Apparatus and method for performing in-phase and quadrature skew calibration in a coherent transceiver

Abstract

A method and apparatus for performing IQ time skew calibration in a coherent transceiver is described. A four-channel signal is received. A set of inputs to a 4x8 MIMO equalizer is constructed by converting the four-channel signal into four complex inputs, each complex input having a phase shift corresponding to an estimated carrier frequency offset. The set of inputs also includes conjugate copies of the four complex inputs. Using the output from the 4x8 MIMO equalizer, equalizer coefficients are calculated by minimizing the error between the MIMO output and a reference signal. The equalizer coefficients are used to estimate the receiver IQ skew and the transmitter IQ skew in the following manner, namely, by converting the equalizer coefficients from the time domain to the frequency domain to determine the receiver IQ differential phase response and the transmitter IQ differential phase response, the receiver IQ differential phase response and the transmitter IQ differential phase response indicating the corresponding receiver IQ skew and transmitter IQ skew in the time domain. Then, skew compensation is performed.

Description

[0001] Cross-reference to related applications

[0002] This application claims priority to U.S. non-provisional application No. 17 / 008,402, filed on August 31, 2020, entitled “APPARATUS AND METHOD FOR IN-PHASE AND QUADRATURE SKEW CALIBRATION IN A COHERENT TRANSCEIVER,” the contents of which are incorporated herein by reference in jurisdictions where incorporation is permitted. Technical Field

[0003] The present invention relates to a method and apparatus for optical transmission, and in particular to a method and apparatus for calibrating IQ time skew in a coherent transceiver. Background Art

[0004] Coherent optical transceivers (also called coherent transceivers) are used to send and receive optical signals by modulating the amplitude and phase of light transmitted through an optical channel such as an optical cable. For example, data can be encoded using quadrature amplitude modulation (QAM), and polarization multiplexing (PM) can be used to double the transmission capacity. One technique for coherent transmission involves modulating the I and Q phase components of an optical signal using two separate electrical data channels, an in-phase (I) data channel and a quadrature (Q) data channel. In a polarization multiplexing IQ modulator, the I and Q channels are used to modulate signals in each of two orthogonal polarizations: an I channel for an X-polarization signal (usually denoted XI); an I channel for a Y-polarization signal (usually denoted YI); a Q channel for an X-polarization signal (usually denoted XQ); and a Q channel for a Y-polarization signal (usually denoted YQ).

[0005] Time misalignment (also called skew) between the I and Q data channels of the IQ modulators at the transmitter and receiver (also called IQ skew) is an impairment that can degrade the performance of coherent transceivers, especially for high-order modulation formats with high symbol rates. IQ skew causes sampling errors at the receiver that cannot be compensated by the traditional 2x2 multiple-input multiple-output (MIMO) equalizer in the receiver digital signal processor (DSP). This sampling error can cause a significant degradation in the signal-to-noise ratio (SNR). In addition, IQ skew greater than half the symbol duration can cause acquisition failures in the receiver DSP because the error can exceed the capacity of the 2x2 MIMO equalizer.

[0006] After traditional 2x2 MIMO equalization, additional IQ equalization can be used to compensate for IQ skew to some extent. However, the equalization performance may be affected by channel impairments such as polarization mode dispersion (PMD), polarization dependent loss (PDL), and amplified spontaneous emission (ASE) noise.

[0007] Some optical receivers may include a digital signal processor (DSP) (also called a DSP unit) designed to measure IQ skew during factory calibration or transceiver self-calibration. Existing methods estimate the IQ skew at the receiver first and then estimate the IQ skew at the transmitter; however, the estimated IQ skew at the receiver is affected by the presence of IQ skew at the transmitter.

[0008] Therefore, it would be useful to provide methods and apparatus for more accurately calibrating IQ skew (both IQ skew at the receiver and IQ skew at the transmitter). Summary of the invention

[0009] In various examples described herein, methods and apparatus are disclosed that provide factory calibration or self-calibration of in-phase (I) and quadrature (Q) time skew (also referred to as IQ skew) in a coherent transceiver. A receiver-side DSP method is described that enables joint calibration of IQ skew at both the transmitter and receiver without requiring additional hardware.

[0010] The disclosed example uses a single-stage 4x8 MIMO equalizer to jointly estimate the transmitter IQ skew and the receiver IQ skew. The transmitter impairment does not affect the estimate of the receiver skew, and vice versa. The 4x8 MIMO equalizer can directly compensate for the estimated transmitter skew and the estimated receiver skew.

[0011] Additionally, other impairments such as XY skew can be estimated and compensated.

[0012] In some examples, the present invention describes an apparatus comprising a receiver having a processor, the receiver being configured to: receive a measurement signal, the measurement signal being a four-channel signal corresponding to an in-phase (I) and a quadrature (Q) channel of each of two orthogonal polarizations; estimate a carrier frequency offset between the measurement signal and a reference signal; construct a set of inputs for a 4x8 multiple-input multiple-output (MIMO) equalizer implemented by the receiver, the set of inputs being constructed by converting the four-channel signal into four complex inputs, a Q channel signal in the four-channel signal being converted into an imaginary input, each of the four complex inputs having a phase shift corresponding to the estimated carrier frequency offset, the set of inputs comprising the four complex inputs, and also comprising corresponding conjugate copies of the four complex inputs; and using the signals from the 4x8 MIMO outputs of a MIMO equalizer, calculating a set of equalizer coefficients by minimizing an error between the MIMO outputs and the reference signal; using the equalizer coefficients to estimate a receiver IQ skew and a transmitter IQ skew by converting the set of equalizer coefficients from the time domain to the frequency domain to determine a receiver IQ differential phase response and a transmitter IQ differential phase response in the frequency domain, the receiver IQ differential phase response and the transmitter IQ differential phase response indicating corresponding receiver IQ skew and transmitter IQ skew in the time domain; performing skew compensation using the estimated receiver IQ skew and the estimated transmitter IQ skew.

