西南大学学报 (自然科学版)  2020, Vol. 42 Issue (2): 129-136.  DOI: 10.13718/j.cnki.xdzk.2020.02.016 0
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1. 贵州电网有限责任公司 电力调度控制中心, 贵阳 550002;
2. 重庆大学 微电子与通信工程学院, 重庆 400044

1 系统模型

 图 1 FD-TPSR网络结构图
2 中继间干扰处理方法 2.1 信道状态信息获取

FD-TPSR网络采用基于导频的信道估计获得信道状态信息，其导频集合为{p1p2p3}，获取步骤如下：

2.2 编码调制符号传输

 $\begin{array}{*{20}{c}} {{y_{R1}}\left( 1 \right) = {f_1}s\left( 1 \right) + {n_1}\left( 1 \right)}\\ {{y_{R2}}\left( 1 \right) = {f_2}s\left( 1 \right) + {n_2}\left( 1 \right)} \end{array}$ (1)

 $\begin{array}{*{20}{c}} {{x_1}\left( 2 \right) = b{y_{{{R}}1}}\left( 1 \right)}\\ {{x_2}\left( 2 \right) = b{y_{{{R}}2}}\left( 1 \right)} \end{array}$ (2)

 $\begin{array}{l} {y_D}\left( 2 \right) = {g_1}{x_1}\left( 2 \right) + {g_2}{x_2}\left( 2 \right) + {n_D}\left( 2 \right) = \\ \;\;\;\;\;\;\;\;\;\;\;\;b\left( {{g_1}{f_1} + {g_2}{f_2}} \right)s\left( 1 \right) + w\left( 2 \right) \end{array}$ (3)

 $\begin{array}{*{20}{c}} {{y_{R1}}\left( 2 \right) = {f_1}s\left( 2 \right) + bh\left[ {{f_2}s\left( 1 \right) + {n_2}\left( 1 \right)} \right] + {c_1}\left( 2 \right) + {n_1}\left( 2 \right)}\\ {{y_{R2}}\left( 2 \right) = {f_2}s\left( 2 \right) + bh\left[ {{f_1}s\left( 1 \right) + {n_1}\left( 1 \right)} \right] + {c_2}\left( 2 \right) + {n_2}\left( 2 \right)} \end{array}$ (4)

 $\begin{array}{*{20}{c}} {{x_1}\left( 3 \right) = b{y_{R1}}\left( 2 \right)}\\ {{x_2}\left( 3 \right) = b{y_{R2}}\left( 2 \right)} \end{array}$ (5)

 $\begin{array}{l} {y_D}\left( 3 \right) = {g_1}{x_1}\left( 3 \right) + {g_2}{x_2}\left( 3 \right) + {n_D}\left( 3 \right) = \\ \;\;\;\;\;\;\;\;\;\;\;b\left( {{g_1}{f_1} + {g_2}{f_2}} \right)s\left( 2 \right) + {b^2}h\left( {{g_1}{f_2} + {g_2}{f_1}} \right)s\left( 1 \right) + w\left( 3 \right) \end{array}$ (6)

 $\tilde c\left( 3 \right) = b\left[ {{g_1}\left( {{c_1}\left( 2 \right) + {g_2}{c_2}\left( 2 \right)} \right]} \right.$
 $\tilde n\left( 3 \right) = {b^2}h\left[ {{g_1}{n_2}\left( 1 \right) + {g_2}{n_1}\left( 1 \right)} \right] + b\left[ {{g_1}{n_1}\left( 2 \right) + {g_2}{n_2}\left( 2 \right)} \right]$

 $\begin{array}{*{20}{c}} {{y_{R1}}\left( 3 \right) = {f_1}s\left( 3 \right) + {a_1}\left( 3 \right) + {c_1}\left( 3 \right) + {n_1}\left( 3 \right)}\\ {{y_{R2}}\left( 3 \right) = {f_2}s\left( 3 \right) + {a_2}\left( 3 \right) + {c_2}\left( 3 \right) + {n_2}\left( 3 \right)} \end{array}$ (7)

