CN112769728B - KDE non-uniform quantization method of multi-carrier modulation optical communication system based on filter bank - Google Patents

KDE non-uniform quantization method of multi-carrier modulation optical communication system based on filter bank Download PDF

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CN112769728B
CN112769728B CN202011638907.2A CN202011638907A CN112769728B CN 112769728 B CN112769728 B CN 112769728B CN 202011638907 A CN202011638907 A CN 202011638907A CN 112769728 B CN112769728 B CN 112769728B
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毕美华
徐杭甬
林嘉芊
杨国伟
周雪芳
胡淼
李齐良
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Hangzhou Dianzi University
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Abstract

The invention relates to a KDE non-uniform quantization method of a multi-carrier modulation optical communication system based on a filter bank, which comprises the following steps: (1) performing a clipping operation on the signal at different clipping ratios; (2) initializing a bandwidth and a kernel function according to the signal distribution characteristics and the non-parameter kernel density estimation requirement; (3) applying a kernel function as a distribution function for each data point; (4) linearly superposing the distribution functions of all the representative data points to obtain a distribution curve of a fitting signal; (5) normalizing the distribution curve of the fitting signal to obtain a probability density function of the fitting signal; (6) solving the optimal quantization level combination under the constraint of the minimum quantization error for the fitted signal probability density function by utilizing nonlinear programming; (7) the quantized input signals are combined according to the optimal quantization levels. The KDE non-uniform quantization method has lower error rate in signal transmission and better system quantization performance.

Description

KDE non-uniform quantization method of multi-carrier modulation optical communication system based on filter bank
Technical Field
The invention belongs to the technical field of optical communication, and particularly relates to a KDE non-uniform quantization method of a multi-carrier modulation optical communication system based on a filter bank.
Background
In recent years, with the development of technologies such as artificial intelligence, big data, cloud computing and the like, the demand of people on access bandwidth is rapidly increasing year by year. The multi-carrier modulation technology has wide application in an optical access network system based on IMDD because the multi-carrier modulation technology is more advantageous in meeting the aspects of high capacity, asynchronous transmission and spectral efficiency. Meanwhile, the multi-carrier modulation technology is one of the research hotspots of the current 5G key technology because of the advantages of high spectrum efficiency, multipath interference resistance and the like. The conventional multi-carrier modulation (OFDM) technique causes a waste of spectrum resources due to the introduction of a Cyclic Prefix (CP), and each subcarrier of the conventional multi-carrier modulation technique must be strictly synchronized to ensure orthogonality and a large side lobe of the carrier, which makes the conventional multi-carrier modulation technique unsuitable for a 5G scenario. Compared with OFDM, the filter bank-based multi-carrier modulation technique includes filter bank-based multi-carrier (FBMC), universal filtering multi-carrier (UFMC), and the like, does not require introduction of a cyclic prefix, and has better asynchronous transmission performance, higher spectral efficiency, and lower out-of-band leakage. In an optical transmission system, a high bit resolution digital-to-analog converter (DAC) converts a digital signal into an analog electrical signal, but a high resolution uniformly quantized DAC causes very high power consumption and system cost, so that it is necessary to adopt a non-uniform quantization method to improve the performance of a low resolution DAC to reduce the system cost.
Non-uniform quantization methods are, in turn, exponential quantization, power quantization, polyline quantization, quantization based on signal distribution estimation, and the like. In "SQNR improved Enabled by non-nuniform DAC Output Levels for IM-DD OFDM Systems" published by IEEE Photonics Journal in 2017, Juzong Peng can use the nonlinear programming function of MATLAB to determine the quantization level according to the property that the OFDM signal conforms to Gaussian distribution. Although the method improves the transmission performance of the system, the quantization effect in the IMDD-UFMC system is not good. In the IMDD filter bank multi-carrier system, after the waveform is processed by the filter, the waveform distribution presents a peak in the direction of zero mean value instead of gaussian distribution, and the waveform distribution cannot be fitted based on the quantization scheme of gaussian distribution. Because the non-uniform quantization scheme based on the gaussian distribution cannot embody the characteristic that the UFMC small signal occupies most parts, the problem of insufficient fitting precision exists, which causes the quantization error to become larger due to the poor matching degree of the optimal quantization level and the signal. In conclusion, there is still room for improvement in quantization step optimization algorithms.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a KDE non-uniform quantization method of a multi-carrier modulation optical communication system based on a filter bank.