[0013] In some examples, the present invention describes a method comprising: receiving a measurement signal, the measurement signal being a four-channel signal corresponding to an in-phase (I) and a quadrature (Q) channel of each of two orthogonal polarizations; estimating a carrier frequency offset between the measurement signal and a reference signal; constructing a set of inputs for a 4x8 multiple-input multiple-output (MIMO) equalizer implemented by the receiver, the set of inputs being constructed by converting the four-channel signal into four complex inputs, a Q channel signal in the four-channel signal being converted into an imaginary input, each of the four complex inputs having a phase shift corresponding to the estimated carrier frequency offset, the set of inputs including the four complex inputs and also including corresponding conjugate copies of the four complex inputs; using the signals from the 4x8 MIMO outputs of a MIMO equalizer, calculating a set of equalizer coefficients by minimizing an error between the MIMO outputs and the reference signal; using the equalizer coefficients to estimate a receiver IQ skew and a transmitter IQ skew by converting the set of equalizer coefficients from the time domain to the frequency domain to determine a receiver IQ differential phase response and a transmitter IQ differential phase response in the frequency domain, the receiver IQ differential phase response and the transmitter IQ differential phase response indicating corresponding receiver IQ skew and transmitter IQ skew in the time domain; performing skew compensation using the estimated receiver IQ skew and the estimated transmitter IQ skew.

[0014] In some examples, the present invention describes a computer-readable medium having instructions thereon. When the instructions are executed by a processor of a receiver, the receiver: receives a measurement signal, the measurement signal being a four-channel signal corresponding to an in-phase (I) and quadrature (Q) channel of each of two orthogonal polarizations; estimates a carrier frequency offset between the measurement signal and a reference signal; constructs a set of inputs for a 4x8 multiple-input multiple-output (MIMO) equalizer implemented by the receiver, the set of inputs being constructed by converting the four-channel signal into four complex inputs, the Q channel signal in the four-channel signal being converted into an imaginary input, each of the four complex inputs having a phase shift corresponding to the estimated carrier frequency offset, the set of inputs including the four complex inputs, and also including corresponding conjugate copies of the four complex inputs; uses the 4x8 MIMO outputs of a MIMO equalizer, calculating a set of equalizer coefficients by minimizing an error between the MIMO outputs and the reference signal; using the equalizer coefficients to estimate a receiver IQ skew and a transmitter IQ skew by converting the set of equalizer coefficients from the time domain to the frequency domain to determine a receiver IQ differential phase response and a transmitter IQ differential phase response in the frequency domain, the receiver IQ differential phase response and the transmitter IQ differential phase response indicating corresponding receiver IQ skew and transmitter IQ skew in the time domain; performing skew compensation using the estimated receiver IQ skew and the estimated transmitter IQ skew.

[0015] In any of the examples, a least squares algorithm may be used to calculate the set of equalizer coefficients to minimize the error between the MIMO output and the reference signal.

[0016] In any of the examples, an adaptive least mean square algorithm may be used to calculate the set of equalizer coefficients to minimize the error between the MIMO output and the reference signal.

[0017] In any of the examples, the set of inputs can be constructed by the following steps: multiplying the Q channel signal among the four channel signals by an imaginary number j to obtain an imaginary-valued Q channel signal; point-by-point multiplying the real-valued I channel signal and each of the imaginary-valued Q channel signals with a carrier frequency offset phasor generated using the estimated carrier frequency offset to obtain the four complex inputs; and applying a conjugate operation to each of the four complex inputs to obtain the corresponding conjugate replica.

[0018] In any of the examples, the receiver IQ skew and the transmitter IQ skew can be estimated by the following steps: converting the equalizer coefficients from the time domain to the frequency domain; determining the receiver IQ differential phase response and the transmitter IQ differential phase response for each polarization; and using the slope of the corresponding differential phase responses as the estimated receiver IQ skew and the estimated transmitter IQ skew for each polarization.

[0019] In any of the examples, the set of equalizer coefficients may also be used to estimate receiver XY skew and transmitter XY skew, the estimated receiver XY skew and the estimated transmitter XY skew further used to perform skew compensation.

[0020] In any of the examples, the receiver XY skew and the transmitter XY skew may be estimated by converting the equalizer coefficients from the time domain to the frequency domain; determining a receiver XY phase difference and a transmitter XY phase difference; and using the slope of the corresponding phase differences as the estimated receiver XY skew and the estimated transmitter XY skew.

[0021] In any of the examples, performing skew compensation may include sending the estimated transmitter IQ skew to another device.

[0022] In any of the examples, performing skew compensation may include performing real-time equalization using the 4x8 MIMO equalizer. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Reference will now be made, by way of example, to the accompanying drawings which show exemplary embodiments of the present application, in which:

[0024] Figure 1 A schematic diagram showing exemplary in-phase and quadrature modulation;

[0025] Figure 2 shows a block diagram of an exemplary digital coherent receiver in which the examples described herein may be implemented;

[0026] Figure 3 It shows that it can be implemented in Figure 2 A block diagram of an exemplary arrangement of a receiver is shown;

[0027] Figure 4A A block diagram showing some details of an exemplary DSP for estimating IQ skew;

[0028] Figure 4B A block diagram showing some details of an exemplary MIMO input builder;

[0029] Figure 5A flow chart of an exemplary method for estimating and compensating for skew in a coherent transceiver is shown.

[0030] Similar reference numerals may be used in different drawings to represent similar components. DETAILED DESCRIPTION

[0031] In the examples disclosed herein, a method and apparatus for performing in-phase and quadrature (IQ) time skew calibration in a coherent transceiver is described. Figure 1 .

[0032] Figure 1 A schematic diagram of an example of IQ modulation is shown, which can be performed using an electro-optical modulator (EOM) such as an IQ Mach-Zehnder Modulator (IQ-MZM) or other suitable optical modulator. The in-phase (I) channel path 106 is modulated by the analog electrical data I channel 102, and the quadrature (Q) channel path 108 is modulated by the analog electrical data Q channel 104.

[0033] For example, an optical carrier input 122 is received in the form of a laser providing a light source at a specific frequency (e.g., about 193 THz). The optical carrier input 122 is divided into the I channel path 106 and the Q channel path 108 according to optical interferometry techniques. The I path 106 receives an analog electrical signal from the I channel 102, which modulates the I component of the optical carrier signal propagating through the I channel path 106. The Q path 108 receives an analog electrical signal from the Q channel 104, which modulates the Q component of the optical carrier signal propagating through the Q channel path 108. The Q path 108 passes through a phase shifter 110 of about 90°. The optical signal output of the I path 106 and the optical signal output of the Q path 108 are coupled or combined to form an optical signal output 124 (i.e., an optical carrier modulated with data). The signal at the output 124 is an optical quadrature amplitude modulation (QAM) signal, where the descriptor "optical" indicates that the QAM signal is carried by an optical carrier. Since there are two polarizations (X polarization and Y polarization), the signal at the output 124 may also be referred to as a dual-polarized light signal.

