CN103036669B

CN103036669B - A kind of symbol timing synchronization method based on particle filter

Info

Publication number: CN103036669B
Application number: CN201210566909.4A
Authority: CN
Inventors: 刘策伦; 安建平; 田露; 卜祥元; 卢继华; 王正欢; 黄彦东; 柯晟
Original assignee: Beijing Institute of Technology BIT
Current assignee: Beijing Institute of Technology BIT
Priority date: 2012-12-24
Filing date: 2012-12-24
Publication date: 2015-09-09
Anticipated expiration: 2032-12-24
Also published as: CN103036669A

Abstract

The invention relates to a particle filter-based symbol synchronization method, in particular to a particle filter-based high-speed satellite communication system symbol synchronization method, which belongs to the technical field of communication signal processing. After the input analog baseband signal is sampled by AD, it becomes a digital signal. The digital signal first passes through an interpolation filter, which is based on the input signal and the timing deviation estimate provided by the particle filter. The value of the best sampling time is calculated, and the output of the interpolation filter is sent to the timing error calculation module to obtain the measurement timing error, and the measurement timing error is passed through the particle filter to obtain the estimated value of the timing deviation then It is sent to the interpolation filter to control the interpolation time, the output x'(rT _s ) of the interpolation filter already contains the value x'(rT) at the best sampling time, and the symbol synchronization is completed by direct output. The method of the invention improves the estimation precision of the timing error without increasing the sampling rate; the particle filter is used to adjust the timing deviation, and the influence of the self-noise is reduced compared with the traditional scheme.

Description

A Symbol Synchronization Method Based on Particle Filter

技术领域technical field

本发明涉及一种基于粒子滤波的符号同步方法，尤其涉及一种基于粒子滤波的高速卫星通信系统符号同步方法，属于通信信号处理技术领域。The invention relates to a particle filter-based symbol synchronization method, in particular to a particle filter-based high-speed satellite communication system symbol synchronization method, which belongs to the technical field of communication signal processing.

背景技术Background technique

同步一直是高速卫星通信系统的研究主题和技术瓶颈，其中，寻找并跟踪码元符号最佳采样时刻的过程即为符号同步。对于高速卫星通信系统，由于调制的符号速率很高，受AD器件的限制，AD的采样率相对于符号速率不能太高，需要能够在相对于符号速率较低的采样率下精确恢复出最佳采样时刻的信号值。1986年5月Gardner在一篇名为“A BPSK/QPSK Timing-Error Detector forSampled Receivers”的论文中提出了一种符号同步算法，简称Gardner算法。Gardner算法中每个符号只需两个采样点参与计算便可准确地实现定时恢复,并且对载波相位不敏感,可先于载波恢复完成定时恢复。但对于高阶调制（例如16APSK），即使采用2008年一篇名为“A Modified Gardner Detector for MultilevelPAM/QAM System”的论文中提出的修正方法，系统性能仍受Gardner算法本身的自噪声影响较大。滤波器的适当选取就变得尤其重要，以往的符号同步结构中仅使用环路滤波器，2005年11月一篇名为“Feedforward Symbol TimingRecovery Technique Using Two Samples Per Symbol”的论文将传统符号同步算法与卡尔曼滤波器相结合，获得了更优的估计性能。而卡尔曼滤波器及扩展的卡尔曼滤波器无法处理非高斯模型及滤波误差和预测误差较大的情况，相比之下，粒子滤波器的应用范围更广，日渐成为学术界的研究热点。2003年9月一篇名为“Particle filtering”的论文简要介绍了粒子滤波的工作原理及其在通信系统中的应用。近年来，粒子滤波逐渐引起信号处理和通信领域的重视。盲均衡，多用户检测，衰落信道中的空时码估计和检测等诸多问题均可建模为粒子滤波问题。如2006年5月公开的专利“基于粒子滤波的信道估计方法”就将粒子滤波应用于信道估计算法中。而本发明将粒子滤波方法应用于符号同步系统以提高估计性能。2005年8月发表的一篇名为“A Sequential Monte Carlo Method forAdaptive Blind Timing Estimation and Data Detection”的论文，尽管采用了粒子滤波的方法估计定时误差进行符号同步，但是无法在低采样率的条件下达到本发明的估计性能。Synchronization has always been the research topic and technical bottleneck of high-speed satellite communication systems. Among them, the process of finding and tracking the best sampling time of symbol symbols is symbol synchronization. For high-speed satellite communication systems, due to the high symbol rate of modulation, limited by the AD device, the AD sampling rate should not be too high relative to the symbol rate, and it is necessary to be able to accurately restore the best signal at a lower sampling rate than the symbol rate. The value of the signal at the sampling instant. In May 1986, Gardner proposed a symbol synchronization algorithm in a paper titled "A BPSK/QPSK Timing-Error Detector for Sampled Receivers", referred to as the Gardner algorithm. In the Gardner algorithm, only two sampling points are needed for each symbol to participate in the calculation, and the timing recovery can be realized accurately, and it is not sensitive to the carrier phase, and the timing recovery can be completed before the carrier recovery. But for high-order modulation (such as 16APSK), even if the modification method proposed in a paper named "A Modified Gardner Detector for MultilevelPAM/QAM System" in 2008 is adopted, the system performance is still greatly affected by the self-noise of the Gardner algorithm itself . The proper selection of the filter becomes particularly important. In the past, only the loop filter was used in the symbol synchronization structure. In November 2005, a paper titled "Feedforward Symbol Timing Recovery Technique Using Two Samples Per Symbol" made the traditional symbol synchronization algorithm Combined with the Kalman filter, better estimation performance is obtained. However, the Kalman filter and the extended Kalman filter cannot deal with non-Gaussian models and the situation where the filtering error and prediction error are large. In contrast, the particle filter has a wider range of applications and has gradually become a research hotspot in the academic community. A paper titled "Particle filtering" in September 2003 briefly introduced the working principle of particle filtering and its application in communication systems. In recent years, particle filter has gradually attracted attention in the field of signal processing and communication. Blind equalization, multi-user detection, space-time code estimation and detection in fading channels and many other problems can be modeled as particle filter problems. For example, the patent "Channel Estimation Method Based on Particle Filter" published in May 2006 applies the particle filter to the channel estimation algorithm. However, the present invention applies the particle filter method to the symbol synchronization system to improve the estimation performance. In a paper titled "A Sequential Monte Carlo Method for Adaptive Blind Timing Estimation and Data Detection" published in August 2005, although the method of particle filtering was used to estimate the timing error for symbol synchronization, it could not be used under the condition of low sampling rate The estimated performance of the present invention is achieved.

