振荡器中引起显著的同相和正交（in-phase and quadrature, IQ）通道失衡。鉴于此，对收发IQ通道失衡引起的信号失真进行数学建模，给出接收机处信干噪比的数学表达式，并给出干扰抑制比的闭合表达式。仿真结果表明，收发IQ通道失衡引起的信号失真的功率远大于热噪声功率。随着收发IQ通道失衡加剧，所提架构的信干噪比和干扰抑制比性能均会急剧下降，当幅度和相位失衡分别达到0.95和π/50时，信干噪比和干扰抑制比均损失了47 dB。

Abstract

A CJ(cooperative jamming) masked secure communication architecture was proposed for confidential communications when malicious interference and illegal eavesdropping coexist. Thereinto, the FH(frequency-hopping) technology was adopted in the transceiver to avoid malicious interference, and the CJ technology was employed to block illegal eavesdropping. Nevertheless, the proposed architecture employs a wide frequency bandwidth, which will raise nonnegligible IQ(in-phase and quadrature) imbalances at the transceiver oscillators. In view of this, the mathematical modeling was conducted on the signal distortion caused by the imbalance of the receiving and transmitting IQ channels, a mathematical expression for SDNR(the signal to distortion-plus-noise ratio) at the receiver was provided, and a closed-form expression for the system CJSR(CJ suppression ratio) was derived. Simulation results show that the power of the signal distortion raised by transceiver IQ imbalance is much greater than that of the thermal noise. Besides, both the SDNR and CJSR will decline sharply as the transceiver IQ imbalance deteriorates, and when the magnitude and phase imbalance are 0.95 and π/50 respectively, both the SDNR and CJSR performance will deteriorate 47 dB.

关键词

协作干扰；跳频；同相和正交通道失衡；干扰抑制比

Keywords

cooperative jamming ； frequency hopping ； in-phase and quadrature imbalance ； jamming suppression ratio

近年来无线通信中网络连接数量迅猛增长^[1]，但无线通信的开放特性使得通信信息容易遭受恶意干扰与非法窃听^[2-3]。物理层安全技术可以有效地提升系统保密性能，因此受到了广泛关注与研究。
跳频与协作干扰技术可以有效地提升系统的物理层安全性能。一方面，跳频技术通过不断改变发射信号的中心频率，有效避免了恶意电磁干扰^[4-5]。但在强窃听的情况下，窃听装置仍能够估计出跳频参数^[6-7]，进而可以窃听到保密信息。另一方面，协作干扰可以有效地恶化窃听信道质量、阻塞非法窃听^[8]。己方接收机可以利用协作干扰的先验信息进行协作干扰重构与抑制，将接收协作干扰抑制到热噪声水平；而非法窃听机做不到这一点，窃听信道急剧恶化，非法窃听遭受阻塞^[9-10]。文献^[11-13]研究了协作干扰对无人机通信、多输入多输出通信安全性能的影响，文献^[10]与文献^[14]分别研究了定频通信系统中相位噪声、时频同步误差下的协作干扰抑制性能。进一步地，文献^[15]研制了协作干扰辅助的安全通信实验测试台，验证了协作干扰技术的工程可行性。然而当遭受恶意干扰时，我方设备将面临通信阻塞的风险。为了在同时存在恶意干扰和非法窃听时保证通信安全，本文提出了一种协作干扰掩护的保密通信架构。其中，发射机同时发送协作干扰和保密信息阻塞非法窃听，并采用跳频技术躲避恶意干扰。在接收端，接收机利用先验信息依次执行跳频同步、协作干扰重构与抑制操作^[10]来消除协作干扰对通信系统性能的影响。
理想情况下，接收机可以利用先验信息将接收信号中的协作干扰分量完美抑制^[16]。但在实际通信系统中，收发信机模拟前端的频率振荡器中不可避免地会存在同相和正交（in-phase and quadrature，IQ）通道失衡^[16]，这会对传输信号造成失真^[17-18]，进而降低系统的协作干扰抑制性能^[19]。同时，跳频架构具有较大的通信带宽，部分通信频点的中心频率很高，这将进一步加剧收发信机处的IQ通道失衡问题^[20]。
鉴于上述问题，本文提出了一种协作干扰掩护的保密通信架构，并对收发信机中的IQ通道失衡问题进行了数学建模。此外，本文给出了接收机处信干噪比的表达式，以衡量收发信机处IQ通道失衡引起的信号失真程度；并给出了干扰抑制比的闭式解，以评估接收机处的协作干扰抑制能力。
1 系统模型
图1展示了协作干扰掩护下的保密通信架构。其中，发射机同时发送协作干扰序列c（n）与保密信息序列s（n）以降低窃听信道质量，并且在收发信机之间采用跳频技术以躲避恶意电磁干扰。发射的协作干扰服从零均值高斯分布并与保密信息不相关，传输信道假设为加性高斯白噪声信道^[14]。
图1 协作干扰掩护的保密通信架构
Fig.1 Cooperative jamming-shielded secure communication architecture
1.1 跳频发射机
在发射机中，经过数模转换后，保密信息和协作干扰的基带复合信号可以表示为

x (t) = s (t) + c (t) = x_{i} (t) + j x_{q} (t)