[0034] The IQ skew is the relative delay between the data path of the I channel 102 and the data path of the Q channel 104, which can be defined as:

[0035] Δτ IQ =Δτ Q -ΔτI

[0036] Among them, Δτ IQ is the time skew, Δτ Q is the time delay of the I data path, Δτ I is the time delay of the Q data path. The IQ skew is caused by the physical time delay difference between the I channel 102 and the Q channel 104. The time delay in these channels (102, 104) may be caused by defects in physical components, such as: a digital-to-analog converter (DAC) for generating an analog channel from a digital input; a driver for driving the EOM; the EOM itself; and / or printed circuit board (PCB) lines used by the transmitter.

[0037] On the receiver side ( Figure 1 (not shown in the figure), the received optical signal is converted into an electrical signal by an optical coherent receiver to recover the data on the I channel and the Q channel. A digital coherent receiver can be implemented in the receiver. The digital coherent receiver includes an integrated coherent receiver (ICR), an analog-to-digital converter (ADC), and a digital signal processor (DSP) that implements an equalization algorithm. Similar to the transmitter, due to component defects, a time skew is introduced between the I channel and the Q channel. In the present invention, the IQ skew introduced at the transmitter is called transmitter IQ skew, and the IQ skew introduced at the receiver is called receiver IQ skew.

[0038] The time difference between the I channel and the Q channel corresponds to the frequency linear phase shift between the I response and the Q response in the frequency domain. Therefore, the time skew is converted into a linear differential phase (in the frequency domain) response between I and Q. At lower frequencies (e.g., up to 15 GHz), the linear differential phase response can be clearly observed. Typically, the differential phase response is not linear in the higher frequency region, resulting in severe distortion of high baud rate signals. For some high-speed systems, time skew in the order of picoseconds can be a serious problem. In the examples disclosed herein, methods and apparatus are described that can jointly measure the transmitter IQ differential phase response and the receiver IQ differential phase response.

[0039] In some examples, the optical signal can be a dual-polarization optical signal. Four modulation components of the optical signal are modulated using four separate electrical data channels, wherein the four orthogonal channels are an X polarization I channel, an X polarization Q channel, a Y polarization I channel, and a Y polarization Q channel. That is, data is modulated on the I component and the Q component of each of the two orthogonal polarization directions (X and Y) of the optical signal. This technology may be referred to as polarization multiplexed optical modulation. At the receiver, the optical signal is converted back to an electrical signal by an optical coherent receiver and separated into four separate channels, and the data is recovered from the four channels. Typically, the DSP implements a 2x2 multiple-input multiple-output (MIMO) equalizer at the receiver to compensate for any channel impairments. Each polarization has a corresponding IQ skew, so that there is a receiver X polarization IQ skew, a receiver Y polarization IQ skew, a transmitter X polarization IQ skew, and a transmitter Y polarization IQ skew.

[0040] Traditionally, a 2x2 MIMO equalizer separates the X-polarization signal and the Y-polarization signal from each other. However, IQ skew can cause sampling errors at the receiver that cannot be compensated by a traditional 2x2 MIMO equalizer in the receiver DSP. This sampling error can cause a significant degradation in the signal-to-noise ratio (SNR). Likewise, an IQ skew greater than half the symbol duration can cause acquisition failures in the receiver DSP. Previous attempts have been made to calibrate and pre-compensate for IQ skew during factory calibration.

[0041] Some existing calibration schemes are hardware-based. Hardware-based schemes often require additional electronic components and / or bias point IQ phase changes. This can be more difficult to implement because of the physical design changes required. In addition, the operating bias point of the device needs to be changed, which may not be convenient for performing factory calibration or transmitter self-calibration because manual operations or special algorithms are required, and additional time is required for the device to stabilize at the new bias point.

[0042] Some other existing calibration schemes are software-based and implemented in the receiver DSP. The transmitter IQ skew and the estimate of the receiver IQ skew can be calculated at the receiver DSP without adding electrical or optical components. Since the IQ skew usually changes slowly, the calibration can be implemented at the software level, such as on a slower processing device connected to a real-time application-specific integrated circuit (ASIC) DSP chip, or by sending the signal to an external service node in the optical network for calibration. Some existing software-based calibration techniques rely on two-stage skew estimation, that is, the receiver IQ skew is first estimated and compensated, and then the transmitter IQ skew is estimated and compensated. However, it has been found that the transmitter IQ skew estimation and the receiver IQ skew estimation affect each other. In addition, two separate stages are required for estimation and compensation, which requires a long calibration time. This may be a problem when there are a large number of transceivers that need to be calibrated in the factory.

[0043] The exemplary methods and apparatus described herein can jointly estimate the transmitter IQ skew and the receiver IQ skew. The examples described herein can be implemented using a single MIMO equalizer (e.g., a 4x8 MIMO equalizer) implemented in the DSP at the receiver, rather than using a two-stage equalization approach.

[0044] Figure 2 A block diagram of an exemplary receiver 200 in which the examples described herein may be implemented is shown. Specifically, the receiver 200 is a digital coherent receiver that includes an optical front end 210, an optoelectronic interface 220, and a DSP 230.

[0045] The optical front end 210 receives an optical signal through an optical channel (e.g., an optical fiber) and is used to separate the received optical signal into four branches (corresponding to the X polarization and Y polarization of each of the I channel and the Q channel). The optical front end 210 includes a 90° optical hybrid 212 and a local oscillator (LO) 214. The four signals from the optical front end 210 are provided to the optoelectronic interface 220. In the optoelectronic interface 220, a group of balanced photodetectors (BPD) 222 are used to detect each of the four optical signals and convert them into corresponding electrical signals. An analog-to-digital converter (ADC) 224 receives the electrical signal and performs signal sampling and quantization to output a digital signal. Although the output of the ADC 224 is shown as a single arrow, it should be understood that the output of the ADC 224 includes four digital signals corresponding to the four channels.

[0046] The digitized signal from the ADC 224 is input to the DSP 230. For example, the DSP 230 can be implemented using a customized ASIC chip. The DSP 230 implements an algorithm to compensate for impairments introduced into the signal, including compensating for the IQ skew. Specifically, as discussed further below, the DSP 230 described in the present invention implements a 4x8 MIMO equalizer in ASIC or software, which enables joint estimation of the transmitter IQ skew and the receiver IQ skew.

