WO2020073387A1 - 基于级联卡尔曼滤波器减少噪声干扰的方法及系统 - Google Patents

基于级联卡尔曼滤波器减少噪声干扰的方法及系统 Download PDF

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WO2020073387A1
WO2020073387A1 PCT/CN2018/113413 CN2018113413W WO2020073387A1 WO 2020073387 A1 WO2020073387 A1 WO 2020073387A1 CN 2018113413 W CN2018113413 W CN 2018113413W WO 2020073387 A1 WO2020073387 A1 WO 2020073387A1
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spiral
signal
point
kalman filter
constellation points
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PCT/CN2018/113413
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French (fr)
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高明义
马媛媛
叶阳
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苏州大学张家港工业技术研究院
苏州大学
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/32—Carrier systems characterised by combinations of two or more of the types covered by groups H04L27/02, H04L27/10, H04L27/18 or H04L27/26
    • H04L27/34—Amplitude- and phase-modulated carrier systems, e.g. quadrature-amplitude modulated carrier systems
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03006—Arrangements for removing intersymbol interference
    • H04L25/03159—Arrangements for removing intersymbol interference operating in the frequency domain
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/32—Carrier systems characterised by combinations of two or more of the types covered by groups H04L27/02, H04L27/10, H04L27/18 or H04L27/26
    • H04L27/34—Amplitude- and phase-modulated carrier systems, e.g. quadrature-amplitude modulated carrier systems
    • H04L27/3405—Modifications of the signal space to increase the efficiency of transmission, e.g. reduction of the bit error rate, bandwidth, or average power

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  • the invention specifically relates to a method and system for reducing noise interference based on a cascaded Kalman filter.
  • the object of the present invention is to provide a network-based real-time rendering strategy to achieve an efficient real-time display virtual simulation environment based on cascaded Kalman filter to reduce noise interference method and system.
  • the method for reducing noise interference based on the cascaded Kalman filter includes:
  • the 16 constellation points of the spiral 16-QAM signal are located on 4 amplitudes, and each amplitude has only 4 constellation points, and the minimum angular distance between adjacent points is ⁇ / 2;
  • the received spiral 16-QAM signal is processed through clock recovery and channel equalization, and the spiral 16-QAM signal is then processed by the Kalman filter.
  • the method for generating the spiral 16-QAM signal specifically includes:
  • Number the four constellation points of the QPSK signal designate one of the four constellation points as point 1, and sequentially number the other constellation points in the counterclockwise direction as point 2, point 3, and point 4;
  • the three numbered points behind each point are used as the centers of the three circles, and use the minimum Euclidean distance r, 2r, 3r of the QPSK signal as the radius of each circle to draw a ⁇ / 2 arc ,
  • the three arcs are connected to each other to generate a spiral line at each point;
  • the constellation points on each spiral line are positioned, and the minimum distance between two adjacent constellation points is greater than or equal to the minimum Euclidean distance r of the QPSK signal.
  • the signal processing method of the Kalman filter includes:
  • the initial value of the filter is given.
  • the predicted filter value of is:
  • Q is the phase noise covariance matrix between pilots
  • the gain of the kth pilot Kalman filter is expressed as:
  • R is the variance of Gaussian white noise
  • the system for reducing noise interference based on cascaded Kalman filter includes:
  • the spiral 16-QAM signal generation module is used to generate a spiral 16-QAM signal.
  • the 16 constellation points of the spiral 16-QAM signal are located at 4 amplitudes, and each amplitude has only 4 constellation points, between adjacent points
  • the minimum angular distance is ⁇ / 2;
  • the Kalman filter processes the spiral 16-QAM signal after clock recovery and channel equalization.
  • spiral 16-QAM signal generation module includes:
  • the numbering unit is used to number the four constellation points of the QPSK signal, designate one of the four constellation points as point 1, and sequentially number the other constellation points in the counterclockwise direction as point 2, point 3, and point 4;
  • Helical line generation unit used to complete each spiral line, the three numbered points behind each point are used as the centers of the three circles, and the minimum Euclidean distance r, 2r, 3r of the QPSK signal is used as each circle in turn
  • the radius of is drawn by ⁇ / 2 arc, and the three arcs are connected to each other to generate a spiral line of each point;
  • Constellation point positioning unit used for positioning constellation points on each spiral line, the minimum distance between two adjacent constellation points is greater than or equal to the minimum Euclidean distance r of QPSK signal, and the minimum between two adjacent points The angular distance should be as large as possible.
