A method for recovering a direct current component of a Kramers-Kronig receiver

Abstract

The application discloses a DC component recovery method of a Kramers-Kronig receiver and relates to the technical field of optical communication; the DC component recovery method of the application firstly obtains a relational expression between photoelectric current and optical carrier power and signal average power through derivation, simultaneously defines a correction coefficient to correct the error of the expression, and then utilizes a calculation formula of a carrier signal power ratio (CSPR) to respectively derive calculation formulas of estimated optical carrier power and signal average power, so that the size of the filtered DC component value when AC coupling photoelectric detection is estimated; the method of the application can well recover the required DC component value in the KK receiver, and has a very small estimation error compared with the correct value.

Description

Technical Field

[0001] This invention relates to the field of optical communication technology, and more specifically, to a method for recovering the DC component of a Kramers-Kronig receiver. Background Technology

[0002] The Kramers-Kronig (KK) receiver, a recently proposed efficient detection scheme suitable for short-range transmission scenarios, can recover the complex electric field of the optical signal from intensity information through digital signal processing (DSP). This receiver not only detects optical single-sideband (SSB) signals, eliminating the effects of signal beat frequency interference (SSBI), but also supports the use of electrical domain equalization techniques to fully compensate for signal quality degradation caused by linear transmission impairments (such as fiber dispersion). The KK receiver has attracted widespread attention because it can recover complex signals using a single photodetector (PD) with a relatively small required CSPR (current-to-frequency response).

[0003] Currently, a common method for DC component estimation in KK receivers is the DC scanning method, which attempts all possible values ​​of the DC component while measuring system performance (such as bit error rate BER or error vector magnitude EVM). However, this search method not only requires a demodulation process but also consumes significant time and power to measure such performance metrics. Therefore, this method is rarely used in KK receiver implementations. Another common method first guesses the lost DC component, checks consistency by comparing the CSPR obtained from the reconstructed signal with the known CSPR of the transmitted signal, and finally updates it for DC recovery. Therefore, this DC component recovery method requires not only iterative computation of the KK algorithm but also a CSPR value. More importantly, it only has good accuracy when the CSPR is high (e.g., >10 dB). Summary of the Invention

[0004] To address the shortcomings of existing technologies, the purpose of this invention is to achieve accurate estimation and recovery of the DC component of a KK receiver after using AC-coupled photoelectric detection.

[0005] To achieve the above objectives, this invention provides a method for recovering the DC component of a KK receiver, which can accurately estimate and recover the DC component after the DC component has been filtered out by AC-coupled photoelectric detection.

[0006] In an optional embodiment, a method for recovering the DC component of a KK receiver includes the following steps:

[0007] The DC component filtered out by AC-coupled photodetector (AC-PD) in the KK receiver mainly consists of two parts: the optical carrier power at the carrier beat frequency and the average signal power at the signal beat frequency. The relationship between photocurrent, optical carrier power, and average signal power is derived, and a correction coefficient is defined to correct the error in this equation. Then, using the formula for calculating the carrier-signal power ratio (CSPR), the formulas for estimating the optical carrier power and average signal power can be derived, thereby estimating the magnitude of the DC component filtered out by AC-coupled photodetector.

[0008] The DC component recovery method for the KK receiver according to claim 1 is characterized by deriving the relationship between the photocurrent, optical carrier power, and average signal power after AC-coupled photodetector (AC-PD), and defining a correction coefficient to correct the error in this equation:

[0009] 2 AC (t)>≈2P c <P S (t)>+α· <P S (t)> 2

[0010] Among them, I AC (t) represents the photocurrent after the detection signal passes through an AC-coupled photodetector, P c =|E0| 2 The optical carrier power for the carrier beat frequency, <P s (t)>=|E s (t)| 2 The signal beat frequency is the average power of the signal, <·> is the averaging operator, and α is the correction coefficient, which ranges from 0 to 1.

[0011] The DC component recovery method for the KK receiver according to claim 1 is characterized by utilizing the following formula for calculating the carrier signal power ratio (CSPR):

[0012]

[0013] Combined with photocurrent I AC (t) and optical carrier power P c and the average power of the signal <P S The relationship between (t) and the estimated value of optical carrier power P c It can be calculated using the following formula:

[0014]

[0015] Similarly, the average power of the signal <P S (t)> can also be estimated by the following formula: ​

[0016]

[0017] The DC component recovery method for the KK receiver according to claim 1 is characterized in that, after obtaining the calculation formulas for the optical carrier power and the average signal power, the magnitude of the DC component filtered out by the AC-coupled photodetector (AC-PD) can be directly estimated:

[0018]

[0019] Among them, DC est This represents the estimated DC component value.

[0020] The main advantage of this invention is that it can effectively recover the DC component filtered out by AC-coupled photodetector even at low CSPR (Collateralized Sensitivity to Resonance), with an estimation error of <1%. By deriving the relationship between photocurrent, optical carrier power, and average signal power, and defining a correction coefficient to correct the error in this equation, the calculation formulas for estimating the optical carrier power and average signal power can be derived using the carrier-signal power ratio (CSPR). This allows for the estimation of the filtered DC component value. Because the correction coefficient significantly reduces the error in the relationship between photocurrent, optical carrier power, and average signal power, the error in the subsequent derived calculations is also very small, thus ensuring that the estimated DC component value error is <1%. Attached Figure Description

[0021] Figure 1 This is a flowchart illustrating the application of the DC component recovery method of the KK receiver in the embodiment in a single-polarization KK receiver system.

[0022] Figure 2 The example shows the error curves of the relationship between photocurrent, optical carrier power, and average signal power under different correction coefficients.