[0047] Figure 3 A block diagram of an exemplary device 300 in which the receiver 200 may be implemented is shown. For example, the device 300 may be an electronic device, such as a server, a computing system, an access point (AP), a terminal device, etc. The device 300 is capable of optical communication and may optionally also have wireless communication capabilities. Other communication devices suitable for implementing the examples described in the present invention may be used, which may include components different from those discussed below. Although Figure 3 A single instance of each component is shown, but there may be multiple instances of each component in the apparatus 300, and the apparatus 300 may be implemented using a parallel and / or distributed architecture.

[0048] In this example, the apparatus 300 may include one or more processing devices 302, such as a processor, a microprocessor, an ASIC, a field-programmable gate array (FPGA), a dedicated logic circuit, or a combination thereof. In addition, the apparatus 300 may also include one or more optional input / output (I / O) interfaces 304, which may be connected to one or more optional input devices 312 and / or output devices 314. The apparatus 300 includes one or more network interfaces 306, which include the receiver 200 for receiving optical signals. In addition, the one or more network interfaces 306 may also include a transmitter (not shown) for sending optical signals. The receiver 200 and the transmitter may be implemented by an optical coherent transceiver.

[0049] Alternatively, if the device 300 has both optical and wireless communication capabilities, the device 300 may include one or more antennas 316 to enable wireless communication. In this example, one antenna 316 is shown, which may be used for both the transmitter and the receiver. However, in other examples, there may be multiple antennas for transmission and reception. In examples where the device 300 does not have wireless communication capabilities, the one or more antennas 316 may be omitted.

[0050] The device 300 includes one or more storage units 308, which may include a large-capacity storage unit, such as a solid-state hard disk, a hard disk drive, a magnetic disk drive, and / or an optical disk drive. In addition, the device 300 also includes one or more memories 310, which may include volatile or non-volatile memory (e.g., flash memory, random access memory (RAM) and / or read-only memory (ROM)). The one or more non-transient memories 310 (and the storage unit 308) can store instructions for execution by the one or more processing devices 302. The one or more memories 310 may include software instructions, such as software instructions for implementing an operating system (OS) and other applications / functions. In some examples, instructions may also be provided by an external memory (e.g., an external drive that performs wired or wireless communication with the device 300), or may be provided by a transient or non-transient computer-readable medium. Examples of the non-transitory computer readable medium include RAM, ROM, erasable programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), flash memory, CD-ROM, or other portable memory.

[0051] The one or more optional input devices 312 (e.g., a keyboard, a mouse, a microphone, a touch screen, and / or keys) and the one or more optional output devices 314 (e.g., a display, a speaker, and / or a printer) are shown as external devices to the apparatus 300 and connected to the optional I / O interface 304. In other examples, one or more of the one or more input devices 312 and / or the one or more output devices 314 may be included as a component of the apparatus 300.

[0052] As described above, the present invention describes an example for jointly estimating and calibrating the transmitter IQ skew and the receiver IQ skew using a 4x8 MIMO equalizer implemented in the receiver DSP. Specifically, the 4x8 MIMO equalizer can be implemented as a 4x8 MIMO finite impulse response (FIR) filter. The coefficients of the MIMO equalizer (also called filter taps) enable the calculation of the transmitter IQ skew and the receiver IQ skew, or more generally, enable the calculation of the transmitter IQ differential phase response and the receiver IQ differential phase response. In the skew estimation technique disclosed herein, transmitter impairments and receiver impairments do not affect each other. The disclosed 4x8 equalizer-based calibration can be integrated on a real-time chip or in calibration software for in-service calibration without the need for additional optical or electrical equipment.

[0053] Figure 4A A block diagram illustrating an example of performing skew calibration using a 4x8 MIMO equalizer in an optical coherent transceiver. Figure 4A The calibration shown can be performed during factory setup, for example, using a simulator and / or test equipment to simulate / generate impairment effects. The factory calibration starts with a 4-channel measurement signal. The overall channel from the 4-channel transmission signal to the 4-channel measurement signal is simplified to have only three ordered blocks, namely the transmitter skew 404, other optical impairments 406 and the receiver skew 408, which in practice represent the coherent transmitter, the optical channel (fiber) and the coherent receiver respectively.

[0054] It is known that a 4-channel transmission signal (which is an electrical signal) is used as a reference signal (ie, a target signal for optimizing the equalizer). The four transmission channels can be represented as i x ,q x 、i y ,q y , each of the transmit channels is a time series at the DSP rate. These transmit channels can be represented by vectors as follows:

[0055]

[0056] The transmitted signal may experience transmitter skew 404, other impairments 406, and receiver skew 408. The transmitter skew 404 and the receiver skew 408 may be introduced by the actual physical components of the optical coherent transceiver. It can be assumed that the time skew is non-zero. Other impairments 406 include impairments other than IQ skew, such as local oscillator frequency offset (LOFO), phase noise (PN), polarization-dependent loss (PDL), polarization mode dispersion (PMD), amplified spontaneous emission (ASE), and other channel impairments. For example, the channel impairment effect can be simulated or created using test equipment. The 4-channel signal (which is an electrical signal) measured by the receiver is received in the DSP 230. The measured signal can be represented as r' XI 、r' XQ 、r' YI 、r' YQ , where the prime number symbol represents the measurement quantity (ie, the real captured data). Each of the measurement channels is also a time series acquired from the ADC 224 in the coherent receiver 200. The measurement signal can be represented by a vector as follows:

[0057]

[0058] Figure 4A The DSP 230 is shown implementing various exemplary software modules, such as frequency offset estimation 232, MIMO input constructor 234, 4x8 MIMO equalizer 236, and equalizer coefficient calculator 238. It should be understood that although shown as separate blocks for ease of understanding, it should be understood that the functionality of these modules may be implemented by the DSP 230 as a single set of instructions.

[0059] At the DSP 230, the measurement signal is input to a frequency offset estimation 232, which estimates the carrier frequency offset between the transmitter and the receiver. The carrier frequency offset may be estimated using various suitable techniques, such as using techniques based on fast Fourier transform (FFT). The estimated carrier frequency offset may be expressed as

[0060] The estimated carrier frequency offset and the measured signal are input to the MIMO input constructor 234, which constructs eight inputs for the 4x8 MIMO equalizer 236 (e.g., 4x8 MIMO-FIR filter) by adding conjugate replicas. At the MIMO input constructor 234, four real-valued time series inputs (r' XI 、r' XQ 、r' YI 、r' YQ ) and the phasor Point-by-point multiplication, the phasor is a complex-valued time series based on the estimated carrier frequency offset. XQ and r' YQ The MIMO input constructor 234 constructs the input of the 4×8 MIMO equalizer 236 using the obtained four complex-valued time series and their corresponding conjugate copies.

