Channel response dependent noise shaping method for pre-equalization dmt transmission system

Abstract

The application discloses a channel response related noise shaping method based on a pre-equalization DMT transmission system, comprising the following steps: S1: considering the influence of a channel, minimizing the difference between a sending signal and a receiving signal, and obtaining optimal feedback filter coefficients; and S2: using the optimal feedback filter coefficients to generate a quantized output signal, wherein the quantized output signal is used to be loaded into a low-quantization digital-to-analog converter to generate an analog signal. ‑1 The application considers the influence of a channel response in the process of obtaining tap coefficients of a feedback filter, and the weighting coefficient changes with the change of the channel H, so that the amplitude response abs|1+G| of the feedback filter changes with the inverse channel response H Changes are made, and unbalanced damage caused by residual quantization noise is effectively avoided. In addition, most of the residual quantization noise is concentrated in the high-frequency part of the signal, so that the residual quantization noise is further attenuated after transmission through the channel, and the SQNR is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of high-speed optical signal processing, and more particularly, to a channel response dependent noise shaping method based on a pre-equalization DMT transmission system. BACKGROUND

[0002] With the emergence of new applications such as social media, cloud computing, and ultra-high-definition television, the traffic of data centers and metropolitan area optical communications has increased dramatically. Discrete multi-tone signals (DMT signals) are widely used to improve the capacity of short-distance optical communication systems due to their efficient spectrum utilization and strong tolerance to inter-channel interference. For DMT signals, digital pre-equalization technology has been widely used at the transmitting end to avoid the problem of excessive compensation of channel noise caused by post-equalization. In addition, pre-equalization technology can also effectively avoid the imbalance caused by bandwidth limitations of electrical / optical devices. However, the peak-to-average power ratio (PAPR) of pre-equalization DMT signals is high, so high-quantization-bit digital-to-analog converters (DACs) are often used to avoid the loss caused by quantization noise during digital-to-analog conversion. Compared with low-quantization-bit DACs, the use of high-quantization-bit DACs undoubtedly increases the system cost and power consumption, which is not conducive to cost-sensitive short-distance optical communication systems. Therefore, in order to promote the use of low-quantization-bit DACs, quantization noise suppression techniques have been continuously researched:

[0003] 1) Delta-sigma modulator

[0004] Delta-sigma modulator is a technique that suppresses the influence of in-band quantization noise by directly designing a high-pass filter for quantization noise. This technique can effectively suppress in-band quantization noise and promote the use of 1 / 2-bit DACs, but Delta-sigma modulator requires an oversampling rate (OSR) of about 8-16 times to achieve quantization noise shaping, so it is not suitable for short-distance high-speed optical communication systems.

[0005] 2) Digital resolution enhancer

[0006] Digital resolution enhancer (DRE) is a technique that suppresses in-band quantization noise by finding the best quantization level at the transmitting end using the Viterbi algorithm. This technique can eliminate the influence of quantization noise with low OSR, but the dynamic quantization process implemented by the Viterbi algorithm requires high computational complexity, which can cause high processing delay and increase system power consumption, so it is not suitable for low-cost high-speed optical communication systems.

[0007] 3) Noise shaping technology

[0008] NS is designed to minimize the in-band quantization noise of the signal before and after quantization, which has the advantages of low OSR, computational complexity and processing delay, but for the DMT signal after pre-equalization, it will cause SQNR uneven phenomenon, resulting in poor performance. SUMMARY

[0009] The application provides a channel response related noise shaping method based on a pre-equalization DMT transmission system, which effectively eliminates the SQNR uneven problem caused by the use of traditional NS technology in the pre-equalization DMT system.

[0010] To solve the above technical problems, the technical scheme of the application is as follows:

[0011] A channel response related noise shaping method based on a pre-equalization DMT transmission system, comprising the following steps:

[0012] S1: considering the influence of the channel, the difference between the transmitted signal and the received signal is minimized to obtain the optimal feedback linear filter coefficient;

[0013] S2: using the optimal feedback linear filter coefficient to generate a quantized output signal, the quantized output signal is used to load into a low quantization digital-to-analog converter to generate an analog signal.

[0014] Preferably, in step S1, when considering the influence of the signal, the mathematical formula of the transmitted signal and the received signal is:

[0015] Y(e jw )=X(e jw )+(1+G(e jw ))H(e jw )E(e jw )

[0016] In the formula, X(e jw ), Y(e jw ) and E(e jw ) represent the transmitted signal, the received signal and the quantization noise respectively, G(e jw )=g1e -jω +g2e -2jω +…+g K e -Kjω represents the channel response of the feedback linear filter, and g1, g2, …, g K is the feedback linear filter coefficient.

[0017] Preferably, in step S1, the difference between the transmitted signal and the received signal is minimized, which is represented as the following problem (1):

[0018]

[0019] Preferably, the quantization noise is modeled as white noise.