  • the method and system for reducing noise interference based on the cascaded Kalman filter have at least the following advantages:
  • the spiral 16-QAM signal has the same maximum modulation amplitude as the spiral 16-QAM signal has the following advantages. For example, the phase difference of ⁇ / 2 at each amplitude is relatively large. The distance between them is larger. Compared with the traditional square 16-QAM signal, these constellation characteristics make the spiral 16-QAM signal have a higher noise tolerance. In addition, the cascaded Kalman filter can effectively reduce the interference caused by the phase noise of the laser line width. Therefore, the present invention has high noise tolerance and robustness to laser linewidth.
  • Figure 1 shows the traditional square 16-QAM signal (a) and spiral 16-QAM signal (b);
  • FIG. 2 is a constellation diagram (b) of the QPSK signal (a) and spiral 16-QAM signal of the present invention
  • Figure 3 shows the BER and laser linewidth (KHz) of the present invention
  • FIG. 4 is a constellation diagram of a spiral 16-QAM signal without any algorithm (a) of the present invention, a spiral 16-QAM signal with a second-order Kalman filter (b), and a conventional square 16-QAM signal without any algorithm (c ) A traditional square 16-QAM signal using a second-order Kalman filter (d);
  • Figure 5 shows the BER and SNR (dB) of the present invention.
  • a spiral 16-QAM signal is generated.
  • the 16 constellation points of the spiral 16-QAM signal are located at 4 amplitudes, and each amplitude has only 4 constellation points, and the minimum angular distance between adjacent points is ⁇ / 2;
  • the received spiral 16-QAM signal is processed through clock recovery and channel equalization, and the spiral 16-QAM signal is then processed by the Kalman filter.
  • the spiral 16-QAM signal has a larger Euclidean distance and minimum angular distance than the conventional square 16-QAM signal.
  • the cascaded Kalman filter can largely suppress the phase noise caused by the laser linewidth.
  • This embodiment is based on a method of reducing noise interference by a cascaded Kalman filter.
  • the method of generating a spiral 16-QAM signal specifically includes:
  • the upper left of the four constellation points is designated as point 1, and the other constellation points are sequentially numbered in the counterclockwise direction.
  • the point 2 is used as the center of the circle, and the minimum Euclidean distance r of the QPSK signal is used as the radius of the ⁇ / 2 arc drawn from the point 1, as shown in FIG. 2 (one).
  • points 3 and 2r as the center and radius of the circle, and then draw the ⁇ / 2 arc, as shown in Figure 2 (a).
  • points 4 and 3r are used as the center and radius of the circle, followed by drawing a ⁇ / 2 arc, as shown in Figure 2 (a). Therefore, the first spiral is completed.
  • the other 3 spiral lines can be drawn similarly.
  • the second step is how to locate the constellation points in the spiral.
  • There are two rules for the arrangement of constellation points that is, the minimum distance between two adjacent constellation points is greater than or equal to the minimum Euclidean distance r of the QPSK signal, and the minimum angular distance between the two adjacent points should be as large as possible. Because the first point in each spiral is known, first arrange and adjust the second point of each line according to the above rules. After that, the third and fourth points of each line are similarly assigned.
  • the complete constellation of the spiral 16-QAM signal is shown in Figure 2 (b).
  • the received signal is first processed by clock recovery and channel equalization, and then processed by the Kalman filter.
  • the traditional Kalman filter is used in linear systems and is not suitable for nonlinear models of phase noise. Therefore, the Taylor series is used to linearize the system equation S (k) and the measurement equation F (k):
  • x is the transmitted signal
  • y is the received signal
  • m is the measurement noise
  • ⁇ is phase noise
  • w is the process noise.
  • Both measurement noise and process noise are Gaussian white noise with mean zero.
  • the initial value of the filter must be given [10].
  • the predicted filter value of the subcarrier of the k-th pilot is:
  • Q is the phase noise covariance matrix between pilots.
  • the gain of the kth pilot Kalman filter is expressed as:
  • R is the variance of Gaussian white noise.