已有的符号同步技术已经有较好的估计性能，但对于低信噪比下的高阶调制，其估计性能仍然不够理想。The existing symbol synchronization technology has good estimation performance, but for high-order modulation with low SNR, its estimation performance is still not ideal.

发明内容Contents of the invention

本发明的目的是为改善现有时域符号同步算法估计性能低的缺陷，提出一种基于粒子滤波的符号同步方法，在不增加采样率和少量增加算法复杂度的前提下，实现高速卫星通信的符号同步。The purpose of the present invention is to improve the defect of low estimation performance of the existing time-domain symbol synchronization algorithm, and propose a symbol synchronization method based on particle filter, to realize high-speed satellite communication without increasing the sampling rate and a small increase in algorithm complexity. Symbol synchronization.

一种基于粒子滤波的符号同步方法，其实现步骤如下：A particle filter-based symbol synchronization method, the implementation steps are as follows:

步骤1、对输入的一路或两路模拟基带信号,进行采样，得到数字信号；其中，采样率为f_s。Step 1. Sampling one or two input analog baseband signals to obtain digital signals; wherein, the sampling rate is f _s .

其中，对于二进制调制，输入的一路模拟基带信号为x(t)，经模数转换得到一路数字信号x(nT_s)；对于多进制调制，输入的基带信号为两路模拟信号x_I(t)和x_Q(t)，经模数转换后得到两路信号x_I(nT_s)和x_Q(nT_s)；采样率为f_s，采样间隔为n为采样点的序号。Wherein, for binary modulation, the input analog baseband signal of one path is x(t), which is obtained through analog-to-digital conversion of one path of digital signal x(nT _s ); for multi-ary modulation, the input baseband signal is two analog signals x _I ( t) and x _Q (t), after analog-to-digital conversion, two signals x _I (nT _s ) and x _Q (nT _s ) are obtained; the sampling rate is f _s , and the sampling interval is n is the serial number of the sampling point.

步骤2、产生粒子。Step 2. Generate particles.

按照设定的概率分布π（π通常选取一个均值为0，方差很大的Gaussian分布）,对每个符号(码元)周期产生N个粒子样本，N个粒子样本对应的定时偏差记为上标i表示样本序号，i=1,2,…,N，下标r为符号周期序号，r=1,2,…。According to the set probability distribution π (π usually chooses a Gaussian distribution with a mean value of 0 and a large variance), N particle samples are generated for each symbol (symbol) period, and the timing deviation corresponding to the N particle samples is recorded as The superscript i represents the sample number, i=1,2,...,N, and the subscript r represents the symbol period number, r=1,2,....

步骤3、粒子滤波初始化。Step 3, particle filter initialization.

步骤3.1，记r=1时产生的N个粒子样本值为其中每一个粒子的重要性权值为 Step 3.1, record the N particle sample values generated when r=1 The importance weight of each particle is

步骤3.2，将步骤3.1输出的每个粒子重要性权值进行归一化Step 3.2, normalize the importance weight of each particle output in step 3.1

${\overset{~ ~}{w w}}_{11}^{((i i))} = = \frac{{w w}_{11}^{((i i))}}{{Σ Σ}_{i i = = 11}^{N N} {w w}_{11}^{((i i))}} = = \frac{11}{N N} - - - - - - ((11))$

步骤3.3，计算定时偏差估计值 Step 3.3, Calculate Timing Offset Estimate

${\overset{^^}{ϵ ϵ}}_{11} = = {Σ Σ}_{i i = = 11}^{N N} {ϵ ϵ}_{11}^{((i i))} {\overset{~ ~}{w w}}_{11}^{((i i))} - - - - - - ((22))$

步骤4、根据当前符号的定时偏差估计值对步骤一输出的数字信号进行插值滤波，得到最佳采样时刻的插值滤波输出值，实现符号同步。Step 4. According to the estimated value of the timing deviation of the current symbol Interpolation filtering is performed on the digital signal output in step 1 to obtain an interpolation filtering output value at an optimal sampling time, and to realize symbol synchronization.

插值滤波采用频域算法，具体步骤如下：The interpolation filter adopts the frequency domain algorithm, and the specific steps are as follows:

步骤4.1，对步骤一输出的x(nT_s)信号进行K点FFT，得到频谱R(kf_s/K)。Step 4.1: Perform K-point FFT on the x(nT _s ) signal output in step 1 to obtain the spectrum R(kf _s /K).