[0020] Preferably, problem (1) can be expressed as problem (2):

[0021]

[0022] Preferably, the definition vector K is:

[0023]

[0024] wherein, Problem (2) is expressed as problem (3):

[0025]

[0026] In the formula, H represents the channel response coefficient of the transmission link.

[0027] Preferably, a weighting matrix is introduced to minimize problem (3):

[0028] W = diag (W1, W2,..., W p , W P+1 , ... W p+q )

[0029] wherein, W1~W p and W p+1 ~W p+q represent the weights of the signal frequency band and the unused frequency band respectively.

[0030] Preferably, W s and W I represent the coefficients of W1~W p and W p+1 ~W p+q respectively, the bandwidth weighted by W s is represented by B s , and W s >>W I .

[0031] Preferably, W I is 1, and the optimal values of W s and B s are obtained through simulation.

[0032] Preferably, problem (3) is converted into problem (4):

[0033]

[0034] In the formula, g is the coefficient of the feedback linear filter, which is a real number, and A is a complex number. The coefficient g is obtained by solving the following equation:

[0035]

[0036] The achievable optimal coefficient g is as follows:

[0037]

[0038] In the formula, This represents the pseudo-inverse of a matrix.

[0039] Compared with the prior art, the beneficial effects of the technical solution of the present invention are:

[0040] This invention, based on low-cost neutral density (NS) technology, further proposes CRD-NS technology to address the problems of traditional NS technology in pre-equalized DMT signals. Compared to traditional NS technology, this technology effectively eliminates the SQNR unevenness caused by using traditional NS technology for pre-equalized DMT signals without increasing computational complexity, and also improves the overall SQNR. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of the method flow of the present invention.

[0042] Figure 2 This is a schematic diagram of the technical structure of the present invention.

[0043] Figure 3 The CRD-NS technology and NS technology feedback linear filter amplitude response and corresponding weighting function are provided for the embodiments.

[0044] Figure 4 A schematic diagram of the experimental setup provided for the example.

[0045] Figure 5 The example provides a curve relating the bit error rate to the number of taps in the feedback linear filter.

[0046] Figure 6 The bit error rate and B of the NS technology provided in the embodiments s The relationship between the curves.

[0047] Figure 7 The bit error rate and B of the CRD-NS technology provided in the embodiments s The relationship between the curves. Detailed Implementation

[0048] The accompanying drawings are for illustrative purposes only and should not be construed as limiting the scope of this patent.

[0049] To better illustrate this embodiment, some parts in the accompanying drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions;

[0050] It is understood by those skilled in the art that some well-known structures and their descriptions in the drawings can be omitted.

[0051] The technical solutions of the present application are further described below in combination with the drawings and examples.

[0052] Example 1

[0053] This example provides a channel response dependent noise shaping method based on a pre-equalized DMT transmission system, as shown in Figure 1 , comprising the following steps:

[0054] S1: considering the influence of the channel, the difference between the transmitted signal and the received signal is minimized to obtain the optimal feedback linear filter coefficient;

[0055] S2: using the optimal feedback linear filter coefficient to generate a quantized output signal, the quantized output signal is used to load into a digital-to-analog converter to generate an analog signal.

[0056] The residual quantization noise exists in the signal generated by the low-quantization-bit DAC combined with the NS technology. For high-order modulation format signals, it still causes serious performance distortion at the hard decision forward error correction (HD-FEC) threshold, especially for pre-equalized DMT signals. The power distribution of the pre-equalized signal follows the reverse channel response obtained by post-equalization, and the quantization noise can be modeled as white noise, so the SQNR will present the characteristics of uneven distribution after the traditional NS technology, thereby causing unbalanced damage to the DMT signal. In view of the above unbalanced damage problem, the present application proposes a CRD-NS technology, which changes the design of the filter to make the residual quantization noise consistent with the power distribution of the pre-equalized signal, thereby effectively avoiding the problem of uneven SQNR. In addition, the residual quantization noise after the CRD-NS technology is mostly concentrated in the high-frequency part of the signal, so after transmission through the channel, the residual quantization noise will be further attenuated, thereby improving the SQNR.