  • phase noise has been largely suppressed.
  • channel estimation is performed on the obtained signal, in which a part of noise can be filtered out and bit error rate (BER) performance is improved.
  • the obtained data is used as measurement signals, and then they are judged according to the minimum distance, and the judged data are regarded as known signals.
  • the measured signal and the known signal are subjected to second-order Kalman filtering, that is, the same Kalman filtering as the first-order Kalman filtering is performed at each data point. Finally, we can get the final phase noise.
  • This embodiment is based on a cascaded Kalman filter to reduce noise interference system, which can be used to run the method described in Embodiment 1 or 2, and the working principle of the Kalman filter is the same as the above embodiment, including:
  • the spiral 16-QAM signal generation module is used to generate a spiral 16-QAM signal.
  • the 16 constellation points of the spiral 16-QAM signal are located at 4 amplitudes, and each amplitude has only 4 constellation points, between adjacent points
  • the minimum angular distance is ⁇ / 2;
  • the Kalman filter processes the spiral 16-QAM signal after clock recovery and channel equalization.
  • the spiral 16-QAM signal generation module includes:
  • the numbering unit is used to number the four constellation points of the QPSK signal, designate one of the four constellation points as point 1, and sequentially number the other constellation points in the counterclockwise direction as point 2, point 3, and point 4;
  • Helical line generation unit used to complete each spiral line, the three numbered points behind each point are used as the centers of the three circles, and the minimum Euclidean distance r, 2r, 3r of the QPSK signal is used as each circle in turn
  • the radius of is drawn by ⁇ / 2 arc, and the three arcs are connected to each other to generate a spiral line of each point;
  • Constellation point positioning unit used for positioning constellation points on each spiral line, the minimum distance between two adjacent constellation points is greater than or equal to the minimum Euclidean distance r of QPSK signal, and the minimum between two adjacent points The angular distance should be as large as possible.
  • the phase noise will generate random phase changes, thereby causing interference between certain constellation points.
  • a traditional square 16-QAM signal there are 8 constellation points in the middle amplitude, as shown in Figure 1 (a). Once the phase noise becomes severe, adjacent constellation points will overlap, resulting in erroneous decision of the signal.
  • FIG. 1 (b) shows the constellation diagram of the spiral 16-QAM signal, where 16 constellation points are located on 4 amplitudes, and each amplitude has only 4 constellation points, and the minimum angular distance between adjacent points is /2.
  • the spiral 16-QAM signal has a larger minimum angular distance and the same minimum Euclidean distance. Therefore, the spiral 16-QAM signal has better noise tolerance.
  • the invention proposes a spiral 16-QAM system based on cascaded Kalman filter.
  • the larger Euclidean distance and minimum angular distance of the spiral 16-QAM signal make it have higher noise tolerance than the traditional square 16-QAM signal.
  • the cascaded Kalman filter can largely suppress the phase noise caused by the laser line width. The following is a simulation experiment comparison between the spiral 16-QAM signal of the present invention and the traditional square 16-QAM signal to verify the feasibility of the invention.
  • the spiral 16-QAM signal and the traditional square 16-QAM signal were simulated. Includes robust measurement of laser linewidth and signal-to-noise ratio (SNR).
  • Figure 3 shows the relationship between BER and laser linewidth at 10dB SNR. As shown in Figure 3, as the laser line width increases, the phase noise becomes severe, causing the BER curve to slope upward. As shown in Figure 3, compared with the traditional square 16-QAM signal, the spiral 16-QAM signal has better BER performance. By applying a cascaded Kalman filter, the noise margin is enhanced, as shown by the diamond-shaped curve, star-shaped curve, and circle-shaped curve in Figure 3.
  • Fig. 4 (a) constellation of spiral 16-QAM signal without any algorithm (b) spiral 16-QAM signal with second-order Kalman filter (c) traditional square 16-QAM signal without any algorithm (d) application The traditional square 16-QAM signal of the second-order Kalman filter.
  • Figure 4 shows the constellation diagram of the spiral 16-QAM signal and the traditional square 16-QAM, where the laser line width is 50-KHz and the SNR is 10-dB.
  • the phase noise of the laser line width makes the phase of the constellation points widely distributed, as shown in Figure 4 (a) and Figure 4 (c).
