Low-complexity Volterra decision feedback equalization method based on clustering pruning lookup table

Abstract

The invention relates to the technical field of optical fiber communication systems, in particular to a low-complexity Volterra decision feedback equalization method based on a cluster pruning lookup table. Comprising the following steps: estimating tap coefficients of VFFE and VDFE based on a training sequence; respectively clustering the linear kernel coefficient and the nonlinear kernel coefficient of the VDFE obtained by estimation by adopting a k-means clustering algorithm; sorting the clustering centers obtained by clustering and trimming the clustering centers of which the absolute values are within a set range; a sub lookup table is constructed for each cluster center after trimming; independently constructing a sub lookup table for the second-order beat frequency item; a received damaged data signal is subjected to VFFE equalization, and then an output signal is superposed on an equalization output signal of the CPLUT-VDFE for joint equalization. According to the method, kernel coefficients in VDFE are clustered and trimmed, and a clustering trimming lookup table is established, so that dispersion and nonlinear distortion in the IM / DD system are effectively compensated, meanwhile, the calculation complexity is remarkably reduced, and the method is suitable for signal distortion processing in the high-speed IM / DD system.

Description

Technical Field

[0001] The present application relates to the technical field of optical fiber communication systems, and more specifically, to a low-complexity Volterra decision feedback equalization method based on a clustered pruning lookup table. Background Art

[0002] With the increasing popularity of emerging bandwidth-intensive applications such as ultra-high-definition video streaming, artificial intelligence, and machine learning, the demand for high-speed signal transmission in optical communication systems is surging. Among the many modulation schemes, intensity-modulated direct detection (IM / DD) systems based on pulse amplitude modulation (PAM) have become the preferred solution for intra- and inter-data center links due to their cost-effectiveness and low power consumption. However, as data rates continue to increase, signal distortion issues facing IM / DD systems are becoming increasingly prominent. Specifically, the combined effects of bandwidth limitations, nonlinear modulation and detection processes, and fiber chromatic dispersion can significantly degrade system performance. The interaction between fiber chromatic dispersion and the square-law response of photodetectors often leads to frequency-selective power fading and severe nonlinear intersymbol interference (ISI), which are the main bottlenecks degrading system performance. To improve the transmission performance of IM / DD systems, nonlinear equalizers based on the Volterra series model are typically used at the receiver to compensate. Common solutions include the combination of a nonlinear feedforward equalizer and a decision feedback equalizer. However, although this type of equalizer has excellent distortion compensation capabilities, its computational complexity increases exponentially with the increase of memory length, resulting in high overall computational complexity of the system, which seriously restricts its real-time processing capabilities and actual deployment. Summary of the Invention

[0003] The purpose of the present invention is to overcome the shortcomings of the prior art that a nonlinear equalizer based on a Volterra series model is used for compensation, which leads to high overall computational complexity of the system. A low-complexity Volterra decision feedback equalization method based on a clustered pruned lookup table is provided, which effectively reduces the computational complexity and thus improves the performance of the system.

[0004] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0005] A low-complexity Volterra decision feedback equalization method based on a clustered pruned lookup table is provided, comprising the following steps:

[0006] S1. Estimate the tap coefficients of the Volterra feedforward equalizer and the Volterra decision feedback equalizer based on the training sequence;

[0007] S2. Using the k-means clustering algorithm to cluster the estimated linear kernel coefficients and nonlinear kernel coefficients of the Volterra decision feedback equalizer, respectively, to obtain a Volterra decision feedback equalizer based on the clustering lookup table;

[0008] S3. Sort the cluster centers obtained by clustering and prune the cluster centers whose absolute values are within the set range;

[0009] S4. Build a sub-lookup table for each pruned cluster center;

[0010] S5. Construct a separate sub-lookup table for the second-order beat frequency term in step S4;

[0011] S6. The output signal of the received impaired data signal after being equalized by the Volterra feedforward equalizer is superimposed on the equalized output signal of the Volterra decision feedback equalizer based on the cluster pruning lookup table to perform joint equalization.

