«上一篇
 文章快速检索 高级检索

 哈尔滨工程大学学报  2018, Vol. 39 Issue (12): 1894-1901, 2016  DOI: 10.11990/jheu.201708007 0

### 引用本文

SHENG Xueli, RUAN Yewu, YIN Jingwei, et al. The equalization technology of adaptive multi-channel decision-feedback equalization using error feedback with time reversal based on single vector[J]. Journal of Harbin Engineering University, 2018, 39(12), 1894-1901, 2016. DOI: 10.11990/jheu.201708007.

### 文章历史

1. 哈尔滨工程大学 水声工程学院, 黑龙江 哈尔滨 150001;
2. 哈尔滨工程大学 水声技术重点实验室, 黑龙江 哈尔滨 150001;
3. 北京系统工程研究院 水声对抗技术重点实验室, 北京 100000

The equalization technology of adaptive multi-channel decision-feedback equalization using error feedback with time reversal based on single vector
SHENG Xueli 1,2,3, RUAN Yewu 1,2, YIN Jingwei 1,2,3, HAN Xiao 1,2
1. College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, China;
2. Science and Technology on Underwater Acoustic Laboratory, Harbin Engineering University, Harbin 150001, China;
3. Key Laboratory of Underwater Acoustic Antagonizing, Beijing Institute of Systems Engineering, Beijing, 100000, China
Abstract: In underwater acoustic communication, complex ocean ambient noise and acoustic channel multipath effect lead to severe limitations in the equalization performance of decision-feedback equalizers (DFEs) using error feedback (EFB) filters. To solve this problem, an adaptive multi-channel decision-feedback equalizer with an error feedback filter (EFB-ADFE) to reduce noise is proposed in this paper. The equalizer operates based on the difference between the coherence of the signal vector field and noise vector field and the physical properties of the dipole directivity found in the velocity channel of the vector hydrophone. Moreover, the time reversals are used to suppress the channel multipath interference. Simulation experiment and field experiment results show that the proposed algorithm retains the advantages of the EFB-ADFE. In addition, its ability to reduce noise and multiple interferences is stronger. It is featured with lower equalization error rate, resulting in a more stable underwater acoustic communication.
Keywords: underwater acoustic communication    channel equalization    decision-feedback equalization technique    vector hydrophone    multi-channel DFE using error feedback    time-reversal mirror technique    adaptive algorithm

1 基于单矢量的时反自适应多通道误差反馈DFE均衡系统 1.1 自适应误差反馈DFE均衡器

 $\mathit{\boldsymbol{X}}\left( N \right) = \left[ {\begin{array}{*{20}{c}} {x\left( n \right)}&{x\left( {n - 1} \right)}& \cdots &{x\left( {n - L} \right)} \end{array}} \right]$ (1)
 $\mathit{\boldsymbol{W}}\left( n \right) = \left[ {\begin{array}{*{20}{c}} {{w_f}\left( 0 \right)}&{{w_f}\left( 1 \right)}& \cdots &{{w_f}\left( {n - L} \right)} \end{array}} \right]$ (2)

 $\mathit{\boldsymbol{D}}\left( n \right) = \left[ {\begin{array}{*{20}{c}} {d\left( {n - 1} \right)}&{d\left( {n - 2} \right)}& \cdots &{d\left( {n - M} \right)} \end{array}} \right]$ (3)
 ${\mathit{\boldsymbol{W}}_b}\left( n \right) = \left[ {\begin{array}{*{20}{c}} {{w_b}\left( 1 \right)}&{{w_b}\left( 2 \right)}& \cdots &{{w_b}\left( {n - M} \right)} \end{array}} \right]$ (4)

EFB在n时刻的输入信号和EBF的权系数向量分别为

 $\mathit{\boldsymbol{E}}\left( n \right) = \left[ {\begin{array}{*{20}{c}} {e\left( {n - 1} \right)}&{e\left( {n - 2} \right)}& \cdots &{e\left( {n - N} \right)} \end{array}} \right]$ (5)
 ${\mathit{\boldsymbol{W}}_e}\left( n \right) = \left[ {\begin{array}{*{20}{c}} {{w_e}\left( 1 \right)}&{{w_e}\left( 2 \right)}& \cdots &{{w_e}\left( {n - N} \right)} \end{array}} \right]$ (6)

 ${\mathit{\boldsymbol{X}}_{{\rm{ine}}}}\left( n \right) = {\left( {\mathit{\boldsymbol{X}}\left( n \right),\mathit{\boldsymbol{D}}\left( n \right),\mathit{\boldsymbol{E}}\left( n \right)} \right)^{\rm{T}}}$ (7)
 ${\mathit{\boldsymbol{W}}_{{\rm{ine}}}}\left( n \right) = {\left( {{\mathit{\boldsymbol{W}}_f}\left( n \right),{\mathit{\boldsymbol{W}}_b}\left( n \right),{\mathit{\boldsymbol{W}}_e}\left( n \right)} \right)^{\rm{T}}}$ (8)

 $y\left( n \right) = \mathit{\boldsymbol{X}}_{{\rm{ine}}}^{\rm{T}}\left( n \right){\mathit{\boldsymbol{W}}_{{\rm{ine}}}}\left( n \right) = \mathit{\boldsymbol{W}}_{{\rm{ine}}}^{\rm{T}}\left( n \right){\mathit{\boldsymbol{X}}_{{\rm{ine}}}}\left( n \right)$ (9)