  • the phase noise can be suppressed to a large extent, so that the constellation points converge, as shown in Figure 4 (b) and Figure 4 (d).
  • the present invention simulates the BER performance under different SNRs, as shown in Figure 5, where the laser line width is 50KHz.
  • the BER performance of the spiral 16-QAM signal is better than the traditional square 16-QAM signal, as shown by the dotted and solid lines.
  • the better BER performance of the spiral 16-QAM signal is caused by the larger Euclidean distance and minimum angular distance, which is illustrated in Figure 1.
  • Applying the Kalman filter can improve the noise tolerance, as shown in Figure 5 with diamond-shaped curve, star-shaped curve and round-shaped curve. It is worth noting that in the case of low SNR, there is no improvement in the cascaded Kalman filter, the star-shaped marking curve and the circular marking curve almost overlap. The main reason is that the Kalman filter cannot handle signals with relatively low signal-to-noise. As the signal-to-noise ratio increases, the second-order Kalman filter can achieve greater BER improvement than the first-order Kalman filter.

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Abstract

一种基于级联卡尔曼滤波器减少噪声干扰的方法及系统，为了抑制由激光线宽引起的相位噪声而设计。该方法包括：产生螺旋16-QAM信号，该螺旋16-QAM信号的16个星座点位于4个幅度上，并且每个幅度上只有4个星座点，相邻点之间的最小角距离为π/2；通过时钟恢复和信道均衡处理接收螺旋16-QAM信号，该螺旋16-QAM信号再经过卡尔曼滤波器处理。该方法和系统具有较高的噪声容限和对激光线宽的鲁棒性。

Description

基于级联卡尔曼滤波器减少噪声干扰的方法及系统 技术领域
本发明具体涉及一种基于级联卡尔曼滤波器减少噪声干扰的方法及系统。
背景技术
高阶调制信号是大容量光通信系统解决容量紧缩比较好的选择。然而，随着信号的调制阶数增加，星座图上星座点的数量也增加。因此，星座点的密集容易受到各种噪声的影响。其中一种严重的噪声是由激光线宽引起的，直观的解决方案是利用高成本的窄线宽激光器而不是低成本的宽线宽激光器。另一方面，对于高阶调制信号，数字信号处理(DSP)对于信号精确解调是必不可少的。因此，一种经济有效的方法是开发基于DSP的方法来减轻激光线宽引起的影响，其中卡尔曼滤波是一种有效的方法。此外，开发具有较大欧氏距离的新调制信号对于高噪声容限也是有帮助的。
发明内容
为解决上述技术问题，本发明的目的是提供一种基于网络的实时渲染策略，实现高效的实时显示虚拟仿真环境的基于级联卡尔曼滤波器减少噪声干扰的方法及系统。