步骤4.2，对步骤4.1得到的频谱R(kf_s/K)进行相位旋转，得到去除定时偏差的频域数据R′(kf_s/K)：Step 4.2, perform phase rotation on the frequency spectrum R(kf _s /K) obtained in step 4.1, and obtain frequency domain data R′(kf _s /K) with timing deviation removed:

${R R}^{' '} (({kf kf}_{s the s} / / K K)) = = R R (({kf kf}_{s the s} / / K K)) exp exp ((j j 22 πk πk {f f}_{s the s} {\overset{^^}{ϵ ϵ}}_{r r} T T / / K K)) - - - - - - ((33))$

步骤4.3，对步骤4.2输出的R′(kf_s/K)进行IFFT，输出当前符号周期下插值滤波器的输出x'(nT_s)，提取其中最佳采样时刻的输出值x′(rT)，T为码元周期，实现当前符号周期的同步。Step 4.3, perform IFFT on R'(kf _s /K) output in step 4.2, output the output x'(nT _s ) of the interpolation filter under the current symbol period, and extract the output value x'(rT) at the best sampling moment , T is the symbol period, which realizes the synchronization of the current symbol period.

若为多进制调制，插值滤波器的输出为x′_I(nT_s)和x′_Q(nT_s)，则最佳采样时刻的输出值为x′_I(r_T)和x′_Q(r_T)。If it is multi-ary modulation, the output of the interpolation filter is x′ _I (nT _s ) and x′ _Q (nT _s ), then the output values at the best sampling moment are x′ _I (r _T ) and x′ _Q ( r _T ).

步骤5、根据步骤4的插值滤波最佳采样时刻输出值，计算r>1时的测量定时误差u(r)。Step 5. Calculate the measurement timing error u(r) when r>1 according to the output value at the best sampling time of the interpolation filter in step 4.

对于二进制调制，第r个符号周期的测量定时误差为：For binary modulation, the measured timing error for the rth symbol period is:

$u u ((r r)) = = u u ((rT rT)) = = {x x}^{' '} ((rT rT - - \frac{11}{22} T T)) [[{x x}^{' '} ((rT rT)) - - {x x}^{' '} ((rT rT - - T T))]] - - - - - - ((44))$

对于多进制调制,第r个符号周期的测量定时误差为：For multi-ary modulation, the measured timing error for the rth symbol period is:

$u u ((r r)) = = u u ((rT rT))$

$= = {x x}_{11}^{' '} ((rT rT - - \frac{11}{22} T T)) [[{x x}_{11}^{' '} ((rT rT)) - - {x x}_{11}^{' '} ((rT rT - - T T))]] + + {x x}_{Q Q}^{' '} ((rT rT - - \frac{11}{22} T T)) [[{x x}_{Q Q}^{' '} ((rT rT)) - - {x x}_{Q Q}^{' '} ((rT rT - - T T))]] - - - - - - ((55))$

步骤6、对步骤5得到的测量定时误差进行粒子滤波，得到对应符号周期的定时偏差估计值。Step 6. Perform particle filtering on the measurement timing error obtained in step 5 to obtain an estimated value of the timing deviation corresponding to the symbol period.

具体步骤如下：Specific steps are as follows:

步骤6.1,根据状态方程及第r-1个符号周期的定时误差，求得第r个符号周期对应的N个粒子样本的定时偏差。Step 6.1, according to the state equation and the timing error of the r-1th symbol period, the timing deviation of the N particle samples corresponding to the r-th symbol period is obtained.

状态方程为：The state equation is:

${ϵ ϵ}_{r r}^{((i i))} = = {ϵ ϵ}_{r r - - 11}^{((i i))} + + {μ μ}_{r r}^{((i i))} - - - - - - ((66))$

其中，为系统噪声。in, is the system noise.

步骤6.2,根据观测方程，建立u(r)与的关系；Step 6.2, according to the observation equation, establish u(r) and Relationship;

观测方程根据u(r)与之间的S曲线得到，表示为The observation equation is based on u(r) and The S-curve between is obtained, expressed as

$u u ((r r)) = = - - ((44 / / T T)) sin sin ((22 π π {ϵ ϵ}_{r r}^{((i i))})) {&Integral; &Integral;}_{00}^{11 / / T T} G G ((f f)) G G ((\frac{11}{T T} - - f f)) sin sin πfTdf πfTdf {+ + γ γ}_{r r}^{((i i))} - - - - - - ((1515))$

其中，G(f)为滤波函数，为观测噪声。Among them, G(f) is the filter function, is the observation noise.

步骤6.3,计算第r个符号周期中每一个粒子的重要性权值；Step 6.3, calculating the importance weight of each particle in the rth symbol period;

${w w}_{r r}^{((i i))} = = {w w}_{r r - - 11}^{((i i))} \frac{p p ((u u ((r r)) | | {ϵ ϵ}_{r r}^{((i i))})) p p (({ϵ ϵ}_{r r}^{((i i))} | | {ϵ ϵ}_{r r - - 11}^{((i i))}))}{π π (({ϵ ϵ}_{r r}^{((i i))} | | {ϵ ϵ}_{00 : : r r - - 11}^{((i i))},, u u ((r r))))} - - - - - - ((77))$

其中，表示第r个符号周期的N个粒子样本点的重要性权值；表示在条件下定时误差u(r)的概率密度。表示在条件下的概率密度。in, Represents the importance weights of the N particle sample points of the r-th symbol period; expressed in The probability density of the timing error u(r) under the condition. expressed in under the condition the probability density of .

