一种低复杂度和便于硬件移植的非线性均衡算法及其UWOC实时补偿实验演示
Underwater wireless optical communication (UWOC) has advantages such as high bandwidth, high data rate, low latency, and small form factor. It can support the transmission of high-speed, high-capacity, real-time, and multimedia services like underwater images and videos. Light-emitting diodes (LEDs) are cost-effective light sources with high energy efficiency, and their wide-angle beam profile relaxes the alignment requirements between the transmitter and receiver. However, high-power LED sources have narrow bandwidth and exhibit strong non-linear effects. Additionally, the underwater optical channel is affected by absorption, scattering, turbulence, and bubbles, while the photodetectors may also exhibit non-linear effects. These factors lead to non-linear distortion of the optical signal, severely affecting communication bandwidth and limiting transmission distance. The Volterra algorithm is commonly used for non-linear compensation in communication systems, but it has high complexity and computational overhead. Most existing research on the Volterra algorithm involves offline processing, which is not conducive to miniaturization and low power consumption in underwater environments. Therefore, we propose a low-complexity, low-power, and hardware-friendly 3l-sVolterra (link and linear list-based sparse Volterra) algorithm for UWOC systems. By combining new data structures based on linked lists and linear lists to store all the parameters of the Volterra algorithm, the on-chip resources required for updating the Volterra algorithm's parameters are effectively reduced. It also facilitates sparse processing of the participating non-linear terms, making it suitable for small-scale hardware systems. Compared with the 3l-Volterra algorithm without sparsity operations, this algorithm reduces resource consumption by 30% while preserving similar non-linear compensation capabilities. We hope that the proposed 3l-sVolterra algorithm can promote miniaturization and real-time underwater applications of UWOC systems.
The 3l-sVolterra algorithm utilizes a combined data format of linked lists and linear lists to store the parameters for Volterra operations. The algorithm achieves parameter updates through N multiplications, one node insertion, and traversal of the remaining N-1 nodes in the linked list, significantly improving the efficiency of each update and operation. The algorithm's sparse operations on the non-linear terms further reduce on-chip resource consumption. We implement and validate the 3l-sVolterra algorithm on a low-power and miniaturize digital signal processing (DSP) chip, the C6748. We also design a DSP subsystem based on the C6748 as the core. In the receiving end, the optical signal is converted into an electrical signal by an avalanche photo diode (APD). The electrical signal is then amplified and input to an analog-to-digital conversion (ADC) module. Finally, the converted digital signal is synchronized, demodulated, and subjected to non-linear equalization by the DSP subsystem.
In a 5 m-long underwater channel, the UWOC system employs the CAP-4 modulation scheme for data transmission. The experiment tests the compensation capability of the 3l-sVolterra algorithm in the entire UWOC system with four different memory lengths (10, 14, 18, and 20) and varying numbers of retained terms (4, 8, 12, and 16). As the memory length increases, the 3l-Volterra algorithm (the 3l-sVolterra algorithm without sparse operations) enhances the compensation capability of the entire UWOC system, achieving a channel bandwidth expansion of up to 20 Mbit/s. While maintaining similar non-linear compensation capabilities to the algorithm without sparsity operations, the 3l-sVolterra algorithm reduces on-chip resource consumption by 30%. When a non-linear compensation algorithm with a memory length of N is processed, the number of retained non-linear terms should be greater than N/2, so as to ensure the majority of non-linear compensation capability. The influence of non-linear terms beyond the N/2 range gradually diminishes. This algorithm is suitable for DSP hardware systems and can be ported to hardware systems of other architectures.