本发明基于级联卡尔曼滤波器减少噪声干扰的方法，包括：
产生螺旋16-QAM信号，该螺旋16-QAM信号的16个星座点位于4个幅度上，并且每个幅度上只有4个星座点，相邻点之间的最小角距离为π/2；
通过时钟恢复和信道均衡处理接收的螺旋16-QAM信号，螺旋16-QAM信号再经过卡尔曼滤波器处理。
进一步地，产生螺旋16-QAM信号的方法具体包括：
对QPSK信号的4个星座点进行编号，将4个星座点中的一个指定为点1，沿逆时针方向顺序编号其他星座点分别为点2、点3、点4；
完成各条螺旋线，各点后面的三个编号的点分别作为三个圆的中心，并依次使用QPSK信号的最小欧几里德距离r、2r、3r作为各圆的半径绘制π/2弧，三段弧相互连接生成各点的螺旋线；
各条螺旋线上星座点定位，两个相邻星座点之间的最小距离大于等于QPSK信号的最小欧几里德距离r。
进一步地，卡尔曼滤波器对信号处理方法包括：
利用泰勒级数来线性化系统方程S(k)和测量方程F(k)：
Figure PCTCN2018113413-appb-000001
Figure PCTCN2018113413-appb-000002
其中，x是发射信号，y是接收信号；
Figure PCTCN2018113413-appb-000003
m是测量噪声；φ是相位噪声，
Figure PCTCN2018113413-appb-000004
其中w是过程噪声；测量噪声和过程噪声均是均值为零的高斯白噪声；
给出滤波器的初始值，第一个导频的滤波器的初始值是φ(0)＝0和P(0)＝0，其中P是误差协方差矩阵；第k个导频的子载波的预测滤波值是：
Figure PCTCN2018113413-appb-000005
p(k)＝p(k-1)+Q
Q是导频之间的相位噪声协方差矩阵；
第k个导频的卡尔曼滤波器增益表示为：
Figure PCTCN2018113413-appb-000006
R是高斯白噪声的方差；
更新第k个导频的
Figure PCTCN2018113413-appb-000007
和P：
Figure PCTCN2018113413-appb-000008
p(k)＝(1-K(k)·S(k))·p(k)
获得这些导频的相位噪声，通过线性插值来计算每个点处的相位噪声，完成一阶卡尔曼滤波；
对获得的信号进行信道估计，将获得的数据用作测量信号，然后根据最小距离判决它们，并将判决后的数据当作已知信号；将测量信号和已知信号进行二阶卡尔曼滤波处理，即在每个数据点处执行与一阶卡尔曼滤波相同的卡尔曼滤波，最终得到最终的相位噪声。
本发明基于级联卡尔曼滤波器减少噪声干扰的系统，包括：
螺旋16-QAM信号产生模块，用于产生螺旋16-QAM信号，该螺旋16-QAM信号的16个星座点位于4个幅度上，并且每个幅度上只有4个星座点，相邻点之间的最小角距离为π/2；
卡尔曼滤波器，对时钟恢复和信道均衡处理后的螺旋16-QAM信号进行处理。
进一步地，螺旋16-QAM信号产生模块包括：
编号单元，用于对QPSK信号的4个星座点进行编号，将4个星座点中的一个指定为点1，沿逆时针方向顺序编号其他星座点分别为点2、点3、点4；
螺旋线生成单元，用于完成各条螺旋线，各点后面的三个编号的点分别作为三个圆的中心，并依次使用QPSK信号的最小欧几里德距离r、2r、3r作为各圆的半径绘制π/2弧，三段弧相互连接生成各点的螺旋线；
星座点定位单元，用于各条螺旋线上星座点定位，两个相邻星座点之间的最小距离大于等于QPSK信号的最小欧几里德距离r，并且两个相邻点之间的最小角距应尽可能大。
借由上述方案，本发明基于级联卡尔曼滤波器减少噪声干扰的方法及系统，至少具有以下优点：
螺旋16-QAM信号与传统的方形16-QAM信号相比，具有相同的最大调制幅度的螺旋16-QAM信号具有以下优点，例如每个幅度上π/2的相位差比较大，相邻点之间的距离较大。与传统的方形16-QAM信号相比，这些星座特征使得螺旋16-QAM信号有着更高的噪声容限。此外，级联卡尔曼滤波器可以有效地减轻由激光线宽的相位噪声引起的干扰。因此，本发明具有高的噪声容限和对激光线宽的鲁棒性。
上述说明仅是本发明技术方案的概述，为了能够更清楚了解本发明的技术手段，并可依照说明书的内容予以实施，以下以本发明的较佳实施例并配合附图详细说明如后。
附图说明