(1)

式中，x_i（t）和x_q（t）分别表示x（t）的实部和虚部，保密信息s（t）和协作干扰c（t）的功率分别为P_s和P_c。
接着，基带复合信号x（t）通过IQ混频器来进行跳频调制。发射机处频率振荡器产生的第k跳载波的IQ分量分别可以表示为

u_{i} (t) = c o s (2 π f_{k} t) g (t - k T)

(2)

u_{q} (t) = β_{T} s i n (2 π f_{k} t + θ_{T}) g (t - k T)

(3)

其中：f_k是第k跳载波的中心频率，k是正整数；β_T和θ_T分别表示发射机处振荡器的幅度失衡和相位失衡；g（t-kT）表示第k跳信号的持续时间，当（k-1）T≤t≤kT时取值为1，否则为0。经过IQ混频器后，得到的第k跳发射信号可以表示为

\begin{matrix} x_{I Q}^{T x} (t) = 2 [x_{i} (t) u_{i} (t) - x_{q} (t) u_{q} (t)] \\ = e^{j 2 π f_{k} t} [x_{i} (t) + j β_{T} e^{j θ_{T}} x_{q} (t)] g (t - k T) + \\ e^{- j 2 π f_{k} t} [x_{i} (t) - j β_{T} e^{- j θ_{T}} x_{q} (t)] g (t - k T) \\ = e^{j 2 π f_{k} t} [G_{T_{1}} x (t) + G_{T_{2}}^{*} x^{*} (t)] g (t - k T) + \\ e^{- j 2 π f_{k} t} [G_{T_{1}}^{*} x^{*} (t) + G_{T_{2}} x (t)] g (t - k T) \end{matrix}

(4)

式中， $G_{T_{1}} = \frac{1 + β_{T} e^{j θ_{T}}}{2} ， G_{T_{2}} = \frac{1 - β_{T} e^{- j θ_{T}}}{2}$ 。
当发射机处不存在IQ通道失衡时，即β_T=1和θ_T=0，式（4）变为

x_{I Q}^{T x} (t) = [x (t) e^{j 2 π f_{k} t} + x^{*} (t) e^{- j 2 π f_{k} t}] g (t - k T)

(5)

通过比较式（4）和式（5）可以发现，发射机处的IQ通道失衡会引起信号失真，引入非预期的失真成分。下一节中，将进一步分析接收机处IQ通道失衡对接收信号造成的失真。
1.2 接收机
1.2.1 IQ混频
假设发射信号在传播过程中经历了平坦慢衰落。跳频接收机处，射频接收信号的数学表达式为

y (t) = h x_{I Q}^{T x} (t - τ) + w_{r} (t)

(6)

式中，h和τ分别表示信道增益和延迟，w_r（t）表示热噪声分量。
为了分离出IQ通道失衡对系统性能的影响，本文假设接收机可以完美地实现跳频同步，即传播延迟的估计值 $\hat{τ}$ 满足 $\hat{τ} = τ$ 。利用估计的时延值对接收频率振荡器产生的跳频载波进行补偿，则第k跳载波的IQ分量经时延补偿后可以表示为

v_{I} (t) = c o s (2 π f_{k}^{'} t) g (t - τ - k T)

(7)

v_{Q} (t) = β_{R} s i n (2 π f_{k}^{'} t + θ_{R}) g (t - τ - k T)

(8)

其中： $f_{k}^{'} = f_{k} - f_{o}$ 表示第k跳本地载波的中心频率， f_o表示接收信号与本地载波间的频率偏移；β_R和θ_R表示接收频率振荡器的幅度失衡和相位失衡。
接收信号依次通过IQ混频、低通滤波后，得到的基带接收信号可以表示为

\begin{matrix} y_{I Q}^{R x} (t) = Φ_{L P F} \{y (t) v_{I} (t)\} - j Φ_{L P F} \{y (t) v_{Q} (t)\} \\ = ({\tilde{h}}_{1} G_{T_{1}} G_{R_{1}} e^{j 2 π f_{o} t} + {\tilde{h}}_{2} G_{T_{2}} G_{R_{2}} e^{- j 2 π f_{o} t}) x (t - τ) + \\ ({\tilde{h}}_{1} G_{T_{2}}^{*} G_{R_{1}} e^{j 2 π f_{o} t} + {\tilde{h}}_{2} G_{T_{1}}^{*} G_{R_{2}} e^{- j 2 π f_{o} t}) x^{*} (t - τ) + \\ {\tilde{w}}_{r} (t) \\ = y_{s} (t) + y_{c} (t) + y_{i m} (t) + {\tilde{w}}_{r} (t) \end{matrix}

