Survey of Differential Chaotic Communications: Signal Design and Performance Optimization
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摘要: 作为一种低复杂度的非相干信息传输方案，差分混沌通信系统以其良好的抗多径衰落性能而受到广泛关注。近年来，研究者围绕着以差分混沌移位键控(DCSK)为代表的差分混沌通信开展了一系列富有成效的研究，逐渐发展了差分混沌通信的信号设计与性能优化方法。为此，该文从信号帧结构设计、正交多级信号设计、信号星座图设计和多载波信号设计4个层面详细综述了差分混沌通信信号设计的主要研究进展。此外，该文重点总结了面向差分混沌通信的噪声抑制辅助性能优化、索引调制辅助性能优化和混沌成形滤波辅助性能优化等方面的研究工作。Abstract: As a kind of low-complexity and non-coherent information transmission schemes, the differential chaotic communication system has been widely studied because of its good performance against multipath fading. Recently, a series of fruitful researches on Differential Chaos Shift Keying (DCSK) have been carried out, and the signal design and performance optimization for differential chaotic communications have also been developed. Therefore, the main research progresses in signal design of differential chaotic communications are surveyed in detail in the paper from the following four perspectives: design of signal frames, design of orthogonal multilevel signals, design of constellation diagrams and design of multicarrier signals. In addition, the research works on noise suppression aided performance optimization, index modulation aided performance optimization and chaotic shape forming aided performance optimization for differential chaotic communications are summarized in the paper.
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1. 引言
涡旋波束在传播方向上携带轨道角动量(Orbital Angular Momentum, OAM)，使得其坡印廷矢量不再是直线，而是围绕传播轴旋转前进的矢量轨迹，因而涡旋波束的相位波前在垂直于传播方向的横截面上呈现螺旋相位，且具有空心环状的能量分布[1,2]。理论上OAM的模式数l可覆盖全部整数空间，根据模式间的卷积可知，不同OAM模式间存在天然的正交性，因此携带多模式OAM的涡旋波束可从物理层面为频谱资源拓展、无线通信技术提供理论途径。