步骤6.4,将步骤6.3输出的第r个符号周期的每个粒子重要性权值进行归一化： ${\tilde{w}}_{r}^{(i)} = \frac{w_{r}^{(i)}}{Σ_{i = 1}^{N} w_{r}^{(i)}} - - - (8)$ Step 6.4, normalize the importance weight of each particle of the rth symbol period output in step 6.3: ${\tilde{w}}_{r}^{(i)} = \frac{w_{r}^{(i)}}{Σ_{i = 1}^{N} w_{r}^{(i)}} - - - (8)$

其中，表示第r个符号周期N个粒子样本点的归一化重要性权值。in, Indicates the normalized importance weight of N particle sample points in the r-th symbol period.

步骤6.5,为消除退化现象，对步骤6.4输出的归一化权值进行重采样。In step 6.5, in order to eliminate the degradation phenomenon, the normalized weights output in step 6.4 are resampled.

每一个符号周期的重采样结果仍为N个粒子，用表示重采样后的N个粒子样本值的定时偏差，重采样后新粒子对应的权值为即 The resampling result of each symbol period is still N particles, using Indicates the timing deviation of the N particle sample values after resampling, and the weight corresponding to the new particle after resampling is Right now

步骤6.6,求取第r个符号周期重采样后的定时偏差估计值 Step 6.6, obtain the estimated value of the timing offset after resampling of the rth symbol period

${\overset{^^}{ϵ ϵ}}_{r r} = = {Σ Σ}_{i i = = 11}^{N N} {ϵ ϵ}_{r r}^{' ' ((i i))} {\overset{~ ~}{w w}}_{r r}^{((i i))} - - - - - - ((99))$

步骤6.7，将步骤6.6计算得到的带入步骤4，继续步骤4至步骤6，直到实现所有符号周期的同步。Step 6.7, the calculated step 6.6 Bringing into step 4, continue step 4 to step 6 until the synchronization of all symbol periods is achieved.

有益效果Beneficial effect

本发明“一种基于粒子滤波的符号同步方法”，具有如下优点：The present invention "a symbol synchronization method based on particle filter" has the following advantages:

1.在不增加采样率的前提下，提高了定时误差估计精度；1. On the premise of not increasing the sampling rate, the timing error estimation accuracy is improved;

2.利用粒子滤波调整定时偏差，相比传统Gardner符号同步方法进一步降低了自噪声的影响；2. The particle filter is used to adjust the timing deviation, which further reduces the influence of self-noise compared with the traditional Gardner symbol synchronization method;

3.其估计方差性能优于使用传统环路滤波器的Gardner符号同步方法；3. Its estimated variance performance is better than the Gardner symbol synchronization method using traditional loop filters;

4.其误码率性能在高信噪比（Eb/N₀>10）的情况下，优于传统Gardner符号同步算法；提高了同步估计精度和系统误码率性能。4. Its bit error rate performance is superior to the traditional Gardner symbol synchronization algorithm in the case of high signal-to-noise ratio (Eb/N ₀ >10); it improves the synchronization estimation accuracy and system bit error rate performance.

附图说明Description of drawings

图1是本发明“一种基于粒子滤波的符号同步方法”及实施例1中的系统实现原理图；Fig. 1 is a schematic diagram of the system implementation in "a particle filter-based symbol synchronization method" and embodiment 1 of the present invention;

图2是本发明“一种基于粒子滤波的符号同步方法”及实施例1和实施例2中不同滚降系数α时u(r)与之间的S曲线，横坐标为定时偏差纵坐标为定时误差u(r)；Fig. 2 is "a kind of symbol synchronization method based on particle filter" of the present invention and embodiment 1 and embodiment 2 in different roll-off coefficient α when u(r) and The S curve between, the abscissa is the timing deviation The ordinate is the timing error u(r);

图3是本发明“一种基于粒子滤波的符号同步方法”的实施例1中采用16APSK调制方式、滚降系数为0.2时，传统Gardner符号同步方法与本发明“一种基于粒子滤波的符号同步方法”的稳态定时误差估计量方差对比图，横坐标为信噪比，纵坐标为定时偏差的估计方差；Fig. 3 is the traditional Gardner symbol synchronization method and the present invention "a symbol synchronization method based on particle filter" when the 16APSK modulation mode is adopted and the roll-off coefficient is 0.2 in Embodiment 1 of the "a particle filter-based symbol synchronization method" Method" steady-state timing error estimator variance comparison graph, the abscissa is the signal-to-noise ratio, and the ordinate is the estimated variance of the timing error;

图4是本发明“一种基于粒子滤波的符号同步方法”的实施例2中采用32APSK调制方式时，传统Gardner符号同步方法与基于粒子滤波的符号同步方法误码率性能的对比图，横坐标为信噪比，纵坐标为系统的误比特率。Fig. 4 is a comparison chart of the bit error rate performance between the traditional Gardner symbol synchronization method and the particle filter-based symbol synchronization method when the 32APSK modulation method is adopted in Embodiment 2 of the "a particle filter-based symbol synchronization method", the abscissa is the signal-to-noise ratio, and the ordinate is the bit error rate of the system.

具体实施方式Detailed ways

为了更好的说明本发明方法的目的和优点，下面结合附图和16APSK、32APSK两种高阶调制方式的实施例对本发明的具体实施过程进行说明。In order to better illustrate the purpose and advantages of the method of the present invention, the specific implementation process of the present invention will be described below in conjunction with the accompanying drawings and embodiments of two high-order modulation modes of 16APSK and 32APSK.

实施例1Example 1

以采用16APSK调制方式，匹配滤波器滚降系数为0.2的调制解调系统为例，采用本发明“一种基于粒子滤波的符号同步方法”实现符号同步。Taking a modulation and demodulation system that adopts 16APSK modulation mode and a matched filter roll-off coefficient of 0.2 as an example, "a symbol synchronization method based on particle filter" of the present invention is used to realize symbol synchronization.