 ${a_1}\left( 3 \right) = bh\left[ {{f_2}s\left( 2 \right) + bh{y_{R1}}\left( 1 \right) + {c_2}\left( 2 \right) + {n_2}\left( 2 \right)} \right]$
 ${a_2}\left( 3 \right) = bh\left[ {{f_1}s\left( 2 \right) + bh{y_{R2}}\left( 1 \right) + {c_1}\left( 2 \right) + {n_1}\left( 2 \right)} \right]$

R1R2利用历史接收信号消除信号传输第1时隙接收信号对信号传输第3时隙接收信号形成的干扰，保留信号传输第2时隙接收信号形成的干扰，即

 $\begin{array}{l} {{y'}_{R1}}\left( 3 \right) = {y_{R1}}\left( 3 \right) - {\left( {^bh} \right)^2}{y_{R1}}\left( 1 \right) = \\ \;\;\;\;\;\;\;\;\;\;\;\;{f_1}s\left( 3 \right) + {{a'}_1}\left( 3 \right) + {c_1}\left( 3 \right) + {n_1}\left( 3 \right)\\ {{y'}_{R2}}\left( 3 \right) = {y_{R2}}\left( 3 \right) - {\left( {^bh} \right)^2}{y_{R2}}\left( 1 \right) = \\ \;\;\;\;\;\;\;\;\;\;\;\;{f_2}s\left( 3 \right) + {{a'}_2}\left( 3 \right) + {c_2}\left( 3 \right) + {n_2}\left( 3 \right) \end{array}$ (8)

 ${{a'}_1}\left( 3 \right) = bh\left[ {{f_2}s\left( 2 \right) + {c_2}\left( 2 \right) + {n_2}\left( 2 \right)} \right]$
 ${{a'}_2}\left( 3 \right) = bh\left[ {{f_1}s\left( 2 \right) + {c_1}\left( 2 \right) + {n_1}\left( 2 \right)} \right]$

 $\begin{array}{l} {x_1}\left( t \right) = b{{y'}_{R1}}\left( {t - 1} \right)\\ {x_2}\left( t \right) = b{{y'}_{R2}}\left( {t - 1} \right) \end{array}$ (9)

 $\begin{array}{l} {y_D}\left( t \right) = {g_1}{x_1}\left( t \right) + {g_2}{x_2}\left( t \right) + {n_D}\left( t \right) = \\ \;\;\;\;\;\;\;\;\;\;\;b\left( {{g_1}{f_1} + {g_2}{f_2}} \right)s\left( {t - 1} \right) + {b^2}h\left( {{g_1}{f_2} + {g_2}{f_1}} \right)s\left( {t - 2} \right) + w\left( t \right) \end{array}$ (10)

 $\tilde c\left( t \right) = {b^2}h\left[ {{g_1}{c_2}\left( {t - 2} \right) + {g_2}{c_1}\left( {t - 2} \right)} \right] + b\left[ {{g_1}{c_1}\left( t \right) + {g_2}{c_2}\left( t \right)} \right]$
 $\tilde n\left( t \right) = {b^2}h\left[ {{g_1}{n_2}\left( {t - 2} \right) + {g_2}{n_1}\left( {t - 2} \right)} \right] + b\left[ {{g_1}{n_1}\left( t \right) + {g_2}{n_2}\left( t \right)} \right]$

 $\begin{array}{*{20}{c}} {{y_{R1}}\left( t \right) = {f_1}s\left( t \right) + {a_1}\left( t \right) + {c_1}\left( t \right) + {n_1}\left( t \right)}\\ {{y_{R2}}\left( t \right) = {f_2}s\left( t \right) + {a_2}\left( t \right) + {c_2}\left( t \right) + {n_2}\left( t \right)} \end{array}$ (11)

 ${a_1}\left( t \right) = bh\left[ {{f_2}s\left( {t - 1} \right) + bh{y_{R1}}\left( {t - 2} \right) + {c_2}\left( {t - 1} \right) + {n_2}\left( {t - 1} \right)} \right]$
 ${a_2}\left( t \right) = bh\left[ {{f_1}s\left( {t - 1} \right) + bh{y_{R2}}\left( {t - 2} \right) + {c_1}\left( {t - 1} \right) + {n_1}\left( {t - 1} \right)} \right]$