目前在微波波段，常用的OAM波束激发方式大致可以分为两种：一是利用螺旋相位板(spiral phase plate, SPP)厚度随方位角的变化，在透射波中加载OAM空间相位分布函数[3,4]；另外一种方法则是利用天线阵中不同单元之间的相位差，在电波传播中产生OAM螺旋波前，如环形阵列天线(Uniform Circular Array, UCA)等[5,6]；通过这些方法，人们已经可以高效地进行OAM波束的激发。然而从应用的角度出发，这些方法目前均存在着无法突破的瓶颈和限制。对于螺旋相位板而言，其厚度表达式为lλθ/2π(n–1)，其中n为螺旋相位波板介质材料的折射率。OAM模式数l较大时，将导致螺旋相位板厚度及重量的急剧增加。另外，螺旋相位板是无源器件，无法实现多模式OAM的切换或可调。对于利用天线阵产生OAM的方法而言，无论天线单元尺寸，还是阵列单元的间距，都是与工作波长可比拟的，无法突破工作波长尺度的极限。天线阵所能产生OAM模式的数量直接受到天线阵单元数的制约，这意味着利用天线阵技术在微波波段无法产生l模式数较大的OAM波束。而产生多模式的OAM，则需要更加复杂的馈电网络、大量的移相器等，这无疑会使系统复杂性及成本大大提高[6]。超构表面为解决上述瓶颈问题提供了一种可行的理论方法[7–10]。通过介质分界面上的相位突变替代特定传播距离上的相位累积，由平面结构替代曲面或平板结构，能够极大程度上减小传统螺旋相位板的厚度及重量[11–13]。而通过将变容二极管、开关二极管等电可调器件引入超构表面的设计中，能够为相位的控制提供更高的自由度，从而实现多个OAM模式的切换及跳变[14–16]。
因此，聚焦于微波波段多模式涡旋波束的集成与高效激发，首先从超表面的相位来源及工作机理出发，揭示了多阶整数、奇数模式涡旋波束的高纯度集成机理，通过实验验证了无源式超表面透镜对多模式OAM的激发与调控作用。与此同时，为了探索多模式涡旋波束的动态可切换调控方式，本课题组聚焦于基于有源超表面的OAM波束的激发方式，搭建加载变容二极管的有源超表面系统，在微波波段验证了模式数为1, 2, 3阶涡旋波前的激发与切换。不仅降低了馈电网络对电磁能量的损耗，也摆脱了加工精度对OAM波束激发纯度的束缚，同时可以实现OAM波束的指向和拓扑荷数实时可调，这使得OAM波束距离实际的通信应用更进一步。并在此基础上，基于超表面的涡旋通信系统信道建模，实现了涡旋通信系统的性能的验证与评估。
2. 基于无源超表面透镜的分数模OAM激发研究
通过改变入射波的极化状态，利用透射场中圆极化电磁波的正交性，实现电磁波传输通道的进一步扩展。本节将以涡旋波束集成为例验证多极化通道复用的理论可行性，设计超构表面，使其在线极化电磁波照射下，利用透射场中的左旋圆极化和右旋圆极化分量分别实现携带轨道角动量拓扑电荷数l = 1.5, 2.5的涡旋波前分布[13]。通过传播相位加载涡旋波束l = 2的相位分布ΦOAM,l=2
Φprop = 12∑φ=ΦOAM,l=2 (1) 与此同时，利用几何相位加载涡旋波束l =±1的相位分布ΦOAM,l=1，并分析其与传播相位对出射场中左旋和右旋圆极化分量波前的调控作用，即有
{ΦL=0.5(∑φ−2θ)=0.5(ΦOAM,l=2 + ΦOAM,l=1)=ΦOAM,l=1.5ΦR=0.5(∑φ+2θ)=0.5(ΦOAM,l=2+ΦOAM,l=3)=ΦOAM,l=2.5 (2) 式中ΦL/ΦL表示在出射场中的左/右旋圆极化相位分布。通过式(2)推导可以看出，通过合理的单元设计可以实现在线极化电磁波的照射下，无源超表面透镜可以通过改变接收端圆极化状态来切换分数模分别为1.5和2.5的涡旋波束。在此基础上，我们可以通过亚波长超表面单元构型的设计，结合几何相位与传播相位调控作用，组建具有分数模OAM的涡旋波前集成。