如图1所示，符号速率为1Mbaud的输入模拟基带信号x_I(t)和x_Q(t)经过采样率固定为200MHz的AD采样后，变为数字信号x_I(nT_s)和x_Q(nT_s)，x_I(nT_s)和x_Q(nT_s)首先经过一个插值滤波器，该滤波器根据输入信号和由粒子滤波器提供的定时偏差估计值计算出最佳采样时刻的值，插值滤波器的输出送入定时误差计算模块，得到u(r)，u(r)经粒子滤波即得定时偏差估计值再将送入插值滤波器以控制插值时刻，插值滤波器的输出x′(rT_s)中已包含了最佳采样时刻的值x′(rT)，直接输出即完成符号同步。As shown in Figure 1, the input analog baseband signals x _I (t) and x _Q (t) with a symbol rate of 1Mbaud become digital signals x _I (nT _s ) and x _Q after being sampled by AD with a fixed sampling rate of 200MHz (nT _s ), x _I (nT _s ) and x _Q (nT _s ) first pass through an interpolation filter based on the input signal and the timing offset estimate provided by the particle filter Calculate the value of the best sampling time, and the output of the interpolation filter is sent to the timing error calculation module to obtain u(r), and u(r) is particle-filtered to obtain the estimated value of the timing deviation then It is sent to the interpolation filter to control the interpolation time, the output x'(rT _s ) of the interpolation filter already contains the value x'(rT) at the best sampling time, and the symbol synchronization is completed by direct output.

步骤1、对输入的两路符号速率为1MBaud、调制方式为16APSK、滚降系数为0.2的模拟基带信号,进行采样，得到数字信号；其中，采样率为200MHz。Step 1. Sampling the two input analog baseband signals with a symbol rate of 1 MBaud, a modulation mode of 16APSK, and a roll-off coefficient of 0.2 to obtain a digital signal; wherein, the sampling rate is 200 MHz.

其中，输入的基带信号为两路模拟信号x_I(t)和x_Q(t)，经模数转换后得到两路信号x_I(nT_s)和x_Q(nT_s)。Among them, the input baseband signals are two analog signals x _I (t) and x _Q (t), and after analog-to-digital conversion, two signals x _I (nT _s ) and x _Q (nT _s ) are obtained.

步骤2、产生粒子.Step 2. Generate particles.

按照设定的概率分布π，选取π服从均值为0，方差为0.01的Gaussian分布,对每个符号(码元)周期产生N=100个粒子样本，100个粒子样本对应的定时偏差记为上标i表示样本序号，i=1,2,…,N，下标r为符号周期序号，r=1,2,…。According to the set probability distribution π, select π to obey the Gaussian distribution with the mean value of 0 and the variance of 0.01, and generate N=100 particle samples for each symbol (symbol) cycle, and the timing deviation corresponding to 100 particle samples is recorded as The superscript i represents the sample number, i=1,2,...,N, and the subscript r represents the symbol period number, r=1,2,....

步骤3、粒子滤波初始化。Step 3, particle filter initialization.

${\overset{~ ~}{w w}}_{r r}^{((i i))} = = \frac{{w w}_{r r}^{((i i))}}{{Σ Σ}_{i i = = 11}^{N N} {w w}_{11}^{((i i))}} = = \frac{11}{N N} = = \frac{11}{100100} - - - - - - ((11))$

${\overset{^^}{ϵ ϵ}}_{11} = = {Σ Σ}_{i i = = 11}^{N N} {ϵ ϵ}_{11}^{((i i))} {\overset{~ ~}{w w}}_{11}^{((i i))} = = 00 - - - - - - ((22))$

步骤4.1，对步骤一输出的x(nT_s)信号进行K=16点FFT，得到频谱R(kf_s/K)。Step 4.1: Perform K=16-point FFT on the x(nT _s ) signal output in step 1 to obtain the spectrum R(kf _s /K).

步骤5、根据步骤4的插值滤波输出值，计算r>1时的测量定时误差u(r)。Step 5. Calculate the measurement timing error u(r) when r>1 according to the interpolation filter output value in step 4.

对于MQAM和MAPSK等高阶调制，需要对中间采样值进行修正：For high-order modulations such as MQAM and MAPSK, the intermediate sampling values need to be corrected:

${x x}_{I I}^{' '' '} ((rT rT - - \frac{11}{22} T T)) = = {x x}_{I I}^{' '} ((rT rT - - \frac{11}{22} T T)) - - β β [[{x x}_{I I}^{' '} ((rT rT - - T T)) + + {x x}_{I I}^{' '} ((rT rT))]] - - - - - - ((44))$

${x x}_{Q Q}^{' '' '} ((rT rT - - \frac{11}{22} T T)) = = {x x}_{Q Q}^{' '} ((rT rT - - \frac{11}{22} T T)) - - β β [[{x x}_{Q Q}^{' '} ((rT rT - - T T)) + + {x x}_{Q Q}^{' '} ((rT rT))]] - - - - - - ((55))$

其中，和为修正后的中间采样值，in, and is the corrected intermediate sampling value,

β=h(T/2)/h(0)=h(-T/2)/h(0)，h(t)为滤波器的冲激响应；β=h(T/2)/h(0)=h(-T/2)/h(0), h(t) is the impulse response of the filter;

第r个符号周期的测量定时误差为：The measured timing error for the rth symbol period is:

$u u ((r r)) = = u u ((rT rT))$

$= = {x x}_{I I}^{' '' '} ((rT rT - - \frac{11}{22} T T)) [[{x x}_{I I}^{' '} ((rT rT)) - - {x x}_{I I}^{' '} ((rT rT - - T T))]] + + {x x}_{Q Q}^{' '' '} ((rT rT - - \frac{11}{22} T T)) [[{x x}_{Q Q}^{' '} ((rT rT)) - - {x x}_{Q Q}^{' '} ((rT rT - - T T))]] - - - - - - ((66))$

步骤6、对步骤5得到的测量定时误差进行粒子滤波，得到对应符号周期的定时偏差估计值。Step 6. Perform particle filtering on the measured timing error obtained in step 5 to obtain an estimated value of the timing deviation corresponding to the symbol period.