Nonparametric Kernel Density Estimation (KDE) is a nonparametric estimation algorithm based on statistical learning theory. The advantage of KDE is that it can get a smoother fit signal distribution than non-parametric histogram estimation. The kernel density estimation improves the condition that the probability of the histogram estimation method possibly occurring in partial intervals is zero, and the problem of discontinuity is improved to a great extent. In addition, the kernel density estimation algorithm can use different kernel functions for estimation, so that the finally obtained fitting signal distribution is closer to the original signal distribution.
Based on this, the invention adopts the following technical scheme:
a KDE non-uniform quantization method of a multi-carrier modulation optical communication system based on a filter bank comprises the following steps:
(1) performing a clipping operation on the signal at different clipping ratios;
(2) initializing a bandwidth and a kernel function according to the signal distribution characteristics and the requirements of nonparametric kernel density estimation;
(3) applying a kernel function as a distribution function for each data point;
(4) linearly superposing the distribution functions of all the representative data points to obtain a distribution curve of a fitting signal;
(5) normalizing the distribution curve of the fitting signal to obtain a probability density function of the fitting signal;
(6) solving the optimal quantization level combination under the constraint of the minimum quantization error for the fitted signal probability density function by utilizing nonlinear programming;
(7) the quantized input signals are combined according to the optimal quantization levels.
Preferably, in step (1), the clipping ratio CR is represented by:
Figure BDA0002877685640000021
wherein σsIs the standard deviation of the signal. The small signals in the signal of UFMC occupy most of the signal, resulting in a great waste of system resources, and in addition, clipping operation is necessary to prevent excessive PAPR.
Preferably, in step (2), the kernel function is a gaussian kernel function.
Each data point can be viewed as a "box" or a "gaussian distribution function" or curve of other functions, depending on the type of kernel function. The functions of each kernel are different, and a gaussian kernel is selected when estimating the UFMC signal.
As a preferred scheme, the kernel function curve is distributed by taking a data point as a center, and the bandwidth is h. If h is selected too large, the final linear overlapping part of the kernel function of the data point is more, so that the probability distribution curve is relatively flat, the proportion of the data point in the curve shape is not obvious enough, and under-fitting is caused; if h is too small, the final linear overlapping part of the kernel function represented by the data points is very small, so that the probability distribution curve is steeper and not smooth enough, and overfitting is caused. In practical application, the relationship between the fitting effect and the curve smoothness needs to be balanced.
Preferably, in step (3), the kernel function is centered on the data point, and the density is a density function value of the domain [ x-h, x + h ] of the data point at h- >0, and is expressed as
Figure BDA0002877685640000031
Nxi∈[x-h,x+h]Is the number of data points in the width 2h, N is the total number of samples, and is guaranteed
Figure BDA0002877685640000032
The integral of (a) is 1; the analogy is a rectangle with a width of 2h and a height of 1/2h, representing the weight of each data point; in a Gaussian distributionThe function is used as the kernel of the KDE, i.e. the rectangle is transformed into a gaussian distribution curve, which represents the same meaning.
Preferably, the kernel functions are linearly superimposed to obtain a fitted signal distribution curve representing the total number of samples N.
Preferably, the probability density function f (x) of the fitting signal obtained by normalizing the fitting signal distribution curve of the total number N of samples is represented as:
Figure BDA0002877685640000033
wherein, Kh(. represents a kernel function, x)iRepresenting data points.
Preferably, in the step (6), the probability density function of the fitting signal is subjected to nonlinear programming to obtain a quantization interval that minimizes quantization noise, and the quantization interval is 2nThen the quantization level also has 2nA plurality of; wherein n is the resolution of the DAC;
the quantization level is the average of the sum of two adjacent quantization intervals;
wherein the quantization interval points are represented as:
[q-(2n-1),…,q-2,q-1,0,q1,q2,…,q2n-1-1]
assuming that the last quantization level is equal to the clipping ratio CR, the quantized discrete output level is expressed as:
Figure BDA0002877685640000034
the quantized values of the discrete outputs are represented as:
Figure BDA0002877685640000041
the non-linear program is represented as:
minf(q)＝eq
s.t.qj+1>qj,j＝1,…,2n-1-1
qj>0,j＝1,…,2n-1
Figure BDA0002877685640000042
wherein minf (q) ═ eqRepresenting the minimization of quantization error, and calculating the optimal quantization level combination under three constraint conditions;
the quantization error is expressed as:
Figure BDA0002877685640000043
preferably, the optimal quantization level combination is used to represent 2nThe numerical points of the quantization intervals. The point of values within these quantization intervals is represented by the optimal combination of quantization levels.