 $e\left( n \right) = d\left( n \right) - y\left( n \right)$ (10)

 ${J_{\min }} = {\rm{E}}\left[ {{\mathit{\boldsymbol{d}}^2}\left( n \right)} \right] - {\mathit{\boldsymbol{P}}^{\rm{T}}}{\mathit{\boldsymbol{R}}^{ - 1}}\mathit{\boldsymbol{P}}$ (11)

 $\begin{array}{*{20}{c}} {{J_{e,\min }} = {\rm{E}}\left[ {{\mathit{\boldsymbol{d}}^2}\left( n \right)} \right] - {\mathit{\boldsymbol{P}}^{\rm{T}}}{\mathit{\boldsymbol{R}}^{ - 1}}\mathit{\boldsymbol{P}} - }\\ {{{\left( {\delta _{\rm{e}}^2} \right)}^{ - 1}}{{\left( {{\rm{E}}\left[ {d\left( n \right)e\left( {n - 1} \right)} \right]} \right)}^2}} \end{array}$ (12)

e(n)平稳时，δe2=E[e2(n)]=E[e2(n-1)]。

1.2 单矢量自适应多通道误差反馈DFE均衡系统

 $\begin{array}{l} p\left( t \right) = x\left( t \right)\\ {v_x}\left( t \right) = \left( {1/\rho c} \right) \cdot x\left( t \right)\cos \theta \\ {v_y}\left( t \right) = \left( {1/\rho c} \right) \cdot x\left( t \right)\sin \theta \end{array}$ (13)

 Download: 图 3 二维矢量水听器的振速偶极子指向性 Fig. 3 The vibrational dipole directivity of the two-dimensional vector hydrophone

 $\begin{array}{l} {n_p}\left( t \right) = \sum\limits_j {{n_j}\left( t \right)} \\ {n_{vx}}\left( t \right) = \sum\limits_j {{n_u}\left( t \right)\cos {\theta _j}} \\ {n_{vy}}\left( t \right) = \sum\limits_j {{n_j}\left( t \right)\sin {\theta _j}} \end{array}$ (14)

 $\begin{array}{l} {\rho _{{\rm{pvx}}}} = \frac{{{\rm{E}}\left[ {{n_p}\left( t \right)n_{vx}^ * \left( t \right)} \right]}}{{\sqrt {{\rm{E}}\left[ {{{\left| {{n_p}\left( t \right)} \right|}^2}} \right]{\rm{E}}\left[ {{{\left| {{n_{vx}}\left( t \right)} \right|}^2}} \right]} }} = \\ \;\;\;\;\;\frac{{\sum\limits_j {\overline {n_j^2\left( t \right)} \cdot \overline {\cos {\theta _j}} } }}{{\sqrt {{\rm{E}}\left[ {{{\left| {{n_p}\left( t \right)} \right|}^2}} \right]{\rm{E}}\left[ {{{\left| {{n_{vx}}\left( t \right)} \right|}^2}} \right]} }} \end{array}$ (15)

1.3 被动时间反转技术

 ${s_r}\left( t \right) = s\left( t \right) \otimes h\left( t \right) + n\left( t \right)$ (16)

 $\begin{array}{*{20}{c}} {r\left( t \right) = {s_r}\left( t \right) \otimes h'\left( { - t} \right) = }\\ {\left[ {s\left( t \right) \otimes h\left( t \right)} \right] \otimes h'\left( { - t} \right) + n\left( t \right) \otimes h'\left( { - t} \right) = }\\ {s\left( t \right) \otimes q\left( t \right) + n\left( t \right) \otimes h'\left( { - t} \right)} \end{array}$ (17)

1.4 矢量EFB-AMDFE-TR均衡系统

 Download: 图 5 矢量时反自适应多通道误差反馈DFE原理框图 Fig. 5 Block diagram of EFB-AMDFE-TR based on single vector hydrophone

2 系统仿真实验结果

 Download: 图 6 仿真信道的信道冲激响应和频率响应 Fig. 6 The channel impulse response and frequency response of simulation channel

2.1 自适应误差反馈DFE的均衡结果

2.2 单矢量自适应多通道误差反馈DFE均衡结果

 Download: 图 9 SNR=0 dB EFB-ADFE和EFB-AMDFE均衡后的星座图 Fig. 9 The balanced constellation of the AMDFE and EFB-AMDFE with SNR=0 dB

2.3 单矢量时反自适应多通道误差反馈DFE均衡结果

 Download: 图 11 SNR=0 dB时，EFB-ADFE、EFB-AMDFE和EFB-AMDFE-TR均衡后星座图和误码率比较曲线 Fig. 11 The balanced constellation of the EFB-ADFE, EFB-AMDFE and EFB-AMDFE-TR with SNR=0 dB and error rate comparison curves

3 实验数据处理结果

2015年12月松花江水下实验，水深5.7 m，发射换能器深度为3 m，接收阵元水深为1.5 m，通信距离1 km。通信速率为2 kbit/s，中心频率为6 kHz，带宽为4 kHz，采样频率为48 kHz，信号长度为12.5 s。