[0061] Figure 4B FIG. 2 shows an exemplary implementation of the MIMO input constructor 234. Figure 4B As shown, each channel of the measurement signal is received as a corresponding input. The four inputs are converted to complex inputs by multiplying the carrier frequency offset phasor of each of the four inputs (using the estimated carrier frequency offset from the frequency offset estimation 232). In addition, the X polarization Q channel input and the Y polarization Q channel input are multiplied by the imaginary number. A conjugate copy is generated for each of the four complex inputs using a conj() operation to obtain a set of eight inputs provided to the 4x8 MIMO equalizer 236.

[0062] These eight time series inputs can be expressed as Where j=1, 2, ..., 8 (not to be confused with the imaginary number j). The input of the 4x8 MIMO equalizer 236 can be expressed as follows:

[0063]

[0064] The symbol "⊙" represents a point-by-point multiplication operation between two vectors of the same length. The eight inputs are input into the 4x8 MIMO equalizer 236, which can be represented as the following 4x8 coefficient matrix:

[0065]

[0066] After filtering in the time domain, the output of the 4x8 MIMO equalizer 236 is four real-valued time series. The filtering can be expressed as:

[0067]

[0068] Wherein, * represents the convolution operation in the time domain, c ij is the time domain coefficient (also called filter tap) between the i-th output and the j-th input, where i = 1, 2, 3, 4, j = 1, 2, ..., 8, i' x ,q' x 、i' y ,q' y is the real-valued time series output by the 4x8 MIMO equalizer 236. It should be noted that each coefficient c ij is actually a vector of n taps, where n is a user-defined hyperparameter (e.g., chosen according to the actual implementation in ASIC or software).

[0069] The MIMO output and a known reference signal (i.e., a known transmitted signal) are input to the equalizer coefficient calculator 238 to calculate the coefficients of the 4x8 MIMO equalizer 236. The coefficients are optimized by minimizing the mean square error between the MIMO output and the known reference signal, which is mathematically written as:

[0070]

[0071] The equalizer coefficient calculator 238 may use a variety of techniques to perform the calculation, including a least-square (LS) technique (e.g., using matrix inversion) or a least-mean-square (LMS) technique, etc. The LS technique may be suitable for implementation during factory calibration. For example, the LMS technique may be suitable for implementation during self-calibration or in-service monitoring.

[0072] An exemplary calculation of the coefficients is now described. The error between the MIMO output and the known reference signal can be expressed as:

[0073] e XI [t] = i x [t]-i′ x [t]

[0074] e XQ [t] = q x [t]-q′ x [t]

[0075] e YI [t] = i y [t]-i′ y [t]

[0076] e YQ [t] = q y[t]-q′ y [t]

[0077] Where t is the time index, e XI 、e XQ 、e YI 、e YQ is the error in the corresponding XI, XQ, YI and YQ channels, i x [t], q x [t]、i y [t], q y [t] is the training time series in training mode (e.g., during calibration) or the decision time series in tracking mode (e.g., for real-time equalization, or for calibration in an ASIC-DSP using adaptive LMS). All the above quantities are scalars.

[0078] It should be noted that in examples where the frequency drift is fast (e.g., due to random laser phase noise), the estimated carrier frequency offset (from the frequency offset estimation 232) may not fully reflect the dynamics of the frequency drift (because the frequency offset estimation 232 is intended to estimate the carrier frequency offset, which is typically slow relative to the symbol rate of the DSP), in which case the frequency dynamics can be considered as phase noise. This phase noise can be estimated by a carrier phase recovery algorithm (not shown).

[0079] The estimated carrier phase can be expressed as In this case, the error of the 4x8 MIMO equalizer 236 can be expressed as:

[0080]

[0081] As mentioned before, each coefficient c ij is an n-tap filter, which can be expressed as:

[0082]

[0083] The coefficient c at time t ij The n taps can be expressed in vectorized form as:

[0084]

[0085] The eight time series inputs of the 4x8 MIMO equalizer 236 can be expressed as in can represent the jth input at time t, where j = 1, 2, ..., 8. For example, It can be expressed as:

[0086]

[0087] The equalizer coefficient calculator 238 may use the following updates to implement an adaptive LMS algorithm for real-time DSP implementations:

[0088]

[0089]

[0090] Wherein, μ is the LMS step size, which can be selected to control the convergence speed. After convergence, the equalizer coefficient calculator 238 outputs a set of 4x8 coefficients c implemented by the 4x8 MIMO equalizer 236. ij . Output the set of 4x8 coefficients c ij , so that the transmitter IQ skew and the receiver IQ skew can be determined in the frequency domain. As mentioned above, the time shift in the time domain is converted to a linear phase shift in the frequency domain, which can be calculated as the differential phase response between I and Q. Therefore, the 4x8 coefficients c of the calculation can be used ij Calculations in the frequency domain (described below) are performed to estimate the IQ skew in the transmitter and the receiver. Using the equalizer coefficients output from the DSP 230, the calculations may be performed by another processing device of the apparatus 300 in which the receiver 200 is implemented (e.g., a slower processing device (not shown) external to the DSP 230) to estimate the IQ skew. In some examples, the estimation of the IQ skew may be performed by the DSP 230 itself. The estimated IQ skew may then be used to compensate for the IQ skew using a suitable technique (e.g., by adding a corresponding phase shift to the sampling clock at the ADC 224).

[0091] In the following equation, C ij (capital, indicating frequency domain) represents the equalizer coefficient c ij (lowercase, indicating time domain) is a fast Fourier transform (FFT). In the following equations, the symbol * is used to represent the conjugate of a complex quantity; the operation "arg" extracts the complex argument (i.e., angel). It should be noted that if the output of "arg" changes abruptly by + / –π, the "unwrap" function needs to be used to correct for this abrupt change.

[0092] To determine the transmitter IQ skew, the transmitter IQ differential phase response (expressed as) for the X polarization can be first estimated by performing the following calculation ) and the transmitter IQ differential phase response for Y polarization (expressed as ):

[0093]

[0094] The transmitter IQ skew (denoted as τ) for the X polarization can then be estimated by performing the following calculation: X,Tx ) and the transmitter IQ skew for Y polarization (denoted as τ Y,Tx ):

[0095]

[0096] It should be noted that although the above equation indicates that the derivative of the differential phase response has been calculated, in actual implementations, the differential phase response may not be completely linear in frequency. Therefore, the slope of a linear fit of the differential phase response may be used instead of the calculated derivative. For example, the slope of the linear fit of the differential phase response may take a value between -Baud / 2 and Baud / 2, divided by 2π (or over the product DSP bandwidth). The same applies to other calculations disclosed herein that use the derivative of the differential phase response.