本文设计了一种多层级联的超表面单元，该单元的结构示意图如图1所示。通过级联多层电容型和电感型等效结构，实现具有多阶带通响应的传输网络。该单元结构由5层金属、4层介质组成，周期大小为a=8.8 mm。单元结构的奇数层金属为矩形贴片结构，矩形贴片的宽度为px，长度为py。奇数层矩形贴片在等效电路模型中可被看作电容元件(Cn)，可实现低通的传输响应。为了小型化设计，贴片上有3条平行且尺寸完全相同的矩形缝隙，贴片缝隙的长宽分别为wx和wy，3条平行缝隙间的距离为g。偶数层金属为网格层结构，在电路模型中可等效为电感元件(Ln)，产生高通的传输响应。为了保证单元结构的旋转不敏感特性，网格设置为圆形缝隙，网格层缝隙半径r=3 mm。4层介质具有完全相同的厚度和材料特性，介电常数为εr=3.5，厚度设置为h=1 mm。其在等效电路中可视为具有匹配阻抗的传输线模型(Zn)。每个相邻的电容层与电感层可组合成一组L-C 谐振元件，多组谐振结构便可实现宽频范围内的高透射率和全相覆盖范围。在该单元结构中，奇数层的矩形贴片作为整体，关于其长、短轴对称，通过调节矩阵贴片的长度与宽度，可实现对正交线极化传输系数的调控。另一方面，当矩形贴片的对角长度小于周期大小时，即px2 + py2 < a2，单元结构视为有效，在此基础上，通过旋转贴片层可为单元结构提供几何相位。
本文所设计的该超表面透镜由25×25个单元结构组合而成。为了进一步验证上述仿真计算结果的有效性，对该超构表面透镜进行了实物加工和实验测试，由于多层介质板的加工需要采用固化片结构对其进行热压合，因此超构透镜的实物样品厚度为4.475 mm，其余结构参数均与仿真模型完全一致。该超构透镜的加工实物照片如图2所示。
图3(a)和3(b)分别给出了分数模式l=1.5和2.5的涡旋波束在传播方向横截面内的能量分布、电场分布、相位分布情况。根据仿真及测试的能量结果可知，分数阶模式涡旋波束的能量呈现开口环状分布，开口方向与图3(a)和3(b)中左侧图示的黄色箭头方向保持一致。开口能量环的暗斑直径仿真结果分别为2.19λ0和2.87λ0，对应测试结果分别为3.82λ0和4.05λ0。值得注意的是，在测试结果中，开口能量环的内径(暗斑直径)略大于仿真结果，这一差异是由测试过程中的测量位置误差和噪声干扰所导致的。然而，不论涡旋波束的能量环是否具有开口，暗斑半径均会随着拓扑电荷数的增大而增大，说明了涡旋波束的发散特性同样存在于分数模式当中。通过对比图3(a)和3(b)中的电场分布可以看出，分数拓扑荷的涡旋波束电场均呈现奇数模式分布，并且缺失的电场模式位置与能量环的开口位置一致。与此同时，仿真和测试的相位分布除中心相位奇点外还会存在一个额外奇异点，引起平面内空间相位分布的不连续性，如图3(a)和3(b)中相位分布的黄色虚线框所标注。分别出现在方位角+135°和–45°方向上，并且分数模式涡旋波束的相位同样满足l×2π分布规律。需要说明的是，该额外奇异点是引起能量环呈现开口环状分布、奇数模式电场，以及相位不连续的根本原因，也是奇数阶涡旋波束与整数阶涡旋波束最大的区别。
对分数模式涡旋波束的纯度进行计算与分析，所得OAM纯度结果如图4所示，在10 GHz处，拓扑电荷数为l = 1.5和2.5的涡旋波束的仿真和测试模式纯度分别为70%，64%和81%，71%。OAM纯度的测试结果略低于仿真结果，主要是由于测试环境中噪声干扰引起的。通过以上的仿真和测试结果的分析，我们实现了利用P-B相位与传输型相位的混合调制，在单一超表面阵列中激发多种模式以及非整数型模式的OAM波束的激发。为接下来的实时动态涡旋波的调控与激发提供了理论上的帮助。
3. 基于有源超表面动态涡旋波抗干扰技术
本节提出了一种加载变容二极管的有源超表面，通过控制变容二极管端口电压值来获得多种螺旋相位分布，从而生成多种模态的高纯度涡旋波束，为基于涡旋电磁波的抗干扰机理研究提供全新的平台。单元具体结构如图5所示，详细参数如下(单位：mm)： p=8，g=4，l1=1.55，l2=0.95，l3=7.4，r=0.15，w=0.2。该单元为一个多层结构，其中包括金属贴片、介质基底、金属过孔以及金属馈线。提供相位补偿的变容二极管加载在“工”形贴片中间的缝隙上，与贴片形成电连接。“工”形金属贴片一侧通过金属通孔与地板连接，另一侧穿过金属过孔与底层的馈线形成电连接，结构整体等效为一个串联谐振电路。单元的馈电结构进行了特殊设计，上层的金属结构中包含15个金属化过孔，这15个过孔中仅有一个与馈电线相连，其余均为盲孔，此设计的目的为保证不同单元具有相同的过孔阵列，抵消过孔位置对单元特性的影响，此外，过孔的大小、位置，以及阵列的间距都进行了调整，以保证单元的高效率、宽带宽特性。
