CN117768037A - Cascading MIMO structure for ultra-high order coherent light transmission system - Google Patents

Abstract

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

Description

Cascading MIMO structure for ultra-high order coherent light transmission system

Technical Field

The invention relates to the technical field of coherent light transmission, in particular to a cascading MIMO structure for an ultra-high order coherent light transmission system.

Background

With the continuous growth of explosive digital application traffic such as artificial intelligence, cloud computing, VR/AR, and even meta-universe, new challenges are certainly presented to the underlying optical transmission system. To meet the ever-increasing demand for channel capacity, the scientific and industrial community continues to expand system capacity to ever-higher values. It is therefore important to find a viable technical solution for a cost-effective optical transmission system.

In an optical communication transmission system, coherent optical communication has become a breakthrough technology, and can achieve a data transmission rate of 400 Gbit/s or higher. Because the high sensitivity of its coherent receiver extends the transmission distance, providing new possibilities for efficient data transmission, high-speed digital coherent optical communication is extremely important in meeting today's throughput requirements. Currently, development and research of 800G and 1.6T coherent optical modules have become 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 be generally adopted. Among them, a direct boosting method of high-speed single carrier transmission is to increase Spectrum Efficiency (SE) by increasing modulation format. At present, research on high-order modulation formats has been carried out at home and abroad, 256QAM, 1024QAM and 4096QAM signals are transmitted on a Standard Single Mode Fiber (SSMF) by a Probability Shaping (PS) technology, and the method is quite applicable to practical application in the future. However, current ultra-high order modulation format operation still faces some challenges.

When using ultra-high order QAM formats, transmission performance is more susceptible to system imperfections such as nonlinearities in the fiber, offset between the transmitting end laser and the local oscillator, and imbalance between IQ in coherent optical transmission. The structure of the conventional MIMO needs to be modified so that it can tolerate any one of the imbalance phenomena mentioned before and correct the defect of any one of the channels in the transmission system, thereby realizing a significant reduction in the error rate.

In-phase (I) and quadrature (Q) impairments in the transceiver caused by component imperfections or misalignment can lead to significant performance degradation when ultra-high order QAM is used. To compensate for IQ impairments in QAM coherent optical communications, many DSP algorithms have been developed. However, the existing research has limitations on the IQ imbalance algorithm in the ultra-high order modulation format, and the research on the IQ imbalance algorithm suitable for the ultra-high order modulation format is urgently needed.

Disclosure of Invention

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

In order to solve the technical problems, the invention provides a cascading MIMO structure for an ultra-high order coherent optical transmission system, which comprises a first-stage structure and a second-stage structure;

the first-stage structure is positioned at a signal receiving end of a coherent light transmission system, a 2×2MIMO equalizer based on a constant modulus algorithm CMA is adopted to perform signal polarization demultiplexing, and partial compensation is performed on first IQ imbalance of coherent light transmission, wherein the 2×2MIMO equalizer is a 2×2 complex-valued filter, and the first IQ imbalance comprises IQ imbalance from the signal receiving end;

the second stage structure is positioned after the first stage structure and before the decision output of the signal receiving end of the coherent optical transmission system, and a 4×4MIMO equalizer based on a constant modulus algorithm CMA is adopted to compensate for the second IQ imbalance of the coherent optical transmission, wherein the 4×4MIMO 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.

In one embodiment of the present invention, 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)

wherein u is _(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 the X polarization, Y represents the Y polarization, i represents the imaginary part, r represents the r tableAn imaginary part, n represents the current time;

calculating the final output v of the real value filter _x (n) and v _y (n) the formula:

v _x (n)＝v _xx (n)+v _xy (n) (15)

v _y (n)＝v _yx (n)+v _yy (n) (16)

and updating tap coefficients based on a constant modulus algorithm CMA to calculate corresponding error signals, wherein the formula is as follows:

e _x,y (n)＝S(n)-v _x,y (n) (17)

wherein S (n) is a training symbol in training mode, v _x,y (n) is v _x (n) or v _y (n)；

Finally, based on a constant modulus algorithm CMA, the tap coefficient of the next time n+1 is updated as follows:

h _ab-ef (n+1)＝h _ab-ef (n)+μe _a-e (n)u _b-f (n) (18)

wherein μ is the step size parameter, e _x-r,y-r (n)，e _x-i,y-i (n) are respectively e _x,y A real part and an imaginary part of (n);

a final 4 x 4 real value filter is obtained based on the updated tap coefficients.

In one embodiment of the present invention, IQ imbalance of the signal receiving end includes IQ phase mismatch, IQ gain mismatch, IQ delay skew, and corresponding transfer matrices are respectively constructed, a first overall transfer function is obtained according to the constructed transfer matrices, a first inverse matrix is obtained according to the first overall transfer function, the first inverse matrix is used for multiplying a received signal to filter IQ imbalance of 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 of the signal receiving end are balanced by a 2×2 complex filter.