[0097] To determine the receiver IQ skew, the receiver IQ differential phase response (expressed as) for the X polarization may be first estimated by performing the following calculation: ) and the receiver IQ differential phase response for Y polarization (expressed as ):

[0098]

[0099] The receiver IQ skew (denoted as τ) for the X polarization can then be estimated by performing the following calculation: X,Rx ) and the receiver IQ skew for Y polarization (denoted as τ Y,Rx ):

[0100]

[0101] Using the estimated transmitter IQ skew and the receiver IQ skew, calibration may be performed on the transceiver to compensate for the estimated skew. For example, the estimated skew of each of the four channels (XI, XQ, YI, and YQ) may be compensated by offsetting the sampling clock at the ADC 224 of the receiver 200 by a corresponding amount. The calibration may be a factory calibration (e.g., before commissioning the transceiver for actual use).

[0102] In some examples, the estimated IQ skew can be used to perform remote calibration on the transmitter. For example, a reference signal known to the transmitting device and the receiving device can be sent from the transmitting device to the receiving device. After the receiving device estimates the transmitter IQ skew (as described above), the receiving device can send the estimated transmitter IQ skew (e.g., as a control signal or as a data packet) to the transmitting device to enable the transmitting device to calibrate itself.

[0103] In some examples, the estimated IQ skew can be used to perform in-service monitoring of the channel. For example, a slower processing device separate from the DSP 230 can be used to estimate slowly varying skew (because channel characteristics are expected to change slowly and be relatively static). In another example, the DSP 230 can perform such monitoring for slowly varying skew.

[0104] It should be noted that the calculated coefficients of the 4x8 MIMO equalizer provide information about the full IQ differential phase response of the transmitter and the receiver, and can also be used to estimate other impairments in addition to estimating IQ skew. For example, the differential phase information provided by the coefficients also enables the calculation of the skew (also referred to as XY skew) between the X polarization and the Y polarization. For example, due to PMD effects, the XY skew can be introduced at the transmitter and the receiver.

[0105] Any skew between the four channels (XI, XQ, YI, and YQ) can be estimated using the following equations. In the following equations, subscripts 1, 2, 3, and 4 represent XI, XQ, YI, and YQ, respectively. Any channel skew at the transmitter and the receiver can be estimated using the following phase difference:

[0106]

[0107] Then, the channel skew at the transmitter (denoted as τ) can be ji,Tx ) and the channel skew at the receiver (denoted as τ ji,Rx ) is estimated to be:

[0108]

[0109] The XY skew at the transmitter and the receiver can be estimated using the following phase difference:

[0110]

[0111]

[0112] The XY deflection at the transmitter (denoted as τ) can then beYX,Tx ) and the XY skew at the receiver (denoted as τ YX,Rx ) is estimated to be:

[0113]

[0114] Such calculations may be performed by another processing device external to the DSP 230 to calibrate the transceiver for the transmitter skew and the receiver skew. For example, such calculations may be performed during factory calibration, and the estimated XY skew at the transmitter and the receiver may be compensated in the transmitter DSP and the receiver DSP, respectively (e.g., by adjusting electrical filter phase response and / or other parameters).

[0115] In some examples, the DSP 230 can be implemented using a real-time ASIC-DSP for real-time estimation of transmitter skew and receiver skew, and for equalizing any linear impairments such as IQ crosstalk, IQ skew, XY skew, gain imbalance, and quadrature phase error.

[0116] Figure 5 An exemplary method 500 for estimating and compensating for skew in a coherent transceiver is shown, which can be performed using the 4x8 MIMO equalizer 236 implemented by the DSP 230. In some examples, some steps of the method 500 can also be performed using a slower processing unit external to the DSP 230. As described above, the method 500 can be used for factory calibration, remote calibration, self-calibration, and / or in-service monitoring. For example, during factory calibration (before the transceiver is deployed for use), the method 500 can be used to calibrate the transceiver (e.g., using a combination of the DSP 230 and an external desktop computing system). After the transceiver has been deployed for use, the method 500 can be implemented by the transceiver itself (e.g., using a combination of the DSP 230 and a slower processor of the transceiver) to calibrate its own impairments. In a coherent transceiver, the transmitter and the receiver are implemented at the same module, so self-calibration can be achieved.

[0117] In 502, a measurement signal is acquired at the DSP 230 of the receiver. For in-service applications, the measurement signal is a digital electrical signal that is the result of detecting and converting an optical signal received by the receiver through an optical channel (corresponding to a known electrical reference signal from a transmitter). For factory calibration, the measurement signal is a digital electrical signal that is the result of detecting and converting an optical signal received by the receiver through a short optical fiber (corresponding to a known electrical reference signal from a transmitter). Typically, the measurement signal is a four-channel signal (r' XI 、r'XQ 、r' YI 、r' YQ ), which contains the information of the transmitted XI, XQ, YI, and YQ channels.

[0118] In 504, a carrier frequency offset between the measurement signal and a reference signal is estimated. The carrier frequency offset may be estimated using various suitable techniques, such as using a FFT-based technique.

[0119] In 506, the inputs of the 4x8 MIMO equalizer 236 are constructed. Constructing eight inputs involves converting the four channels of the measured signal into four complex inputs (wherein the X polarization and Y polarization signals on the I channel are real inputs, and the X polarization and Y polarization signals on the Q channel are converted into imaginary inputs), each of the eight inputs having a phase shift corresponding to the estimated carrier frequency offset. Then, a corresponding conjugate replica is generated for each of the four complex inputs. Then, the eight inputs are provided to the 4x8 MIMO equalizer.

[0120] In 508, equalizer coefficients are calculated to minimize the error between the MIMO output and the known reference signal. Various optimization techniques may be used. For example, an adaptive LMS technique may be used in multiple iterations until convergence. The calculated equalizer coefficients are then output for estimating skew.

[0121] In 510, the transmitter IQ skew and the receiver IQ skew are estimated using the equalizer coefficients. The skew estimation may be performed by the DSP 230 or by another processing device external to the DSP 230. The IQ skew estimation involves converting the time domain equalizer coefficients to frequency domain equalizer coefficients (e.g., using an FFT). A differential phase response is determined at each of the receiver and the transmitter (and for each polarization), and the slope of the corresponding differential phase response is used as an estimate of the corresponding IQ skew at each of the receiver and the transmitter (and for each polarization). The calculations for estimating the IQ skew may be performed according to the above equations.

