﻿ OFDM多载波系统中子载波调制识别新方法
 计算机系统应用  2018, Vol. 27 Issue (11): 120-127 PDF
OFDM多载波系统中子载波调制识别新方法

OFDM Signal Subcarrier Recognition in OFDM Multi-Carrier System
LIU Gao-Hui, XU Ming-Tao
Faculty of Automation and Information Engineering, Xi'an University of Technology, Xi’an 710048, China
Foundation item: National Natural Science Foundation of China (61671375)
Abstract: A new method of classifying and identifying sub-carriers is proposed for Orthogonal Frequency Division Multiplexing (OFDM) signals in non-cooperative communication systems, because there are many sub-carrier modulation types and some sub-carrier modulation types are difficult to be identified in OFDM signals. This method combined and improved the constellation cluster projection method and Logarithmic Likelihood Function (LLF) algorithm. The method first performed constellation clustering projection on different subcarrier modulation signals to recognize the common subcarrier modulation, then calculated the LLF to recognize Offset QAM (OQAM) subcarrier signal and common subcarrier signals. On the basis of the previous step, the LLF of subcarrier group was derived to make the LLF calculation easier to be classified by the decision threshold. Theoretical deduction and computer simulation results showed that the method could recognize the subcarrier modulation when the SNR is 15 dB.
Key words: multi-carrier modulation system     modulation recognition     constellation clustering projection     Offset QAM (OQAM)     Logarithmic Likelihood Function (LLF)

OFDM多载波调制系统是基于频分复用(Frequency Division Multiplexing, FDM)技术的通信系统. 其原理是通过对多路调制信号进行不同载频的调制, 使得多路信号的频谱在同一个传输信道的频率特性中互不重叠, 从而完成在一个信道中同时传输多路信号的目的[1]. 目前, OFDM是使用最广泛的多载波调制技术, OFDM采用矩形窗作为原型滤波器和正交子载波的设计方案, 其调制方式正好与快速傅里叶算法(Fast Fourier Transform, FFT)相匹配[2], 并且因为其简单易实现和高效的频谱利用率得到了普遍应用, 而且在理想情况中, 利用子载波的正交特性, 接收端系统可以完全无损的恢复出发射信号.

1 信号模型

OFDM调制系统中, 子载波的调制方式由系统需求所决定, 对于其子载波的调制识别也会存在一定难度. 在加性高斯白噪声信道中, 接收端OFDM信号模型如下:

 $X\left( t \right) = \mathop \sum \limits_{k = 1}^N \left ({a_k}\cos{w_c}t + {b_k}\sin{w_c t} \right ) + {{n}}\left( t \right)$ (1)

 \begin{aligned}r\left( t \right) = \sqrt {{p_t}} \left( {\mathop \sum \limits_{n = - \infty }^\infty {a_n}h\left( {t - nT} \right)} \right)\cos {w_c}t \\\;\;\;\; -\sqrt {{p_t}} \left( {\mathop \sum \limits_{n = - \infty }^\infty {b_n}h\left( {t - nT} \right)} \right)\sin{w_c}t\end{aligned} (2)

2 基于星座图聚类投影与对数似然函数的算法 2.1 算法流程

(1) 对子载波调制信号的星座图进行聚类投影, 并利用聚类投影结果的最大距离点与最小距离点的比值最为特征参数, 对MPSK和MQAM调制类型进行粗分类.

(2) 根据调制类型的不同, 得到MPSK和MQAM的条件概率 ${{p}}\left( {\theta |{m_i}} \right)$ , 求得MPSK和MQAM子载波接收信号的条件似然函数 ${{p}}\left( {{{{X}}_k}\left( n \right)|{m_i}} \right)$ 和OQAM的条件似然函数 ${{p}}\left( {{{{X}}_k}\left( n \right){\rm{|\theta }}} \right)$ .

(3) 由子载波接收信号的 ${{p}}\left( {{{{X}}_k}\left( n \right)|{m_i}} \right)$ 推导出多个子载波接收信号的条件似然函数 ${{p}}\left( {{{X}}\left( n \right)|{m_i}} \right)$ 降低误分类概率, 并求其对数似然函数.