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

the I path and the Q path of the X polarization component of the received signal are respectively set as r _X-I (t) and r _X-Q (t) setting the I and Q paths of the Y polarization component as r respectively _Y-I (t) and r _Y-Q (t); modeling the complex amplitude of the received signal 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 in the complex plane are respectively denoted as θ _X-I And theta _X-Q The rotation angle of the Y polarization component is used as theta _Y-I And theta _Y-Q The IQ phase mismatch and the angle 90 DEG from the correct angle are denoted as θ _X-I 、θ _X-Q And theta _Y-I 、θ _Y-Q The method comprises the steps of carrying out a first treatment on the surface of the To solve IQ phase mismatch, a transfer matrix of IQ phase mismatch is defined as:

P _X,Y ＝(-sin(θ _X-Q,Y-Q )cos(θ _X-Q,Y-Q )) (5)。

in one embodiment of the present invention, the IQ gain mismatch transfer matrix construction method includes:

for IQ gain mismatch, use beta _X-I And beta _X-Q Representing the gain of the X-polarized I and Q ports, using beta _Y-I And beta _Y-Q Representing the gains of the Y-polarized I-port and Q-port, the IQ gain mismatch is expressed as:

when beta is _X-I≠ β _X-Q Indicating that IQ gain imbalance exists in the X polarization; when beta is _Y-I≠ β _Y-Q When IQ gain imbalance is indicated in the Y polarization, the transfer matrix of IQ gain imbalance is defined as:

in one embodiment of the present invention, the IQ delay skew transfer matrix construction method includes:

for IQ delay skew, the received signal is divided into X-polarized and Y-polarized, and then the time delays of the X-polarized I and Q signals, the Y-polarized I and Q signals, respectively, are τ _X-I 、τ _X-Q 、τ _Y-I And τ _Y-Q The complex amplitude of the signal is thus modeled as:

when τ is _X-I≠ τ _X-Q When IQ delay skew exists in the X-polarized component; when τ is _Y-I≠ τ _Y-Q When IQ delay skew exists in the Y-polarized component; for IQ delay skew, transform equation (8) to the frequency domain is:

wherein 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 respectively ^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 Fourier transform of (t), then IQ delay skew transfer matrix is expressed as:

in one embodiment of the present invention, the method obtains an overall transfer function according to the constructed transfer matrix, and finds an inverse matrix of the overall transfer function, where the method includes:

by modeling IQ phase mismatch, IQ gain imbalance, and IQ delay offset, the overall transfer function is reduced to:

I _X,Y (ω)＝P _X,Y G _X,Y D _X,Y (ω) (11)

wherein P is _X,Y ,G _X,Y ,D _X,Y (ω) are respectively the transfer matrices of IQ phase mismatch, IQ gain imbalance and IQ delay offset;

then inverse matrix I ^-1 _X,Y The expression of (ω) is:

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

Compared with the prior art, the technical scheme of the invention has the following advantages:

the cascade MIMO structure can compensate the great reduction of the error rate caused by IQ imbalance due to the hardware damage of the transmitter and the receiver, and can compensate the signal degradation caused by IQ imbalance due to the accumulation of an ultra-high order algorithm, so that the quality of the transmission signal is greatly improved, and the error rate is obviously reduced;

the cascading MIMO structure can enhance signals with different modulation formats, and for ultra-high order signals, the structure can enable PS-PDM-1024QAM signals transmitted on 80km single-mode fiber to reach a judgment threshold of 3.8E-3 under the condition of lower signal to noise ratio, but the original structure can not reach a hard judgment line, and the structure can also obviously improve the quality of PS-PDM-4096QAM signals;

the research work of the cascade MIMO structure can greatly save cost, make up for signal attenuation caused by hardware damage, and obviously improve the error rate, thereby having great significance for putting the ultra-high order modulation format into practical application in the future.

Drawings

In order that the invention may be more readily understood, a more particular description of the invention will be rendered by reference to specific embodiments thereof that are illustrated in the appended drawings.

Fig. 1 is an overall architecture diagram of a cascaded MIMO structure for a coherent optical transmission system in accordance with an embodiment of the present invention;

fig. 2 is a schematic diagram illustrating an effect of IQ imbalance based on 16QAM on constellation points in an embodiment of the present invention;

FIG. 3 is a schematic diagram of a 4×4 real-valued filter according to an embodiment of the present invention;

FIG. 4 is a schematic diagram of an experimental setup for 4GBd PS-1024QAM over 80km of optical fiber according to an embodiment of the present invention;

fig. 5 is a graph of error rate versus OSNR (dB) for different modulation formats for BTB transmission for use or not for cascaded MIMO in an embodiment of the present invention;

FIG. 6 is a graph of error rate versus OSNR (dB) for different transmission distances for whether a cascaded MIMO structure is used or not over PS-PDM-1024QAM in an embodiment of the present invention;

FIG. 7 is a graph of error rate versus OSNR (dB) for a transmission distance of 80km when a cascading MIMO structure is used or not on PS-PDM-4096QAM in an embodiment of the present invention;

fig. 8 is a graph of error rate versus OSNR for a transmission distance of 80km using different MIMO configurations on PS-PDM-1024QAM in an embodiment of the present invention.

Detailed Description

The present invention will be further described with reference to the accompanying drawings and specific examples, which are not intended to be limiting, so that those skilled in the art will better understand the invention and practice it.