[0057] Example 2

[0058] This example is based on example 1 and further discloses the following content:

[0059] The traditional NS technology determines the coefficient of the feedback linear filter by minimizing the difference between the signals before and after quantization. Unlike the traditional NS technology, the principle of the CRD-NS technology is to minimize the difference between the transmitted and received signals, that is, the influence of the channel is considered to obtain the coefficient of the feedback linear filter. The architecture of the CRD-NS technology is as shown in Figure 2 , H(e jw ) and H -1 (e jwrespectively represent the channel response of the transmission link and its reverse channel response. Q, which is achieved by rounding off the criteria, represents the quantization process in the DAC, and it also limits the maximum output of the quantization process to 2 bit -1. The clipping module at the end of the feedback path can reduce the impact of excessive feedback noise to some extent, and the mathematical expressions of the transmitted signal and the received signal are as follows:

[0060] Y(e jw )=X(e jw )+(1+G(e jw ))H(e jw )E(e jw )

[0061] wherein X(e jw ), Y(e jw ) and E(e jw ) represent the transmitted signal, the received signal and the quantization noise respectively, G(e jw ) = g1e -jω + g2e -2jω + … + g K e -Kjω represents the channel response of the feedback linear filter, g1, g2, …, g K are the feedback linear filter coefficients.

[0062] The minimization of the difference between the transmitted signal and the received signal in step S1 is represented as the following problem (1):

[0063]

[0064] The quantization noise is modeled as white noise.

[0065] Problem (1) can be represented as problem (2):

[0066]

[0067] The vector K is defined as:

[0068]

[0069] wherein Problem (2) is represented as problem (3):

[0070]

[0071] wherein H represents the channel response coefficient of the transmission link.

[0072] A weighting matrix is introduced to minimize problem (3):

[0073] W = diag(W1, W2, …, W pW P+1 W p+q )

[0074] wherein W1~W p and W p+1 ~W p+q represent the weights of the signal frequency band and the unused frequency band, respectively.

[0075] For simplicity, W s and W I represent the coefficients of W1~W p and W p+1 ~W p+q , respectively, the bandwidth weighted by W s is denoted by B s , and W s >>W I .

[0076] W I is set to 1, and the optimal values of W s and B s are obtained through simulation.

[0077] Problem (3) is converted to problem (4):

[0078]

[0079] wherein g is the coefficient of the feedback linear filter, is constrained to be a real number, A is a complex number, and the coefficient g is obtained by solving the following equation:

[0080]

[0081] The optimal coefficient g that can be obtained is as follows:

[0082]

[0083] wherein represents the pseudo-inverse of a matrix.

[0084] For the conventional NS technology, due to the problem of unbalanced impairment, the residual quantization noise still brings obvious distortion to the pre-equalization high-order QAM-DMT signal. For the CRD-NS technology proposed in the embodiment, the channel response is considered in the process of obtaining the tap coefficient of the feedback linear filter, so that the residual quantization noise power distribution in the signal band after the CRD-NS technology follows the pre-equalization signal power variation, to avoid the problem of uneven SQNR. Figure 3The amplitude response of the feedback linear filter abs|1+G| and the corresponding weight function of the NS and CRD-NS techniques are given. It is noted that the weight function of the CRD-NS is defined by WH. The amplitude response of the transmission link H is simulated by the experimental channel under test. Unlike the conventional NS technique, the weighting coefficients of the CRD-NS technique vary with the channel H, so that the amplitude response of the feedback linear filter abs|1+G| varies with the inverse channel response H -1 The changes are made so that the unbalanced impairment caused by the residual quantization noise can be effectively avoided. In addition, the residual quantization noise after the CRD-NS technique is mostly concentrated in the high frequency part of the signal, so that the residual quantization noise will be further attenuated after transmission through the channel, thereby achieving the improvement of the SQNR.

[0085] Embodiment 3

[0086] This embodiment gives the digital signal processing (DSP) flow and experimental device, as shown in Figure 4

[0087] (1) Transmit-end DSP

[0088] The 100 Gb / s 16-QAM signal is first generated offline by a pseudo-random binary sequence (PRBS) generated by MATLAB, then converted from serial to parallel, and the digital pre-equalization technology is used to avoid the channel noise amplification in the post-equalization process at the receiving end. In order to obtain the 16 QAM-DMT signal, the 1024-point inverse fast Fourier transform (IFFT) algorithm is used for frequency-time conversion, and the generated parallel DMT signal is converted from parallel to serial for signal transmission. Before loading the data to the DAC for digital-to-analog conversion, the conventional NS, CRD-NS and DRE techniques are combined with a 3-bit quantizer for quantization, and the quantization noise in the band is shaped, and finally the shaped signal is input to the experimental DAC for experimental verification.

[0089] (2) Receiving-end DSP

[0090] At the receiving end, the DSP flow of the directly detected signal includes synchronization, serial-to-parallel conversion, time-frequency conversion using the FFT algorithm, post-equalization based on the zero-forcing algorithm, parallel-to-serial conversion, signal demapping, and error code calculation.