We propose a low-complexity, low-power, and hardware-friendly 3l-sVolterra algorithm. The algorithm adopts a new data structure that combines linked lists and linear lists to store all the parameters of the Volterra algorithm, effectively reducing the on-chip resources required for parameter updates. It also allows sparse operations on the non-linear terms of the Volterra algorithm and facilitates portability to different small-scale hardware systems. Furthermore, a DSP subsystem based on the 3l-sVol algorithm is implemented on the C6748 chip, and a UWOC system is constructed using a 5 m-long water tank to test the designed DSP subsystem. Compared with the 3l-Vol algorithm, the proposed algorithm reduces on-chip resource consumption by 30% while maintaining similar non-linear compensation capability. By changing the memory length and the number of retained terms in the Volterra algorithm, the variation of the algorithm's non-linear compensation capability in the constructed UWOC system is tested. Reducing the number of retained terms can effectively reduce the on-chip resource consumption of the Volterra algorithm. This is the first time that a non-linear equalization algorithm has been ported to a DSP chip, achieving synchronous data transmission and real-time non-linear compensation in the DSP-based UWOC system. The DSP subsystem has good compensation capability for both linear and non-linear distortions, as well as system bandwidth extension ability, which is of great significance for miniaturizing the UWOC system and promoting its real-time underwater applications.
1 引言
海洋的探索与保护、资源的开发和利用等都离不开水下信息的高效采集与通信[1]。常见的水下无线通信主要有水声通信、水下射频通信和水下无线光通信,相较于前二者,水下无线光通信具有带宽大、速率高、时延短、设备功耗低、体积小等优点,能支持水下图像、视频等高速率、大容量、实时多媒体业务的传输,在未来高速局域组网或与长距离水声通信混合组网中,必将发挥重要作用[2]。发光二极管(LED)和激光二极管(LD)被广泛用作水下无线光通信(UWOC)系统的光源。LED具有成本低、能效高的特点,而且它的宽角度光束轮廓可以放宽光发射机与光接收机之间对准的要求。由于成本低、对温度不敏感,且可通过增加LED光源的输出功率或采用LED阵列来延长通信距离,LED作为光源能在水下中/短距离通信中发挥重要作用。