(9)

式中：Φ_LPF{·}表示低通滤波操作； ${\tilde{h}}_{1} = h e^{- j 2 π f_{k} τ} ， {\tilde{h}}_{2} = h e^{j 2 π f_{k} τ}; G_{R_{1}} = \frac{1 + β_{R} e^{- j θ_{R}}}{2} ， G_{R_{2}} = \frac{1 - β_{R} e^{j θ_{R}}}{2}; {\tilde{w}}_{r} （ t ）$ 表示复热噪声分量；y_s（t）、y_c（t）和y_im（t）分别表示保密信号分量、协作干扰分量和镜像分量，且满足式（10）~（12）。

\begin{matrix} y_{s} (t) = ({\tilde{h}}_{1} G_{T_{1}} G_{R_{1}} e^{j 2 π f_{o} t} + {\tilde{h}}_{2} G_{T_{2}} G_{R_{2}} e^{- j 2 π f_{o} t}) s (t - τ) \\ \overset{(a)}{\approx} {\tilde{h}}_{1} G_{T_{1}} G_{R_{1}} e^{j 2 π f_{o} t} s (t - τ) \end{matrix}

(10)

\begin{matrix} y_{c} (t) = ({\tilde{h}}_{1} G_{T_{1}} G_{R_{1}} e^{j 2 π f_{o} t} + {\tilde{h}}_{2} G_{T_{2}} G_{R_{2}} e^{- j 2 π f_{o} t}) c (t - τ) \\ \overset{(a)}{\approx} {\tilde{h}}_{1} G_{T_{1}} G_{R_{1}} e^{j 2 π f_{o} t} c (t - τ) \end{matrix}

(11)

y_{i m} (t) = ({\tilde{h}}_{1} G_{T_{2}}^{*} G_{R_{1}} e^{j 2 π f_{o} t} + {\tilde{h}}_{2} G_{T_{1}}^{*} G_{R_{2}} e^{- j 2 π f_{o} t}) x^{*} (t - τ)

(12)

由于 $G_{T_{2}} G_{R_{2}}$ 的幅值远小于 $G_{T_{1}} G_{R_{1}}$ 的幅值^[21]，式（10）、式（11）中近似操作（a）不影响所得结论的正确性。
1.2.2 协作干扰抑制
完成IQ混频后，需要进行协作干扰重构与抑制操作，以抑制基带接收信号 $y_{I Q}^{R x} （ t ）$ 中的协作干扰分量。协作干扰抑制过程主要分为三个阶段^[10]：
1）接收协作干扰参数估计：利用本地参考协作干扰，估计接收干扰的信道衰落^[22]、时频偏移^[23-24]等信道信息；
2）本地协作干扰特征重构：将第一阶段估得的信道信息补偿到本地参考协作干扰中，完成本地协作干扰特征重构；
3）协作干扰抑制：将接收混合信号减去本地重构的协作干扰，完成协作干扰抑制。
为了分离出IQ通道失衡的影响，假设等效信道增益 ${\tilde{h}}_{1}$ 和频率偏移f_o已被完美估计。将估计值补偿到本地参考协作干扰，得到的本地重构协作干扰可以表示为

{\hat{y}}_{c} (t) = {\tilde{h}}_{1} e^{j 2 π f_{o} t} c (t - τ)

(13)

从 $y_{I Q}^{R x} （ t ）$ 中减去 ${\hat{y}}_{c} （ t ）$ ，可以抑制掉接收信号中的协作干扰分量，所得基带接收信号可以表示为

\tilde{y} (t) = y_{s} (t) + Δ y_{c} (t) + y_{i m} (t) + {\tilde{w}}_{r} (t)

(14)

其中

Δ y_{c} (t) = y_{c} (t) - {\hat{y}}_{c} (t) \overset{(a)}{\approx} {\tilde{h}}_{1} (G_{T_{1}} G_{R_{1}} - 1) e^{j 2 π f_{o} t} c (t - τ)

(15)