[0012] The present invention provides a low-complexity Volterra decision feedback equalization method based on clustering and pruning lookup tables. It combines clustering and lookup table technologies, introduces a pruning strategy to reduce the size of the lookup table, solves the problem of high computational complexity in the equalization process, and thus improves system performance.

[0013] Furthermore, step S1 includes: estimating the tap coefficients of the Volterra feedforward equalizer and the Volterra decision feedback equalizer using an adaptive estimation algorithm according to the training sequence signal of the transmitting and receiving ends, wherein the input-output relationship of the VDFE is expressed as:

[0014]

[0015] Where d(nk) represents the previous hard-decision output signal, n represents the time when the equalizer outputs the signal, and k represents the number of samples of signal delay. ω1(k) represents the first-order kernel coefficient of the Volterra decision feedback equalizer, D1 represents the memory length of the linear part of the Volterra decision feedback equalizer, ω2(k,u) represents the second-order kernel coefficient of the Volterra decision feedback equalizer, u represents the relative delay, and its value range is limited by the truncation factor U, which is used to truncate high-order kernel coefficients and beat frequency terms with large relative delays and insignificant impact on the system. D2 represents the memory length of the nonlinear part of the Volterra decision feedback equalizer.

[0016] Furthermore, step S2 includes: clustering the D1 linear kernel coefficients and U(2D2-U+1) / 2 nonlinear kernel coefficients obtained in step S1 using a k-means clustering algorithm to obtain a Volterra decision feedback equalizer based on a clustering lookup table, and the input-output relationship is expressed as:

[0017]

[0018] Where g1(i) and C1 represent the cluster centers and number of cluster centers obtained by clustering the linear kernel coefficients, g2(i) and C2 represent the cluster centers and number of cluster centers obtained by clustering the nonlinear kernel coefficients. d1(n,i) represents the sum of the first-order decision feedback terms d(nk) corresponding to the linear kernel coefficients belonging to the i-th cluster, and d2(n,i) represents the sum of the second-order decision feedback terms d(nk) and d(nku) corresponding to the nonlinear kernel coefficients belonging to the i-th cluster. The first and second terms in the formula represent the outputs of the linear and nonlinear clustering lookup tables, respectively. After clustering, the D1 linear kernel coefficients and U(2D2-U+1) / 2 nonlinear kernel coefficients are reduced to C1 and C2, respectively. The number of required real multiplications is reduced from D1+U(2D2-U+1) to 0, and the number of real additions is reduced from D1+U(2D2-U+1) / 2-1 to C1+C2-1.

[0019] Furthermore, step S3 includes: using a cluster center sorting strategy to sort the absolute values of the cluster centers, and pruning the cluster centers whose absolute values in step S2 are less than the set range. The number of cluster centers of the linear kernel coefficient and the nonlinear kernel coefficient after pruning are P1 and P2 respectively. The output of the Volterra decision feedback equalizer based on the cluster pruning lookup table is:

[0020]

[0021] Where g′1(i) and d′1(n,i) represent the sum of the linear cluster centers and their corresponding linear decision feedback terms after pruning the linear clustering lookup table, and g′2(i) and d′2(n,i) represent the sum of the nonlinear cluster centers and their corresponding nonlinear decision feedback terms after pruning the nonlinear clustering lookup table. After pruning, the number of real addition operations required is reduced from C1+C2-1 to P1+P2-1.

[0022] Furthermore, step S4 includes: constructing a sub-lookup table for each cluster center obtained after cluster pruning in step S3, and the m-th output element of the i-th sub-lookup table in the linear cluster lookup table is expressed as:

[0023]

[0024] The mth output element of the i-th sub-lookup table in the nonlinear clustering lookup table is expressed as:

[0025]

[0026] Where N L (i) and NNL (i) represents the number of kernel coefficients in the i-th cluster of the linear kernel coefficient and the nonlinear kernel coefficient, respectively. c1(m,j) and c2(m,j) represent the j-th element in the m-th sequence of the i-th sub-lookup table in the linear cluster pruning lookup table and the nonlinear cluster pruning lookup table, respectively. The size of the sub-table established is Much smaller than the subtable size without pruning