Example 1

Referring to fig. 3, the present invention relates to a cascade MIMO structure for an ultra-high order coherent optical transmission system, the cascade MIMO structure including a first-stage structure and a second-stage structure;

the first-stage structure is located at a signal receiving end of the coherent light transmission system, and performs signal polarization demultiplexing by adopting a 2×2MIMO equalizer based on a constant modulus algorithm CMA, and performs partial compensation (i.e., except for IQ delay skew of the signal receiving end) on first IQ imbalance of coherent light transmission, where the 2×2MIMO equalizer is a 2×2 complex-valued filter, and the first IQ imbalance includes IQ imbalance from the signal receiving end;

the second stage structure is positioned after the first stage structure and before the decision output of the signal receiving end of the coherent optical transmission system, and a 4×4MIMO equalizer based on a constant modulus algorithm CMA is adopted to compensate for the second IQ imbalance of the coherent optical transmission, wherein the 4×4MIMO 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.

The present embodiment is described in detail below:

1. the embodiment aims at researching the unbalance problem among IQ components of the ultra-high-order QAM signal, and provides a new cascade structure, and the structure of the traditional MIMO is modified, so that any unbalance phenomenon mentioned in the background art can be solved, the defect of any channel in a transmission system can be corrected, and the obvious reduction of the error rate is realized.

2. Principle of two-stage MIMO structure

In this section, the basic principle of a cascaded MIMO architecture will be analyzed from three aspects, fig. 1 shows an overall receiver-side offline DSP architecture for ultra-high order coherent optical transmission, where iqorthoonalization represents quadrature normalization of IQ components, CD compensation represents fiber dispersion compensation, clock Recovery represents Clock synchronization and Recovery, CMA represents a 2 x 2 complex-valued filter, FOE is used to remove frequency bias, CPR is used to remove phase noise, volterra equalizer is used to compensate for nonlinear impairments, and the architecture of fig. 1 takes into account IQ imbalance (i.e., algorithm-induced IQ imbalance) resulting from the algorithm's separate processing (i.e., FOE, CPR, VE) of the X, Y polarized IQ components. The emphasis of this embodiment is on 2×2 complex-valued filters and 4×4 real-valued filters in the MIMO architecture. This embodiment has three major IQ imbalances: respectively, the IQ imbalance of the transmitting end, the IQ imbalance of the receiving end and the IQ imbalance caused by algorithm. The present embodiment equalizes algorithm IQ imbalance caused by the separate processing of X, Y polarized IQ components in a coherent optical transmission system by a 4×4 real-valued filter.

First, higher order modulated signals are generally more susceptible to impairments caused by imperfections from either the transmitter (Tx) or receiver (Rx) devices, including offset between in-phase (I) and quadrature (Q) components, IQ phase imbalance, IQ gain imbalance, and non-uniform IQ frequency characteristics. Therefore, a more stringent calibration or more accurate equalization of the ultra-high order modulated signal is required to compensate for these IQ impairments. The nature of these injuries may change slightly with changing environments due to imperfections in the equipment. For these dynamic effects, the present embodiment desirably uses adaptive equalization to automatically compensate. In a conventional coherent optical transmission system, a butterfly structure of a Finite Impulse Response (FIR) filter is generally adopted, and polarization demultiplexing is realized through an adaptive algorithm and an equalization function is exerted, so that time-varying transmission impairments are compensated. However, in these conventional butterfly complex-valued filters, the I component and Q component are not handled independently, considering the impairments from the hardware. To better compensate for IQ imbalance, such as offset, phase, gain imbalance, and frequency characteristics, the present embodiment contemplates replacing complex-valued MIMO filters with real-valued MIMO filters.

A. Equalizer structure principle

First, a discussion starts with the structure of a polarization receiver adaptive equalizer, the most general structure of which is shown in the following formula:

it corresponds to a 4X 4 real-valued mimo system, the inputs being the real and imaginary parts of the received complex-valued polarized signal (X, Y): x is X _I ＝Re(X)，X _Q ＝Im(X)，Y _I ＝Re(Y)，Y _Q =im (Y). For convenience, a matrix H is defined:

obviously, the general reversible channel response can be compensated in the original equalizer structure. However, in the existing coherent optical system, since IQ mixing impairment is not considered, the conventional equalizer simplifies the original 4×4 real-valued filter to a standard 2×2 complex-valued equalizer, and its structure is defined as:

it can be seen from an examination of the above formulae that, in general, formula (1) and formula (3) are not equivalent. The present embodiment considers the case that when hardware is damaged, damage may be caused to the real part or the imaginary part of a certain signal. In this case, the conventional structure cannot compensate for the damage, and thus it is considered to use a 4×4 real-valued structure in the structure.

The present embodiment then discusses the necessity of using a 4 x 4 real-valued filter in terms of impairment compensation. At the receiving end, a defective 90-degree mixer, balanced photodiodes or any other device may cause IQ-imbalance. The imbalance here is not just XY path IQ imbalance correction, which is generally considered to be performed by GSOP or Lowdin algorithm, respectively, in the first step of the DSP. It also includes phase mismatch between IQ ports; and timing mismatch due to IQ port physical path length differences, i.e., delay offset in IQ. If the receiver's DSP unit is unable to compensate for these IQ imbalance, the system performance can be severely degraded. In low order modulation formats, the effect of these imbalances on signal quality may be less pronounced. However, experiments have shown that in the case of ultra-high orders, if these imbalances are ignored, they will seriously impair the quality of the transmitted signal.