[0023] Figure 3 The example shows the error curves of the relationship between photocurrent, optical carrier power, and average signal power under different CSPRs with the optimal correction coefficient.

[0024] Figure 4 This is a graph showing the error between the preset DC component and the estimated DC component. Detailed Implementation

[0025] To further understand the present invention, a detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the embodiments are merely illustrative and not limiting of the invention.

[0026] like Figure 1As shown, this embodiment provides an application of a DC component recovery method for a KK receiver in a single-polarization KK receiving system. This KK receiving system utilizes the KK algorithm to recover the phase and amplitude of the detection signal. A single-channel 28GBaud 16-QAM signal is generated using a root-raised cosine (RRC) pulse shaping filter with a roll-off factor of 0.1. Subsequently, a virtual carrier with a frequency f0 = 1.1 × 28Gbaud / 2 = 15.4GHz is added to the edge of the 28GBaud 16-QAM signal in the digital domain. The added digital virtual carrier coincides with the right edge of the transmitted signal spectrum to generate a single-sideband signal. The amplitude E0 of the virtual carrier should be kept sufficiently high to satisfy the minimum phase condition (MPC) during KK algorithm detection. Then, an arbitrary waveform generator (AWG) is used to generate the signal, followed by a digital-to-analog converter (DAC). The generated electrical signal is modulated onto a 1550nm optical carrier using a single-polarization IQ modulator (IQM). The modulated optical signal generated by the IQM is directly transmitted to a standard single-mode fiber optic cable (SSMF). After a distance of SSMF transmission, the optical signal is amplified by an erbium-doped fiber amplifier (EDFA) and detected using a 40GHz AC-coupled photodetector, followed by sampling using an oscilloscope. Finally, the experimental data acquired by the oscilloscope is processed offline for data recovery. Next, the DC component is estimated and recovered according to the steps of this invention:

[0027] S1. The photocurrent after the signal passes through the DC-coupled photodetector (DC-PD) is expressed as:

[0028]

[0029] Where φ is the signal phase. The DC component (DC) is then expressed as:

[0030] DC =<I(t)> =P c + <P S (t)>=|E0| 2 +<|E S (t)| 2 >

[0031] The photocurrent of AC-coupled photodetector can then be expressed as:

[0032]

[0033] Furthermore, the relationship between the photocurrent after AC-coupled photodetector and the optical carrier power and the average power of the signal is derived:

[0034] 2 AC (t)>≈2P c <P S (t)>+α· <P S (t)> 2 ​

[0035] Figure 2 The error curves of the relationship between photocurrent, optical carrier power, and average signal power under different correction coefficients show that the optimal correction coefficient when using a 16-QAM signal is approximately α = 0.54. Figure 3 The approximate error of the proposed relationship between photocurrent, optical carrier power, and average signal power under the optimal correction coefficient with different CSPRs is [not specified].

[0036] S2. Using the above equations and the formula for calculating the carrier signal power ratio, the formulas for estimating the optical carrier power and the average signal power can be derived respectively, where the CSPR calculation formula is:

[0037]

[0038] Therefore, the estimated optical carrier power P c It can be calculated using the following formula:

[0039]

[0040] Similarly, the average power of the signal <P S (t)> can also be estimated by the following formula:

[0041]

[0042] S3. After obtaining the optical carrier power P c and average signal power <P S After calculating (t)>, the magnitude of the DC component filtered out by the AC-coupled photoelectric detector can be directly calculated:

[0043]

[0044] Among them, DC est This represents the estimated DC component value.

[0045] In the receiver DSP, after the DC component is recovered, resampling, KK algorithm, dispersion compensation, adaptive equalization, matched filtering downsampling are performed before calculating BER.

[0046] To evaluate the accuracy of the DC component recovery of this invention, Figure 4 The graph shows the error relationship between the preset DC component and the DC component estimated by the present invention. It can be seen that under any CSPR, the present invention can make the error of the estimated DC component <1%.

[0047] It should be noted that the DC component recovery method for the KK receiver provided in the embodiments of the present invention may include more or fewer parts, and the optimal correction coefficient can also be obtained for different modulation codes, which will not be elaborated here.

[0048] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for recovering the DC component of a Kramers-Kronig receiver, characterized in that, Includes the following steps: The DC component filtered out by AC-coupled photodetector (AC-PD) in KK receiver mainly includes two parts: the optical carrier power at the carrier beat frequency and the average signal power at the signal beat frequency. The relationship between photocurrent, optical carrier power, and average signal power is derived, and a correction coefficient is defined to correct the error of the equation. Then, the calculation formula of carrier signal power ratio (CSPR) can be used to derive the calculation formula of estimated optical carrier power and average signal power, so that the magnitude of the DC component filtered out by AC-coupled photodetector can be estimated. The relationship between the photocurrent, optical carrier power, and average signal power after AC-coupled photodetector (AC-PD) is derived, and a correction coefficient is defined to correct the error in this equation. ； in, To detect the photocurrent after the signal passes through an AC-coupled photodetector, The optical carrier power for the carrier beat frequency, The average power of the signal at the beat frequency. For averaging operators, This is a correction factor, with a value ranging from 0 to 1; The following formula is used to derive the carrier signal power ratio (CSPR): ； Combined with photocurrent With optical carrier power and the average power of the signal The relationship between the two values, and the estimated value of the optical carrier power. It can be calculated using the following formula: ； Similarly, the average power of the signal It can also be estimated using the following formula: ； Optical carrier power was obtained respectively and average signal power After calculating the formula, the magnitude of the DC component filtered out by the AC-coupled photodetector (AC-PD) can be directly estimated: ； in, This represents the estimated DC component value.

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