Compared with the prior art, the invention has the following beneficial effects:
(1) compared with the traditional uniform quantization method, the KDE non-uniform quantization method has better quantization performance, thereby improving the performance of a multi-carrier modulation optical communication system based on a filter bank;
(2) compared with a non-uniform quantization method based on Gaussian distribution, the KDE non-uniform quantization method disclosed by the invention has the advantages that the probability density of signals can be better fitted, and the performance of small signals is highlighted;
(3) the KDE non-uniform quantization method fully considers the characteristics of a high-speed general filtering multi-carrier system, finds a quantization mode suitable for the system aiming at the characteristics of general filtering multi-carrier waveforms, and further greatly improves the DAC quantization performance.
Drawings
Fig. 1 is a schematic diagram of the DAC quantization principle based on KDE;
FIG. 2 is a schematic diagram of an IMDD general filtering multi-carrier optical communication application system;
fig. 3 shows a KDE-based and gaussian-distribution-based non-uniform quantization method for IMDD general filtering multi-carrier optical communication system using different bits, (a) shows a BER performance comparison diagram for back-to-back transmission (B2B) system under different received optical powers, and (B) shows a BER performance comparison diagram for system with a transmission distance of 80 km.
Detailed Description
The present invention will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the invention, but are not intended to limit the invention in any way. It should be noted that variations and modifications can be made by persons skilled in the art without departing from the concept of the invention. All falling within the scope of the present invention.
The invention provides a KDE non-uniform quantization algorithm for a filter bank multi-carrier modulation optical communication system. As shown in fig. 1, a signal to be processed is input, after amplitude limiting, kernel functions of all data points of the signal are linearly superposed and normalized to obtain a fitted kernel density probability density function f (x), then nonlinear programming is performed to obtain a quantization level combination which minimizes quantization noise, and finally the input signal is quantized according to the optimal quantization level combination. Specifically, the method comprises the following steps:
step 1: and (4) clipping, wherein the signal is subjected to clipping operation by using different clipping ratios.
Step 2: and (4) parameter initialization, namely initializing the bandwidth h and the kernel function according to the signal distribution characteristics and the non-parameter kernel density estimation requirement.
And step 3: kernel function application, applying a kernel function as a distribution function for each data point.
And 4, step 4: and linearly overlapping, namely linearly overlapping distribution function curves of all the representative data points to obtain a distribution curve of a fitting signal.
And 5: and (5) normalizing the curve, and fitting the distribution curve of the signal to obtain a probability density function f (x) of the fitted signal.
Step 6: and (4) calculating the optimal quantization level, and solving the optimal quantization level combination under the constraint of the minimum quantization error by using a nonlinear programming function.
And 7: and quantizing, namely quantizing the input signals according to the optimal quantization level combination.
Further, the terms to be used hereinafter are first introduced:
1) the probability distribution function for the kernel density estimate can be expressed as:
Figure BDA0002877685640000051
wherein, Kh(. represents a kernel function, x)iRepresenting data points.
2) The choice of bandwidth h depends largely on subjective judgments: if the true probability distribution curve is relatively flat, a larger bandwidth is generally selected; if the true probability distribution curve is steeper, a smaller bandwidth is selected. The magnitude of the Mean Integrated Square Error (MISE) can also be used to measure the relative merits of h, which can be expressed as:
Figure BDA0002877685640000061
3) the quantization error is expressed as:
Figure BDA0002877685640000062
4) the quantization interval points are represented as:
[q-(2n-1),…,q-2,q-1,0,q1,q2,…,q2n-1-1]
5) the quantized discrete output level is represented as:
Figure BDA0002877685640000063
6) the quantized value of the discrete output is represented as:
Figure BDA0002877685640000064
7) the non-linear program is represented as:
minf(q)＝eq
s.t.qj+1>qj,j＝1,…,2n-1-1
qj>0,j＝1,…,2n-1
Figure BDA0002877685640000065
wherein minf (q) ═ eqWhich means that the quantization error is minimized and the best combination of quantization levels is calculated under three constraints.
In the step 1: the small signals in the signal of UFMC occupy most of the signal, resulting in a great waste of system resources, while clipping operation is necessary to prevent excessive PAPR. The Clipping Ratio (CR) is obtained by normalizing the clipping value by the standard deviation of the signal.
In the step 2: each data point can be viewed as a "box" or a "gaussian distribution function" or curve of other functions, depending on the type of kernel function. The functions of each kernel are different, and a gaussian kernel is selected when estimating the UFMC signal. Meanwhile, the kernel function curve is distributed by taking the data point as the center, and the bandwidth is h. If h is selected too large, the final linear overlapping part of the kernel function of the data point is more, so that the probability distribution curve is relatively flat, the proportion of the data point in the curve shape is not obvious enough, and under-fitting is caused; if h is too small, the final linear overlapping part of the kernel function represented by the data points is very small, so that the probability distribution curve is steeper and not smooth enough, and overfitting is caused. In practical application, the relationship between the fitting effect and the curve smoothness needs to be balanced.