表示残余协作干扰分量，并且由式（11）可知，近似操作（a）不影响所得结论的正确性。
理想情况下，收发信机的频率振荡器中不存在IQ通道失衡，即β_T=β_R=1且θ_T=θ_R=0，由此可以得到 $G_{T_{1}}$ = $G_{R_{1}}$ =1且 $G_{T_{2}}$ = $G_{R_{2}}$ =0。在这种情况下，Δy_c（t）=0，此时接收信号中的协作干扰分量可以被完美抑制。但在实际系统中，频率振荡器处总会存在IQ通道失衡问题。从式（15）可以看出，收发频率振荡器中的IQ通道失衡会引入残余协作干扰分量，进而会降低干扰抑制性能。在下一节中，将详细分析跳频系统中IQ通道失衡对干扰抑制性能的影响。
2 IQ通道失衡下系统性能分析
在混频操作中，频率振荡器中的IQ通道失衡会引起信号失真，进而会降低协作干扰抑制效果。本部分先通过信干噪比来衡量IQ通道失衡引起的信号失真，再通过干扰抑制比来分析所提架构的干扰抑制性能。为了简便而不失一般性，文中假设 $y_{I Q}^{R x} （ t ）$ 不同分量之间具有频率无关性^[21]。
2.1 接收信号成分分析
在接收机处，复合信号 $y_{I Q}^{R x} （ t ）$ 中的保密信息分量、协作干扰分量、镜像分量的功率分别如式（16）~（19）所示，其中， $P {\cdot}$ 表示求功率操作，近似操作（b）成立的条件是收发频率振荡器处的IQ通道失衡可以忽略不计，即β_T≈β_R≈1，θ_T≈θ_R≈0。该近似操作展示了具有理想收发频率振荡器的系统特例，此时保密信息与协作干扰的功率分别为 $h^{2} P_{s}$ 和 $h^{2} P_{c}$ 。

\begin{matrix} P \{y_{s} (t)\} = \frac{h^{2} P_{s}}{16} (1 + β_{T}^{2} + 2 β_{T} c o s θ_{T}) (1 + β_{R}^{2} + \\ 2 β_{R} c o s θ_{R}) \\ \overset{(b)}{\approx} h^{2} P_{s} \end{matrix}

(16)

\begin{matrix} P \{y_{c} (t)\} = \frac{h^{2} P_{c}}{16} (1 + β_{T}^{2} + 2 β_{T} c o s θ_{T}) (1 + β_{R}^{2} + \\ 2 β_{R} c o s θ_{R}) \\ \overset{(b)}{\approx} h^{2} P_{c} \end{matrix}

(17)

\begin{matrix} P \{Δ y_{c} (t)\} = \frac{h^{2} P_{c} (1 + β_{T}^{2} + 2 β_{T} c o s θ_{T}) (1 + β_{R}^{2} + 2 β_{R} c o s θ_{R})}{16} + \\ \frac{h^{2} P_{c}}{2} [1 - β_{T} c o s θ_{T} - β_{R} c o s θ_{R} - β_{T} β_{R} c o s (θ_{T} - θ_{R})] \end{matrix}

(18)

\begin{matrix} P \{y_{i m} (t)\} = \frac{h^{2} (P_{s} + P_{c})}{16} (1 + β_{T}^{2} - 2 β_{T} c o s θ_{T}) \cdot \\ (1 + β_{R}^{2} + 2 β_{R} c o s θ_{R}) + \\ \frac{h^{2} (P_{s} + P_{c})}{16} (1 + β_{T}^{2} + 2 β_{T} c o s θ_{T}) \cdot \\ (1 + β_{R}^{2} - 2 β_{R} c o s θ_{R}) + \\ \frac{h^{2} (P_{s} + P_{c})}{8} \{c o s 4 π (f_{o} t - f_{k} τ) + \\ β_{T}^{2} β_{R}^{2} c o s [4 π (f_{o} t - f_{k} τ) + 2 θ_{T} - 2 θ_{R}]\} - \\ \frac{h^{2} (P_{s} + P_{c})}{8} \{β_{T}^{2} c o s [4 π (f_{o} t - f_{k} τ) + 2 θ_{T}] + \\ β_{R}^{2} c o s [4 π (f_{o} t - f_{k} τ) - 2 θ_{R}]\} \end{matrix}

(19)

此外，由于收发信机之间存在频率偏移，可以发现y_im（t）的功率是关于时间t的函数，其平均功率如式（20）所示，其中 $E {\cdot}$ 表示求期望操作。
$\begin{matrix} P \{\bar{y_{i m} (t)}\} = E \{P \{y_{i m} (t)\}\} \\ = \frac{h^{2} (P_{s} + P_{c})}{16} (1 + β_{T}^{2} - 2 β_{T} c o s θ_{T}) \cdot \end{matrix}$

\begin{matrix} (1 + β_{R}^{2} + 2 β_{R} c o s θ_{R}) + \\ \frac{h^{2} (P_{s} + P_{c})}{16} (1 + β_{T}^{2} + 2 β_{T} c o s θ_{T}) \cdot \\ (1 + β_{R}^{2} - 2 β_{R} c o s θ_{R}) \end{matrix}

(20)