在电容的可变化范围内选取C=0.12 pF进行仿真，图6(a)展示了单元在y极化波入射下的反射系数。可以观察到整个工作频段内反射幅度均大于0.94，带宽内的相位响应十分平滑；在观察了单元的初步特性之后，为了进一步确定反射系数与电容值之间的关系，对工作频率10.1 GHz下电容值由0.02 pF变化到0.22 pF的幅度和相位响应进行仿真，如图6(b)所示，在电容变化范围内，幅度曲线均可以保持在0.94以上，同时可以获得约320°的相位覆盖。根据有源超表面的电容-相位变化曲线可以建立单元库，方便后续相位编码中单元的选取。图6(c)为不同频点下的相位覆盖，从9.8 GHz至11 GHz，提出的单元均能实现较为良好的相位覆盖。值得注意的是，有源器件的等效电路模型以及寄生参数都会对结果产生一定影响，在仿真中一般将变容二极管等效成串联RLC电路，寄生参数也可以被认为是这三类无源器件的组合。其中等效电容会使得宏观单元的谐振频点产生偏移，引起实测相位突变与仿真结果的差异，但可结合实测结果对部分单元的相位响应进行优化与补偿，从而保证波前调控的准确性。此外，等效电阻会引起有源超表面的反射系数的损耗，但不会对波形保真度产生负面影响。
根据上述提出的超表面单元构建了一个由30×30单元组成的超表面阵列，并利用其产生动态可调的涡旋波束。产生涡旋波束需要在超表面上实现螺旋的相位分布，其相位分布与单元所在的方位角相关，阵列中单元相位可以表示为
φ(x,y)=l⋅arctan(y,x) (3) 式中，(x,y)表示单元中心坐标，arctan(y,x)表示坐标下方位角，l表示涡旋电磁波模态。
根据式(5)计算出的结果是连续相位分布，还需要将其离散化才能在超表面上编码，从构造难易程度、相位覆盖精度等多方面考虑，最终选择了将相位进行2 bit编码，以90°为间隔，选择4个不同的电容值，具体参数如表1。
表 1 选取超表面单元具体参数序号 变容二极管对应电容值(pF) 离散相位(°) 连续相位取值范围(°) 1 0.02 0 0～90 2 0.09 90 90～180 3 0.12 180 180～270 4 0.17 270 270～360 对超表面进行仿真，并根据离散相位分布进行布阵。图7展示了拓扑电荷 l=+1到+3 时超表面在10.1 GHz的远场方向图。可以看出不同模态的涡旋波束具有环形能量分布的特点，同时所有波束的峰值能量都比中心能量高 15dB，证明这些光束具有良好的抗干扰特性。此外，通过提取仿真结果中的近场相位并计算纯度可得，l=+1到+3 的纯度分别为70.6%, 79%和71.8%，均超过了70% ，OAM波束的频谱如图8所示。仿真结果证明了可重构超表面具备产生高质量多模态OAM波束的能力，产生的3种不同模态的波束均可作为 OAM 通信系统的信道。
为了验证上述仿真结果，将上述超表面加工成实物并在微波暗室中对远场方向图以及近场相位进行测试，如图9所示，观察远场结果可知，生成的涡旋波束能量均匀，且中心能量很低，符合涡旋波的特征。此外，近场相位测试结果很好地展示了涡旋光束的螺旋相位特征，当l=+1时，在相位分布中可以看到一个旋转臂，随着拓扑电荷数的增加，旋转臂的个数也在依次增加。测试结果与仿真结果具有较好的一致性，证明了有源超表面能够产生多种高纯度的涡旋波束，为未来高质量OAM通信提供了坚实的基础。
4. 基于涡旋调制通信系统的理论分析
涡旋调制与传统的调制并不相同，它是将由信源产生的传统信号加载到携带轨道角动量(Orbital Angular Momentum)的涡旋波束上的。OAM调制不仅与信源产生信号的相位和幅度有关，而且和电磁波传播方向上波前空间位置有关。OAM调制由于携带不同拓扑荷的涡旋波束之间天然正交，有利于无线通信抗干扰。采用的OAM调制的方式为传统信号调制+涡旋相位调制的方式。具体过程如图10所示。