In the step 3: if the kernel function is regarded as a density function value with the data point as the center, wherein the density is the density function value of the field [ x-h, x + h ] of the data point when h- >0
Figure BDA0002877685640000071
Nxi∈[x-h,x+h]Is the number of data points in the width 2h, N is the total number of samples, and is guaranteed
Figure BDA0002877685640000072
The integral of (a) is 1; the kernel function for the analog data points is a rectangle of width 2h and height 1/2h, which represents the weight of each data point. The Gaussian distribution function is used as the kernel of kernel density estimation, which is equivalent to changing a rectangle into a Gaussian distribution curve, and the meaning represented by the Gaussian distribution curve is unchanged.
In the step 4: the kernel functions are linearly superposed. The distribution function curves for all data points are linearly superimposed to obtain a fitted signal distribution curve representing the total number of samples N.
In the step 5: and (6) normalizing. The normalization process is to divide the distribution curve of the estimation function obtained in step 3 by the total number of samples N, in order to obtain the probability density function of the fitted signal.
In the step 6: and (4) nonlinear programming. The quantization interval, which is typically 2, is determined by performing a non-linear programming based on the probability density function of the signal to minimize quantization noisenAnd n is the resolution of the DAC, and the last stage quantization interval is typically taken to be equal to the Clipping Ratio (CR). The quantization level is the average of the sum of two adjacent quantization intervals.
In step 7: and (6) quantizing. Quantization is to divide the signal amplitude range into 2nAnd (4) quantizing intervals, and expressing the numerical points in the quantizing intervals by using the optimal quantization level obtained in the step 6.
As shown in fig. 2, the multi-carrier modulation optical communication system based on a filter bank according to the embodiment of the present invention includes: the device comprises a light emitting module, a light receiving module and a light channel. In the optical transmitting module, a digital signal containing data information is input into a quantization module based on KDE non-uniform quantization to obtain an analog signal, the analog signal is converted into a high-speed optical signal through an optical modulator and is sent to an optical fiber channel, the optical receiving module converts the optical signal into a corresponding electric signal, and information data is obtained through demodulation.
The light emitting module includes: the device comprises a digital signal module, a baseband modulation module, a KDE-based non-uniform quantization module and an optical modulator; the digital signal module is connected with the baseband modulation module, carries out coding and mapping processing on the input data sequence and generates a high-speed digital electric signal to be transmitted. The baseband modulation module outputs digital signals to a KDE-based non-uniform quantization module, inputs signals to be processed, linearly superposes and normalizes kernel functions of all data points of the signals after amplitude limiting to obtain a fitted kernel density probability density function f (x), then carries out non-linear programming to obtain quantization level combination which enables quantization noise to be minimum, and finally quantizes the input signals according to the optimal quantization level combination. And inputting the fitted signal distribution as a quantization result into the optical modulator to complete the electro-optical conversion.
The light receiving module includes: the device comprises a light spot detector, a real-time oscilloscope, a baseband demodulation module and a data output unit; after the light spot detector samples the received electric signal through the real-time oscilloscope, the output signal of the real-time oscilloscope is processed and output through the baseband demodulation module, and the user data is received.
Fig. 3 is a diagram showing BER performance comparison of the high-speed optical filter bank multi-carrier system for back-to-back transmission and a transmission distance of 80km under different received optical powers respectively by 3-5-bit non-uniform quantization based on gaussian distribution and non-uniform quantization based on KDE. In the figure: the horizontal axis is the received optical power, and the unit is dBm; the vertical axis BER represents the bit error rate. It can be seen that the algorithm of the present invention can achieve the FEC bit error rate threshold requirement under the condition of lower received optical power when the BER is the same, and is superior to the non-uniform quantization scheme based on gaussian distribution in both cases of B2B and the transmission distance of 80 km.
In summary, the non-uniform quantization algorithm based on KDE of the present invention can better consider the influence factors of small signals in signal quantization. Compared with the DAC based on the non-uniform quantization of the Gaussian distribution, the method has better quantization effect. And meanwhile, the principle of the KDE is simple and easy to realize. Therefore, the algorithm of the invention can be better applied to the requirements of a filter bank multi-carrier optical communication system.