[0091] (3) Experimental device

[0092] ​The experimental system is an IM / DD system. Firstly, in the transmitting end, the offline data generated by MATLAB is loaded into a DAC with a sampling rate of 80-GSa / s and a 3-dB bandwidth of 16.7 GHz for digital-to-analog conversion, and then a electrical amplifier (EA) with a gain of 23 dB is used to amplify the signal. Then, a Mach-Zehnder modulator (MZM) is used to realize photoelectric conversion. The output optical signal of the modulator is guided into a 2-kilometer optical fiber and transmitted. An optical attenuator (VOA) is used in the receiving end to adjust the received power of the signal, and the attenuated optical signal is detected by a photodetector (PD). The analog electrical signal output by the PD is collected by an oscilloscope with a cutoff bandwidth of 36 GHz and a sampling rate of 80-GSa / s. Finally, the collected data is imported into MATLAB for offline DSP.

[0093] In order to verify the effectiveness of the CRD-NS technology in this embodiment, 25-GHz QAM-DMT signals generated by 3 / 4 / 5 / 6-bit DACs combined with NS, CRD-NS, and DRE technologies are used for simulation comparison. Firstly, the parameters of the traditional NS and CRD-NS technologies are optimized, and the optimization results are as shown in Figure 5 . Figure 5 The optimization of the above parameters is based on 25-GHz 16-QAM-DMT signals generated by 80-GSa / s 3-bit DACs. Figure 5 The curve relationship between BER and the number of taps of the feedback linear filter is given, and it can be found that for NS and CRD-NS technologies, when the number of taps reaches 7, the BER no longer has obvious improvement. Therefore, for NS and CRD-NS technologies, the optimal number of taps for subsequent simulation and experiment is set to 7. Based on the optimized number of taps, the BER s and W s parameters of NS and CRD-NS technologies are simulated and optimized, and the simulation is as shown in Figure 6 and Figure 7 . It can be found that the BER will decrease with the increase of B s , and a larger B s will reduce the BER performance, because the unused frequency band becomes too small, resulting in poor noise shaping ability. From the simulation results, it can be seen that the optimal B s of the traditional NS and CRD-NS technologies is 0.6 and 0.65, respectively. A smaller W s will reduce the ability of noise shaping, and a larger W s will cause excessive feedback noise. Therefore, the W sThe values of both are optimized to 24. For the DRE technology, the required computational complexity increases sharply with the dynamic quantization possible quantization level number M and the channel length L, so after comprehensively considering the computational complexity and the BER performance, the dynamic quantization possible quantization level number M and the channel length L of the DRE are both set to 3, which is also the current mainstream parameter setting of the DRE technology.

[0094] The same or similar reference signs correspond to the same or similar components;

[0095] The terms describing the positional relationship in the drawings are only used for illustrative description, and should not be understood as a limitation on the patent;

[0096] Obviously, the above embodiments of the present application are only examples for clearly illustrating the present application, and are not intended to limit the implementation modes of the present application. Based on the above description, other different forms of changes or variations can be made by those skilled in the art. Here, it is not necessary and also impossible to exhaust all the implementation modes. Any modification, equivalent replacement and improvement made within the spirit and principle of the present application should be included in the protection scope of the claims of the present application.

Claims

1. A method for shaping the channel response dependent noise of a pre-equalized DMT transmission system, characterized in that, The method comprises the following steps: S1: considering the influence of the channel, minimizing the difference between the transmitted signal and the received signal to obtain optimal feedback linear filter coefficients; S3: using the optimal feedback linear filter coefficients to generate a quantized output signal, which is used to load into a low-quantization digital-to-analog converter to generate an analog signal; In step S1, when considering the influence of the signal, the mathematical formula of the transmitted signal and the received signal is: Y(e jw ) = X(e jw ) + (1 + G(e jw )) H(e jw ) E(e jw ) where X(e jw ), Y(e jw ) and E(e jw ) represent a transmission signal, a reception signal and quantization noise, respectively, G(e jw ) = g1e -jω + g2e -2jω +... + g K e -Kjω represents a channel response of a feedback linear filter, and g1, g2,..., g K are coefficients of the feedback linear filter; In step S1, minimizing the difference between the transmitted signal and the received signal is expressed as the following problem (1): The quantization noise is modeled as white noise; Problem (1) can be expressed as problem (2): The vector K is defined as: wherein Problem (2) is then represented as problem (3): In the formula, H represents the channel response coefficient of the transmission link; A weighted matrix is introduced to minimize problem (3): W = diag(W1, W2,..., W p , P+1 W p+q ) wherein W1-W p and W p+1 -W p+q represent the weight of the signal frequency band and the unused frequency band, respectively. W s and W I represent coefficients of W p 1 to W p+1 4, respectively, the bandwidth weighted with W p+q is denoted by B s , and W s > W s > W I > W W I takes the value 1, while W s and B s are obtained by simulation. Problem (3) is converted into problem (4): In the formula, g is the coefficient of the feedback linear filter, which is constrained to be a real number, and A is a complex number, which is obtained by solving the following equation: The optimal coefficient g that can be obtained is as follows: In the formula, denotes the pseudo-inverse of a matrix.

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