图1为传统方形16-QAM信号(a)，螺旋16-QAM信号(b)；
图2为本发明QPSK信号(a)，螺旋16-QAM信号的星座图(b)；
图3为本发明BER与激光线宽(KHz)；
图4为本发明没有任何算法的螺旋16-QAM信号的星座图(a)，应用二阶卡尔曼滤波器的螺旋16-QAM信号(b)，没有任何算法的传统方形16-QAM信号(c)应用二阶卡尔曼滤波器的传统方形16-QAM信号(d)；
图5为本发明BER与SNR(dB)。
具体实施方式
下面结合附图和实施例，对本发明的具体实施方式作进一步详细描述。以下实施例用于说明本发明，但不用来限制本发明的范围。
实施例1
本实施例基于级联卡尔曼滤波器减少噪声干扰的方法，包括：
产生螺旋16-QAM信号，该螺旋16-QAM信号的16个星座点位于4个幅度 上，并且每个幅度上只有4个星座点，相邻点之间的最小角距离为π/2；
通过时钟恢复和信道均衡处理接收的螺旋16-QAM信号，螺旋16-QAM信号再经过卡尔曼滤波器处理。
本实施例中，螺旋16-QAM信号比传统方形16-QAM信号具有更大的欧几里德距离和最小的角距离。级联卡尔曼滤波器能够在很大程度上抑制由激光线宽引起的相位噪声。这些优点增强了所提出系统的噪声容限。
实施例2
本实施例基于级联卡尔曼滤波器减少噪声干扰的方法，在实施例1的基础上，产生螺旋16-QAM信号的方法具体包括：
首先，将4个星座点中的左上一个指定为点1，并且沿逆时针方向顺序编号其他星座点。接下来，将点2用作圆的中心，并使用QPSK信号的最小欧几里德距离r作为从点1绘制π/2弧的半径，如图2中的所示(一个)。然后将点3和2r用作圆的中心和半径，接着画π/2弧，如图2(a)中所示。最后，点4和3r用作圆的中心和半径，接着绘制π/2弧，如图2(a)中的所示。因此，完成了第一条螺旋线。其他3条螺旋线可以类似地绘制。第2步是如何定位螺旋线中的星座点。星座点布置有两个规则，即两个相邻星座点之间的最小距离大于等于QPSK信号的最小欧几里德距离r，并且两个相邻点之间的最小角距应尽可能大。因为每条螺旋线中的第一点是已知的，所以首先根据上述规则排列和调整每条线的第二点。之后，每行的第三和第四点被类似地分配。螺旋16-QAM信号的完整星座图如图2(b)所示。
在接收器部分，首先通过时钟恢复和信道均衡处理接收信号，然后再经过卡尔曼滤波器处理。传统的卡尔曼滤波器用于线性系统，不适用于相位噪声的非线性模型。因此，利用泰勒级数来线性化系统方程S(k)和测量方程F(k)：
Figure PCTCN2018113413-appb-000009
Figure PCTCN2018113413-appb-000010
其中，x是发射信号，y是接收信号。
Figure PCTCN2018113413-appb-000011
m是测量噪声。φ是相位噪声，
Figure PCTCN2018113413-appb-000012
其中w是过程噪声。测量噪声和过程噪声均是均值为零的高斯白噪声。
而且，对于卡尔曼滤波器，须给出滤波器的初始值[10]。在本文里，第一个导频的滤波器的初始值是φ(0)＝0和P(0)＝0，其中P是误差协方差矩阵。第k个导频的子载波的预测滤波值是：
Figure PCTCN2018113413-appb-000013
p(k)＝p(k-1)+Q      (4)
这里，Q是导频之间的相位噪声协方差矩阵。
第k个导频的卡尔曼滤波器增益表示为：
Figure PCTCN2018113413-appb-000014
R是高斯白噪声的方差。
最后更新第k个导频的
Figure PCTCN2018113413-appb-000015
和P：
Figure PCTCN2018113413-appb-000016
p(k)＝(1-K(k)·S(k))·p(k)    (7)
因此，我们可以获得这些导频的相位噪声，并且可以通过线性插值来计算每个点处的相位噪声。上述过程就是一阶卡尔曼滤波。
通过一阶卡尔曼滤波，相位噪声已经很大程度地抑制。接下来，对获得的信号进行信道估计，其中可以滤除一部分噪声并且改善误码率(BER)性能。将获得的数据用作测量信号，然后根据最小距离判决它们，并将判决后的数据当作已 知信号。接下来，将测量信号和已知信号进行二阶卡尔曼滤波处理，即在每个数据点处执行与一阶卡尔曼滤波相同的卡尔曼滤波。最后，我们可以得到最终的相位噪声。