[0122] Optionally, in 512, the equalizer coefficients may be used to estimate other channel skews, such as XY skew. Frequency domain equalizer coefficients (e.g., converted from time domain equalizer coefficients in 510 above) may be used to estimate other channel skews. A phase difference between channels may be determined, and the slope of the phase difference may be used as an estimate of the corresponding channel skew. Calculations for estimating channel skews (including XY skew) may be performed according to the above equations.

[0123] In 514, skew compensation is performed using the estimates calculated in 510 and (optionally) in 512. For example, skew compensation may be performed by adjusting the phase of the sampling clock at the ADC. For full compensation, the IQ differential phase response may be compensated at the expense of higher computational cost. For remote calibration, transmitter skew compensation may be performed by sending information about the estimated transmitter skew from the receiver back to the transmitter to enable the transmitter to achieve a corresponding phase shift in its channel.

[0124] As previously described, the method 500 may be implemented for performing factory calibration on an optical coherent transceiver, performing self-calibration on the transceiver, and / or performing real-time equalization on a receiver module within the transceiver. For example, the method 500 may be implemented entirely by the ASIC-DSP of the receiver (e.g., for performing real-time equalization or self-calibration on the transceiver). The method 500 may also be implemented by the ASIC-DSP of the receiver together with a slower processor of the receiver, the slower processor being communicatively coupled to the ASIC-DSP (e.g., for performing self-calibration on the transceiver). The method 500 may also be implemented by the ASIC-DSP running under the control of an external processor (e.g., a central processing unit (CPU) of a desktop computing system that sends data to and from the ASIC-DSP) (e.g., for performing factory calibration). It should be understood that the method 500 may also be implemented in other scenarios (e.g., remote calibration of a transmitter).

[0125] In various examples, the present disclosure describes the use of a single-stage 4x8 MIMO equalizer (e.g., implemented as a 4x8 MIMO-FIR filter) to jointly estimate the transmitter IQ differential phase response and the receiver IQ differential phase response (and therefore the transmitter IQ skew and the receiver IQ skew). The transmitter impairments do not affect the estimate of the receiver skew, and vice versa.

[0126] Examples described herein enable a set of 4x8 equalizer coefficients to be used to estimate IQ skew as well as other channel skews (e.g., XY skew), thereby enabling the 4x8 MIMO equalizer to directly compensate for transmitter skew and receiver skew. Since the channel skew can be directly estimated from the phase response, the disclosed examples can be robust to optical polarization rotation, IQ phase error, and IQ gain imbalance (e.g., the skew estimate may not be affected by the presence of such impairments).

[0127] The examples described herein can be implemented to perform real-time equalization (e.g., on an ASIC-DSP chip) to compensate for linear impairments such as IQ crosstalk, IQ quadrature phase error, IQ gain imbalance, and IQ skew. The examples described herein can also be implemented in calibration software to perform factory calibration, remote transmitter calibration, or in-service calibration of transmitter skew and receiver skew (including IQ skew, XY skew, and IQ differential phase response).

[0128] The examples described herein can be implemented in a single-stage 4x8 MIMO equalizer implemented in the DSP (rather than requiring two stages as in some other existing solutions), which can provide a faster, more efficient solution for calibrating IQ skew in coherent transceivers. Being able to implement the disclosed examples in a DSP (without requiring additional hardware components) can make implementation relatively simple and low cost.

[0129] Although the present invention describes the method and process in a specific order, one or more steps of the method and process may be omitted or modified as appropriate. One or more steps may be performed in sequence, but not in the order described (as appropriate).

[0130] Although the present invention has been described, at least in part, in terms of methods, it will be understood by those of ordinary skill in the art that the present invention also relates to various components for performing at least some aspects and features of the described methods by hardware components, software, or any combination of the two. Accordingly, the technical solution of the present invention may be embodied in the form of a software product. Suitable software products may be stored in a pre-recorded storage device or other similar non-volatile or non-transient computer-readable medium, including, for example, a DVD, CD-ROM, USB flash drive, removable hard disk, or other storage medium. The software product includes instructions tangibly stored thereon that enable a processing device (e.g., a personal computer, a server, or a network device) to execute examples of the methods disclosed herein.

[0131] The present invention may be embodied in other specific forms without departing from the subject matter of the claims. The described exemplary embodiments are merely illustrative and not restrictive in all respects. Selected features from one or more of the above embodiments may be combined to create alternative embodiments not explicitly described, and it is understood that features suitable for such combinations are within the scope of the present invention.

[0132] All values ​​and sub-ranges within the disclosed range are also disclosed. In addition, although the systems, devices and processes disclosed and shown herein may include a specific number of elements / assemblies, the systems, devices and assemblies may be modified to include more or less elements / assemblies in such elements / assemblies. For example, although any disclosed element / assembly may be cited as a singular, the embodiments disclosed herein may be modified to include a plurality of such elements / assemblies. The subject matter described herein is intended to cover and encompass all appropriate technical changes.

Claims

1. A device for optical transmission, characterized in that: A receiver having a processor is included, the receiver being configured to: receiving a measurement signal, the measurement signal being a four-channel signal corresponding to an in-phase (I) and a quadrature (Q) channel for each of two orthogonal polarizations; estimating a carrier frequency offset between the measurement signal and a reference signal; constructing a set of inputs for a 4x8 multiple-input multiple-output (MIMO) equalizer implemented by the receiver, the set of inputs being constructed by converting the four-channel signal into four complex inputs, a Q-channel signal of the four-channel signal being converted into an imaginary input, each of the four complex inputs having a phase shift corresponding to the estimated carrier frequency offset, the set of inputs including the four complex inputs and also including corresponding conjugate copies of the four complex inputs; using a MIMO output from the 4x8 MIMO equalizer, calculating a set of equalizer coefficients by minimizing an error between the MIMO output and the reference signal; estimating a receiver IQ skew and a transmitter IQ skew using the equalizer coefficients by converting the set of equalizer coefficients from the time domain to the frequency domain to determine a receiver IQ differential phase response and a transmitter IQ differential phase response in the frequency domain, the receiver IQ differential phase response and the transmitter IQ differential phase response indicating respective receiver IQ skew and transmitter IQ skew in the time domain; Skew compensation is performed using the estimated receiver IQ skew and the estimated transmitter IQ skew.

2. The device according to claim 1, characterized in that The set of equalizer coefficients is calculated using a least squares algorithm to minimize the error between the MIMO output and the reference signal.