值得注意的是，随着硬件的升级与制作工艺的提升，实际收发频率振荡器中的IQ通道失衡比较小。由式（16）和式（17）可知，经过IQ调制后，y_s（t）和y_c（t）的功率基本保持不变。然而从式（18）和式（19）中可以发现，即使IQ通道失衡很微弱，Δy_c（t）和y_im（t）的功率也会随着IQ通道失衡的变化而急剧变化。
可以发现，接收信号 $y_{I Q}^{R x} （ t ）$ 和干扰抑制后的基带接收信号 ${\hat{y}}_{c} （ t ）$ 均包含两类分量。一类是仅包含期望的保密信号分量y_s（t）；另一类包含非期望的干扰分量，包括y_c（t）、Δy_c（t）、y_im（t）和 ${\tilde{w}}_{r} （ t ）$ 。鉴于此，本文采用信干噪比来表征 $y_{I Q}^{R x} （ t ）$ 和 ${\hat{y}}_{c} （ t ）$ 中两类分量的功率比，以衡量由IQ通道失衡引起的信号失真程度。
协作干扰抑制前，接收信号 $y_{I Q}^{R x} （ t ）$ 中的信干噪比可以表示为

Λ = \frac{P \{y_{s} (t)\}}{P \{y_{c} (t)\} + P \{\bar{y_{i m} (t)}\} + P \{{\tilde{w}}_{r} (t)\}}

(21)

协作干扰抑制后，所得基带信号 ${\hat{y}}_{c} （ t ）$ 处的信干噪比为

Λ_{Δ} = \frac{P \{y_{s} (t)\}}{P \{Δ y_{c} (t)\} + P \{\bar{y_{i m} (t)}\} + P \{{\tilde{w}}_{r} (t)\}}

(22)

当协作干扰分量被彻底抑制， ${\hat{y}}_{c} （ t ）$ 处的信干噪比将达到上界，为

Λ_{U} = \frac{P \{y_{s} (t)\}}{P \{\bar{y_{i m} (t)}\} + P \{{\tilde{w}}_{r} (t)\}}

(23)

由式（21）~（23）可知，协作干扰抑制操作可以有效地抑制协作干扰分量，进而提升接收机处的信干噪比性能。但IQ通道失衡会降低接收机的干扰抑制能力，使得在接收机处无法达到预期的信干噪比上界。
2.2 协作干扰抑制性能
在采用协作干扰技术的通信系统中，常常采用干扰抑制比来分析系统的协作干扰抑制性能^[25-26]。干扰抑制比的定义为协作干扰抑制前后非期望信号分量的功率比，其中非期望信号分量包含协作干扰分量、镜像分量和热噪声。
根据上述定义，存在IQ通道失衡时，协作干扰掩护下的保密通信系统中的干扰抑制比为

Γ ≜ \frac{P \{y_{c} (t)\} + P \{\bar{y_{i m} (t)}\} + P \{{\tilde{w}}_{r} (t)\}}{P \{Δ y_{c} (t)\} + P \{\bar{y_{i m} (t)}\} + P \{{\tilde{w}}_{r} (t)\}}

(24)

当仅考虑接收频率振荡器处的IQ通道失衡，即β_T=1且θ_T=1时，干扰抑制比可以简化为

Γ^{R} ≜ \frac{P \{y_{c}^{R} (t)\} + P \{\bar{y_{i m}^{R} (t)}\} + P \{{\tilde{w}}_{r} (t)\}}{P \{Δ y_{c}^{R} (t)\} + P \{\bar{y_{i m}^{R} (t)}\} + P \{{\tilde{w}}_{r} (t)\}}

(25)

其中，

P \{y_{c}^{R} (t)\} = \frac{h^{2} P_{c}}{4} (1 + β_{R}^{2} + 2 β_{R} c o s θ_{R})

(26)

P \{Δ y_{c}^{R} (t)\} = h^{2} P_{c} (\frac{1 + β_{R}^{2} + 2 β_{R} c o s θ_{R}}{4} - β_{R} c o s θ_{R})

(27)

P \{\bar{y_{i m}^{R} (t)}\} = \frac{h^{2} (P_{s} + P_{c})}{4} (1 + β_{R}^{2} - 2 β_{R} c o s θ_{R})

(28)

当仅考虑发射频率振荡器处的IQ通道失衡，即β_R=1且θ_R=1时，干扰抑制比可以简化为

Γ^{T} = \frac{P \{y_{c}^{T} (t)\} + P \{\bar{y_{i m}^{T} (t)}\} + P \{{\tilde{w}}_{r} (t)\}}{P \{Δ y_{c}^{T} (t)\} + P \{\bar{y_{i m}^{T} (t)}\} + P \{{\tilde{w}}_{r} (t)\}}

(29)

其中，

P \{y_{c}^{T} (t)\} = \frac{h^{2} P_{c}}{4} (1 + β_{T}^{2} + 2 β_{T} c o s θ_{T})