实施例3
本实施例基于级联卡尔曼滤波器减少噪声干扰的系统，可以用于运行实施例1或2所述的方法，且卡尔曼滤波器的工作原理与上述实施例相同，包括：
螺旋16-QAM信号产生模块，用于产生螺旋16-QAM信号，该螺旋16-QAM信号的16个星座点位于4个幅度上，并且每个幅度上只有4个星座点，相邻点之间的最小角距离为π/2；
卡尔曼滤波器，对时钟恢复和信道均衡处理后的螺旋16-QAM信号进行处理。
螺旋16-QAM信号产生模块包括：
编号单元，用于对QPSK信号的4个星座点进行编号，将4个星座点中的一个指定为点1，沿逆时针方向顺序编号其他星座点分别为点2、点3、点4；
螺旋线生成单元，用于完成各条螺旋线，各点后面的三个编号的点分别作为三个圆的中心，并依次使用QPSK信号的最小欧几里德距离r、2r、3r作为各圆的半径绘制π/2弧，三段弧相互连接生成各点的螺旋线；
星座点定位单元，用于各条螺旋线上星座点定位，两个相邻星座点之间的最小距离大于等于QPSK信号的最小欧几里德距离r，并且两个相邻点之间的最小角距应尽可能大。
上述各实施例原理，相位噪声会产生随机的相位变化，从而在某些星座点之间产生干扰。对于传统的方形16-QAM信号，中间的幅度上有8个星座点，如图1(a)所示。一旦相位噪声变得严重，相邻的星座点将重叠，从而导致信号的错误判决。
为了增强传统方形16-QAM信号的噪声容限，在无线单载波通信中提出了螺旋16-QAM调制。图1(b)展示出了螺旋16-QAM信号的星座图，其中16个星座点位于4个幅度上，并且每个幅度上只有4个星座点，相邻点之间的最小角距离为π/2。与图1(a)中的传统方形16-QAM信号相比，螺旋16-QAM信号具有较大的最小角距离和相同的最小欧氏距离。因此，螺旋16-QAM信号具有更好的噪声容限。
本发明提出了一个基于级联卡尔曼滤波器的螺旋16-QAM系统。螺旋16-QAM信号较大的欧几里德距离和最小角距离使得其比传统方形16-QAM信号有着更高的噪声容限。此外，级联卡尔曼滤波器能够在很大程度上抑制由激光线宽引起的相位噪声。以下通过本发明的螺旋16-QAM信号和传统的方形16-QAM信号进行了仿真实验对比验证该发明的可行性。
对螺旋16-QAM信号和传统的方形16-QAM信号进行了仿真实验。包括对激光线宽和信噪比(SNR)的鲁棒性测量。
图3显示了BER与激光线宽在10dB SNR条件下的关系曲线。如图3所示，随着激光线宽的增加，相位噪声变得严重，导致BER曲线向上倾斜。如图3所示，与传统的方形16-QAM信号相比，螺旋线16-QAM信号具有更好的BER性能。通过应用级联卡尔曼滤波器，噪声容限得到了增强，如图3中的菱形标记曲线，星形标记曲线和圆形标记曲线所示。
图4(a)没有任何算法的螺旋16-QAM信号的星座图(b)应用二阶卡尔曼滤波器的螺旋16-QAM信号(c)没有任何算法的传统方形16-QAM信号(d)应用二阶卡尔曼滤波器的传统方形16-QAM信号。
图4显示了螺旋16-QAM信号和传统方形16-QAM的星座图，其中激光线宽为50-KHz，SNR为10-dB。很明显，激光线宽产生相位噪声，使得星座点的相 位广泛分布，如图4(a)和图4(c)所示。通过应用二阶卡尔曼滤波器，可以在很大程度上抑制相位噪声，使得星座点会聚，如图4(b)和图4(d)所示。
接下来，本发明模拟不同SNR下的BER性能，如图5所示，其中激光线宽为50KHz。结果与图3的结果一致，螺旋16-QAM信号的BER性能优于传统的方形16-QAM信号，如虚线和实线所示。螺旋16-QAM信号有更好的BER性能是由更大的欧几里德距离和最小角距离导致的，在图1中阐述过。应用卡尔曼滤波器，可以改善噪声容限，如图5中菱形标记曲线、星形标记曲线和圆形标记曲线所示。值得注意的是，在SNR较低的情况下，级联卡尔曼滤波器没有什么改进，星形标记曲线和圆形标记曲线几乎重叠。主要原因是卡尔曼滤波器不能很好地处理信噪比较低的信号。随着信噪比的提高，二阶卡尔曼滤波器可以实现比一阶卡尔曼滤波器更大的BER改善。
以上所述仅是本发明的优选实施方式，并不用于限制本发明，应当指出，对于本技术领域的普通技术人员来说，在不脱离本发明技术原理的前提下，还可以做出若干改进和变型，这些改进和变型也应视为本发明的保护范围。