(4) 根据多个子载波调制方式的 ${{LL}}{{{F}}_X}$ 计算值来设置检测门限并分类不同子载波调制方式.

2.2 基于星座图聚类算法的子载波调制识别

 图 1 调制信号星座图

 ${D_{{i}}} = \sum\limits_{j = {\rm{1}}}^n {\exp \left( - \frac{{{{\left\| {{x_i} - {x_j}} \right\|}^2}}}{{{{\left(\displaystyle\frac{{{r_a}}}{2}\right)}^2}}}\right)}$ (3)

 ${D_{{i}}} = {D_{{i}}} - {D_{c1}}\exp \left( - \frac{{{{\left\| {{x_i} - {x_{c1}}} \right\|}^2}}}{{{{\left(\displaystyle\frac{{{r_b}}}{2}\right)}^2}}}\right)$ (4)
2.3 基于对数似然函数的多载波信号调制识别

Xk(n)表示第k个子载波的接收信号, 使用 ${m_i}$ ( $i$ =2, 4, 8, 16,…)表示识别出的子载波调制类型, 则:

 ${{p}}\left( {{{{X}}_k}\left( n \right)|{m_i}} \right) = {{p}}\left( {{{{X}}_k}\left( n \right){\rm{|\theta }}} \right) \times {{p}}\left( {{\rm{\theta }}|{m_i}} \right)$ (5)

 $\begin{array}{l}{{P}}\left( {{{r}}\left( t \right)|{a_n},{b_n},h\left( t \right),{\theta _c}} \right) = \\\!\!\!\!{\rm{Cexp}}\left( { - {{N\gamma }}} \right)\exp\left[ {\displaystyle\frac{{2\sqrt {{p_t}} }}{{{N_0}}}\mathop \sum \limits_{n = 0}^{N - 1} {a_n}\mathop \smallint \limits_{nT}^{\left( {n + 1} \right)T} r\left( t \right)h\left( {t - nT} \right)\cos {w_c}tdt} \right]\\ \times \exp\left[ { - \displaystyle\frac{{2\sqrt {{p_t}} }}{{{N_0}}}\mathop \sum \limits_{n = 0}^{N - 1} {b_n}\mathop \smallint \limits_{nT}^{\left( {n + 1} \right)T} r\left( t \right)h\left( {t - nT} \right)\sin {w_c}tdt} \right]\end{array}$ (6)

 $\left\{ \begin{array}{l}{{\tilde r}_{{\rm{I}}n}} = \displaystyle\frac{1}{T}\int_{nT}^{(n + 1)T} {\tilde r(t)p(t - nT)} dt\\{{\tilde r}_{{\rm{Q}}n}} = \displaystyle\frac{1}{T}\int_{nT}^{(n + 1)T} {\tilde r(t)p[t - nT]} dt\end{array} \right.$ (7)

 $\begin{array}{l}\!\!\!\!\!{{P}}\left( {{{r}}\left( t \right){\rm{|}}{\theta _c}} \right) = {\rm{Cexp}}\left( { - {{N\gamma }}} \right) \times \exp\displaystyle\mathop \sum \limits_{n = 0}^{N - 1} \ln \cosh\left[ {\displaystyle\frac{{\sqrt {{p_t}} }}{{{\sigma ^2}}}{\rm{Re}}\left( {{{{r}}_{{\rm{I}}n}}{e^{ - {\rm{j}}{\theta _c}}}} \right)} \right]\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \times \exp\displaystyle\mathop \sum \limits_{n = 0}^{N - 1} \ln \cosh\left[ {\displaystyle\frac{{\sqrt {{p_t}} }}{{{\sigma ^2}}}{\rm{Im}}\left( {{{{r}}_{{\rm{Q}}n}}{e^{ - {{j}}{\theta _c}}}} \right)} \right]\\ = {\rm{Cexp}}\left\{ { - {{N\gamma }} + \displaystyle\mathop \sum \limits_{n = 0}^{N - 1} \left[ {\ln \cosh{{\rm{x}}_{{\rm{I}}n}}\left( {{\theta _c}} \right) + \ln \cosh{{\rm{x}}_{{\rm{Q}}n}}\left( {{\theta _c}} \right)} \right]} \right\}\end{array}$ (8)

 $\left\{ {\begin{array}{*{20}{c}} {{{\rm{x}}_{{\rm{I}}n}}\left( {{\theta _c}} \right) \triangleq \displaystyle\frac{{\sqrt {{p_t}} }}{{{\sigma ^2}}}{\rm {Re}}\left( {{{\rm{r}}_{{\rm{I}}n}}{e^{ - {\rm{j}}{\theta _c}}}} \right)} \\ {{{\rm{x}}_{{\rm{Q}}n}}\left( {{\theta _c}} \right) \triangleq \displaystyle\frac{{\sqrt {{p_t}} }}{{{\sigma ^2}}}{\rm {Im}}\left( {{{\rm{r}}_{{\rm{Q}}n}}{e^{ - {\rm{j}}{\theta _c}}}} \right)} \end{array}} \right.$ (9)

 ${\rm{ln}}\left\{ {\frac{1}{2}\left[ {\cosh\left( {X + Y} \right) + \cosh\left( {X - Y} \right)} \right]} \right\} = \ln \cosh X + \ln \cosh Y$ (10)

 $\begin{array}{l}\!\!\!\!\!P\left( {r( t )|{\theta _c}} \right) = C\exp \{ { - N\gamma } + \displaystyle\mathop \sum \limits_{n = 0}^{N - 1} \ln \frac{1}{2} \left[ {\cosh ( {{x_{{\rm I}n}}( {{\theta _c}}) }} \right.\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;+{x_{{\rm Q}n}}\left( {{\theta _c}} \right)\left. {\left. { + \cosh \left( {{x_{{\rm I}n}}\left( {{\theta _c}} \right) - {x_{{\rm Q}n}}\left( {{\theta _c}} \right)} \right)} \right]} \right\}\end{array}$ (11)

 $\left\{ {\begin{array}{*{20}{c}} {{\rm{cosh}}x \approx 1 + \displaystyle\frac{{{x^2}}}{2}} \\ {\ln \left( {1 + {\rm{x}}} \right) \approx x} \end{array}} \right.$ (12)

 $\begin{array}{l}P\left( {{{r}}\left( t \right){\rm{|}}{\theta _c}} \right) = \exp\left\{ {\displaystyle\mathop \sum \limits_{n = 0}^{N - 1} \displaystyle\frac{{{p_t}}}{{2{\sigma ^4}}}} \right.\left[ {{{\left( {{\rm{Re}}\left( {{{{r}}_{{\rm{I}}n}}{e^{ - {{j}}{\theta _{{c}}}}}} \right)} \right)}^2}} \right.\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\left. {\left. { + {\rm{Im}}{{\left( {{{{r}}_{{\rm{Q}}n}}{e^{ - {{j}}{\theta _{{c}}}}}} \right)}^2}} \right]} \right\}\end{array}$ (13)

 \left\{ {\begin{aligned}&{p\left( {{\rm{\theta }}|{m_i}} \right) = \displaystyle\frac{1}{M}\;\;\;\;{\rm {MPSK}}{\text{调制信号}}}\\&{p\left( {{\rm{\theta }}|{m_i}} \right) = \displaystyle\frac{1}{{12}}\;\;\;\;{\rm {16QAM}}{\text{调制信号}}}\\&{p\left( {{\rm{\theta }}|{m_i}} \right) = \displaystyle\frac{1}{{28}}\;\;\;\;{\rm {32QAM}}{\text{调制信号}}}\\&{p\left( {{\rm{\theta }}|{m_i}} \right) = \displaystyle\frac{1}{{44}}\;\;\;\;{\rm {64QAM}}{\text{调制信号}}}\end{aligned}} \right. (14)

${\rm{\alpha }} \triangleq {\rm{p}}\left( {{\rm{\theta }}|{m_i}} \right)$ , 则:

 \begin{aligned}&{{p}}\left( {{{{X}}_k}\left( n \right)|{m_i}} \right) = {{p}}\left( {{{{X}}_k}\left( n \right){\rm{|\theta }}} \right) \times {{p}}\left( {{\rm{\theta }}|{m_i}} \right)\\& = {{p}}\left( {{{r}}\left( t \right){\rm{|}}{\theta _c}} \right) \times \alpha \\& = \alpha \exp\left\{ {\displaystyle\mathop \sum \limits_{n = 0}^{N - 1} \displaystyle\frac{{{p_t}}}{{2{\sigma ^4}}}\left[ {{{\left( {{\rm{Re}}\left( {{{{r}}_{{\rm{I}}n}}{e^{ - {{j}}{\theta _c}}}} \right)} \right)}^2}{\rm{ + Im}}{{\left( {{{{r}}_{{\rm{Q}}n}}{e^{ - {{j}}{\theta _c}}}} \right)}^2}} \right]} \right\}\end{aligned} (15)

 $LL{F_{{X_k}}} = {\rm{ln}}\left( {\rm{\alpha }} \right)\mathop \sum \limits_{n = 0}^{N - 1} \frac{{{p_t}}}{{2{\sigma ^4}}}\left[ {{{\left( {{\rm{Re}}\left( {{{{r}}_{{\rm{I}}n}}{e^{ - {{j}}{\theta _c}}}} \right)} \right)}^2} + {\rm{Im}}{{\left( {{{{r}}_{{\rm{Q}}n}}{e^{ - {{j}}{\theta _c}}}} \right)}^2}} \right]$ (16)

 \begin{aligned}{{p}}\left( {{{X}}\left( {{n}} \right)|{m_i}} \right) &= \mathop \prod \limits_{k = 1}^K {{p}}\left( {{{{X}}_k}\left( n \right)|{m_i}} \right) = \mathop \prod \limits_{k = 1}^K {\rm{\alpha exp}}\left\{ {\displaystyle\mathop \sum \limits_{n = 0}^{N - 1} \displaystyle\frac{{{p_t}}}{{2{\sigma ^4}}}\left[ {{{\left( {{\rm{Re}}\left( {{{{r}}_{{\rm{I}}n}}{e^{ - {{j}}{\theta _c}}}} \right)} \right)}^2} + {\rm{Im}}{{\left( {{{{r}}_{{\rm{Q}}n}}{e^{ - {{j}}{\theta _{{c}}}}}} \right)}^2}} \right]} \right\}\\& = {\alpha ^K}\exp\left\{ {\displaystyle\mathop \sum \limits_{k = 0}^K \displaystyle\mathop \sum \limits_{n = 0}^{N - 1} \displaystyle\frac{{{p_t}}}{{2{\sigma ^4}}}\left[ {{{\left( {{\rm{Re}}\left( {{{{r}}_{{\rm{I}}n}}{e^{ - {{j}}2{\rm{\pi }}{f_k}t}}} \right)} \right)}^2} + {\rm{Im}}{{\left( {{{{r}}_{{\rm{Q}}n}}{e^{ - {{j}}2{\rm{\pi }}{f_k}t}}} \right)}^2}} \right]} \right\}\end{aligned} (17)

 \begin{aligned}{{LL}}{{{F}}_X} = &{\rm{ln}}\left( {{\alpha ^K}} \right)\displaystyle\mathop \sum \limits_{k = 0}^K \displaystyle\mathop \sum \limits_{n = 0}^{N - 1} \displaystyle\frac{{{p_t}}}{{2{\sigma ^4}}}\left[ {{{\left( {{\rm{Re}}\left( {{{{r}}_{{\rm{I}}n}}{e^{ - {\rm{j}}2{\rm{\pi }}{f_k}t}}} \right)} \right)}^2}} \right.\\&\left. { + {\rm{Im}}{{\left( {{{\rm{r}}_{{\rm{Q}}n}}{e^{ - {{j}}2{\rm{\pi }}{f_k}t}}} \right)}^2}} \right]\end{aligned} (18)

3 仿真结果与分析

3.1 基于星座图的聚类算法的调制识别

 图 2 BPSK, QPSK, 8PSK, 16QAM, 32QAM, 64QAM的星座图聚类并投影结果

3.2 基于对数似然函数的多载波信号识别仿真

 图 3 文献[9]中方法在不进行星座图恢复情况下8PSK信号的星座图聚类投影结果

4 结论与展望

 图 4 文献[9]中方法在不进行星座图恢复情况下16QAM信号的星座图聚类投影结果

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