具体步骤如下：Specific steps are as follows:

状态方程为：The state equation is:

${ϵ ϵ}_{r r}^{((i i))} = = {ϵ ϵ}_{r r - - 11}^{((i i))} + + {μ μ}_{r r}^{((i i))} - - - - - - ((77))$

其中，为系统噪声，设定其服从均值为0，方差为0.00001的Gaussian分布。in, As the system noise, it is set to obey the Gaussian distribution with mean value 0 and variance 0.00001.

观测方程根据u(r)与之间的S曲线得到，可表示为The observation equation is based on u(r) and The S-curve between is obtained, which can be expressed as

$u u ((r r)) = = - - ((44 / / T T)) sin sin ((22 π π {ϵ ϵ}_{r r}^{((i i))})) {&Integral; &Integral;}_{00}^{11 / / T T} G G ((f f)) G G ((\frac{11}{T T} - - f f)) sin sin πfTdf πfTdf {+ + γ γ}_{r r}^{((i i))} - - - - - - ((88))$

当G(f)为升余弦滚降滤波器时，When G(f) is a raised cosine roll-off filter,

$u u ((r r)) = = sin sin ((πα πα / / 22)) sin sin ((22 π π {ϵ ϵ}_{r r}^{((i i))})) / / [[π π ((11 - - {α α}^{22} / / 44))]] + + {γ γ}^{((i i))} - - - - - - ((99))$

其中，α为升余弦滤波器的滚降系数，不同滚降系数对应的S曲线见图2。本实施例中α=0.2。Among them, α is the roll-off coefficient of the raised cosine filter, and the S-curves corresponding to different roll-off coefficients are shown in Figure 2. In this embodiment, α=0.2.

${w w}_{r r}^{((i i))} = = {w w}_{r r - - 11}^{((i i))} \frac{p p ((u u ((r r)) | | {ϵ ϵ}_{r r}^{((i i))})) p p (({ϵ ϵ}_{r r}^{((i i))} | | {ϵ ϵ}_{r r - - 11}^{((i i))}))}{π π (({ϵ ϵ}_{r r}^{((i i))} | | {ϵ ϵ}_{00 : : r r - - 11}^{((i i))},, u u ((r r))))} - - - - - - ((1010))$

由于选取的先验概率密度函数为重要性函数，即，Since the selected prior probability density function is an importance function, that is,

$π π (({ϵ ϵ}_{r r}^{((i i))} | | {ϵ ϵ}_{00 : : r r - - 11}^{((i i))},, u u ((r r)))) = = p p (({ϵ ϵ}_{r r}^{((i i))} | | {ϵ ϵ}_{r r - - 11}^{((i i))})) - - - - - - ((1111))$

因此， $w_{r}^{(i)} = w_{r - 1}^{(i)} p (u (r) | ϵ_{r}^{(i)}) - - - (12)$ therefore, $w_{r}^{(i)} = w_{r - 1}^{(i)} p (u (r) | ϵ_{r}^{(i)}) - - - (12)$

由于存在观测噪声与系统噪声，且它们之间相互独立，因此，Since there are observation noise and system noise, and they are independent of each other, therefore,

$p p ((u u ((r r)) | | {ϵ ϵ}_{r r}^{((i i))})) = = p p (({γ γ}_{r r} | | {ϵ ϵ}_{r r}^{((i i))})) = = p p ((u u ((r r)) - - sin sin ((πα πα / / 22)) sin sin ((22 π π {ϵ ϵ}_{r r}^{((i i))})) / / [[π π ((11 - - {α α}^{22} / / 44))]])) - - - - - - ((1313))$

假设观测噪声服从均值为0的高斯分布，则权值计算为Assuming that the observation noise obeys a Gaussian distribution with a mean of 0, the weight is calculated as

${w w}_{r r}^{((i i))} = = {w w}_{r r - - 11}^{((i i))} exp exp [[- - \frac{11}{{22 σ σ}^{22}} ((u u ((r r)) - - sin sin ((πα πα / / 22)) sin sin ((22 π π {ϵ ϵ}_{r r}^{((i i))})) / / [[π π ((11 - - {α α}^{22} / / 44))]]))]] - - - - - - ((1414))$

步骤6.4,将步骤6.3输出的第r个符号周期的每个粒子重要性权值进行归一化：Step 6.4, normalize the importance weight of each particle of the rth symbol period output in step 6.3:

${\overset{~ ~}{w w}}_{r r}^{((i i))} = = \frac{{w w}_{r r}^{((i i))}}{{Σ Σ}_{i i = = 11}^{N N} {w w}_{r r}^{((i i))}} - - - - - - ((1515))$

本实施例采用系统采样方法进行重采样：In this embodiment, the system sampling method is used for resampling:

根据下式生成N=100个随机数，Generate N=100 random numbers according to the following formula,

其中，q服从[0，1]的均匀分布，m=1,2,…,100； Among them, q obeys the uniform distribution of [0, 1], m=1,2,...,100;

如果直接拷贝a个粒子为重采样粒子。if directly copy a particle for resampled particles.