[0027] Furthermore, step S5 includes: for the second-order beat frequency term c2(m,j)c2(m,j+N NL (i)) Construct a separate sub-lookup table and update the m-th output element of the i-th sub-lookup table in the nonlinear clustering lookup table as follows:

[0028]

[0029] Where c3(m,j) represents the pre-calculated product value of the second-order beat frequency term. Further reducing the size of the established sub-table to

[0030] Furthermore, the transmitted data signal undergoes digital-to-analog conversion, electro-optical modulation, optical fiber channel transmission, photoelectric detection, and analog-to-digital conversion to obtain a receiving-end data signal. The output signal of the received impaired data signal after equalization by the Volterra feedforward equalizer is superimposed on the equalized output signal of the Volterra decision feedback equalizer based on the clustered pruning lookup table for joint equalization.

[0031] The present invention also provides a low-complexity Volterra decision feedback equalization system based on a clustered pruning lookup table, comprising:

[0032] Tap coefficient estimation module: used to estimate the tap coefficients of Volterra feedforward equalizer and Volterra decision feedback equalizer based on the training sequence;

[0033] K-means clustering module: used to cluster the estimated linear kernel coefficients and nonlinear kernel coefficients of the Volterra decision feedback equalizer using the K-means clustering algorithm, and obtain a Volterra decision feedback equalizer based on the clustering lookup table;

[0034] Sorting and pruning module: used to sort the cluster centers obtained by clustering and prune the cluster centers whose absolute values are within the set range;

[0035] The first sub-lookup table building module is used to build a sub-lookup table for each cluster center after pruning;

[0036] A second sub-lookup table establishment module: used to separately construct a sub-lookup table for the second-order beat frequency term in the first sub-lookup table establishment module;

[0037] Joint equalization module: used to perform joint equalization by superimposing the output signal of the received damaged data signal after being equalized by the Volterra feedforward equalizer on the equalized output signal of the Volterra decision feedback equalizer based on the cluster pruning lookup table.

[0038] The present invention also provides a computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above method when executing the computer program.

[0039] The present invention also provides a computer-readable storage medium having a computer program stored thereon, and when the computer program is executed by a processor, the steps of the method described above are implemented.

[0040] Compared with the prior art, the present invention has the following beneficial effects:

[0041] The present invention proposes a low-complexity Volterra decision feedback equalization method and system based on clustered and pruned lookup tables. Combining clustering with lookup table techniques, this method introduces a pruning strategy to reduce the size of the lookup table, addressing the issue of excessive computational complexity during the equalization process and thereby improving system performance. While maintaining equalization performance, this method significantly reduces the computational complexity required to compensate for fiber chromatic dispersion and nonlinear distortion in IM / DD systems, effectively addressing the real-time processing requirements of high-speed data transmission scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 Schematic diagram of the method flow of the present invention;

[0043] Figure 2 This is a flowchart of the experimental device and the digital signal processing (DSP) at the receiving end in an embodiment of the present invention.

[0044] Figure 3 This is a graph showing the relationship between the bit error rate characteristics and the total table size and the number of cluster centers after a 112Gb / s PAM-4 signal is transmitted over 50km of standard single-mode optical fiber, after VFFE equalization, and CLUT-VDFE equalization under the parameter conditions (D1=30, D2=22, U=13) in an embodiment of the present invention. (a) The linear DFE items in the corresponding VDFE are replaced with a linear cluster lookup table, and (b) The nonlinear DFE items in the corresponding VDFE are replaced with a nonlinear cluster lookup table. The horizontal axis is the number of cluster centers, and the vertical axis represents the bit error rate and the total table size, respectively;

[0045] Figure 4This graph shows the relationship between the bit error rate (BER), total table size, and number of cluster centers for a 112Gb / s PAM-4 signal transmitted over 50km of standard single-mode fiber, after VFFE equalization and CPLUT-VDFE equalization under the parameter conditions (D1=30, D2=22, U=13) in an embodiment of the present invention. (a) corresponds to replacing the linear DFE terms in the VDFE with a linear cluster lookup table, and (b) corresponds to replacing the nonlinear DFE terms in the VDFE with a nonlinear cluster lookup table. The horizontal axis represents the number of cluster centers retained after pruning, and the vertical axis represents the bit error rate and total table size, respectively. DETAILED DESCRIPTION

[0046] The present invention will be further described below with reference to specific embodiments. The accompanying drawings are for illustrative purposes only and are schematic, not actual, representations. They should not be construed as limiting the present invention. To better illustrate the embodiments of the present invention, some components in the drawings may be omitted, enlarged, or reduced in size, and do not represent the actual dimensions of the products. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted from the drawings.