R1R2利用历史信号消除信号传输第t-2时隙接收信号对信号传输第t时隙接收信号造成的干扰，保留信号传输第t-1时隙接收信号形成的干扰，即：

 $\begin{array}{l} {{y'}_{R1}}\left( t \right) = {y_{R1}}\left( t \right) - {\left( {^bh} \right)^2}{y_{R1}}\left( {t - 2} \right) = \\ \;\;\;\;\;\;\;\;\;\;\;{f_1}s\left( t \right) + {{a'}_1}\left( t \right) + {c_1}\left( t \right) + {n_1}\left( t \right)\\ {{y'}_{R2}}\left( t \right) = {y_{R2}}\left( t \right) - {\left( {^bh} \right)^2}{y_{R2}}\left( {t - 2} \right) = \\ \;\;\;\;\;\;\;\;\;\;\;{f_2}s\left( t \right) + {{a'}_2}\left( t \right) + {c_2}\left( t \right) + {n_2}\left( t \right) \end{array}$ (12)

 ${{a'}_1}\left( t \right) = bh\left[ {{f_2}s\left( {t - 1} \right) + {c_2}\left( {t - 1} \right) + {n_2}\left( {t - 1} \right)} \right]$
 ${{a'}_2}\left( t \right) = bh\left[ {{f_1}s\left( {t - 1} \right) + {c_1}\left( {t - 1} \right) + {n_1}\left( {t - 1} \right)} \right]$

R1R2依次对各信号传输时隙的接收信号处理，消除部分干扰后转发至D，直到t=T+1，编码调制符号传输结束.

3 信号检测算法

 $\mathit{\boldsymbol{y}} = \mathit{\boldsymbol{Hs}} + \mathit{\boldsymbol{w}}$ (13)

 $\mathit{\boldsymbol{H}} = \left[ {\begin{array}{*{20}{c}} {{h_1}}&0&0& \cdots &0\\ {{h_2}}&{{h_1}}&0& \cdots &0\\ 0&{{h_2}}& \ddots & \ddots & \vdots \\ \vdots & \vdots & \vdots &{{h_1}}&0\\ 0&0& \cdots &{{h_2}}&{{h_1}} \end{array}} \right]$

 $\begin{array}{*{20}{c}} {{h_1} = b\left( {{g_1}{f_1} + {g_2}{f_2}} \right)}&{{h_2} = b{h^2}\left( {{g_1}{f_2} + {g_2}{f_1}} \right)} \end{array}$

 图 2 MF-PSIC结构框图

 $\mathit{\boldsymbol{K}} = {\left( {{\mathit{\boldsymbol{H}}^{\rm{T}}}\mathit{\boldsymbol{H}}} \right)^{ - 1}}{\mathit{\boldsymbol{H}}^{\rm{T}}}$ (14)

 $\tilde s = \mathit{\boldsymbol{Ky}}$ (15)

t时隙源节点发送符号的粗估计为

 $\tilde s\left( t \right) = {\mathit{\boldsymbol{w}}_t}\mathit{\boldsymbol{y}}$ (16)

 $\eta \left( t \right) = \ln \left( {\frac{{pr\left( {s'\left( t \right)\left| {s\left( t \right) = + 1} \right.} \right)}}{{pr\left( {s'\left( t \right)\left| {s\left( t \right) = - 1} \right.} \right)}}} \right)$ (17)

 $s'\left( t \right) = \tanh \left( {\eta \left( t \right)/2} \right)$ (18)

 $\hat s\left( t \right) = \tilde s\left( t \right) - \sum\limits_{i = 1,i \ne t}^T {{\mathit{\boldsymbol{k}}_t}{\mathit{\boldsymbol{h}}_t}s'\left( i \right)}$ (19)

4 差错性能分析

 $\mathit{\boldsymbol{y}} = \mathit{\boldsymbol{Sfg}} + \mathit{\boldsymbol{w}}$ (20)