每一个符号周期的重采样结果仍为N=100个粒子，用表示重采样后的100个粒子样本值的定时偏差，重采样后新粒子对应的权值为即 The resampling result of each symbol period is still N=100 particles, using Indicates the timing deviation of 100 particle sample values after resampling, and the weight corresponding to the new particle after resampling is Right now

${\overset{^^}{ϵ ϵ}}_{r r} = = {Σ Σ}_{i i = = 11}^{N N} {ϵ ϵ}_{r r}^{' ' ((i i))} {\overset{~ ~}{w w}}_{r r}^{((i i))} - - - - - - ((1616))$

基于本发明“一种基于粒子滤波的符号同步方法”中的同步方法，对采用16APSK调制方式，滚降系数为0.2的系统实现同步，可以得出图3的传统Gardner符号同步算法与基于粒子滤波的符号同步算法的稳态定时误差估计量的方差对比图，其中，传统Gardner同步算法中所用的环路滤波器的归一化带宽为B_LT=10^-3。观察发现，采用基于粒子滤波的符号同步算法的稳态定时误差估计量的方差比采用传统Gardner符号同步算法的稳态定时误差估计量的方差性能提升近8dB。Based on the synchronization method in "a kind of symbol synchronization method based on particle filter" of the present invention, to adopt 16APSK modulation mode, the system that roll-off coefficient is 0.2 realizes synchronization, can draw the traditional Gardner symbol synchronization algorithm of Fig. 3 and based on particle filter The comparison chart of the variance of the steady-state timing error estimator of the symbol synchronization algorithm, where the normalized bandwidth of the loop filter used in the traditional Gardner synchronization algorithm is B _L T=10 ^-3 . It is observed that the variance performance of the steady-state timing error estimator using the particle filter-based symbol synchronization algorithm is nearly 8dB higher than that of the traditional Gardner symbol synchronization algorithm.

实施例2Example 2

为了进一步验证该同步方法，针对存在频偏和相偏的系统采用本发明所述的“一种基于粒子滤波的符号同步方法”中的方法实现同步。该系统采用STM-4标准，信息速率为622.08Mbps，采用32APSK调制方式，符号速率为154MB，每帧帧头120个符号、有效数据3936个符号，滚降系数为0.5。In order to further verify the synchronization method, the method in "a particle filter-based symbol synchronization method" described in the present invention is used to achieve synchronization for a system with frequency offset and phase offset. The system adopts the STM-4 standard, the information rate is 622.08Mbps, the 32APSK modulation method is adopted, the symbol rate is 154MB, each frame has 120 symbols at the beginning of the frame, 3936 symbols of effective data, and the roll-off coefficient is 0.5.

步骤1、对输入的两路符号速率为154MBaud、调制方式为32APSK、滚降系数为0.5的模拟基带信号,进行采样，得到数字信号；其中，采样率为1.54GHz。Step 1. Sampling the two input analog baseband signals with a symbol rate of 154MBaud, a modulation mode of 32APSK, and a roll-off coefficient of 0.5 to obtain a digital signal; wherein, the sampling rate is 1.54GHz.

步骤2、产生粒子。Step 2. Generate particles.

步骤3、粒子滤波初始化。Step 3, particle filter initialization.

${\overset{~ ~}{w w}}_{11}^{((i i))} = = \frac{{w w}_{11}^{((i i))}}{{Σ Σ}_{i i = = 11}^{N N} {w w}_{11}^{((i i))}} = = \frac{11}{N N} = = \frac{11}{100100} - - - - - - ((11))$

可知 It can be seen

步骤4.1，对步骤一输出的x(nT_s)信号进行K=32点FFT，得到频谱R(kf_s/K)。Step 4.1: Perform K=32-point FFT on the x(nT _s ) signal output in step 1 to obtain the spectrum R(kf _s /K).

若为多进制调制，插值滤波器的输出为x′_I(nT_s)和x′_Q(nT_s)，则最佳采样时刻的输出值为x′_I(rT)和x′_Q(rT)。If it is multi-ary modulation, the output of the interpolation filter is x′ _I (nT _s ) and x′ _Q (nT _s ), then the output values at the best sampling moment are x′ _I (rT) and x′ _Q (rT ).

$u u ((r r)) = = u u ((rT rT))$

具体步骤如下：Specific steps are as follows:

状态方程为：The state equation is:

其中，α为升余弦滤波器的滚降系数，不同滚降系数对应的S曲线见图3。本实施例中α=0.5。Among them, α is the roll-off coefficient of the raised cosine filter, and the S-curves corresponding to different roll-off coefficients are shown in Figure 3. In this embodiment, α=0.5.

因此，therefore,

${w w}_{r r}^{((i i))} = = {w w}_{r r - - 11}^{((i i))} p p ((u u ((r r)) | | {ϵ ϵ}_{r r}^{((i i))})) - - - - - - ((1212))$

图4为在该系统下，设定频偏为3MHz，相偏为π/12时，传统Gardner符号同步算法与基于粒子滤波的符号同步算法误码率性能的对比图。由图3和图4可见，基于粒子滤波的符号同步算法的误码率性能优于传统Gardner符号同步算法的误码率性能，在高信噪比的条件下优势尤其明显。Fig. 4 is a comparison chart of bit error rate performance between the traditional Gardner symbol synchronization algorithm and the particle filter-based symbol synchronization algorithm when the frequency offset is set to 3MHz and the phase offset is π/12 under the system. It can be seen from Figure 3 and Figure 4 that the bit error rate performance of the particle filter-based symbol synchronization algorithm is better than that of the traditional Gardner symbol synchronization algorithm, especially under the condition of high signal-to-noise ratio.