[0047] The same or similar numbers in the drawings of the embodiments of the present invention correspond to the same or similar parts; in the description of the present invention, it should be understood that if the terms "up", "down", "left", "right", etc. indicate directions or positional relationships, they are based on the directions or positional relationships shown in the drawings. This is only for the convenience of describing the present invention and simplifying the description, and does not indicate or imply that the device or element referred to must have a specific direction, be constructed and operated in a specific direction. Therefore, the terms describing the positional relationship in the drawings are only used for illustrative purposes and cannot be understood as limiting the present invention. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to specific circumstances.

[0048] Example 1

[0049] This embodiment is a first embodiment of a low-complexity Volterra decision feedback equalization method based on a clustered pruning lookup table, comprising the following steps:

[0050] Step S1: Estimate tap coefficients of a Volterra feedforward equalizer and a Volterra decision feedback equalizer based on a training sequence.

[0051] Before data signal transmission, the training sequence signal generated by the transmitter undergoes digital-to-analog conversion, electro-optical modulation, fiber channel transmission, photoelectric detection, and analog-to-digital conversion to obtain the training sequence signal at the receiver. Based on the training sequence signal at the transmitter and receiver, an adaptive estimation algorithm such as the recursive least squares (RLS) algorithm is used to estimate the tap coefficients of the Volterra feedforward equalizer (VFFE) and Volterra decision feedback equalizer (VDFE). The input-output relationship of the VDFE can be expressed as:

[0052]

[0053] Where d(nk) represents the previous hard-decision output signal, n represents the time when the equalizer outputs the signal, and k represents the number of samples of signal delay. ω1(k) represents the first-order kernel coefficient of the Volterra decision feedback equalizer, D1 represents the memory length of the linear part of the Volterra decision feedback equalizer, ω2(k,u) represents the second-order kernel coefficient of the Volterra decision feedback equalizer, u represents the relative delay, and its value range is limited by the truncation factor U, which is used to truncate high-order kernel coefficients and beat frequency terms with large relative delays and insignificant impact on the system. D2 represents the memory length of the nonlinear part of the Volterra decision feedback equalizer.

[0054] Step S2. Cluster the estimated linear kernel coefficients and nonlinear kernel coefficients of the Volterra decision feedback equalizer using the k-means clustering algorithm to obtain a clustering lookup table-based Volterra decision feedback equalizer (CLUT-VDFE). Cluster the D1 linear kernel coefficients and U(2D2-U+1) / 2 nonlinear kernel coefficients obtained in step S1 using the k-means clustering algorithm to obtain a clustering lookup table-based Volterra decision feedback equalizer (CLUT-VDFE). The input-output relationship is expressed as:

[0055]

[0056] Where g1(i) and C1 represent the cluster centers and number of cluster centers obtained by clustering the linear kernel coefficients, g2(i) and C2 represent the cluster centers and number of cluster centers obtained by clustering the nonlinear kernel coefficients. d1(n,i) represents the sum of the first-order decision feedback terms d(nk) corresponding to the linear kernel coefficients belonging to the i-th cluster, and d2(n,i) represents the sum of the second-order decision feedback terms d(nk) and d(nku) corresponding to the nonlinear kernel coefficients belonging to the i-th cluster. The first and second terms in the formula represent the outputs of the linear and nonlinear clustering lookup tables, respectively. After clustering, the D1 linear kernel coefficients and U(2D2-U+1) / 2 nonlinear kernel coefficients are reduced to C1 and C2, respectively. The number of required real multiplications is reduced from D1+U(2D2-U+1) to 0, and the number of real additions is reduced from D1+U(2D2-U+1) / 2-1 to C1+C2-1.

[0057] Step S3: sort the cluster centers obtained by clustering and prune the cluster centers whose absolute values are within a set range.

[0058] A cluster center sorting strategy is used to sort the absolute values of the cluster centers and prune the cluster centers whose absolute values are within the set range in step S2, thereby reducing unnecessary computation and minimizing the size of the constructed table. The number of cluster centers for the pruned linear kernel coefficient and nonlinear kernel coefficient is P1 and P2, respectively. The output of the Volterra decision feedback equalizer based on the cluster pruning lookup table (CPLUT-VDFE) is:

[0059]

[0060] Where g′1(i) and d′1(n,i) represent the sum of the linear cluster centers and their corresponding linear decision feedback terms after pruning the linear clustering lookup table, and g′2(i) and d′2(n,i) represent the sum of the nonlinear cluster centers and their corresponding nonlinear decision feedback terms after pruning the nonlinear clustering lookup table. After pruning, the number of real addition operations required is reduced from C1+C2-1 to P1+P2-1.

[0061] Step S4. Construct a sub-lookup table for each pruned cluster center.

[0062] In order to further reduce the size of the lookup table, a sub-lookup table is constructed for each cluster center obtained after cluster pruning in step S3. The m-th output element of the i-th sub-lookup table in the linear clustering lookup table is expressed as:

[0063]

[0064] The mth output element of the i-th sub-lookup table in the nonlinear clustering lookup table is expressed as:

[0065]

[0066] Where N L (i) and N NL (i) represents the number of kernel coefficients in the i-th cluster of the linear kernel coefficient and the nonlinear kernel coefficient, respectively. c1(m,j) and c2(m,j) represent the j-th element in the m-th sequence of the i-th sub-lookup table in the linear cluster pruning lookup table and the nonlinear cluster pruning lookup table, respectively. The size of the sub-table established is Much smaller than the subtable size without pruning

[0067] Step S5: construct a separate sub-lookup table for the second-order beat frequency term in step S4.

[0068] is the second-order beat frequency term c2(m,j)c2(m,j+N NL (i)) Construct a separate sub-lookup table and update the m-th output element of the i-th sub-lookup table in the nonlinear clustering lookup table as follows:

[0069]

[0070] Where c3(m,j) represents the pre-calculated product of the second-order beat frequency term. Further reducing the size of the established sub-table to

[0071] Step S6: The output signal of the received impaired data signal after being equalized by the Volterra feedforward equalizer is superimposed on the equalized output signal of the Volterra decision feedback equalizer based on the cluster pruning lookup table to perform joint equalization.

[0072] The transmitted data signal undergoes digital-to-analog conversion, electro-optical modulation, fiber channel transmission, photoelectric detection, and analog-to-digital conversion to obtain the receiving end data signal. The received impaired data signal is equalized by the Volterra feedforward equalizer, and the equalized output signal of the Volterra decision feedback equalizer based on the clustered pruning lookup table is superimposed on it for joint equalization.

[0073] This embodiment provides a low-complexity Volterra decision feedback equalization method based on clustering and pruning lookup tables. It combines clustering and lookup table technologies, introduces a pruning strategy to reduce the size of the lookup table, solves the problem of high computational complexity in the equalization process, and thus improves system performance.

[0074] Example 2

[0075] This embodiment is a second embodiment of a low-complexity Volterra decision feedback equalization method based on a cluster pruning lookup table. This embodiment is similar to the first embodiment. In this embodiment, Figure 2 The figure shows the experimental setup and the digital signal processing (DSP) flow chart for this embodiment. At the transmitter, a 56 GBaud Gray-coded PAM-4 signal is first generated offline and loaded into an arbitrary waveform generator (AWG Keysight M8194A) with a sampling rate of 120 GSa / s to generate an electrical signal. This electrical signal is amplified by an electrical amplifier (EA, SHF M807) and then drives a Mach-Zehnder modulator (MZM, FTM7938EZ) for double-sideband (DSB) electro-optical conversion. This modulator operates at the quadrature point and modulates a 1550.12 nm optical carrier generated by an external cavity laser (ECL). After transmission over 50 km of standard single-mode fiber, the optical signal is adjusted for received optical power (ROP) via a variable optical attenuator (VOA) and amplified to 7 dBm using an erbium-doped fiber amplifier (EDFA). A photodetector then converts the optical signal into an electrical signal, which is acquired and stored by a real-time oscilloscope (OSC, Keysight UXR0804A) with a sampling rate of 256GSa / s. Finally, offline digital signal processing is performed, including data resampling to two samples per symbol, signal synchronization, equalization using a Volterra feedforward equalizer (VFFE) and a clustered pruned lookup table Volterra decision feedback equalizer (CPLUT-VDFE), symbol decision making, PAM-4 signal demapping, and bit error rate calculation.

[0076] Figure 3 The following is a graph showing the relationship between the bit error rate, total table size, and the number of cluster centers after a 112Gb / s PAM-4 signal is transmitted over 50km of standard single-mode fiber, and then processed by CLUT-VDFE under the parameter conditions (D1=30, D2=22, U=13). (a) The linear DFE item in the corresponding VDFE is replaced by a linear cluster lookup table, and (b) The nonlinear DFE item in the corresponding VDFE is replaced by a nonlinear cluster lookup table. The horizontal axis is the number of cluster centers, and the vertical axis represents the bit error rate and total table size, respectively. Figure 3It can be analyzed that as the number of cluster centers increases, the bit error rate in both cases initially shows a downward trend, and then stabilizes after reaching a certain threshold. At the same time, the increase in the number of cluster centers helps to reduce the size of each sub-lookup table, thereby reducing the size of the total lookup table. However, it is worth noting that the increase in the number of cluster centers will also lead to a significant increase in the number of real number addition operations required to achieve the equalization process. Therefore, after comprehensively weighing the bit error rate performance and computational complexity, the present invention chooses to set the number of cluster centers of the linear cluster lookup table to C1=20 and the number of cluster centers of the nonlinear cluster lookup table to C2=90. Under this condition, the number of real number addition operations required for equalization is 109 times, and the total table size of the lookup table is 922987.

[0077] Attachment Figure 4 Figure 1 shows the relationship between the bit error rate (BER) and the total table size, as well as the number of cluster centers, after a 112Gb / s PAM-4 signal is transmitted over 50km of standard single-mode fiber, using VFFE equalization, and then processed by CPLUT-VDFE under the parameter conditions (D1 = 30, D2 = 22, U = 13). (a) corresponds to replacing the linear DFE terms in the VDFE with a linear cluster lookup table, while (b) corresponds to replacing the nonlinear DFE terms in the VDFE with a nonlinear cluster lookup table. The horizontal axis represents the number of cluster centers retained after pruning, while the vertical axis represents the BER and total table size, respectively. As shown in (a), as the number of linear cluster centers retained after pruning (P1) decreases, the system's BER increases dramatically, while the total lookup table size changes little. This indicates that pruning the cluster centers in the linear DFE portion of the VDFE can slightly reduce computational complexity, but has a significant negative impact on BER performance. Therefore, the present invention focuses on pruning the number of cluster centers in the nonlinear DFE portion of the VDFE, while keeping the number of cluster centers in the linear portion unchanged (P1=C1=20). As shown in (b), pruning the cluster centers in the nonlinear portion can significantly reduce computational complexity while still maintaining good bit error rate performance. Specifically, under the condition that the number of nonlinear cluster centers P2=62 is retained, its bit error rate performance is close to that of the unpruned condition with the number of cluster centers C2=90. In addition, the number of cluster centers in the linear and nonlinear lookup tables is reduced from the original 110 to 82, and the number of real number addition operations is reduced from 109 to 81, a reduction of approximately 25.7%. At the same time, in terms of computational complexity optimization, the total table size is reduced from 922987 to 266315, a reduction of up to 71.1%.

[0078] Example 3

[0079] This embodiment is an embodiment of a low-complexity Volterra decision feedback equalization system based on a clustered pruning lookup table. This embodiment is based on the method described in the first embodiment and includes:

[0080] Tap coefficient estimation module: used to estimate the tap coefficients of Volterra feedforward equalizer and Volterra decision feedback equalizer based on the training sequence;

[0081] K-means clustering module: used to cluster the estimated linear kernel coefficients and nonlinear kernel coefficients of the Volterra decision feedback equalizer using the K-means clustering algorithm, and obtain a Volterra decision feedback equalizer based on the clustering lookup table;

[0082] Sorting and pruning module: used to sort the cluster centers obtained by clustering and prune the cluster centers whose absolute values are within the set range;

[0083] The first sub-lookup table building module is used to build a sub-lookup table for each cluster center after pruning;

[0084] A second sub-lookup table establishment module: used to separately construct a sub-lookup table for the second-order beat frequency term in the first sub-lookup table establishment module;

[0085] Joint equalization module: used to perform joint equalization by superimposing the output signal of the received damaged data signal after being equalized by the Volterra feedforward equalizer on the equalized output signal of the Volterra decision feedback equalizer based on the cluster pruning lookup table.

[0086] Example 4

[0087] This embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of the method described in the first embodiment are implemented.

[0088] Example 5

[0089] This embodiment provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the steps of the method described in the first embodiment are implemented.

[0090] In the specific contents of the above-mentioned specific implementation methods, the various technical features can be combined in any non-contradictory manner. In order to make the description concise, not all possible combinations of the above-mentioned technical features are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0091] Obviously, the above embodiments of the present invention are merely examples for the purpose of clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Those skilled in the art will appreciate that other variations or modifications can be made based on the above description. It is not necessary and impossible to enumerate all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the claims of the present invention.

Claims

1. A low-complexity Volterra decision feedback equalization method based on clustered pruned lookup tables, characterized in that: The following steps are involved: S1. Estimate the tap coefficients of the Volterra feedforward equalizer and the Volterra decision feedback equalizer based on the training sequence; S2. Using the k-means clustering algorithm to cluster the estimated linear kernel coefficients and nonlinear kernel coefficients of the Volterra decision feedback equalizer, respectively, to obtain a Volterra decision feedback equalizer based on the clustering lookup table; S3. Sort the cluster centers obtained by clustering and prune the cluster centers whose absolute values are within the set range; S4. Build a sub-lookup table for each pruned cluster center; S5. Construct a separate sub-lookup table for the second-order beat frequency term in step S4; S6. The output signal of the received impaired data signal after being equalized by the Volterra feedforward equalizer is superimposed on the equalized output signal of the Volterra decision feedback equalizer based on the cluster pruning lookup table to perform joint equalization.

2. The low-complexity Volterra decision feedback equalization method based on clustered pruning lookup table according to claim 1, characterized in that: Step S1 includes: estimating the tap coefficients of the Volterra feedforward equalizer and the Volterra decision feedback equalizer using an adaptive estimation algorithm based on the training sequence signal of the transmitting and receiving ends, wherein the input-output relationship of the VDFE is expressed as: Where d(nk) represents the previous hard decision output signal, n represents the time when the equalizer outputs the signal, and k is the number of samples of signal delay; ω1(k) represents the first-order kernel coefficient of the Volterra decision feedback equalizer, D1 represents the memory length of the linear part of the Volterra decision feedback equalizer, ω2(k,u) represents the second-order kernel coefficient of the Volterra decision feedback equalizer, u is the relative delay, and its value range is limited by the truncation factor U, which is used to truncate high-order kernel coefficients and beat frequency terms with large relative delay and insignificant impact on the system; D2 represents the memory length of the nonlinear part of the Volterra decision feedback equalizer.

3. The low-complexity Volterra decision feedback equalization method based on clustered pruning lookup table according to claim 2, characterized in that: The k-means clustering algorithm is used to cluster the D1 linear kernel coefficients and U(2D2-U+1) / 2 nonlinear kernel coefficients obtained in step S1, and a Volterra decision feedback equalizer based on the clustering lookup table is obtained. The input-output relationship is expressed as: Where g1(i) and C1 represent the cluster centers and the number of cluster centers obtained after clustering the linear kernel coefficients, g2(i) and C2 represent the cluster centers and the number of cluster centers obtained after clustering the nonlinear kernel coefficients; d1(n,i) represents the sum of the first-order decision feedback terms d(nk) corresponding to the linear kernel coefficients belonging to the i-th cluster, and d2(n,i) represents the sum of the second-order decision feedback terms d(nk)d(nku) corresponding to the nonlinear kernel coefficients belonging to the i-th cluster; the first and second terms in the formula represent the outputs of the linear clustering lookup table and the nonlinear clustering lookup table, respectively.

4. The low-complexity Volterra decision feedback equalization method based on clustered pruning lookup table according to claim 3, characterized in that: Step S3 includes: using a cluster center sorting strategy to sort the absolute values of the cluster centers, and pruning the cluster centers whose absolute values in step S2 are less than the set range. The number of cluster centers of the linear kernel coefficient and the nonlinear kernel coefficient after pruning are P1 and P2 respectively. The output of the Volterra decision feedback equalizer based on the cluster pruning lookup table is: where g′1(i) and d′1(n,i) represent the sum of the linear cluster centers and their corresponding linear decision feedback terms after the linear clustering lookup table is pruned, respectively; g′2(i) and d′2(n,i) represent the sum of the nonlinear cluster centers and their corresponding nonlinear decision feedback terms after the nonlinear clustering lookup table is pruned, respectively.

5. The low-complexity Volterra decision feedback equalization method based on clustered pruning lookup table according to claim 4, characterized in that: Step S4 includes: constructing a sub-lookup table for each cluster center obtained after cluster pruning in step S3, and the m-th output element of the i-th sub-lookup table in the linear cluster lookup table is expressed as: The mth output element of the i-th sub-lookup table in the nonlinear clustering lookup table is expressed as: Where N L (i) and N NL (i) represents the number of kernel coefficients in the i-th cluster in the linear kernel coefficient and the nonlinear kernel coefficient, respectively. c1(m,j) and c2(m,j) represent the j-th element in the m-th sequence of the i-th sub-lookup table in the linear cluster pruning lookup table and the nonlinear cluster pruning lookup table, respectively.

6. The low-complexity Volterra decision feedback equalization method based on clustered pruning lookup table according to claim 5, characterized in that: Step S5 includes: the second-order beat frequency term c2(m,j)c2(m,j+N NL (i)) Construct a separate sub-lookup table and update the m-th output element of the i-th sub-lookup table in the nonlinear clustering lookup table as follows: Where c3(m,j) represents the pre-calculated product value of the second-order beat frequency term.

7. The low-complexity Volterra decision feedback equalization method based on clustered pruning lookup table according to any one of claims 1 to 6, characterized in that: The transmitted data signal undergoes digital-to-analog conversion, electro-optical modulation, fiber channel transmission, photoelectric detection, and analog-to-digital conversion to obtain the receiving end data signal. The received impaired data signal is equalized by the Volterra feedforward equalizer, and the output signal is superimposed on the equalized output signal of the Volterra decision feedback equalizer based on the clustered pruning lookup table for joint equalization.

8. A low-complexity Volterra decision feedback equalization system based on clustered pruned lookup tables, characterized in that: include: Tap coefficient estimation module: used to estimate the tap coefficients of Volterra feedforward equalizer and Volterra decision feedback equalizer based on the training sequence; K-means clustering module: used to cluster the estimated linear kernel coefficients and nonlinear kernel coefficients of the Volterra decision feedback equalizer using the K-means clustering algorithm, and obtain a Volterra decision feedback equalizer based on the clustering lookup table; Sorting and pruning module: used to sort the cluster centers obtained by clustering and prune the cluster centers whose absolute values are within the set range; The first sub-lookup table building module is used to build a sub-lookup table for each cluster center after pruning; A second sub-lookup table establishment module: used to separately construct a sub-lookup table for the second-order beat frequency term in the first sub-lookup table establishment module; Joint equalization module: used to perform joint equalization by superimposing the output signal of the received damaged data signal after being equalized by the Volterra feedforward equalizer on the equalized output signal of the Volterra decision feedback equalizer based on the cluster pruning lookup table.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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