大功率LED光源不仅带宽窄,而且存在较强的非线性效应。同时,水下光信道也存在吸收、散射、湍流和气泡等不良现象[3-4],光电探测器可能还存在非线性效应等[5],这些都会造成光信号的非线性失真,严重影响通信带宽、限制传输距离[6]。在自由空间光通信中,不少研究通过离线仿真的方式,验证了调制方式的复杂程度同样会影响LED光源的非线性,进而影响整个通信系统的性能,如脉冲幅度调制(PAM)[7]、无载波幅度相位(CAP)调制[8]和多载波系统[如正交频分复用(OFDM)]等[9-10]。文献[11]离线分析了无载波幅度相位调制、正交频分复用[12]以及离散傅里叶变化扩频(DFT-S)OFDM这3种调制方式在UWOC系统中的传输性能。文献[13]在实验中测试了开关键控调制(OOK)和16进制的正交幅度调制[14](QAM)在UWOC系统中的性能。当采用高阶调制方式时,系统所受的总非线性效应的影响会加剧。
针对UWOC系统非线性效应的影响,大多数研究是在接收端采用Volterra算法进行后均衡处理,以增加系统的复杂度为代价换取系统性能的提升。为了降低Volterra算法的复杂度,文献[15]在离线处理中通过减少参与运算项来降低Volterra算法的复杂度,以对基于LD的UWOC系统进行非线性均衡。文献[16]在离线解调中将Volterra算法中的交叉项乘法操作替换为两个输入样本和的绝对值,并展示了一种基于绝对值操作的稀疏剪枝项非线性决策反馈均衡方法。但是,现有的非线性均衡算法大多是在接收端通过高速数字存储示波器(DSO)采集数据后,在PC端离线处理以实现均衡补偿[15-18],而离线处理无法满足UWOC系统水下小型化部署的实际需求。此外,在实现小型硬件系统时,Volterra算法的复杂度高、占用片上资源多以及数据处理计算开销大。
为了满足UWOC光端机的小型化、低成本和强鲁棒性的实用需求,本文提出一种低复杂度、低功耗且便于硬件移植的3l-sVolterra算法,它结合链表与线性表的数据结构来存储Volterra算法中的所有参数,且对参数中非线性项进行稀疏操作处理,并在功耗低、小型化的DSP芯片C6748上进行实验验证。随后,在实验室搭建了基于所设计的DSP子系统的5 m长的UWOC实验系统,对其进行性能测试。结果表明,与基于链表和线性表的无稀疏操作Volterra算法(即3l-Volterra算法)相比,所提出的3l-sVolterra算法能在保留与3l-Volterra算法相近的非线性补偿能力的同时,将资源消耗降低30%,在CAP-4调制方式下将UWOC系统的传输速率增大至20 Mbit/s。此外,该算法还便于移植到不同的硬件系统,利于UWOC系统的实时处理与小型化。本文将非线性均衡算法移植到DSP芯片上,实现了基于DSP的UWOC系统的同步数据传输和实时非线性补偿。
2 UWOC系统构成
在强度调制/直接检测(IM/DD)光通信系统中,CAP是一种提高数据传输速率的低成本、低复杂度的调制技术[19],可以在带宽有限的情况下大幅提升通信系统的传输速率。与传统的单载波调制技术相比,CAP在调制过程中不存在载波相乘的过程,而是直接利用两组相互正交的成型滤波器来产生带通脉冲信号,通过改变同相和正交支路的波形来反映传输的数据流,故被称为“无载波”调制技术。IM/DD光通信CAP调制原理框图如
发送端输入二进制数据比特流进行QAM星座图映射。将映射生成的复数信号分成同相I路和正交Q路两路信号,这两路信号可以生成M进制的CAP调制星座图,称为CAP-M调制。对I(n)和Q(n)两路信号分别进行上采样后,让它们再分别通过同相滤波器
式中:T为符号周期;同相滤波器
式中:g(t)为根升余弦滤波器;fc为载波频率(与码元速率相同)。
3 非线性均衡算法及其实现
3.1 Volterra算法
由于Volterra均衡算法具有灵活的线性和非线性补偿能力,本文选择Volterra非线性均衡算法来提高UWOC系统的通信性能。在接收端,DSP的输入信号x(n)与输出信号y(n)之间的关系为
式中:x(n)为需要进行均衡处理的序列;y(n)为经过均衡算法处理的结果;w1(i)和w2(i,j)分别对应Volterra算法的线性项和二阶非线性项的权重;N1和N2分别为线性和二阶非线性的记忆长度。若增加高阶项或者延长记忆长度,Volterra算法对信道的拟合和补偿效果更好,但是其算法的复杂度会呈指数式增加。为此,本文提出一种低复杂度、低功耗且便于硬件移植的3l-sVolterra算法,它结合链表与线性表的数据结构来存储Volterra算法中的所有参数,且对参数中的非线性项进行稀疏操作。
3.2 3l-sVolterra均衡补偿算法
3.2.1 数据结构的更新操作
为了方便处理数据,通常使用线性表来存储一阶线性项和二阶交叉项的参数,并将各阶项首尾相连地拼接在一起,方便后续的DSP点乘运算。假定记忆长度N为6,当前时刻采样值为xn,存储当前数据的顺序表和未来更新的数据表如
图 2. Volterra算法各阶项线性表存储格式。(a)当前时刻;(b)下一时刻
Fig. 2. Linear list storage format for each order term in the Volterra algorithm. (a) Current time; (b) next time