Fig. 2 shows the effect of the various IQ-imbalance on a 16 QAM-based constellation ((a) ideal constellation, (b) constellation variation of gain imbalance, (c) constellation variation of phase imbalance, (d) constellation variation of IQ-tilt (with eye diagram)). IQ gain imbalance can cause the constellation to exhibit rectangular distortion; IQ phase imbalance can cause the constellation to exhibit parallelogram-like distortion; IQ skew is not obvious for constellations, but obvious phenomena can be observed from the eye diagram. For higher order modulation formats, any IQ imbalance may result in the signal being unrecoverable.

When IQ imbalance does not exist, the I path and the Q path of the X polarization component of the received signal are respectively r _X-I (t) and r _X-Q (t). Similarly, the Y polarization component is also denoted as r _Y-I (t) and r _Y-Q (t). The complex amplitude of the optical signal can then be modeled as:

r _X,Y (t)＝r _X-I,Y-I (t)+jr _X-Q,Y-Q (t)(4)

consider first the IQ phase mismatch case described above. For IQ phase mismatch, the rotation angles of the I and Q axes of the X polarization component in the complex plane are respectively denoted as θ _X-I And theta _X-Q . Also, the rotation angle of the Y polarization component is θ _Y-I And theta _Y-Q And (3) representing. The IQ phase mismatch and the angle 90 DEG from the correct angle are denoted as θ respectively _X-I 、θ _X-Q And theta _Y-I 、θ _Y-Q . To solve the phase mismatch problem, a transfer matrix derived from the phase mismatch is defined as:

next, consider the case of IQ gain mismatch. In this case, beta is used _X-I And beta _X-Q Indicating the gain of the X polarized I and Q ports, again using beta _Y-I And beta _Y-Q The gains of the Y polarized I and Q ports are shown. IQ gain mismatch is generally represented by:

when beta is _X-I≠ β _X-Q When IQ gain imbalance is considered to exist in the X polarization; also, when beta _Y-I≠ β _Y-Q When IQ gain imbalance is considered to exist in the Y polarization. In this case, the transfer matrix of IQ gain imbalance can be defined as:

finally, since other structures cannot compensate for IQ skew, the portions related to IQ skew are described in detail herein. Due to the time delay of the four output ports at the front end being tau _X-I 、τ _X-Q 、τ _Y-I And τ _Y-Q The complex amplitude of the signal can thus be modeled as:

when τ is _X-I≠ τ _X-Q When IQ delay skew exists in the X-polarized component; similarly, when τ _Y-I≠ τ _Y-Q When IQ impairment exists in the Y-polarized component. To compensate for this impairment, transform equation (8) to the frequency domain is:

wherein 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 respectively ^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 Fourier transform of (t), transmission matrix expressed as:

by modeling IQ phase mismatch, IQ gain imbalance, and IQ delay offset, the overall transfer function can be further reduced to:

I _X,Y (ω)＝P _X,Y G _X,Y D _X,Y (ω) (11)

in summary, the problem is reduced to: to compensate for all of the above IQ imbalance, the inverse matrix I needs to be found ^-1 _X,Y (ω) multiplying it by the received signal to eliminate these imbalances, as follows:

the structure of the 4 x 4 real value filter can well find the required inverse matrix I ^-1 _X,Y (ω) to compensate for the various IQ impairments described above. Theory further proves that the real part and the imaginary part of the complex component are separated into four real numbers, so that the full freedom degree of four-dimensional rotation can be better covered, and the loss of the polarization element related to polarization is more comprehensively considered. This conclusion is drawn by four-dimensional (4D) signal space reasoning in communication theory, again corroborating the necessity of the present embodiment to use a 4 x 4 real-valued filter.

It should be noted that, the above formula (4) -formula (12) is 3 IQ imbalance of the signal receiving end, and the (2×2 complex filter is first used for partial compensation of IQ impairment of the receiving end and the 4*4 real filter is used for compensation of mixed IQ impairment of the receiving end and the transmitting end) needs to be balanced together by a 2×2 complex filter (IQ delay skew cannot be compensated) and a 4*4 real filter.

Principle of MIMO cascade architecture

Transmitter (Tx) imbalance may also cause severe performance degradation. Currently, only some calibration methods requiring complex operations or expensive equipment are reported to compensate for the transmitting-end imbalance. In conventional coherent optical transmission systems, the transmit-side imbalance is typically ignored, and only the receive-side skew is of concern. In fact, there may be a potential imbalance at both the transmitting and receiving ends. In the cascade MIMO structure of the present embodiment, the first stage structure uses a CMA-based 2×2MIMO equalizer to perform imbalance compensation on the Rx end, and the Tx end defect is compensated by the CMA-based 4×4MIMO equalizer after passing through the Volterra Equalizer (VE) (i.e., the second stage structure), and the cascade MIMO structure of the present embodiment can compensate various impairments.