3. The device according to claim 1, characterized in that The set of equalizer coefficients is calculated using an adaptive least mean square algorithm to minimize the error between the MIMO output and the reference signal.

4. The device according to claim 1, characterized in that The set of inputs is constructed by the following steps: Multiplying the Q channel signal among the four channel signals by an imaginary number j to obtain an imaginary-valued Q channel signal; multiplying each of the real-valued I channel signal and the imaginary-valued Q channel signal point-by-point by a carrier frequency offset phasor generated using the estimated carrier frequency offset to obtain the four complex inputs; A conjugate operation is applied to each of the four complex inputs to obtain the corresponding conjugate replica.

5. The device according to claim 1, characterized in that The receiver IQ skew and the transmitter IQ skew are estimated by the following steps: converting the equalizer coefficients from the time domain to the frequency domain; determining the receiver IQ differential phase response and the transmitter IQ differential phase response for each polarization; The slopes of the corresponding differential phase responses are used as the estimated receiver IQ skew and the estimated transmitter IQ skew for each polarization.

6. The device according to claim 1, characterized in that The set of equalizer coefficients is further used to estimate receiver XY skew and transmitter XY skew, and the estimated receiver XY skew and the estimated transmitter XY skew are further used to perform skew compensation.

7. The device according to claim 6, characterized in that The receiver XY skew and the transmitter XY skew are estimated by the following steps: converting the equalizer coefficients from the time domain to the frequency domain; Determine the receiver XY phase difference and the transmitter XY phase difference; The slope of the corresponding phase difference is used as the estimated receiver XY skew and the estimated transmitter XY skew.

8. The device according to claim 1, characterized in that Performing skew compensation involves: The estimated transmitter IQ skew is sent to another device.

9. The device according to claim 1, characterized in that Performing skew compensation includes performing real-time equalization using the 4x8 MIMO equalizer.

10. A method for optical transmission, characterized in that include: receiving a measurement signal, the measurement signal being a four-channel signal corresponding to an in-phase (I) and a quadrature (Q) channel for each of two orthogonal polarizations; estimating a carrier frequency offset between the measurement signal and a reference signal; constructing a set of inputs for a 4x8 multiple-input multiple-output (MIMO) equalizer implemented in a receiver, the set of inputs being constructed by converting the four-channel signal into four complex inputs, a Q-channel signal of the four-channel signal being converted into an imaginary input, each of the four complex inputs having a phase shift corresponding to the estimated carrier frequency offset, the set of inputs including the four complex inputs, and also including corresponding conjugate copies of the four complex inputs; using a MIMO output from the 4x8 MIMO equalizer, calculating a set of equalizer coefficients by minimizing an error between the MIMO output and the reference signal; estimating a receiver IQ skew and a transmitter IQ skew using the equalizer coefficients by converting the set of equalizer coefficients from the time domain to the frequency domain to determine a receiver IQ differential phase response and a transmitter IQ differential phase response in the frequency domain, the receiver IQ differential phase response and the transmitter IQ differential phase response indicating respective receiver IQ skew and transmitter IQ skew in the time domain; Skew compensation is performed using the estimated receiver IQ skew and the estimated transmitter IQ skew.

11. The method according to claim 10, characterized in that The set of equalizer coefficients is calculated using a least squares algorithm to minimize the error between the MIMO output and the reference signal.

12. The method according to claim 10, characterized in that The set of equalizer coefficients is calculated using an adaptive least mean square algorithm to minimize the error between the MIMO output and the reference signal.

13. The method according to claim 10, characterized in that The set of inputs is constructed by the following steps: Multiplying the Q channel signal among the four channel signals by an imaginary number j to obtain an imaginary-valued Q channel signal; multiplying each of the real-valued I channel signal and the imaginary-valued Q channel signal point-by-point by a carrier frequency offset phasor generated using the estimated carrier frequency offset to obtain the four complex inputs; A conjugate operation is applied to each of the four complex inputs to obtain the corresponding conjugate replica.

14. The method according to claim 10, characterized in that The receiver IQ skew and the transmitter IQ skew are estimated by the following steps: converting the equalizer coefficients from the time domain to the frequency domain; determining the receiver IQ differential phase response and the transmitter IQ differential phase response for each polarization; The slopes of the corresponding differential phase responses are used as the estimated receiver IQ skew and the estimated transmitter IQ skew for each polarization.

15. The method according to claim 10, characterized in that The set of equalizer coefficients is further used to estimate receiver XY skew and transmitter XY skew, and the estimated receiver XY skew and the estimated transmitter XY skew are further used to perform skew compensation.

16. The method according to claim 15, characterized in that The receiver XY skew and the transmitter XY skew are estimated by the following steps: converting the equalizer coefficients from the time domain to the frequency domain; Determine the receiver XY phase difference and the transmitter XY phase difference; The slopes of the corresponding phase differences are used as the estimated receiver XY skew and the estimated transmitter XY skew.

17. The method according to claim 10, characterized in that Performing skew compensation involves: The estimated transmitter IQ skew is sent to another device.

18. The method according to claim 10, characterized in that Performing skew compensation includes performing real-time equalization using the 4x8 MIMO equalizer.

19. A computer readable medium having instructions thereon, characterized in that: The instructions, when executed by a processor of a receiver, cause the receiver to: receiving a measurement signal, the measurement signal being a four-channel signal corresponding to an in-phase (I) and a quadrature (Q) channel for each of two orthogonal polarizations; estimating a carrier frequency offset between the measurement signal and a reference signal; constructing a set of inputs for a 4x8 multiple-input multiple-output (MIMO) equalizer implemented by the receiver, the set of inputs being constructed by converting the four-channel signal into four complex inputs, a Q-channel signal of the four-channel signal being converted into an imaginary input, each of the four complex inputs having a phase shift corresponding to the estimated carrier frequency offset, the set of inputs including the four complex inputs and also including corresponding conjugate copies of the four complex inputs; using a MIMO output from the 4x8 MIMO equalizer, calculating a set of equalizer coefficients by minimizing an error between the MIMO output and the reference signal; estimating a receiver IQ skew and a transmitter IQ skew using the equalizer coefficients by converting the set of equalizer coefficients from the time domain to the frequency domain to determine a receiver IQ differential phase response and a transmitter IQ differential phase response in the frequency domain, the receiver IQ differential phase response and the transmitter IQ differential phase response indicating respective receiver IQ skew and transmitter IQ skew in the time domain; Skew compensation is performed using the estimated receiver IQ skew and the estimated transmitter IQ skew.

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