为了优化算法、降低复杂度,通常进行剪枝操作来稀疏需要运算的参数[10-11],这可以通过将权重较小的参数设置为0或移除该参数来实现。但在DSP芯片架构中,置0操作并不能降低算法的复杂度。此外,如果使用线性表[
设定的节点包含整型数据(表示当前节点指向线性表中有效数据的个数)、指向数据浮点型指针和指向下一个节点的指针。该数据结构将交叉项以xn-i(i=0,1,2,…,n)为键值进行划分。如
图 3. 数据结构参数更新流程。(a)设计的数据结构;(b)执行操作①后的数据结构;(c)执行操作②后的数据结构;(d)执行操作③后的数据结构
Fig. 3. Data structure parameter update process. (a) Designed data structure; (b) data structure after executing operation ①; (c) data structure after executing operation ②; (d) data structure after executing operation ③
所提出的数据结构参数更新流程如下:①将要更新的数据加入指针头部,同时将更新的二阶交叉项覆盖尾指针的数据,更新尾指针的有效值为N,如
3l-sVolterra算法通过N次乘法、一次节点插入和对链表中剩下的N-1个节点的遍历,同时重置尾指针来完成参数更新,从而显著提高每次更新和运算的效率。随着记忆长度的增加,由更新带来片上消耗的复杂度降低为O(N)。后续可以通过增加链表的节点来对三阶级数交叉项进行存储和操作,以适应不同的环境需求。当面对高速率的UWOC系统需要较长的记忆长度时,所设计的数据结构能够直接映射到硬件系统的寄存器、内存上,更适合在DSP硬件系统上实现,并可以移植到其他架构的硬件系统上。
3.2.2 非线性项稀疏操作
3l-sVolterra算法稀疏操作的原理是通过剔除Volterra算法中“不重要”的权重,以减少参数的存储量和计算量,同时尽量保证算法的非线性补偿能力不受影响。根据设计的数据结构,将交叉项数据以xn-i(i>0)划分为最小操作单位。如
图 4. 各阶参数权重w(n)存储结构。(a)w(n)的存储结构;(b)稀疏操作后的数据结构
Fig. 4. Storage structure for the weights of each order parameter w(n). (a) Storage structure of w(n); (b) data structure after sparse operation
随后,根据记忆长度N和需求确定保留项m(比如N为6时,m为4),再设计一个节点数为m、以链表head1指向进行稀疏操作的数据结构。根据
4 UWOC系统实验原理与装置
所搭建的基于绿色LED光源的DSP-based UWOC实验系统框图如
图 6. UWOC系统的实验装置和实验现场图。(a)发送端;(b)实验的水箱环境;(c)接收端
Fig. 6. Experimental setup and site of UWOC system. (a) Transmitter; (b) water tank for the experiment; (c) receiver
到达光接收端的光束经过凸透镜聚焦后,由型号为LSSAPD9-500-C1-NF-1-1的雪崩光电二极管(APD)进行光/电转换,如
5 实验结果与分析
5.1 非线性均衡算法消耗
实验测试了所提出5组记忆长度为10、12、14、16、18的非线性均衡算法在保留项为8组(Base-8)和4组(Base-4)时芯片上的时间周期消耗,其中Traditional Vol表示使用乘法运算来更新参数的Volterra算法,3l-Vol表示基于链表和线性表无稀疏操作的Volterra算法,3l-sVol-Base-m表示基于链表和线性表稀疏操作的Volterra算法,其保留项为m组。DSP子系统在得到采样数据时标记一个时间戳,在存储完算法补偿的结果后再标记一个时间戳,将两个时间戳之差作为算法的片上资源消耗记录。各种算法的片上资源消耗结果如
图 7. Volterra算法消耗实验结果。(a)不同修剪长度在不同记忆长度Volterra算法的片上消耗;(b)权值估计后二阶参数的权重
Fig. 7. Experimental results of Volterra algorithm consumption. (a) On-chip consumption of different pruning conditions in Volterra algorithm with different memory lengths; (b) weights of second-order parameters after weight estimation
表 1. 不同修剪长度在不同记忆长度Volterra算法的片上消耗