This embodiment must first consider the impairments that occur at the transmitting end and how to compensate for them. At the transmitting end, damage caused by device defects, such as IQ offset of the modulator or frequency characteristics of the driving amplifier, may occur. Of course, nonlinear distortion due to kerr effect may also occur, but for simplicity, this embodiment does not take these factors into account. The remaining lesions were linear after ignoring the kerr effect. This includes the effect of IQ skew, and thus IQ components are different. Therefore, the present embodiment contemplates employing a real-valued MIMO structure, using real-valued signal vectors to represent the I and Q components of the X and Y polarizations 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. Importantly, the signal carrying Tx defect information can only be compensated after removal of frequency deviation (removed by FOE) and phase noise (removed by CPR). Thus, a 4 x 4 real-valued filter of 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 impairment block by block in the reverse order. This also confirms the effectiveness of the structure.

According to the above part a, the structure has completed unbalance compensation at the Rx end. For the Tx side, the IQ imbalance inverse matrix is derived similarly to the formulas (4) - (12), and the derivation process is not given any more in this embodiment due to the space limitation, which is similar to the Tx side overall transfer function matrix I in the formula (11) _X,Y (ω) setting the Rx-side integral transfer function matrix asAnd abbreviated as H, wherein each element is H _ab (a, b.epsilon. {1,2 }). A compensation matrix W in the frequency domain (corresponding to I in equation (12) can be used ^-1 _X,Y (ω)), each element W _ab (a, b e {1,2 }) to compensate for the imbalance at the sender. In the case of Gao Guangxin to noise ratio, the frequency domain matrix W may be approximated as an inverse of H, i.e., w=h ^-1 。

Wherein 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 a one-to-one correspondence of matrix parameters, the imbalance of the Tx end can be monitored by calculating the IQ delay skew, IQ gain mismatch, and IQ phase mismatch of the Tx through the matrix. The present embodiment considers only the damage compensating portion. In order to compensate for the 3 IQ-imbalance at the signal transmitting end, the frequency domain matrix W has to be found to eliminate the transmitting end imbalance, the function of which is implemented by a 4 x 4 real-valued filter.

The present embodiment also considers the reason why the 4×4 real-valued filter is put behind from another point of view. For signal recovery in low order modulation format, the steps of the DSP processing section may not be too many; but for ultra-high order modulation formats, more equalizers are typically used in order to better recover the signal, as shown in fig. 2. However, in the carrier recovery step and the subsequent Volterra equalizer step, the two IQ signals of XY are processed separately, and it is considered that IQ imbalance caused by the algorithm processing after these processing steps is also a problem to be considered. A 4 x 4 real value filter is placed before the decision output. It can effectively compensate the unbalance caused by the algorithm.

C. IQ compensation architecture based on CMA

DSP-based receivers employing butterfly-structured Finite Impulse Response (FIR) filters can compensate for time-varying transmission impairments using adaptive algorithms for polarization demultiplexing and equalization. According to the prior art, the adaptive algorithm applied to the butterfly equalizer mainly comprises CMA and LMS. Since the LMS algorithm is sensitive to FO errors, the accuracy requirements of the FO estimator are high. Thus, the CMA algorithm is used in the structure proposed in the present embodiment.

Indeed, constant Modulus Algorithms (CMAs) are often used in coherent optical transmission systems for their simplicity and immunity to phase noise. However, CMAs also have their frustrating singularity feature, i.e., two outputs may be locked to the same input. Since CMA adjusts FIR filters of two branches independently, it is greatly affected by the initial tap. The present embodiment selects the appropriate initial tap to prevent the two signals from converging to a unified input, ensuring successful demultiplexing of the two channels.

In the cascaded MIMO architecture, the first stage architecture uses a conventional CMA-based 2 x 2 complex-valued filter, and this embodiment will not be described in detail since it is the prior art. The second stage structure, i.e. the 4×4 real-valued filter based on CMA, is mainly described in this embodiment, the structure of the 4×4 real-valued filter is shown in fig. 3, the coherent light transmitted signal in fig. 3 is divided into X-polarized signals u _x (n) and Y polarization signal u _y (n) performing the following processes:

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

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)

wherein u is _(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 instant. The output v of the filter (i.e., real filter) can then be calculated _x (n) and v _y (n) is as follows:

v _x (n)＝v _xx (n)+v _xy (n) (15)

v _y (n)＝v _yx (n)+v _yy (n) (16)

next, a corresponding error signal is calculated based on the iterative formula coefficients of the CMA algorithm, i.e

e _x,y (n)＝S(n)-v _x,y (n) (17)

Where S (n) is a training symbol in training mode. It should be noted that the error function here is calculated without taking absolute values, so that the signal here carries vector information instead of scalar information.

Finally, according to the CMA algorithm, the tap coefficient at the next time n+1 is updated as follows:

h _ab-ef (n+1)＝h _ab-ef (n)+μe _a-e (n)u _b-f (n) (18)

wherein μ is the step size parameter, e _x-r,y-r (n),e _x-i,y-i (n) are respectively e _x,y And (n) real and imaginary parts.

3. Experimental device

The validity of the architecture is verified through experiments. Fig. 4 shows an experimental architecture of a coherent communication system transmitting 4GBd PS-1024QAM over 80km of optical fiber. An offline DSP flow-block diagram from the transmitter to the receiver is included.