The KDE non-uniform quantization algorithm of the filter bank-based multi-carrier modulation optical communication system comprises the following steps: inputting a signal to be processed, after amplitude limiting, linearly superposing and normalizing kernel functions of all data points of the signal to obtain a fitted kernel density probability density function, then carrying out nonlinear programming to obtain a quantization level combination which minimizes quantization noise, and finally quantizing the input signal according to the optimal quantization level combination. The invention solves the problem of poor small amplitude signal quantization performance in the high-speed signal transmission process. Compared with a non-uniform quantization method based on Gaussian distribution, the method can better fit a signal distribution function, highlight a small-amplitude signal and have good quantization performance, so that the method is suitable for a filter bank multi-carrier modulation optical communication system.
The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes or modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention. The embodiments and features of the embodiments of the present application may be combined with each other arbitrarily without conflict.

Claims (9)

1. A KDE non-uniform quantization method of a multi-carrier modulation optical communication system based on a filter bank is characterized by comprising the following steps:
(1) performing a clipping operation on the signal at different clipping ratios;
(2) initializing a bandwidth and a kernel function according to the signal distribution characteristics and the requirements of nonparametric kernel density estimation;
(3) applying a kernel function as a distribution function for each data point;
(4) linearly superposing the distribution functions of all the representative data points to obtain a distribution curve of a fitting signal;
(5) normalizing the distribution curve of the fitting signal to obtain a probability density function of the fitting signal;
(6) solving the optimal quantization level combination under the constraint of the minimum quantization error for the fitted signal probability density function by utilizing nonlinear programming;
(7) the quantized input signals are combined according to the optimal quantization levels.
2. The KDE non-uniform quantization method for a filterbank-based multicarrier modulation optical communication system according to claim 1, characterized in that in step (1), the clipping ratio CR is expressed as:
Figure FDA0002877685630000011
wherein σsIs the standard deviation of the signal.
3. The KDE non-uniform quantization method for filter bank based multi-carrier modulated optical communication system according to claim 2, wherein in the step (2), the kernel function is a gaussian kernel function.
4. The KDE non-uniform quantization method for filterbank-based multicarrier modulation optical communication system according to claim 3, wherein the kernel function curve is distributed with a data point as a center and has a bandwidth of h.
5. The KDE non-uniform quantization method for filter bank based multi-carrier modulated optical communication system according to claim 3, wherein in step (3), the kernel function is centered around the data point, and the density is the density function value of the domain [ x-h, x + h ] of the data point when h- >0, and is expressed as
Figure FDA0002877685630000012
Nxi∈[x-h,x+h]Is the number of data points in the width 2h, N is the total number of samples, and is guaranteed
Figure FDA0002877685630000013
Is integrated into1; the kernel function of the analog data points is a rectangle with a width of 2h and a height of 1/2h, representing the weight of each data point; and taking a Gaussian distribution function as the kernel of the KDE, namely transforming the rectangle into a Gaussian distribution curve.
6. The KDE non-uniform quantization method for a filterbank-based multicarrier modulation optical communication system according to claim 3, characterized in that the kernel functions are linearly added to obtain a fitted signal profile representing the total number N of samples.
7. The KDE non-uniform quantization method for filter bank based multi-carrier modulated optical communication system according to claim 6, wherein the probability density function f (x) of the fitted signal obtained by normalizing the fitted signal distribution curve of the total number of samples N is represented as:
Figure FDA0002877685630000021
wherein, Kh(. represents a kernel function, x)iRepresenting data points.
8. The KDE non-uniform quantization method for filterbank-based multicarrier modulation optical communication system according to claim 7, wherein in step (6), the probability density function of the fitted signal is non-linearly programmed to find a quantization interval that minimizes quantization noise, and the quantization interval is 2nThen the quantization level also has 2nA plurality of; wherein n is the resolution of the digital-to-analog converter DAC;
the quantization level is the average of the sum of two adjacent quantization intervals;
wherein the quantization interval points are represented as:
Figure FDA0002877685630000022
assuming that the last quantization level is equal to the clipping ratio CR, the quantized discrete output level is expressed as:
Figure FDA0002877685630000023
the quantized values of the discrete outputs are represented as:
Figure FDA0002877685630000024
the non-linear program is represented as:
minf(q)＝eq
s.t.qj+1>qj,j＝1,…,2n-1-1
qj>0,j＝1,…,2n-1
Figure FDA0002877685630000025
wherein minf (q) ═ eqExpressing the minimized quantization error, and calculating the optimal quantization level combination under three constraint conditions;
the quantization error is expressed as:
Figure FDA0002877685630000031
9. the KDE non-uniform quantization method for filterbank-based multicarrier modulated optical communication system according to claim 8, wherein the optimal quantization level combination is used to represent 2nThe numerical points of the quantization intervals.
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