Table 1. On-chip consumption of different pruning conditions in Volterra algorithm with different memory lengths unit: machine cycle
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5.2 稀疏操作的效果
所使用的稀疏操作是一种粗剪枝策略,通过将交叉项数据以xn-i(i>0)为单位进行剪枝,如
图 8. Volterra算法在不同剪枝情况下随着码元速率变化的误码率曲线。(a)记忆长度为10;(b)记忆长度为14
Fig. 8. BER of Volterra algorithm with different pruning conditions as a function of symbol rate. (a) Memory length of 10; (b) memory length of 14
图 9. 记忆长度为18和20时Volterra算法在不同剪枝情况下随着码元速率变化的误码率曲线。(a)记忆长度为18;(b)记忆长度为20
Fig. 9. BER of Volterra algorithm with memory lengths of 18 and 20 under different pruning conditions as a function of symbol rate. (a) Memory length of 18; (b) memory length of 20
记忆长度为10的非线性均衡算法的误码率曲线如
如
稀疏算法能够通过删除权重较小的项来减少算法的资源消耗。由于Base-4算法保留的非线性项数较少,其性能近似于线性均衡,无法有效地补偿高速UWOC系统的非线性畸变。在本研究中,3种记忆长度下Base-4算法的误码率都无法满足通信性能的要求。在记忆长度N为10和14的情况下,Base-8算法保留的非线性项数大于N/2,能够在减少片上消耗的同时,保留Volterra算法非线性补偿的大部分性能。当记忆长度为18和20时,Base-8算法由于保留的非线性项数小于N/2,无法将UWOC系统的信道带宽展宽至20 Mbit/s以上。在记忆长度为18和20的情况下,Base-12算法由于保留的非线性项数大于N/2,其误码率曲线逼近未经稀疏操作的情况。对于记忆长度为20的情况,随着通信速率的提高,Base-12算法与Base-16算法对UWOC系统的非线性均衡补偿能力相当,这是因为它们都保留了超过N/2的权重较大的非线性项。面对记忆长度为N的非线性补偿算法时,为了保证大部分非线性补偿能力,所保留的非线性项数要大于N/2,而超出N/2范围的非线性项对非线性补偿能力的影响逐渐变小。
当通信速率超过20 Mbit/s时,非线性均衡算法无法通过提高记忆长度来有效地降低误码率。从
6 结论
提出一种低复杂度、低功耗且便于硬件移植的3l-sVolterra算法。该算法采用新的数据结构,将链表和线性表相结合,以存储Volterra算法的所有参数,有效降低了Volterra算法参数更新所需的片上资源,还能对Volterra算法非线性项进行稀疏操作,且便于移植到不同的小型硬件系统上。此外,在C6748芯片实现了基于3l-sVol算法的DSP子系统,利用5 m长水箱搭建一个UWOC系统来测试所设计的DSP子系统。与3l-Vol算法相比,所提出的算法在保持与其相近的非线性补偿能力的同时,将片上资源消耗降低了30%。通过更改Volterra算法的记忆长度和保留项数量,在搭建的UWOC系统中测试算法对系统非线性补偿能力的变化。通过减少保留项能有效降低Volterra算法的片上资源消耗。将非线性均衡算法移植到DSP芯片上,实现了基于DSP的UWOC系统的同步数据传输和实时非线性补偿。该DSP子系统具有较好的线性和非线性失真的补偿能力以及系统带宽扩展能力,对于UWOC系统的小型化和推动其水下实时应用,具有重要意义。
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Article Outline
肖胡浩, 殷洪玺, 王建英, 黄安, 季秀阳. 一种低复杂度和便于硬件移植的非线性均衡算法及其UWOC实时补偿实验演示[J]. 光学学报, 2024, 44(6): 0606004. Huhao Xiao, Hongxi Yin, Jianying Wang, An Huang, Xiuyang Ji. A Low-Complexity and Hardware-Portable Non-Linear Equalization Algorithm and Experimental Demonstration of Its Real-Time Compensation for UWOC[J]. Acta Optica Sinica, 2024, 44(6): 0606004.