 $\mathit{\boldsymbol{S}} = \left[ {\begin{array}{*{20}{c}} {s\left( 1 \right)}&0&0& \cdots &0\\ {{h^2}s\left( 1 \right)}&{s\left( 2 \right)}&0& \cdots &0\\ 0&{{h^2}s\left( 2 \right)}& \ddots & \ddots & \vdots \\ \vdots & \vdots & \vdots &{s\left( {T - 1} \right)}&0\\ 0&0& \cdots &{{h^2}s\left( {T - 1} \right)}&{s\left( T \right)} \end{array}} \right]$
 $\begin{array}{*{20}{c}} {\mathit{\boldsymbol{f}} = \left[ {\begin{array}{*{20}{c}} {{f_1}}&{{f_2}}\\ {{f_2}}&{{f_1}} \end{array}} \right]}&{\mathit{\boldsymbol{g}} = \left[ {\begin{array}{*{20}{c}} {{g_1}}\\ {{g_2}} \end{array}} \right]} \end{array}$

 ${d^2}\left( {\mathit{\boldsymbol{S}},\mathit{\boldsymbol{S'}}} \right) = {\mathit{\boldsymbol{g}}^H}{\mathit{\boldsymbol{f}}^H}\Delta {\mathit{\boldsymbol{S}}^H}{\mathit{\boldsymbol{ \boldsymbol{\varSigma} }}^{ - 1}}\Delta \mathit{\boldsymbol{Sfg}}$ (21)

 $PEP = Q\left( {\frac{{\sqrt {{d^2}\left( {\mathit{\boldsymbol{S}},\mathit{\boldsymbol{S'}}} \right)} }}{2}} \right)$ (22)

 $\overline {PEP} = \mathop E\limits_{f,g} \left\{ {\exp \left( { - \frac{{{\mathit{\boldsymbol{g}}^H}{\mathit{\boldsymbol{f}}^H}\Delta {\mathit{\boldsymbol{S}}^H}{\mathit{\boldsymbol{ \boldsymbol{\varSigma} }}^{ - 1}}\Delta \mathit{\boldsymbol{Sfg}}}}{4}} \right)} \right\}$ (23)

 $\overline {PEP} = \mathop E\limits_f \left\{ {{{\det }^{ - 1}}\left( {\mathit{\boldsymbol{I}} + \frac{{{\mathit{\boldsymbol{f}}^H}\left( {\Delta {\mathit{\boldsymbol{S}}^H}\Delta \mathit{\boldsymbol{S}}} \right)\mathit{\boldsymbol{f}}}}{{4{\rm{tr}}\left( \Sigma \right)}}} \right)} \right\}$ (24)

 ${\rm{tr}}\left( \mathit{\boldsymbol{ \boldsymbol{\varSigma} }} \right) \sim O\left( {{P^\lambda }} \right)$ (25)

5 仿真实验与结果分析

 图 3 不同IRI处理方法的误码性能对比

 图 4 不同信号检测算法的误码性能对比

 图 5 不同信号检测算法的计算复杂度对比
6 结论

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An IRI Processing and Signal Detection Algorithm for Full-Duplex Two-Path Successive Relay Networks
LIU Kang1, LIU Lu1, YANG Chong-hai2, TANG Wei1, FENG Wen-jiang2, LIU Huan1
1. Power Distribution and Control Center, Guizhou Power Grid Co., Ltd., Guiyang 550002, China;
2. College of Microelectronics and Communication Engineering, Chongqing University, Chongqing 400044, China
Abstract: Full-duplex two-path successive relay (FD-TPSR) networks have high spectral efficiency and simple state control. However, there is residual self-interference (RSI) in full duplex relay, and there will also be inter-relay interference (IRI) between transmitting relay and receiving relay, which will lead to the degradation of communication performance. In this paper, an IRI processing method is proposed, in which the relay nodes eliminate partial IRI to improve the end-to-end signal-to-interference-to-noise ratio (SINR) and reserve partial IRI to form a delayed forwarding coding structure at the destination node to provide time diversity gain. A matched-filter with parallel soft interference cancellation (MF-PSIC) algorithm is proposed, in which the structure of the matched filter is simple and the implementation complexity is low, and the parallel interference cancellation based on soft output can simultaneously detect all time slot symbols in parallel, and the processing delay is small. The simulation results show that the proposed IRI processing method takes into account diversity gain, cumulative interference and noise effects and, compared with non-IRI cancellation and full IRI cancellation, its bit error rate is the lowest. The implementation complexity of MF-PSIC detection algorithm is low, and there is little performance loss compared with ML detection algorithm.
Key words: relay network    two-path successive relay network    full-duplex    inter-relay interference    signal detection