(30)

P \{Δ y_{c}^{T} (t)\} = h^{2} P_{c} (\frac{1 + β_{T}^{2} + 2 β_{T} c o s θ_{T}}{4} - β_{T} c o s θ_{T})

(31)

P \{\bar{y_{i m}^{T} (t)}\} = \frac{h^{2} (P_{s} + P_{c})}{4} (1 + β_{T}^{2} - 2 β_{T} c o s θ_{T})

(32)

当收发频率振荡器处的IQ通道失衡均可以忽略不计，即β_T=β_R=1，θ_T=θ_R=0时，可得 $P \{Δ y_{c} （ t ）\} = P \{\bar{y_{i m} （ t ）}\} = 0 且 P \{y_{c} （ t ）\} = h^{2} P_{c}$ 。此时，干扰抑制比可以简化为

Γ^{P} = \frac{h^{2} P_{c} + P \{{\tilde{w}}_{r} (t)\}}{P \{{\tilde{w}}_{r} (t)\}}

(33)

由式（24）~（33）可知，收发频率振荡器处的IQ通道失衡会引起干扰抑制比性能损失，并且系统中使用的频率振荡器越多，IQ通道失衡造成的干扰抑制比损失越严重。
3 系统仿真与性能分析
基于图1所示的保密架构，本节利用MATLAB工具进行了数值仿真，仿真条件如表1所示。在本节中，先仿真了接收复合信号中各分量之间的功率关系，然后分别仿真了系统的信干噪比和干扰抑制比性能。为了结果的简洁且不失一般性，假设收发频率振荡器性能一致，即β_T=β_R=β且θ_T=θ_R=θ。
表1 仿真参数设置
Tab.1 Simulation conditions
图2给出了干扰抑制前后接收信号中不同分量之间的功率关系。由图可以发现，在给定的仿真条件下，协作干扰功率约等于保密信息功率，并且对于不同的幅度、相位失衡，它们的功率都近似保持恒定，验证了式（16）和式（17）中的结论。此外，除了在零点附近，残余协作干扰和镜像分量的功率都远大于噪声功率，表明系统中的IQ通道失衡会引起显著的信号失真和干扰抑制性能损失。此外，镜像分量的功率会随着|β-1|或θ的增加而增加，表明随着收发频率振荡器中幅度失衡或相位失衡的增大，非期望的镜像分量功率也会显著增加，进而加剧系统性能损失。
图2 接收混合信号中各成分的功率分析
Fig.2 Power analysis of various components in the received composite signal
图3给出了在不同的收发幅度、相位失衡下，干扰抑制前后接收机处的信干噪比性能仿真。可以发现，接收机中干扰抑制操作可以有效地提升接收机处信干噪比性能，即 $Λ_{Δ} ≫ Λ \approx 0 d B$ ，验证了协作干扰抑制操作的有效性。此外，收发频率振荡器处的IQ通道失衡会降低系统的信干噪比性能，并且随着IQ通道失衡的恶化，信干噪比性能损失加剧。由于IQ通道失衡的存在，干扰抑制后的信干噪比通常达不到其理论上限；仅当接收信号中的协作干扰分量被完美抑制时才会达到上界，此时有 $Λ_{Δ} = Λ_{U} = h^{2} P / σ^{2}$ 。
图3 收发IQ通道失衡下信干噪比性能变化趋势
Fig.3 SDNR performance under transceiver IQ imbalances
图4给出了在不同的IQ通道失衡下，所提架构协作干扰抑制能力的变化趋势。可以发现，即使存在IQ通道失衡，所采用方法的干扰抑制能力也远大于其理论下界，验证了协作干扰抑制操作的有效性。但是，干扰抑制比总是小于其理论上界，并且随着IQ通道失衡的加剧，它们之间的差距会变大，表明干扰抑制比性能损失会随着IQ通道失衡的增大而加剧。此外，与只有发射或接收频率振荡器处存在IQ通道失衡的情形相比，当收发振荡器处均存在IQ通道失衡时，系统的干扰抑制比性能会进一步降低，表明系统中使用的频率振荡器越多，IQ通道失衡引起的性能损失越严重。
图4 收发IQ通道失衡下干扰抑制比性能变化趋势
Fig.4 CJSR performance under transceiver IQ imbalances
4 结论
本文提出了一种协作干扰掩护的保密通信架构，适应于同时存在恶意干扰与窃听的通信环境。在此基础上，对收发频率振荡器处由IQ通道失衡引起的信号失真程度进行了建模，并给出了信干噪比和干扰抑制比的闭合表达式。理论分析与仿真结果表明，由IQ通道失衡引起的信号失真功率远大于热噪声功率。此外，随着幅度或相位失衡的不断恶化，接收机处信干噪比和干扰抑制比性能均会急剧恶化。
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- [13] 孙惜媛,解志斌,宋科宁,等.基于MIMO协作干扰对齐网络的保密通信算法[J].火力与指挥控制,2021,46(6):21-26,31.SUN X Y,XIE Z B,SONG K N,et al.Secure communication method in MIMO cooperative interference alignment network[J].Fire Control & Command Control,2021,46(6):21-26,31.(in Chinese)
- [14] 郭文博,宋长庆,文荣,等.不完美时间同步下物理层安全协同干扰功率分配[J].通信学报,2019,40(11):86-93.GUO W B,SONG C Q,WEN R,et al.Cooperative interference power allocation in physical layer security under imperfect time synchronization[J].Journal on Communications,2019,40(11):86-93.(in Chinese)
- [15] 郭文博,宋长庆,张译丹,等.电磁频谱伞罩自干扰抑制实验验证[J].系统工程与电子技术,2021,43(9):2637-2641.GUO W B,SONG C Q,ZHANG Y D,et al.Experimental testbed of self-interference suppression in electromagnetic spectrum umbrella[J].Systems Engineering and Electronics,2021,43(9):2637-2641.(in Chinese)