First, at the transmitting end, a Pseudo Random Binary Sequence (PRBS) is sent to the PS encoder for CCDM encoding to generate a specified amplitude sequence, enabling mapping of signals from bits to symbols. In this step, non-uniform amplitude symbols are mapped to pulse amplitude modulation. Pilot symbols are then added to the processed sequence, and this portion of the pilot signal will be used in subsequent receiver DSPs, playing an important role in signal recovery. The amplitude sequence is then sampled at 2 sample points per symbol, up-sampled twice, and pulse shaped using a root cosine (RRC) FIR filter with a roll-off factor of 0.35 to eliminate the effects of inter-symbol interference (ISI). So far, the basic procedure of the transmitting end DSP is completed.

The experiment uses an 8Gsa/s, 14-bit high-precision AWG to perform digital-to-analog conversion (DAC), and four signals are loaded into a Mach-Zehnder modulator (MZM) for modulation, so as to generate 1024-QAM signals. After modulating the signal into an optical carrier, the signal is amplified by an Erbium Doped Fiber Amplifier (EDFA). A first Variable Optical Attenuator (VOA) is used to attenuate the optical power to the appropriate access optical power of a Standard Single Mode Fiber (SSMF), the best incoming optical power being tested during link testing. For experimental 1024-QAM signals, the best incident optical power tested was about-4 dBm. The transmission distance of the modulated 1024-QAM signal in the SSMF is 80 km. The present embodiment uses a second VOA to vary the output signal optical power of the transmitted QAM signal.

This step is mainly to change the OSNR of the signal to map the bit error rate. The signal is then amplified by the EDFA, attenuated by the third VOA to a fixed power of about 6dBm, and transmitted to the receiving end. At the receiving end, the signal is first passed through an optical bandpass filter (OBPF), and after passing through a Polarization Controller (PC), it is transmitted to the coherent receiver together with the local oscillating Light (LO). The experiment used laser light with a laser linewidth of 1KHz and a wavelength of 1500.112nm as the local oscillating Light (LO). The coherent receiver consists of a 90-degree optical mixer and four balanced photodetectors. Then, a 50GSa/s real time sampling oscilloscope is used for completing analog-digital conversion, and the acquired data is subjected to an off-line digital signal processing step for signal recovery.

The offline digital signal processing of the receiving end mainly comprises preliminary processing such as resampling, RRC matched filtering, I/Q orthogonalization based on GSOP and the like. For dispersion, dispersion compensation is performed from the frequency domain. In order to keep the transmitter clock and the receiver sample clock at the same frequency and phase, a clock recovery algorithm is performed using the gardner algorithm and the auxiliary symbols. In the polarization equalization stage, the proposed optimization algorithm structure is adopted. Channel equalization is performed using 1 filter tap, thereby completing polarization demultiplexing. Then, a carrier recovery algorithm is performed in which the data is modified with an accurate frequency offset using a frequency offset estimation algorithm in combination with a fourth power Fast Fourier Transform (FFT) and a derivative-assisted FFT. For phase recovery of the signal, the phase noise of the laser is estimated from the pilot information of the consecutive short code blocks, and the phase variation is tracked by the pilot signal to find the approximate phase shift of each symbol to compensate.

In addition, in order to alleviate distortion caused by nonlinearity of the optoelectronic device, after the carrier recovery algorithm, a Volterra nonlinear equalization (VNLE) algorithm based on the second-order Volterra level is performed, because the algorithm used by the higher-order modulation format is more, and the I/Q independent operation is performed in the processing process, so that the imbalance of the I/Q signal is easily caused. After using the VNLE algorithm, it is supplemented to the second order VNLE algorithm.

4. Experimental results and discussion

To verify the two-stage MIMO structure proposed above, experiments were performed on the double offset 64, 256, 1024 and 4096-QAM of 4GBd in a coherent optical transmission system, respectively.

Fig. 5 shows experimental results of 64, 256, and 1024-QAM in back-to-back (BTB) transmission. Since the present embodiment focuses on various mixed IQ imbalance problems, in the experimental result section, the difference in bit error rate between XY paths due to IQ imbalance problems is demonstrated.

Referring to fig. 5 ((a) PS-PDM-64QAM-XY, (b) PS-PDM-256QAM-XY, (c) PS-PDM-1024QAM-XY, (d) PS-PDM-64QAM-ALL, (e) PS-PDM-256 QAM-ALL) in fig. 5 (a) (b) (c), and the error rate of XY components added with the proposed structure is represented by a graph of numerals 3 and 4. It can be found that the XY imbalance caused by such IQ mixing imbalance is not significant in the low order modulation format, and the effect on the error rate is not significant in the ultra-high order experiments, however, as shown in fig. 5 (c), the error rate of two XY signals caused by such imbalance is very different, and even an order of magnitude is different in the error rate of the two signals in the observation of data, which is also considered to be one of the reasons why the error rate is required in the ultra-high order modulation format.

In fig. 5 (d) (e) (f), the error rate curves without and with the addition of the secondary structure are represented by the lines of numerals 1 and 2, respectively, showing the overall error rate curves of general interest. It can be seen that in all of 64, 256 and 1024QAM, the two-level structure significantly reduces the bit error rate. Especially in 1024QAM, the increase in the total error rate due to XY imbalance is properly solved after adding the structure. The 1024QAM cannot reach the decision threshold of 3.8E-3 before adding the structure, but reaches the decision threshold when osnr=27 or more after adding the secondary structure. This shows that this structure has a significant impact on the ultra high order modulation format.