如图10所示，信源产生语音、文字等信号，由信源产生的信号经由编码变成二进制信号，转换成的二进制信号经过PSK调制，在经过涡旋调制将传统的调制信号加载到携带轨道角动量的涡旋波束上。载有调制后的信号的涡旋波束经由高斯噪声信道到达接收端，在接收端，首先进行OAM解调称为正弦信号，涡旋解调后的信号经过PSK解调和译码后到达信宿。对于一串信源产生的信号，在接收端的信号表达式为
y(k,t,φ)=s(t)+n(t) (4) 式中，y(k,t,φ)表示接收端接收的信号；s(t)表示信源发出的信号；n(t)表示信号在信道传输过程中加入的高斯白噪声。
经过涡旋调制后，发送天线发送的信号为
y(k,t,φ)=s(t)⋅ejlφ+n(t) (5) 式中，φ表示涡旋调制中的空间方位角；l表示涡旋相位的拓扑电荷。
接下来经过涡旋解调进入PSK解调，涡旋解调基本方法是用与调制涡旋波束的拓扑荷值符号相反的超表面与之相干，涡旋波束就可以恢复到原始的正弦波。该过程可用式(8)简略表示：
yr=y⋅e−jkφ (6) 通过以上的涡旋解调，涡旋信号恢复成原本的正弦信号，进而进行PSK解调、译码，最终被恢复的信号到达信宿。利用数学仿真软件进行涡旋调制的信道仿真。在进行涡旋调制信道仿真之前，本课题组利用软件进行了传统调制方式的信道仿真并和理论的误码率和误比特率进行了比较，采用的PSK调制方式为2PSK调制，仿真得到的结果如图11所示。
从图12可以分析得到，采用纯度为1的涡旋调制后，误码率和误比特率均小于传统调制的误码率和误比特率，且当信噪比大于8时，涡旋调制的误码率和误比特率几乎为0。这表明信号经过纯度为1的涡旋调制后可以实现更低的误码率和误比特率，抗干扰的能力相较于传统调制方式大大增强。
当负责载波功能的涡旋波束的纯度小于1时，可将载波等价于归一化幅度小于1的涡旋波束和归一化幅度小于1的平面波同时传输相同的信号，且涡旋波束和平面波的归一化幅度之和为1。根据之前的公式推导，利用代码将该过程实现并进行信道仿真，得到的结果如图13所示，当纯度为0.6时，OAM通信的误码率在相同的环境信噪比中有了明显的升高。
综上，通过以上的仿真可以将原本并不相关的信号处理和场分布的内容进行结合，数值计算仿真可以了解到，在OAM通信这种特殊的通信模式下，影响整个系统通信效果的因素除了传统的噪声影响外还与电磁波在空间中的传播特性和场分布有关。
传统抗干扰技术采用扩频通信的方式，扩频通信主要依据香农原理，在信道环境中的噪声功率增加时，可以通过将通信频带展宽来实现信道容量的不变。这种方式可以实现通信系统抗干扰能力的增强，但是由于其需要的频带较宽，不利于现阶段频谱资源日益紧张的情况。涡旋调制通信是利用将信号加载到携带轨道角动量(Orbital Angular Momentum, OAM)的电磁波上的一种通信方式，它可以利用不同拓扑荷的涡旋波束之间天然正交这一其独有的性质实现信道容量的增加。根据香农信道容量定理，当N路同轴涡旋信号同时进行复用和传输时，其会同时产生N个涡旋信道。在通信系统占用频带带宽不变的情况下，噪声功率增加，我们可以将涡旋波束的模式数增加来维持信道容量稳定。基于此我们提出扩模通信这一理念来实现通信系统抗干扰。通信系统可以通过扩展涡旋调制中所采用的涡旋波的模式数来实现信道容量的增大，换言之，在信道中的噪声增大的情况下，可以利用增加涡旋波的模式数来维持信道的容量保持不变。为了分析整个涡旋通信系统在抗干扰方面的表现，我们引入了处理增益的概念，在对处理增益进行推导后分析出：涡旋通信中所采用的激发涡旋波的天线或超表面对方位角划分得越精细，通信系统的处理增益越高，系统的抗干扰性能越好，即激发通信系统所需的涡旋波的天线或超表面的相位精度越高，系统的抗干扰性就越强。跳模通信是在原有涡旋通信的基础上加入了跳模的模块，令涡旋调制过程中不同时刻采用的涡旋波的模式数随机跳变。利用仿真软件进行数值仿真得到的结果如图11所示。