- [16] 刘思琦,王天宇,王少尉.OFDM系统中深度神经网络指导的IQ不平衡补偿算法[J].国防科技大学学报,2020,42(4):7-11.LIU S Q,WANG T Y,WANG S W.IQ imbalance compensation algorithm with deep neural network in OFDM systems[J].Journal of National University of Defense Technology,2020,42(4):7-11.(in Chinese)
- [17] SAKAI M,LIN H,YAMASHITA K.Adaptive cancellation of self-interference in full-duplex wireless with transmitter IQ imbalance[C]//Proceedings of 2014 IEEE Global Communications Conference,2014:3220-3224.
- [18] HAKKARAINEN A,WERNER J,DANDEKAR K R,et al.Widely-linear beamforming and RF impairment suppression in massive antenna arrays[J].Journal of Communications and Networks,2013,15(4):383-397.
- [19] MOHAMMADIAN A,TELLAMBURA C,VALKAMA M.Analysis of self-interference cancellation under phase noise,CFO,and IQ imbalance in GFDM full-duplex transceivers[J].IEEE Transactions on Vehicular Technology,2020,69(1):700-713.
- [20] TARIGHAT A,SAYED A H.MIMO OFDM receivers for systems with IQ imbalances[J].IEEE Transactions on Signal Processing,2005,53(9):3583-3596.
- [21] KORPI D,ANTTILA L,SYRJÄLÄ V,et al.Widely linear digital self-interference cancellation in direct-conversion full-duplex transceiver[J].IEEE Journal on Selected Areas in Communications,2014,32(9):1674-1687.
- [22] HUSSEIN H S,HUSSEIN S,MOHAMED E M.Efficient channel estimation techniques for MIMO systems with 1-bit ADC[J].China Communications,2020,17(5):50-64.
- [23] D′AMICO A A,COLAVOLPE G,FOGGI T,et al.Timing synchronization and channel estimation in free-space optical OOK communication systems[J].IEEE Transactions on Communications,2022,70(3):1901-1912.
- [24] SIMON E P,ROS L,HIJAZI H,et al.Joint carrier frequency offset and channel estimation for OFDM systems via the EM algorithm in the presence of very high mobility[J].IEEE Transactions on Signal Processing,2012,60(2):754-765.
- [25] GUO W B,SONG C Q,XIA X J,et al.Analysis of cooperative jamming cancellation with imperfect time synchronization in physical layer security[J].IEEE Wireless Communications Letters,2021,10(2):335-338.
- [26] LI C X,ZHAO H Z,WU F,et al.Digital self-interference cancellation with variable fractional delay FIR filter for full-duplex radios[J].IEEE Communications Letters,2018,22(5):1082-1085.

图1 协作干扰掩护的保密通信架构

Fig.1 Cooperative jamming-shielded secure communication architecture

表1 仿真参数设置

Tab.1 Simulation conditions

图2 接收混合信号中各成分的功率分析

Fig.2 Power analysis of various components in the received composite signal

图3 收发IQ通道失衡下信干噪比性能变化趋势

Fig.3 SDNR performance under transceiver IQ imbalances

图4 收发IQ通道失衡下干扰抑制比性能变化趋势

Fig.4 CJSR performance under transceiver IQ imbalances

图表 1/1

基本信息

中图分类号: TN975
文献标识码: A
DOI: 10.11887/j.cn.202306009
文章编号: 1001-2486(2023)06-064-07