To further investigate the effect of this structure on transmission distance, fig. 6 shows the experimental results of 1024QAM without and with the secondary structure in BTB transmission and 80km transmission experiments ((a) BTB-XY, (b) BTB-ALL, (c) constellation before and after addition of secondary structure at osnr=28, (d) 80km-XY, (e) 80km-ALL, and (f) constellation before and after addition of secondary structure at osnr=33. In order to better understand the quality of signal recovery, the present embodiment also shows the comparison of different constellations of XY components before and after the secondary structure in the figure. The most representative points at different distances are chosen for presentation.

Fig. 6 (a) (b) (c) shows experimental results of BTB transmission using 1024 QAM; fig. 6 (d) (e) (f) shows experimental results of 80km transmission using 1024 QAM. By observing the error rate graphs of the XY components of the two, the XY error rate difference caused by IQ mixed damage is found to be more and more obvious in the transmission distance of 80 km. Even in the case where the signal-to-noise ratio is low, the difference between XY can be observed. However, the secondary structure proposed in this embodiment can well compensate for these damages regardless of whether the difference becomes large or not, and the XY difference after compensation is significantly reduced. In the constellation shown in fig. 6 (c) (f), a gap is observed in the constellation of the XY-differential signal. Without the use of ancillary structures, the recovered constellation points are ambiguous. After the structure proposed by the embodiment is used, the recovery of the constellation diagram becomes very clear, and the situation of XY imbalance is greatly relieved. In the bit error rate curve shown in fig. 6 (b) (E), the structure can well make the bit error rate curve reach the decision threshold of 3.8E-3 from the original decision line, and the original decision line can only reach 2E-2 no matter how far the transmission distance is. Therefore, the transmission performance of the proposed secondary structure is far superior to that of the original conventional structure. The structure can greatly improve the transmission performance of the ultra-high order modulation format.

To further verify the application of this structure in ultra-high order modulation formats, experiments were also performed on 4096 QAM. FIG. 7 shows the results of experiments performed on PS-PDM-4096QAM ((a) 80km-XY (b) 80 km-ALL).

It can be observed from fig. 7 that the XY error rate difference caused by IQ mixing imbalance is not large, since the error rate is kept at a low level. In this regard, the proposed secondary structure does not function well, and other algorithms should be used to restore the bit error rate to a better range in order to further exert its effect. But it can be seen that, even in this case, the structure proposed in this embodiment greatly reduces the error rate of the signal compared with the conventional structure, so that the structure has good applicability to the higher order modulation format.

By comparing the experimental results of the 64, 256, 1024 and 4096QAM different modulation format signals, the validity of the second stage structure was verified, and it was found that the structure was indispensable for the ultra high order modulation format. The algorithm can obviously improve the signal transmission quality, compensate hardware damage and save the actual cost.

Finally, comparative experiments of different MIMO structures were performed. The data of PS-PDM-1024QAM was processed with different structures and the experimental results are shown in fig. 8. Line 1 shows the data error rate curve without the second level MIMO structure. It is clear from the figure that it is basically ineffective if a conventional MIMO structure is added in the second stage of the MIMO structure. For the 8 x 2mimo 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 4×4mimo structure. Therefore, compared with other structures, the structure proposed by the present embodiment has a more superior compensation effect on IQ hybrid impairment.

While preferred embodiments of the present application have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. It is therefore intended that the following claims be interpreted as including the preferred embodiments and all such alterations and modifications as fall within the scope of the application.

It is apparent that the above examples are given by way of illustration only and are not limiting of the embodiments. Other variations and modifications of the present invention will be apparent to those of ordinary skill in the art in light of the foregoing description. It is not necessary here nor is it exhaustive of all embodiments. And obvious variations or modifications thereof are contemplated as falling within the scope of the present invention.

Claims (8)

1. A cascaded MIMO structure for an ultra-high order coherent optical transmission system, characterized by: the cascade MIMO structure comprises a first-stage structure and a second-stage structure;

the first-stage structure is positioned at a signal receiving end of a coherent light transmission system, a 2×2MIMO equalizer based on a constant modulus algorithm CMA is adopted to perform signal polarization demultiplexing, and partial compensation is performed on first IQ imbalance of coherent light transmission, wherein the 2×2MIMO equalizer is a 2×2 complex-valued filter, and the first IQ imbalance comprises IQ imbalance from the signal receiving end;

the second stage structure is positioned after the first stage structure and before the decision output of the signal receiving end of the coherent optical transmission system, and a 4×4MIMO equalizer based on a constant modulus algorithm CMA is adopted to compensate for the second IQ imbalance of the coherent optical transmission, wherein the 4×4MIMO 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 structure for an ultra-high order coherent optical transmission system of claim 1, wherein:

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)

wherein u is _(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, n represents the current time instant;

calculating the final output v of the real value filter _x (n) and v _y (n) the formula:

v _x (n)＝v _xx (n)+v _xy (n) (15)

v _y (n)＝v _yx (n)+v _yy (n) (16)

and updating tap coefficients based on a constant modulus algorithm CMA to calculate corresponding error signals, wherein the formula is as follows:

e _x,y (n)＝S(n)-v _x,y (n) (17)

wherein S (n) is a training symbol in training mode, v _x,y (n) is v _x (n) or v _y (n)；

Finally, based on a constant modulus algorithm CMA, the tap coefficient of the next time n+1 is updated as follows:

h _ab-ef (n+1)＝h _ab-ef (n)+μe _a-e (n)u _b-f (n) (18)

wherein μ is the step size parameter, e _x-r,y-r (n)，e _x-i,y-i (n) are respectively e _x,y A real part and an imaginary part of (n);

a final 4 x 4 real value filter is obtained based on the updated tap coefficients.

3. The cascaded MIMO structure for an ultra-high order coherent optical transmission system of claim 1, wherein: the IQ imbalance of the signal receiving end comprises IQ phase mismatch, IQ gain mismatch and IQ delay deflection, corresponding transfer matrixes are respectively constructed, a first integral transfer function is obtained according to the constructed transfer matrixes, a first inverse matrix is obtained according to the first integral transfer function, the first inverse matrix is used for multiplying a received signal to filter the IQ imbalance of the signal receiving end, and the first inverse matrix is realized through a 4 multiplied by 4 real-value filter;

the IQ phase mismatch and IQ gain mismatch of the signal receiving end are balanced by a 2×2 complex filter.

4. A cascaded MIMO structure for an ultra-high order coherent optical transmission system according to claim 3, wherein: the IQ phase mismatch transfer matrix construction method comprises the following steps:

the I path and the Q path of the X polarization component of the received signal are respectively set as r _X-I (t) and r _X-Q (t) dividing the I and Q paths of the Y polarization componentLet the difference be r _Y-I (t) and r _Y-Q (t); modeling the complex amplitude of the received signal 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 in the complex plane are respectively denoted as θ _X-I And theta _X-Q The rotation angle of the Y polarization component is used as theta _Y-I And theta _Y-Q The IQ phase mismatch and the angle 90 DEG from the correct angle are denoted as θ _X-I 、θ _X-Q And theta _Y-I 、θ _Y-Q The method comprises the steps of carrying out a first treatment on the surface of the To solve IQ phase mismatch, a transfer matrix of IQ phase mismatch is defined as:

5. a cascaded MIMO structure for an ultra-high order coherent optical transmission system according to claim 3, wherein: the transmission matrix construction method for IQ gain mismatch comprises the following steps:

for IQ gain mismatch, use beta _X-I And beta _X-Q Representing the gain of the X-polarized I and Q ports, using beta _Y-I And beta _Y-Q Representing the gains of the Y-polarized I-port and Q-port, the IQ gain mismatch is expressed as:

when beta is _X-I≠ β _X-Q Indicating that IQ gain imbalance exists in the X polarization; when beta is _Y-I≠ β _Y-Q When IQ gain imbalance is indicated in the Y polarization, the transfer matrix of IQ gain imbalance is defined as:

6. a cascaded MIMO structure for an ultra-high order coherent optical transmission system according to claim 3, wherein: the IQ delay skew transfer matrix construction method comprises the following steps:

for IQ delay skew, the received signal is divided into X-polarized and Y-polarized, and then the time delays of the X-polarized I and Q signals, the Y-polarized I and Q signals, respectively, are τ _X-I 、τ _X-Q 、τ _Y-I And τ _Y-Q The complex amplitude of the received signal is thus modeled as:

when τ is _X-I≠ τ _X-Q When IQ delay skew exists in the X-polarized component; when τ is _Y-I≠ τ _Y-Q When IQ delay skew exists in the Y-polarized component; for IQ delay skew, transform equation (8) to the frequency domain is:

wherein 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 respectively ^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 Fourier transform of (t), then IQ delay skew transfer matrix is expressed as:

7. a cascaded MIMO structure for an ultra-high order coherent optical transmission system according to claim 3, wherein: the overall transfer function is obtained according to the constructed transfer matrix, and the inverse matrix of the overall transfer function is found out, and the method comprises the following steps:

by modeling IQ phase mismatch, IQ gain imbalance, and IQ delay offset, the overall transfer function is reduced to:

I _X,Y (ω)＝P _X,Y G _X,Y D _X,Y (ω) (11)

wherein P is _X,Y ,G _X,Y ,D _X,Y (ω) are respectively the transfer matrices of IQ phase mismatch, IQ gain imbalance and IQ delay offset;

then inverse matrix I ^-1 _X,Y The expression of (ω) is:

8. the cascaded MIMO structure for an ultra-high order coherent optical transmission system of claim 1, wherein: the IQ imbalance of the signal transmitting end comprises IQ delay deflection, IQ gain mismatch and IQ phase mismatch, corresponding transfer matrixes are respectively constructed, an overall transfer function is obtained according to the constructed transfer matrixes, a second inverse matrix is obtained according to the second overall transfer function, the second inverse matrix is used for multiplying a received signal to filter the IQ imbalance of the signal transmitting end, and the second inverse matrix is realized through a 4 multiplied by 4 real-value filter.