由图11可以分析出，通过跳模通信的方式，OAM通信系统可以在不外加复杂的算法的情况下实现误码率和误比特率的降低，从而实现更好的抗干扰能力。
5. 结束语
该文简要回顾了近期关于微波波段多模式涡旋波束的激发与调控研究进展。首先，基于传播相位与几何相位的综合调控作用，利用接收端圆极化状态的切换，基于无源超表面透镜实现了分数阶OAM的激发与集成，对应工作频点处的分数模式纯度达到64%和71%。其次，组建了微波段有源可调超表面原理样机，通过加载变容二极管等有源可调谐式器件，实现模式数为1，2，3阶涡旋波束的动态切换与人工调控。最终，通过对基于超表面的涡旋通信系统的信道建模，对涡旋通信系统的性能做出了理论分析与评估，为现代通信系统信道扩容及信息传输速率提升提供理论途径。该文总结并对比了与现有涡旋波束激发与调控工作，如表2所示。可以看出，UCA可以产生固定模式数的OAM波束，相对带宽为9％，但是需要8个天线和精确的控制网络。SPP的方法通过电磁波在介质中相位的累积作用实现相位调控进而实现OAM波束的激发，但是这种方式的带宽一般较低，较难在现实中应用。Metasurface这种方式可以在宽带内激发高纯度的OAM波束，且设计简单，剖面较低；但是其相位响应的分布一经确定就无法改变了，它只可以激发固定模式的OAM波束。该文采用的RIS方法在继承了Metasurface的优点的基础上，实现OAM波束的模式数的任意实时可调。此外，OAM波束通信目前已经不再仅仅停留在理论层面的技术，而是已经利用OAM波束的独特性能对现代的无线通信技术赋能。然而，尽管目前已经有了许多有关OAM无线通信方面的理论研究或实际测试，但是这些研究基本都是基于UCA的多天线的MIMO无线通信。这种方式可以极大地提升无线通信的信道容量，但由于用于无线通信的OAM波束需要多个天线进行激发和接收，所以现行的OAM通信无法获得比传统MIMO天线更高的信道增益或通信性能的提升[12]。有源超表面作为一种自身并不辐射的超表面的电磁器件，在调控电磁波的波前相位分布这一点上，可以与天线透镜相比。也就是说，相比于现行的UCA技术，有源超表面在不增加天线数目的同时，可以增大接收的信噪比，从而使无线通信的抗干扰能力大大增强，这是与目前主流的OAM通信技术相比最大的优势。
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表 1 差分混沌通信不同信号设计的对比
信号设计方法 优势 劣势 信号帧结构设计 实现简单，硬件成本较低 多径时延较大时将导致信号间干扰增大 正交多级信号设计 参考信号和信息承载信号在相同时隙中传输，提高系统的频谱效率 接收端需要Walsh码同步，误码率性能与同步质量密切相关 信号星座图设计 一个多元传输符号可传输多个信息比特，提高系统的数据传输速率 误码率性能随数据传输速率增大而恶化 多载波信号设计 多个信息承载信号子载波共享一个参考信号，提高系统的能量效率 峰均功率比较大，影响系统总体性能 
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表 2 不同噪声抑制方案的对比
噪声抑制方案 基本原理 优势 劣势 NR-DCSK [59]
SA-MC-DCSK [60]利用冗余信息进行平滑滤波降噪 系统实现相对简单，硬件成本较低 引入冗余信息，降低系统的能量效率和频谱效率 ND-MDCSK-DHT [62] 利用信息比特的再调制和迭代算法降噪 能够估计出噪声强度且降噪性能良好 系统复杂度高，高阶调制下的噪声抑制效果差 MC-DCSK-IR [63]
NS-MC-MDCSK [64]利用传输信号的似然信息实现迭代降噪 少量迭代就能获得良好的误码率性能 载波同步要求精度高，其质量直接影响系统性能 LRAM-MC-DCSK [65]
I-OFDM-DCSK [66]利用传输信号矩阵的低秩特性实现降噪 能够大幅度地提高系统的误码率性能 接收端需要额外的信号处理电路，系统复杂度高
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