Claims (5)

  1. 一种基于级联卡尔曼滤波器减少噪声干扰的方法，其特征在于，包括：
    产生螺旋16-QAM信号，该螺旋16-QAM信号的16个星座点位于4个幅度上，并且每个幅度上只有4个星座点，相邻点之间的最小角距离为π/2；
    通过时钟恢复和信道均衡处理接收的螺旋16-QAM信号，螺旋16-QAM信号再经过卡尔曼滤波器处理。
  2. 根据权利要求1所述的基于级联卡尔曼滤波器减少噪声干扰的方法，其特征在于，产生螺旋16-QAM信号的方法具体包括：
    对QPSK信号的4个星座点进行编号，将4个星座点中的一个指定为点1，沿逆时针方向顺序编号其他星座点分别为点2、点3、点4；
    完成各条螺旋线，各点后面的三个编号的点分别作为三个圆的中心，并依次使用QPSK信号的最小欧几里德距离r、2r、3r作为各圆的半径绘制π/2弧，三段弧相互连接生成各点的螺旋线；
    各条螺旋线上星座点定位，两个相邻星座点之间的最小距离大于等于QPSK信号的最小欧几里德距离r。
  3. 根据权利要求1所述的基于级联卡尔曼滤波器减少噪声干扰的方法，其特征在于，卡尔曼滤波器对信号处理方法包括：
    利用泰勒级数来线性化系统方程S(k)和测量方程F(k)：
    Figure PCTCN2018113413-appb-100001
    Figure PCTCN2018113413-appb-100002
    其中，x是发射信号，y是接收信号；
    Figure PCTCN2018113413-appb-100003
    m是测量噪声；φ是相位噪声，
    Figure PCTCN2018113413-appb-100004
    其中w是过程噪声；测量噪声和过程噪声均是均值为零的高斯白噪声；
    给出滤波器的初始值，第一个导频的滤波器的初始值是φ(0)＝0和P(0) ＝0，其中P是误差协方差矩阵；第k个导频的子载波的预测滤波值是：
    Figure PCTCN2018113413-appb-100005
    p(k)＝p(k-1)+Q
    Q是导频之间的相位噪声协方差矩阵；
    第k个导频的卡尔曼滤波器增益表示为：
    Figure PCTCN2018113413-appb-100006
    R是高斯白噪声的方差；
    更新第k个导频的
    Figure PCTCN2018113413-appb-100007
    和P：
    Figure PCTCN2018113413-appb-100008
    p(k)＝(1-K(k)·S(k))·p(k)
    获得这些导频的相位噪声，通过线性插值来计算每个点处的相位噪声，完成一阶卡尔曼滤波；
    对获得的信号进行信道估计，将获得的数据用作测量信号，然后根据最小距离判决它们，并将判决后的数据当作已知信号；将测量信号和已知信号进行二阶卡尔曼滤波处理，即在每个数据点处执行与一阶卡尔曼滤波相同的卡尔曼滤波，最终得到最终的相位噪声。
  4. 一种基于级联卡尔曼滤波器减少噪声干扰的系统，其特征在于，包括：
    螺旋16-QAM信号产生模块，用于产生螺旋16-QAM信号，该螺旋16-QAM信号的16个星座点位于4个幅度上，并且每个幅度上只有4个星座点，相邻点之间的最小角距离为π/2；
    卡尔曼滤波器，对时钟恢复和信道均衡处理后的螺旋16-QAM信号进行处理。
  5. 根据权利要求4所述的基于级联卡尔曼滤波器减少噪声干扰的系统，其特征在于，螺旋16-QAM信号产生模块包括：
    编号单元，用于对QPSK信号的4个星座点进行编号，将4个星座点中的一个指定为点1，沿逆时针方向顺序编号其他星座点分别为点2、点3、点4；
    螺旋线生成单元，用于完成各条螺旋线，各点后面的三个编号的点分别作为三个圆的中心，并依次使用QPSK信号的最小欧几里德距离r、2r、3r作为各圆的半径绘制π/2弧，三段弧相互连接生成各点的螺旋线；
    星座点定位单元，用于各条螺旋线上星座点定位，两个相邻星座点之间的最小距离大于等于QPSK信号的最小欧几里德距离r，并且两个相邻点之间的最小角距应尽可能大。
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