以上所述为本发明的较佳实施例而已，本发明不应该局限于该实施例和附图所公开的内容。凡是不脱离本发明所公开的精神下完成的等效或修改，都落入本发明保护的范围。The above description is only a preferred embodiment of the present invention, and the present invention should not be limited to the content disclosed in this embodiment and the accompanying drawings. All equivalents or modifications accomplished without departing from the disclosed spirit of the present invention fall within the protection scope of the present invention.

Claims

1. A symbol synchronization method based on particle filtering is characterized in that: the method comprises the following implementation steps:

step 1, sampling one or two paths of input analog baseband signals to obtain digital signals;

for binary modulation, an input analog baseband signal is x (t), and a digital signal x (nT) is obtained through analog-to-digital conversion_s) (ii) a For multi-system modulation, the input baseband signal is two analog signals x_I(t) and x_Q(t), obtaining two paths of signals x after analog-to-digital conversion_I(nT_s) And x_Q(nT_s) (ii) a Sampling rate of f_sAt sampling intervals ofn is the serial number of the sampling point;

step 2, generating particles;

generating N particle samples for each symbol period according to a set probability distribution pi, and recording the corresponding timing deviation of the N particle samples asThe superscript i denotes a sample number, i is 1,2, …, N, the subscript r denotes a symbol period number, r is 1,2, …;

step 3, initializing the particle filter;

step 3.1, the N particle sample values generated when r is 1 are recorded asWherein each particle has an importance weight of

Step 3.2, normalizing the importance weight of each particle output in step 3.1

Step 3.3, calculating the timing deviation estimated value

Step 4, according to the timing deviation estimated value of the current symbolPerforming interpolation filtering on the digital signal output in the first step to obtain an interpolation filtering output value at the optimal sampling moment, and realizing symbol synchronization;

the interpolation filtering adopts a frequency domain algorithm, and the specific steps are as follows:

step 4.1, for x (nT) output from step one_s) Performing K-point FFT on the signal to obtain a frequency spectrum R (kf)_s/K)；

Step 4.2, the frequency spectrum R (kf) obtained in the step 4.1_s/K) to obtain frequency domain data R' (kf) with timing deviation removed_s/K)：

Step 4.3, for R' (kf) output in step 4.2_s/K) performs IFFT and outputs the output x' (nT) of the interpolation filter in the current symbol period_s) Extracting an output value x' (rT) of the optimal sampling moment, wherein T is a code element period, and realizing synchronization of the current code element period;

step 5, calculating a measurement timing error u (r) when r is greater than 1 according to the output value of the interpolation filtering optimal sampling moment in the step 4;

for binary modulation, the measured timing error for the r-th symbol period is:

step 6, carrying out particle filtering on the measurement timing error obtained in the step 5 to obtain a timing deviation estimated value corresponding to the symbol period;

the method comprises the following specific steps:

step 6.1, obtaining the timing deviation of N particle samples corresponding to the r-th symbol period according to the state equation and the timing error of the r-1 th symbol period;

the state equation is:

wherein,is the system noise;

step 6.2, according to the observation equation, establish u (r) andthe relationship of (1);

the observation equation is based on u (r) andthe S-curve between the two is obtained and is expressed as

<math> <mrow> <mi>u</mi> <mrow> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>/</mo> <mi>T</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>π</mi> <msubsup> <mi>ϵ</mi> <mi>r</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mo>)</mo> </mrow> <munderover> <mo>&Integral;</mo> <mn>0</mn> <mrow> <mn>1</mn> <mo>/</mo> <mi>T</mi> </mrow> </munderover> <mi>G</mi> <mrow> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> <mi>G</mi> <mrow> <mo>(</mo> <mfrac> <mn>1</mn> <mi>T</mi> </mfrac> <mo>-</mo> <mi>f</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mi>πfTdf</mi> <mo>+</mo> <msubsup> <mi>γ</mi> <mi>r</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> </mrow> </math>

Wherein G (f) is a filter functionThe number of the first and second groups is,to observe noise;

6.3, calculating the importance weight of each particle in the r-th symbol period;

wherein,representing importance weights of the N particle sample points of the r-th symbol period;is shown inProbability density of timing error u (r) under the conditions;is shown inUnder the condition ofThe probability density of (d);is a priori selectedThe probability density function is an importance function;

step 6.4, normalizing each particle importance weight of the r-th symbol period output in step 6.3:

wherein,expressing the normalized importance weight of N particle sample points in the r-th symbol period;

6.5, resampling the normalized weight output in the step 6.4;

representing the timing deviation of the sampled values of N particles after resampling, and the weight value corresponding to the new particles after resampling is

Step 6.6, obtainTiming deviation estimated value after resampling in the r-th symbol period

Step 6.7, calculating the result obtained in the step 6.6And step 4 is carried over, and the steps 4 to 6 are continued until the synchronization of all the symbol periods is realized.

2. The symbol synchronization method based on particle filtering as claimed in claim 1, wherein: pi is Gaussian distribution, 0 mean, large variance.

3. The symbol synchronization method based on particle filtering as claimed in claim 1, wherein:

4. the symbol synchronization method based on particle filtering as claimed in claim 1, wherein: if the modulation is multi-system modulation, the output of the interpolation filter is x'_I(nT_s) And x'_Q(nT_s) The output value at the optimum sampling time is x'_I(rT) and x'_Q(rT); the measured timing error for the r-th symbol period is: