A cascaded MIMO device for ultra-high-order coherent optical transmission system

Abstract

The present invention relates to a cascaded MIMO structure for an ultra-high-order coherent optical transmission system, comprising a first-level structure and a second-level structure; the first-level structure is located at the front end of a signal receiving end of the coherent optical transmission system, and a 2×2 MIMO equalizer is used to perform signal polarization demultiplexing and partially compensate for the first IQ imbalance (signal receiving end) of the coherent optical transmission, and the 2×2 MIMO equalizer is a 2×2 complex-valued filter; the second-level structure is after the first-level structure and before the decision output of the signal receiving end of the coherent optical transmission system, and a 4×4 MIMO equalizer is used to compensate for the second IQ imbalance (signal transmitting end and signal receiving end) of the coherent optical transmission, and the 4×4 MIMO equalizer is a 4×4 real-valued filter. The cascaded MIMO structure constructed by the present invention can effectively remove the IQ imbalance of the transmitting end and the receiving end of the coherent optical transmission system.

Description

Technical Field

[0001] The present invention relates to the technical field of coherent optical transmission, and in particular to a cascaded MIMO structure for an ultra-high order coherent optical transmission system. Background Art

[0002] The continued growth of traffic from explosive digital applications such as artificial intelligence, cloud computing, VR / AR, and even the metaverse has undoubtedly posed new challenges to the underlying optical transmission system. In order to meet the growing demand for channel capacity, the scientific and industrial communities continue to expand system capacity to higher and higher values. Therefore, it is crucial to find viable technical solutions for cost-effective optical transmission systems.

[0003] In optical communication transmission systems, coherent optical communication has become a breakthrough technology that can achieve data transmission rates of 400 Gbit / s or higher. Since the high sensitivity of its coherent receiver extends the transmission distance and provides new possibilities for efficient data transmission, high-speed digital coherent optical communication is extremely important in meeting today's throughput requirements. At present, the development and research of 800G and 1.6T coherent optical modules has become the mainstream. In order to further expand the higher system capacity, methods such as increasing the signal modulation order, increasing the signal single channel transmission rate, and increasing the number of signal parallel transmission channels (wavelength division multiplexing) can usually be adopted. Among them, the direct way to improve high-speed single-carrier transmission is to increase the spectral efficiency (SE) by increasing the modulation format. At present, research on high-order modulation formats has been carried out at home and abroad. Through probability shaping (PS) technology, 256QAM, 1024QAM and 4096QAM signals are transmitted on standard single-mode optical fiber (SSMF). This method has great potential in future practical applications. However, the current work on ultra-high-order modulation formats still faces some challenges.

[0004] When using ultra-high-order QAM formats, transmission performance is more susceptible to system defects, such as nonlinearity in optical fibers, offsets between the transmitter laser and the local oscillator, and imbalances between IQ in coherent optical transmission. The structure of traditional MIMO needs to be modified so that it can tolerate any of the imbalances mentioned by predecessors and correct the defects of any channel in the transmission system, thereby achieving a significant reduction in bit error rate.

[0005] When using ultra-high-order QAM, in-phase (I) and quadrature (Q) impairments caused by component defects or misalignment in the transceiver can lead to significant performance degradation. In order to compensate for IQ impairments in QAM coherent optical communications, many DSP algorithms have been developed. However, existing research has limitations on IQ imbalance algorithms in ultra-high-order modulation formats, and there is an urgent need to study IQ imbalance algorithms suitable for ultra-high-order modulation formats. Summary of the invention

[0006] Therefore, the technical problem to be solved by the present invention is to overcome the IQ imbalance problem of the coherent optical transmission system in the prior art.

[0007] In order to solve the above technical problems, the present invention provides a cascaded MIMO structure for an ultra-high order coherent optical transmission system, wherein the cascaded MIMO structure includes a first-level structure and a second-level structure;

[0008] The first-level structure is located at a signal receiving end of a coherent optical transmission system, and uses a 2×2 MIMO equalizer based on a constant modulus algorithm (CMA) to perform signal polarization demultiplexing and partially compensate for a first IQ imbalance of coherent optical transmission, wherein the 2×2 MIMO equalizer is a 2×2 complex-valued filter, and the first IQ imbalance includes an IQ imbalance from a signal receiving end;

[0009] The second-level structure is after the first-level structure and before the decision output of the signal receiving end of the coherent optical transmission system, and adopts a 4×4 MIMO equalizer based on a constant modulus algorithm CMA to compensate for the second IQ imbalance of the coherent optical transmission, wherein the 4×4 MIMO equalizer is a 4×4 real-valued filter, and the second IQ imbalance includes IQ imbalance from the signal transmitting end and the signal receiving end.

[0010] In one embodiment of the present invention, the iterative formula of the output signal of the 4×4 real-valued filter is:

[0011] v ab (n) = h ab-rr (n)u b-r (n)+h ab-ri (n)u b-i (n)

[0012] +j{h ab-ir (n)u b-r (n)+h ab-ri (n)u b-i (n)} (14)

[0013] Among them, u (a,b)-(e,f) (n) is a vector of four input columns, h ab-ef (n) is a vector of sixteen filter tap coefficients, ab = xx, xy, yx or yy, ef = rr, ri, ir or ii, x represents X polarization, y represents Y polarization, i represents imaginary part, r represents imaginary part, and n represents the current time;

[0014] Calculate the final output v of the real-valued filter x (n) and v y (n), the formula is:

[0015] vx (n) = v xx (n)+v xy (n) (15)

[0016] v y (n) = v yx (n)+v yy (n) (16)

[0017] Based on the constant modulus algorithm CMA, the tap coefficients are updated to calculate the corresponding error signal. The formula is:

[0018] e x,y (n) = S (n) - v x,y (n) (17)

[0019] Among them, S(n) is the training symbol in training mode, v x,y (n) is v x (n) or v y (n);

[0020] Finally, based on the constant modulus algorithm CMA, the tap coefficient of the next moment n+1 is updated to:

[0021] h ab-ef (n+1)=h ab-ef (n)+μe a-e (n)u b-f (n) (18)

[0022] Among them, μ is the step size parameter, e x-r,y-r (n), e x-i,y-i (n) are respectively e x,y The real and imaginary parts of (n);

[0023] The final 4×4 real-valued filter is obtained based on the updated tap coefficients.

[0024] In one embodiment of the present invention, the IQ imbalance at the signal receiving end includes IQ phase mismatch, IQ gain mismatch, and IQ delay skew, and corresponding transfer matrices are constructed respectively, a first overall transfer function is obtained according to the constructed transfer matrix, and a first inverse matrix is ​​obtained according to the first overall transfer function, the first inverse matrix is ​​used to multiply the received signal to filter out the IQ imbalance at the signal receiving end, and the first inverse matrix is ​​implemented by a 4×4 real-valued filter;

[0025] The IQ phase mismatch and IQ gain mismatch at the signal receiving end are also equalized by a 2×2 complex-valued filter.

[0026] In one embodiment of the present invention, the IQ phase mismatch transfer matrix construction method includes:

[0027] The I and Q paths of the X-polarization component of the received signal are set to r X-I (t) and r X-Q (t), the I and Q paths of the Y polarization component are set to r Y-I (t) and r Y-Q (t); The complex amplitude of the received signal is modeled as:

[0028] r X,Y (t) = r X-I,Y-I (t)+jr X-Q,Y-Q (t) (4)

[0029] For IQ phase mismatch, the rotation angles of the I and Q axes of the X polarization component on the complex plane are denoted as θ X-I and θ X-Q , the rotation angle of the Y polarization component is θ Y-I and θ Y-Q The IQ phase mismatch and the angle of deviation from the correct angle of 90° are represented as θ X-I ,θ X-Q and θ Y-I ,θ Y-Q ; To solve the IQ phase mismatch, the transfer matrix of IQ phase mismatch is defined as:

[0030] P X,Y =(-sin(θ X-Q,Y-Q )cos(θ X-Q,Y-Q )) (5).

[0031] In one embodiment of the present invention, the IQ gain mismatch transfer matrix construction method includes:

[0032] For IQ gain mismatch, use β X-I and β X-Q The gains of the I and Q ports at X polarization are expressed as β Y-I and β Y-Q represents the gain of the Y-polarization I port and Q port, and the IQ gain mismatch is expressed as:

[0033]

[0034] When β X-I≠ β X-Q When β Y-I≠ β Y-Q When , it indicates that there is IQ gain imbalance in the Y polarization, and the transfer matrix of IQ gain imbalance is defined as:

[0035]

[0036] In one embodiment of the present invention, the method for constructing a transfer matrix of IQ delay skew includes:

[0037] For IQ delay skew, the received signal is divided into X polarization and Y polarization. The time delays of the I and Q signals of X polarization and the I and Q signals of Y polarization are τ respectively. X-I , τ X-Q , τ Y-I and τ Y-Q , so the complex amplitude of the signal is modeled as:

[0038]

[0039] When τ X-I≠ τ X-Q When τ Y-I≠ τ Y-Q When , IQ delay skew exists in the Y polarization component; is the IQ delay skew, transforming equation (8) into the frequency domain is:

[0040]

[0041] Where ω is the angular frequency R of the optical signal measured from the carrier frequency D X-I,Y-I (ω), R D X-Q,Y-Q (ω), R X-I,Y-I (ω) and R X-Q,Y-Q (ω) are r D X-I,Y-I (t), r D X-Q,Y-Q (t), r X-I,Y-I (t) and r X-Q,Y-Q (t), r X-Q,Y-Q The Fourier transform of (t) is then expressed as:

[0042]

[0043] In one embodiment of the present invention, the method of obtaining the overall transfer function according to the constructed transfer matrix and finding the inverse matrix of the overall transfer function comprises:

[0044] By modeling IQ phase mismatch, IQ gain imbalance, and IQ delay offset, the overall transfer function simplifies to:

[0045] I X,Y (ω)=P X,Y G X,Y D X,Y (ω) (11)

[0046] Among them, PX,Y ,G X,Y ,D X,Y (ω) are the transfer matrices of IQ phase mismatch, IQ gain imbalance and IQ delay offset respectively;

[0047] Then the inverse matrix I -1 X,Y The expression of (ω) is:

[0048]

[0049] In one embodiment of the present invention, the IQ imbalance of the signal transmitting end includes IQ delay skew, IQ gain mismatch, and IQ phase mismatch, and corresponding transfer matrices are constructed respectively, an overall transfer function is obtained according to the constructed transfer matrix, and a second inverse matrix is ​​obtained according to the second overall transfer function. The second inverse matrix is ​​used to multiply the received signal to filter out the IQ imbalance of the signal transmitting end, and the second inverse matrix is ​​implemented by a 4×4 real-valued filter.

[0050] The above technical solution of the present invention has the following advantages compared with the prior art:

[0051] The cascaded MIMO structure of the present invention can compensate for the significant drop in the bit error rate caused by IQ imbalance due to hardware damage in the transmitter and receiver parts, and can compensate for the signal degradation caused by IQ imbalance due to the accumulation of ultra-high-order algorithms, greatly improving the transmission signal quality and significantly reducing the bit error rate;

[0052] The cascaded MIMO structure of the present invention can enhance signals of different modulation formats. For ultra-high-order signals, the structure can enable the PS-PDM-1024QAM signal transmitted on 80km single-mode optical fiber to reach a decision threshold of 3.8E-3 under a low signal-to-noise ratio, which was originally impossible to reach the hard decision line. The structure can also significantly improve the quality of PS-PDM-4096QAM signals.

[0053] The research work on the cascaded MIMO structure of the present invention can greatly save costs, compensate for signal attenuation caused by hardware damage, and significantly improve the bit error rate, which is of great significance for putting ultra-high-order modulation formats into practical applications in the future. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to make the contents of the present invention more clearly understood, the present invention is further described in detail below based on specific embodiments of the present invention in conjunction with the accompanying drawings.

[0055] Figure 1 It is an overall architecture diagram of a cascaded MIMO structure for a coherent optical transmission system in an embodiment of the present invention;

[0056] Figure 2Schematic diagram of the influence of IQ imbalance on constellation points based on 16QAM in an embodiment of the present invention;

[0057] Figure 3 is a schematic diagram of the structure of a 4×4 real-valued filter in an embodiment of the present invention;

[0058] Figure 4 Schematic diagram of an experimental device for 4GBd PS-1024QAM on 80km optical fiber according to an embodiment of the present invention;

[0059] Figure 5 is a comparison diagram of bit error rate and OSNR (dB) of different modulation formats for BTB transmission using cascaded MIMO and not using it in an embodiment of the present invention;

[0060] Figure 6 is a relationship diagram between bit error rate and OSNR (dB) at different transmission distances with or without a cascaded MIMO structure on PS-PDM-1024QAM in an embodiment of the present invention;

[0061] Figure 7 is a comparison diagram of bit error rate and OSNR (dB) at a transmission distance of 80 kilometers when a cascaded MIMO structure is used or not on PS-PDM-4096QAM in an embodiment of the present invention;

[0062] Figure 8 This is a comparison chart of bit error rate and OSNR at a transmission distance of 80 kilometers when different MIMO structures are used on PS-PDM-1024QAM in an embodiment of the present invention. DETAILED DESCRIPTION

[0063] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it, but the embodiments are not intended to limit the present invention.

[0064] Embodiment 1

[0065] Reference Figure 3 As shown, the present invention relates to a cascaded MIMO structure for an ultra-high order coherent optical transmission system, wherein the cascaded MIMO structure comprises a first level structure and a second level structure;

[0066] The first-level structure is located at a signal receiving end of a coherent optical transmission system, and uses a 2×2 MIMO equalizer based on a constant modulus algorithm (CMA) to perform signal polarization demultiplexing, and partially compensates for a first IQ imbalance of coherent optical transmission (i.e., except for an IQ delay skew at a signal receiving end), wherein the 2×2 MIMO equalizer is a 2×2 complex-valued filter, and the first IQ imbalance includes an IQ imbalance from a signal receiving end;

[0067] The second-level structure is after the first-level structure and before the decision output of the signal receiving end of the coherent optical transmission system, and adopts a 4×4 MIMO equalizer based on a constant modulus algorithm CMA to compensate for the second IQ imbalance of the coherent optical transmission, wherein the 4×4 MIMO equalizer is a 4×4 real-valued filter, and the second IQ imbalance includes IQ imbalance from the signal transmitting end and the signal receiving end.

[0068] The following is a detailed introduction to this embodiment:

[0069] 1. This embodiment is dedicated to studying the imbalance problem between the IQ components of ultra-high-order QAM signals, and proposes a new cascade structure, which modifies the structure of traditional MIMO so that it can solve any imbalance phenomenon mentioned in the background technology and correct the defects of any channel in the transmission system, thereby achieving a significant reduction in the bit error rate.

[0070] 2. Principle of two-stage MIMO structure

[0071] In this section, the basic principles of the cascaded MIMO architecture will be analyzed from three aspects: Figure 1 The entire receiving-end offline DSP architecture for ultra-high-order coherent optical transmission is demonstrated, where IQOrthogonalization represents the orthogonal normalization of IQ components, CD compenation represents fiber dispersion compensation, Clock Recovery represents clock synchronization and recovery, CMA represents a 2×2 complex-valued filter, FOE is used to remove frequency deviation, CPR is used to remove phase noise, and Volterra equalizer is used to compensate for nonlinear damage. Figure 1 The architecture takes into account the IQ imbalance caused by the algorithm's separate processing of the X and Y polarization IQ components (i.e., FOE, CPR, VE) (i.e., IQ imbalance caused by the algorithm). The focus of this embodiment is the 2×2 complex-valued filter and the 4×4 real-valued filter in the MIMO architecture. This embodiment has three major IQ imbalances: IQ imbalance at the transmitter, IQ imbalance at the receiver, and IQ imbalance caused by the algorithm. This embodiment uses a 4×4 real-valued filter to equalize the algorithmic IQ imbalance caused by the separate processing of the X and Y polarization IQ components in the coherent optical transmission system.

[0072] First, high-order modulated signals are usually more sensitive to damage caused by defects from transmitter (Tx) or receiver (Rx) equipment, including offset between in-phase (I) and quadrature (Q) components, IQ phase imbalance, IQ gain imbalance, and uneven IQ frequency characteristics. Therefore, it is necessary to perform more rigorous calibration or more precise equalization on ultra-high-order modulated signals to compensate for these IQ impairments. Due to the imperfections of the equipment, the characteristics of these impairments may change slightly as the environment changes. For these dynamic effects, this embodiment hopes to use adaptive equalization to automatically compensate. In traditional coherent optical transmission systems, a butterfly structure of a finite impulse response (FIR) filter is usually used, and polarization demultiplexing and equalization are achieved through an adaptive algorithm to compensate for time-varying transmission impairments. However, considering the damage from hardware, in these traditional butterfly structure complex-valued filters, the I component and the Q component are not processed independently. In order to better compensate for IQ imbalances such as offset, phase, gain imbalance and frequency characteristics, this embodiment considers replacing the complex-valued MIMO filter with a real-valued MIMO filter.

[0073] A. Equalizer structure principle

[0074] First, let's start with the structure of the polarization receiver adaptive equalizer. The most general structure of the polarization multiplexing receiver adaptive equalizer is shown in the following formula:

[0075]

[0076] It corresponds to a 4×4 real-valued multiple-input multiple-output system, where the input is the real and imaginary parts of the received complex-valued polarization signal (X, Y): X I =Re(X),X Q =Im(X),Y I =Re(Y),Y Q =Im(Y). For convenience, define a matrix H:

[0077]

[0078] Obviously, general reversible channel responses can be compensated in the original equalizer structure. However, in existing coherent optical systems, since IQ mixed impairments are not considered, the commonly used equalizer simplifies the original 4×4 real-valued filter into a standard 2×2 complex-valued equalizer, whose structure is defined as:

[0079]

[0080] By observing the above formula, it can be found that, generally speaking, formula (1) and formula (3) are not equivalent. The situation considered in this embodiment is that when the hardware is damaged, the real part or imaginary part of a signal may be damaged. In this case, the commonly used structure cannot compensate for the damage, so it is considered to adopt a 4×4 real value structure in the structure.

[0081] Then, this embodiment discusses the necessity of using a 4×4 real-valued filter in terms of damage compensation. At the receiving end, a defective 90-degree mixer, a balanced photodiode, or any other device can cause IQ imbalance. The imbalance here is not just the XY path IQ imbalance correction that is generally considered to be performed by the GSOP or Lowdin algorithm in the first step of DSP. It also includes the phase mismatch between the IQ ports; and the timing mismatch caused by the difference in the physical path length of the IQ ports, that is, the delay offset in IQ. If the DSP unit of the receiver cannot compensate for these IQ imbalances, the system performance will be seriously degraded. In low-order modulation formats, the impact of these imbalances on signal quality may not be obvious. However, experiments have shown that in ultra-high-order cases, if these imbalances are ignored, they will seriously damage the quality of the transmitted signal.

[0082] Figure 2 The effects of the various IQ imbalances mentioned above on the 16QAM-based constellation diagram are shown ((a) Ideal constellation diagram. (b) Constellation diagram variation due to gain imbalance. (c) Constellation diagram variation due to phase imbalance. (d) Constellation diagram variation due to IQ tilt (with eye diagram)). IQ gain imbalance will cause the constellation diagram to present a rectangular distortion; IQ phase imbalance will cause the constellation diagram to present a parallelogram-like distortion; IQ skew is not obvious in the constellation diagram, but an obvious phenomenon can be observed from the eye diagram. For high-order modulation formats, any type of IQ imbalance may make the signal unrecoverable.

[0083] When there is no IQ imbalance, the I path and Q path of the X-polarization component of the received signal are set to r X-I (t) and r X-Q (t). Similarly, the Y polarization component is also set to r Y-I (t) and r Y-Q (t). Then, the complex amplitude of the optical signal can be modeled as:

[0084] r X,Y (t) = r X-I,Y-I (t)+jr X-Q,Y-Q (t)(4)

[0085] First, consider the above IQ phase mismatch. For IQ phase mismatch, the rotation angles of the I and Q axes of the X polarization component on the complex plane are denoted as θ X-I and θ X-QSimilarly, the rotation angle of the Y polarization component is θ Y-I and θ Y-Q The IQ phase mismatch and the angle of deviation from the correct angle of 90° are represented as θ X-I ,θ X-Q and θ Y-I ,θ Y-Q In order to solve the phase mismatch problem, the transfer matrix caused by the phase mismatch is defined as:

[0086]

[0087] Next, consider the case where the IQ gain does not match. In this case, use β X-I and β X-Q represents the gain of the I port and Q port at X polarization. Similarly, β Y-I and β Y-Q It represents the gain of the I port and Q port of Y polarization. The IQ gain mismatch is usually expressed as follows:

[0088]

[0089] When β X-I≠ β X-Q When , it is considered that there is IQ gain imbalance in the X polarization; similarly, when β Y-I≠ β Y-Q When , it is considered that there is IQ gain imbalance in the Y polarization. In this case, the transfer matrix of IQ gain imbalance can be defined as:

[0090]

[0091] Finally, since other structures cannot compensate for IQ skew, the IQ skew is described in detail here. Since the time delays of the four output ports of the front end are τ X-I , τ X-Q , τ Y-I and τ Y-Q , so the complex amplitude of the signal can be modeled as:

[0092]

[0093] When τ X-I≠ τ X-Q When τ Y-I≠ τ Y-Q When , IQ impairment exists in the Y polarization component. In order to compensate for this impairment, transform equation (8) into the frequency domain:

[0094]

[0095] Where ω is the angular frequency R of the optical signal measured from the carrier frequency D X-I,Y-I (ω), R D X-Q,Y-Q (ω), R X-I,Y-I (ω) and R X-Q,Y-Q (ω) are r D X-I,Y-I (t), r D X-Q,Y-Q (t), r X-I,Y-I (t) and r X-Q,Y-Q (t), r X-Q,Y-Q The Fourier transform of (t) and the transfer matrix are expressed as:

[0096]

[0097] By modeling IQ phase mismatch, IQ gain imbalance, and IQ delay offset, the overall transfer function can be further simplified to:

[0098] I X,Y (ω)=P X,Y G X,Y D X,Y (ω) (11)

[0099] In summary, the problem is simplified to: To compensate for all the above IQ imbalances, we need to find the inverse matrix I -1 X,Y (ω), which is multiplied by the received signal to cancel these imbalances as follows:

[0100]

[0101] The structure of the 4×4 real-valued filter can well find the required inverse matrix I -1 X,Y (ω) to compensate for the various IQ impairments mentioned above. Theory further proves that separating the real and imaginary parts of the complex components into four real numbers can better cover all degrees of freedom of real four-dimensional rotation and more carefully consider the polarization-related losses of polarization components. This conclusion is obtained through four-dimensional (4D) signal space reasoning in communication theory, which once again confirms the necessity of using a 4×4 real-valued filter in this embodiment.

[0102] It should be noted that the above formulas (4) to (12) are three types of IQ imbalance at the signal receiving end, which need to be equalized by a 2*2 complex-valued filter (IQ delay skew cannot be compensated) and a 4*4 real-valued filter (the 2*2 complex-valued filter first partially compensates for the IQ damage at the receiving end, and the 4*4 real-valued filter realizes compensation for the mixed IQ damage at the receiving end and the transmitting end).

[0103] B. Principles of MIMO Cascade Architecture

[0104] Transmitter (Tx) imbalance may also lead to serious performance degradation. Currently, only some calibration methods that require complex operations or expensive equipment have been reported to compensate for transmitter imbalance. In traditional coherent optical transmission systems, transmitter imbalance is usually ignored and only receiver skew is focused on. In fact, both the transmitter and receiver may have potential imbalance. In the cascaded MIMO structure of this embodiment, the first-level structure uses a CMA-based 2×2 MIMO equalizer to compensate for the imbalance at the Rx end, and the Tx end defects are compensated by a CMA-based 4×4 MIMO equalizer after passing through the Volterra equalizer (VE) (ie, the second-level structure). The cascaded MIMO structure of this embodiment can compensate for various impairments.

[0105] This embodiment must first consider the impairments that occur at the transmitting end and how to compensate for them. At the transmitting end, there will be damage caused by device defects, such as the IQ offset of the modulator or the frequency characteristics of the driving amplifier. Of course, nonlinear distortion caused by the Kerr effect may also occur, but for simplicity, this embodiment does not consider these factors. After ignoring the Kerr effect, the remaining impairments are linear. This includes the influence of IQ skew, so the IQ components are different. Therefore, this embodiment considers using a real-valued MIMO structure and using real-valued signal vectors to represent the I and Q components of X polarization and Y polarization to handle these linear impairments. In theory, all these impairments can be compensated by a 4×4 real-valued MIMO filter with IQ and XY cross terms. It is important that the signal carrying Tx defect information can only be compensated after removing the frequency deviation (removed by FOE) and phase noise (removed by CPR). Therefore, a 4×4 real-valued filter with a MIMO cascade structure is added after the carrier recovery algorithm (i.e., FOE and CPR). In this embodiment, it is proposed that each impairment should compensate all linear impairments block by block in reverse order. This also confirms the effectiveness of the structure.

[0106] According to the above part A, the structure has completed the imbalance compensation at the Rx end. For the Tx end, the derivation of its IQ imbalance inverse matrix is ​​similar to formula (4)-formula (12). Due to space limitations, this embodiment will not give the derivation process. Analogously, the Tx end overall transfer function matrix I in formula (11) X,Y (ω), and the overall transfer function matrix of the Rx end is set to And abbreviated as H, where each element is H ab (a, b∈{1, 2}). The compensation matrix W in the frequency domain (equivalent to I in formula (12)) can be used -1 X,Y (ω)), where each element is W ab(a, b∈{1, 2}) to compensate for the imbalance at the transmitter. In the case of high optical signal-to-noise ratio, the frequency domain matrix W can be approximated as the inverse matrix of H, that is, W = H -1 .

[0107]

[0108] Where C = β X-I,Y-I β X-Q,Y-QCOS (θ X-I,Y-I－ θ X-Q,Y-Q ) e jw(τ X-I,Y-I +τ X-Q,Y-Q ), with the one-to-one correspondence between the matrix parameters, the IQ delay skew, IQ gain mismatch and IQ phase mismatch of Tx can be calculated through the matrix to monitor the imbalance at the Tx end. This embodiment only considers the damage compensation part. In order to compensate for the three types of IQ imbalance at the signal transmitter, the frequency domain matrix W must be found to eliminate the imbalance at the transmitter. The function of the frequency domain matrix W is implemented by a 4×4 real-valued filter.

[0109] This embodiment also considers the reason for placing the 4×4 real-valued filter at the end from another perspective. For signal recovery of low-order modulation formats, the steps of the DSP processing part may not be too many; but for ultra-high-order modulation formats, in order to make the signal recovery better, more equalizers are generally used, such as Figure 2 As shown. However, in the carrier recovery step and the subsequent Volterra equalizer step, the two IQ signals of XY are processed separately. It is considered that after these processing steps, the IQ imbalance caused by the algorithm processing is also a problem that needs to be considered. A 4×4 real-valued filter is placed before the decision output. It can effectively compensate for the imbalance caused by the algorithm.

[0110] C. IQ compensation architecture based on CMA

[0111] A DSP-based receiver using a butterfly structure finite impulse response (FIR) filter can use an adaptive algorithm of polarization demultiplexing and equalization to compensate for time-varying transmission impairments. According to existing literature, the adaptive algorithms used in butterfly structure equalizers mainly include CMA and LMS. Since the LMS algorithm is very sensitive to FO errors, the algorithm has high requirements on the accuracy of the FO estimator. Therefore, the CMA algorithm is used in the structure proposed in this embodiment.

[0112] Indeed, the constant modulus algorithm (CMA) is often used in coherent optical transmission systems due to its simplicity and immunity to phase noise. However, CMA also has its frustrating singularity feature, that is, the two outputs may lock to the same input. Since CMA independently adjusts the FIR filters of the two branches, it is greatly affected by the initial tap. This embodiment selects a suitable initial tap to prevent the two signals from converging to a unified input, ensuring successful demultiplexing of the two channels.

[0113] In the cascaded MIMO structure, the first-level structure uses a traditional CMA-based 2×2 complex-valued filter. Since it is a prior art, this embodiment will not be described in detail. This embodiment mainly introduces the second-level structure, that is, a CMA-based 4×4 real-valued filter. The structure of the 4×4 real-valued filter is as follows: Figure 3 As shown, Figure 3 The signal of coherent optical transmission is divided into X polarization signal u x (n) and Y polarization signal u y (n), and perform the following processing respectively:

[0114] For a 4×4 real-valued filter, the iterative formula for the output signal is as follows:

[0115] v ab (n) = h ab-rr (n)u b-r (n)+h ab-ri (n)u b-i (n)

[0116] +j{h ab-ir (n)u b-r (n)+h ab-ri (n)u b-i (n)} (14)

[0117] Among them, u (a,b)-(e,f) (n) is a vector of four input columns, h ab-ef (n) is the vector of sixteen filter tap coefficients, ab = xx, xy, yx or yy, ef = rr, ri, ir or ii, x represents X polarization, y represents Y polarization, i represents imaginary part, r represents imaginary part, and n represents the current time. Then, the output v of the filter (i.e., real-valued filter) can be calculated x (n) and v y (n) are as follows:

[0118] v x (n) = v xx (n)+v xy (n) (15)

[0119] v y (n) = v yx (n)+vyy (n) (16)

[0120] Next, the corresponding error signal is calculated according to the iterative formula coefficients of the CMA algorithm, that is,

[0121] e x,y (n) = S (n) - v x,y (n) (17)

[0122] Among them, S(n) is the training symbol in the training mode. It should be noted that the error function here is calculated without taking the absolute value, so the signal here carries vector information rather than scalar information.

[0123] Finally, according to the CMA algorithm, the tap coefficient of n+1 at the next moment is updated as:

[0124] h ab-ef (n+1)=h ab-ef (n)+μe a-e (n)u b-f (n) (18)

[0125] Among them, μ is the step size parameter, e x-r,y-r (n),e x-i,y-i (n) are respectively e x,y (n) is the real and imaginary part of

[0126] 3. Experimental Setup

[0127] The effectiveness of the architecture is verified through experiments. Figure 4 The experimental architecture of a coherent communication system for 4GBd PS-1024QAM transmission over 80km of fiber is shown. The figure includes the off-line DSP block diagram from transmitter to receiver.

[0128] First, at the transmitter, a pseudo-random binary sequence (PRBS) is sent to the PS encoder for CCDM encoding to generate a specified amplitude sequence to achieve the mapping of the signal from bits to symbols. In this step, the non-uniform amplitude symbols are mapped to pulse amplitude modulation. Then, pilot symbols are added to the processed sequence. This part of the pilot signal will be used in the subsequent receiving DSP and plays an important role in signal recovery. Then, the amplitude sequence is sampled into 2 sampling points for each symbol, up-sampled twice, and a root cosine (RRC) FIR filter with a roll-off factor of 0.35 is used for pulse shaping to eliminate the influence of inter-symbol interference (ISI). At this point, the basic program of the transmitter DSP has been completed.

[0129] The experiment uses an 8Gsa / s, 14-bit high-precision AWG for digital-to-analog conversion (DAC), and loads four signals into a Mach-Zehnder modulator (MZM) for modulation to generate a 1024-QAM signal. After the signal is modulated into an optical carrier, it is amplified by an erbium-doped fiber amplifier (EDFA). The first variable optical attenuator (VOA) is used to attenuate the optical power to the appropriate access optical power of the standard single-mode fiber (SSMF) to test the optimal incoming optical power during the link test. For the experimental 1024-QAM signal, the optimal incident optical power tested was approximately -4dBm. The transmission distance of the modulated 1024-QAM signal in the SSMF is 80 kilometers. This embodiment uses a second VOA to change the output signal optical power of the transmitted QAM signal.

[0130] This step is mainly to change the OSNR of the signal in order to draw a bit error rate graph. The signal is then amplified by the EDFA, attenuated to a fixed power of about 6dBm by the third VOA, and then transmitted to the receiving end. At the receiving end, the signal first passes through an optical bandpass filter (OBPF), and after passing through a polarization controller (PC), it is sent to a coherent receiver together with the local oscillator light (LO). The experiment uses a laser with a linewidth of 1KHz and a wavelength of 1500.112nm as the local oscillator light (LO). The coherent receiver consists of a 90-degree optical mixer and four balanced photodetectors. Then, the analog-to-digital conversion is completed by a 50GSa / s real-time sampling oscilloscope, and the acquired data undergoes an offline digital signal processing step for signal recovery.

[0131] The offline digital signal processing at the receiving end mainly includes preliminary processing such as resampling, RRC matched filtering and I / Q orthogonalization based on GSOP. For dispersion, dispersion compensation is performed in the frequency domain. In order to keep the transmitter clock and the receiver sampling clock at the same frequency and phase, the clock recovery algorithm is performed using the Gardner algorithm and auxiliary symbols. In the polarization equalization stage, the proposed optimization algorithm structure is adopted. Channel equalization is performed using 1 filter tap to complete polarization demultiplexing. Then, the carrier recovery algorithm is executed, in which the frequency offset estimation algorithm is used, combined with the fourth power fast Fourier transform (FFT) and derivative-assisted FFT to correct the data with accurate frequency offset. For the phase recovery of the signal, the phase noise of the laser is estimated based on the pilot information of the continuous short code block, and the phase change is tracked by the pilot signal to find the approximate phase shift of each symbol for compensation.

[0132] In addition, in order to reduce the distortion caused by the nonlinearity of optoelectronic devices, the Volterra nonlinear equalization (VNLE) algorithm based on the second-order Volterra level was performed after the carrier recovery algorithm, because high-order modulation formats use more algorithms, and I / Q independent operations are performed during the processing process, which easily causes an imbalance in the I / Q signal. After using the VNLE algorithm, it is supplemented to the second-order VNLE algorithm.

[0133] 4. Experimental results and discussion

[0134] In order to verify the proposed two-stage MIMO structure, experiments were carried out on 4GBd double-biased 64, 256, 1024 and 4096-QAM in a coherent optical transmission system.

[0135] Figure 5 The experimental results of 64, 256 and 1024-QAM in back-to-back (BTB) transmission are shown. Since the focus of this embodiment is on various mixed IQ imbalance problems, the difference in bit error rate between XY paths caused by IQ imbalance problems is shown in the experimental results section.

[0136] See also Figure 5 ((a)PS-PDM-64QAM-XY; (b) PS-PDM-256QAM-XY; (c) PS-PDM-1024QAM-XY; (d) PS-PDM-64QAM-ALL; (e) PS-PDM-256QAM-ALL; (f) PS-PDM-1024QAM-ALL. Figure 5 In (a), (b), and (c), the curves 3 and 4 show the bit error rate of the XY component with the proposed structure added. Figure 5 (a)(b)(c) It can be seen that in low-order modulation formats, the XY imbalance caused by this IQ mixing imbalance is not obvious and has little impact on the bit error rate. However, when conducting ultra-high-order experiments, such as Figure 5 As shown in (c), the bit error rates of the two XY signals caused by this imbalance are very different. When observing the data, the bit error rates of the two signals even differ by an order of magnitude, which has a huge impact on the final total bit error rate. This is also one of the reasons why it is believed that this experiment is necessary for ultra-high-order modulation formats.

[0137] exist Figure 5In (d)(e)(f), the lines with numbers 1 and 2 represent the bit error rate curves before and after adding the secondary structure, respectively, showing the total bit error rate curve that is usually of interest. It can be seen that in 64, 256 and 1024QAM, the secondary structure will significantly reduce the bit error rate. Especially in 1024QAM, the increase in the total bit error rate caused by XY imbalance is also properly resolved after adding the structure. Before adding this structure, 1024QAM could not reach the decision threshold of 3.8E-3, but after adding the secondary structure, the decision threshold can be reached when OSNR=27 or above. This shows that the structure has a significant impact on ultra-high-order modulation formats.

[0138] In order to further study the effect of this structure on the transmission distance, Figure 6 The experimental results of 1024QAM without and with secondary structure in BTB transmission and 80km transmission experiments are shown ((a) BTB-XY; (b) BTB-ALL; (c) constellation diagram before and after adding secondary structure at OSNR=28; (d) 80km-XY; (e) 80km-ALL; (f) constellation diagram before and after adding secondary structure at OSNR=33). In order to better understand the quality of signal recovery, this embodiment also shows the comparison of different constellation diagrams of XY components before and after the secondary structure in the figure. The most representative points at different distances are selected for display here.

[0139] Figure 6 (a)(b)(c) show the experimental results of BTB transmission using 1024QAM; Figure 6 (d)(e)(f) show the experimental results of 80km transmission using 1024QAM. By observing the bit error rate diagrams of the XY components of the two, it can be found that at a transmission distance of 80km, the difference in XY bit error rate caused by IQ mixing damage becomes more and more obvious. Even in the case of low signal-to-noise ratio, the difference between XY can be observed. However, regardless of whether the difference becomes larger, the secondary structure proposed in this embodiment can compensate for these damages well, and the compensated XY difference is significantly reduced. Figure 6 In the constellation diagrams shown in (c) and (f), it can be observed that the constellation diagrams of signals with XY differences also have gaps. Without using an auxiliary structure, the recovered constellation points are fuzzy. However, after using the structure proposed in this embodiment, the recovery of the constellation diagram becomes very clear, and the XY imbalance is greatly alleviated. Figure 6 In the bit error rate curves shown in (b) and (e), the structure can well make the bit error rate curve reach the judgment threshold of 3.8E-3 from the original judgment line, while the original judgment line can only reach 2E-2 regardless of the transmission distance. Therefore, the transmission performance of the proposed two-level structure is far better than the original traditional structure. This structure can greatly improve the transmission performance of ultra-high-order modulation formats.

[0140] In order to further verify the application of this structure in ultra-high-order modulation formats, experiments were also conducted on 4096QAM. Figure 7 Experimental results performed on PS-PDM-4096QAM are shown ((a) 80km-XY (b) 80km-ALL).

[0141] from Figure 7 It can be observed that the difference in the XY bit error rate caused by the IQ mixing imbalance is not large, because the bit error rates are kept at a very low level. At this point, the proposed secondary structure does not work well. To further exert its effect, other algorithms should be used to restore the bit error rate to a better range. But at the same time, it can be seen that even in this case, the structure proposed in this embodiment greatly reduces the bit error rate of the signal compared with the traditional structure, so the structure is also very suitable for high-order modulation formats.

[0142] By comparing the experimental results of signals with different modulation formats of 64, 256, 1024 and 4096QAM, the effectiveness of the second-level structure is verified, and it is found that the structure is indispensable for ultra-high-order modulation formats. The algorithm can significantly improve the signal transmission quality, compensate for hardware damage, and save actual costs.

[0143] Finally, a comparative experiment of different MIMO structures was conducted. The PS-PDM-1024QAM data was processed using different structures. Figure 8 The experimental results are shown. Line 1 shows the data bit error rate curve without the second-level MIMO structure. It can be clearly seen from the figure that if the traditional MIMO structure is added to the second level of the MIMO structure, it is basically ineffective. For the 8*2 MIMO structure, it does have a certain effect on reducing the bit error rate. However, it can be clearly seen that the compensation effect of the 8*2 structure is not stable enough, and is far from the effect of the actual value 4*4 MIMO structure. Therefore, compared with other structures, the structure proposed in this embodiment has a better compensation effect on IQ mixed damage.

[0144] Although the preferred embodiments of the present application have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present application.

[0145] Obviously, the above embodiments are merely examples for clear explanation and are not intended to limit the implementation methods. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the implementation methods here. The obvious changes or modifications derived from these are still within the protection scope of the invention.

Claims

1. A cascaded MIMO device for an ultra-high order coherent optical transmission system, characterized in that: The cascaded MIMO device includes a first-stage component and a second-stage component; The first-stage component is located at a signal receiving end of a coherent optical transmission system, and uses a 2×2 MIMO equalizer based on a constant modulus algorithm (CMA) to perform signal polarization demultiplexing and partially compensate for a first IQ imbalance of coherent optical transmission, wherein the 2×2 MIMO equalizer is a 2×2 complex-valued filter, and the first IQ imbalance includes an IQ imbalance from a signal receiving end; The second-stage component is located after the first-stage component and before the decision output of the signal receiving end of the coherent optical transmission system, and adopts a 4×4 MIMO equalizer based on a constant modulus algorithm CMA to compensate for the second IQ imbalance of the coherent optical transmission, wherein the 4×4 MIMO equalizer is a 4×4 real-valued filter, and the second IQ imbalance includes IQ imbalance from the signal transmitting end and the signal receiving end.

2. The cascaded MIMO device for an ultra-high order coherent optical transmission system according to claim 1, characterized in that: The iterative formula of the output signal of the 4×4 real-valued filter is: v ab (n)=h ab-rr (n)u b-r (n)+h ab-ri (n)u b-i (n) +j{h ab-ir (n)u b-r (n)+h ab-ri (n)u b-i (n)}(14) Among them, u (a,b)-(e,f) (n) is a vector of four input columns, h ab-ef (n) is a vector of sixteen filter tap coefficients, ab = xx, xy, yx or yy, ef = rr, ri, ir or ii, x represents X polarization, y represents Y polarization, i represents imaginary part, r represents imaginary part, and n represents the current time; Calculate the final output v of the real-valued filter x (n) and v y (n), the formula is: v x (n)=v xx (n)+v xy (n)(15) v y (n)=v yx (n)+v yy (n)(16) Based on the constant modulus algorithm CMA, the tap coefficients are updated to calculate the corresponding error signal. The formula is: e x,y (n)=S(n)-v x,y (n)(17) Among them, S(n) is the training symbol in training mode, v x,y (n) is v x (n) or v y (n); Finally, based on the constant modulus algorithm CMA, the tap coefficient of the next moment n+1 is updated to: h ab-ef (n+1)=h ab-ef (n)+μe a-e (n)u b-f (n)(18) Among them, μ is the step size parameter, e x-r,y-r (n), e x-i,y-i (n) are respectively e x,y The real and imaginary parts of (n); The final 4×4 real-valued filter is obtained based on the updated tap coefficients.

3. The cascaded MIMO device for an ultra-high order coherent optical transmission system according to claim 1, characterized in that: The IQ imbalance at the signal receiving end includes IQ phase mismatch, IQ gain mismatch, and IQ delay skew, and corresponding transfer matrices are constructed respectively, a first overall transfer function is obtained according to the constructed transfer matrix, and a first inverse matrix is ​​obtained according to the first overall transfer function, the first inverse matrix is ​​used to multiply the received signal to filter out the IQ imbalance at the signal receiving end, and the first inverse matrix is ​​implemented by a 4×4 real-valued filter; The IQ phase mismatch and IQ gain mismatch at the signal receiving end are also equalized by a 2×2 complex-valued filter.

4. The cascaded MIMO device for an ultra-high order coherent optical transmission system according to claim 3, characterized in that: The IQ phase mismatch transfer matrix construction method comprises: The I and Q paths of the X-polarization component of the received signal are set to r X-I (t) and r X-Q (t), the I and Q paths of the Y polarization component are set to r Y-I (t) and r Y-Q (t); the complex amplitude of the received signal is modeled as: r X,Y (t)=r X-I,Y-I (t)+jr X-Q,Y-Q (t)(4) For IQ phase mismatch, the rotation angles of the I and Q axes of the X polarization component on the complex plane are denoted as θ X-I and θ X-Q , the rotation angle of the Y polarization component is θ Y-I and θ Y-Q The IQ phase mismatch and the angle of deviation from the correct angle of 90° are represented as θ X-I ,θ X-Q and θ Y-I ,θ Y-Q ; To solve the IQ phase mismatch, the transfer matrix of IQ phase mismatch is defined as:

5. The cascaded MIMO device for an ultra-high order coherent optical transmission system according to claim 3, characterized in that: The IQ gain mismatch transfer matrix construction method comprises: For IQ gain mismatch, use β X-I and β X-Q The gains of the I and Q ports at X polarization are expressed as β Y-I and β Y-Q represents the gain of the Y-polarization I port and Q port, and the IQ gain mismatch is expressed as: When β X-I≠ β X-Q When β Y-I≠ β Y-Q When , it indicates that there is IQ gain imbalance in the Y polarization, and the transfer matrix of IQ gain imbalance is defined as:

6. The cascaded MIMO device for an ultra-high order coherent optical transmission system according to claim 3, characterized in that: The transfer matrix construction method of IQ delay skew includes: For IQ delay skew, the received signal is divided into X polarization and Y polarization. The time delays of the I and Q signals of X polarization and the I and Q signals of Y polarization are τ respectively. X-I , τ X-Q , τ Y-I and τ Y-Q , so the complex amplitude of the received signal is modeled as: When τ X-I≠ τ X-Q When τ Y-I≠ τ Y-Q When , IQ delay skew exists in the Y polarization component; is the IQ delay skew, transforming equation (8) into the frequency domain is: Where ω is the angular frequency of the optical signal measured from the carrier frequency R X-I,Y-I (ω) and R X-Q,Y-Q (ω) are r X-I,Y-I (t) and r X-Q,Y-Q (t), r X-Q,Y-Q The Fourier transform of (t) is then expressed as:

7. The cascaded MIMO device for an ultra-high order coherent optical transmission system according to claim 3, characterized in that: The method of obtaining a first overall transfer function according to the constructed transfer matrix and obtaining a first inverse matrix according to the first overall transfer function comprises: By modeling IQ phase mismatch, IQ gain imbalance, and IQ delay offset, the first overall transfer function is simplified to: I X,Y (ω)=P X,Y G X,Y D X,Y (oh)(11) Among them, P X,Y ,G X,Y ,D X,Y (ω) are the transfer matrices of IQ phase mismatch, IQ gain imbalance and IQ delay offset respectively; Then the first inverse matrix I -1 X,Y The expression of (ω) is:

8. The cascaded MIMO device for an ultra-high order coherent optical transmission system according to claim 1, characterized in that: The IQ imbalance at the signal transmitting end includes IQ delay skew, IQ gain mismatch, and IQ phase mismatch, and corresponding transfer matrices are constructed respectively. A second overall transfer function is obtained according to the constructed transfer matrix. A second inverse matrix is ​​obtained according to the second overall transfer function. The second inverse matrix is ​​used to multiply the received signal to filter out the IQ imbalance at the signal transmitting end. The second inverse matrix is ​​implemented by a 4×4 real-valued filter.

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