基金信息

国家自然科学基金资助项目（U19B2014，62071094，61901396）；

稿件历史

收稿日期: 2021-11-29

参考文献

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[10] QUAN X,LIU Y,SHAO S H,et al.Impacts of phase noise on digital self-interference cancellation in full-duplex communications[J].IEEE Transactions on Signal Processing,2017,65(7):1881-1893.
[11] ZHANG G C,WU Q Q,CUI M,et al.Securing UAV communications via joint trajectory and power control[J].IEEE Transactions on Wireless Communications,2019,18(2):1376-1389.
[12] CAI Y L,CUI F Y,SHI Q J,et al.Dual-UAV-enabled secure communications:joint trajectory design and user scheduling[J].IEEE Journal on Selected Areas in Communications,2018,36(9):1972-1985.
[13] 孙惜媛,解志斌,宋科宁,等.基于MIMO协作干扰对齐网络的保密通信算法[J].火力与指挥控制,2021,46(6):21-26,31.SUN X Y,XIE Z B,SONG K N,et al.Secure communication method in MIMO cooperative interference alignment network[J].Fire Control & Command Control,2021,46(6):21-26,31.(in Chinese)
[14] 郭文博,宋长庆,文荣,等.不完美时间同步下物理层安全协同干扰功率分配[J].通信学报,2019,40(11):86-93.GUO W B,SONG C Q,WEN R,et al.Cooperative interference power allocation in physical layer security under imperfect time synchronization[J].Journal on Communications,2019,40(11):86-93.(in Chinese)
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[16] 刘思琦,王天宇,王少尉.OFDM系统中深度神经网络指导的IQ不平衡补偿算法[J].国防科技大学学报,2020,42(4):7-11.LIU S Q,WANG T Y,WANG S W.IQ imbalance compensation algorithm with deep neural network in OFDM systems[J].Journal of National University of Defense Technology,2020,42(4):7-11.(in Chinese)
[17] SAKAI M,LIN H,YAMASHITA K.Adaptive cancellation of self-interference in full-duplex wireless with transmitter IQ imbalance[C]//Proceedings of 2014 IEEE Global Communications Conference,2014:3220-3224.
[18] HAKKARAINEN A,WERNER J,DANDEKAR K R,et al.Widely-linear beamforming and RF impairment suppression in massive antenna arrays[J].Journal of Communications and Networks,2013,15(4):383-397.
[19] MOHAMMADIAN A,TELLAMBURA C,VALKAMA M.Analysis of self-interference cancellation under phase noise,CFO,and IQ imbalance in GFDM full-duplex transceivers[J].IEEE Transactions on Vehicular Technology,2020,69(1):700-713.
[20] TARIGHAT A,SAYED A H.MIMO OFDM receivers for systems with IQ imbalances[J].IEEE Transactions on Signal Processing,2005,53(9):3583-3596.
[21] KORPI D,ANTTILA L,SYRJÄLÄ V,et al.Widely linear digital self-interference cancellation in direct-conversion full-duplex transceiver[J].IEEE Journal on Selected Areas in Communications,2014,32(9):1674-1687.
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[23] D′AMICO A A,COLAVOLPE G,FOGGI T,et al.Timing synchronization and channel estimation in free-space optical OOK communication systems[J].IEEE Transactions on Communications,2022,70(3):1901-1912.
[24] SIMON E P,ROS L,HIJAZI H,et al.Joint carrier frequency offset and channel estimation for OFDM systems via the EM algorithm in the presence of very high mobility[J].IEEE Transactions on Signal Processing,2012,60(2):754-765.
[25] GUO W B,SONG C Q,XIA X J,et al.Analysis of cooperative jamming cancellation with imperfect time synchronization in physical layer security[J].IEEE Wireless Communications Letters,2021,10(2):335-338.
[26] LI C X,ZHAO H Z,WU F,et al.Digital self-interference cancellation with variable fractional delay FIR filter for full-duplex radios[J].IEEE Communications Letters,2018,22(5):1082-1085.

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保密通信中同相和正交通道失衡对干扰抑制性能的影响*

Impact of transceiver IQ imbalances on cooperative jamming suppression in confidential communications

摘要

Abstract

关键词

Keywords

1 系统模型

1.1 跳频发射机

(1)

(2)

(3)

(4)

(5)

1.2 接收机

1.2.1 IQ混频

(6)

(7)

(8)

(9)

(10)

(11)

(12)

1.2.2 协作干扰抑制

(13)

(14)

(15)

2 IQ通道失衡下系统性能分析

2.1 接收信号成分分析

(16)

(17)

(18)

(19)

(20)

(21)

(22)

(23)

2.2 协作干扰抑制性能

(24)

(25)

(26)

(27)

(28)

(29)

(30)

(31)

(32)

(33)

3 系统仿真与性能分析

4 结论

参考文献

基本信息

基金信息

稿件历史

参考文献

保密通信中同相和正交通道失衡对干扰抑制性能的影响^*