Offset angle insensitive fast adaptive linearization method for microwave photonic link

Abstract

The invention discloses a microwave photonic link-oriented offset angle insensitive rapid adaptive linearization method. The method specifically comprises the following steps of: injecting a continuous optical carrier output by a laser into a Mach-Zehnder modulator; an optical carrier in the Mach-Zehnder modulator is modulated by an input electric signal x; after the modulated optical signal is transmitted through an optical fiber, the signal is completely received through a photoelectric detector and is converted into an electric signal y; performing data sampling on the electric signal y output by the photoelectric detector through an analog-to-digital conversion module, and sending the electric signal y into a DSP (Digital Signal Processor); the method comprises the following steps: firstly, finishing suppression of second-order distortion in a DSP; and the suppression of the third-order distortion is further completed in the DSP. The method can flexibly adapt to the change of the offset angle, can be quickly and adaptively applied to various microwave photon links which have different input signals and are based on the Mach-Zehnder modulator, only needs to know the upper cut-off frequency and the lower cut-off frequency of the bandwidth of the input electric signal, does not need other prior parameters of the link or the input electric signal, and does not need complex training or iterative optimization.

Description

Technical Field

[0001] The present invention belongs to the field of microwave photonics, and in particular relates to a bias-angle-insensitive fast adaptive linearization method for microwave photonic links. Background Art

[0002] Microwave photonic (MWP) technology is widely used in radar, communications, satellites, and other fields due to its advantages such as large bandwidth, low loss, and immunity to electromagnetic interference. However, concerns remain regarding the widespread application of MWP technology. One of the most challenging obstacles is the inherent nonlinearity (e.g., second-order and third-order distortion) of the components used (e.g., Mach-Zehnder modulators), which causes signal distortion and hinders the application of MWP technology in microwave links that require high spurious-free dynamic range.

[0003] Therefore, to alleviate the nonlinearity problem of MWP links, many linearization methods have been proposed. These methods can be simply divided into two categories of technologies, namely optical domain and electrical domain technologies. People's interest in optical domain linearization technology is largely due to its unique large bandwidth advantage. Most reported optical domain linearization methods mainly focus on the nonlinearity of link modulation devices, using cascaded or parallel modulation structures, combined with parameter optimization settings to obtain two modulation paths with opposite or identical nonlinear characteristics, and achieve link linearization by canceling out the nonlinear distortion of the two paths. However, these optical domain linearization methods all require complex and specific link design and parameter settings, and have problems such as high implementation cost and low flexibility.

[0004] Alternatively, electrical linearization converts analog signals to the digital domain, utilizing DSP algorithms to pre- or post-compensate for link nonlinear distortion without modifying the existing link structure. Compared to optical-domain methods, electrical-domain methods offer superior cost, link complexity, and implementation difficulty, making them highly practical in practical microwave links. Of all linearization techniques, digital linearization offers unparalleled flexibility and accuracy in addressing arbitrary nonlinear distortion. Furthermore, the rapid advancement of digital-to-analog (DAC) / analog-to-digital (A / D) converter hardware has alleviated the primary limitations of digital linearization, namely processing speed and bandwidth. Therefore, digital linearization has become an effective and powerful solution for achieving high linearity in MWP links. However, directly applying existing digital linearization methods to the nonlinearity issues of various MWP links carrying diverse signals as a practical and universal solution is difficult. Obstacles include: (1) the need for precise static physical parameters of the link (input optical power, modulator bias angle, photodetector responsivity, link loss, etc.), which are difficult to accurately determine in actual links, not to mention dynamic and unpredictable parameter changes caused by device aging, environmental interference, etc.; (2) dependence on long training cycles and large amounts of high-quality training data sets; (3) considering practical implementation, the computational complexity, power / time consumption and tedious parameter adjustment are unacceptable. Summary of the Invention

[0005] In view of the above problems, the present invention provides a bias-angle-insensitive fast adaptive linearization method for microwave photonic links.

[0006] The present invention provides a bias-angle-insensitive fast adaptive linearization method for microwave photonic links, comprising the following steps:

[0007] Step 1: The continuous optical carrier output by the laser is injected into the Mach-Zehnder modulator.

[0008] Step 2: The optical carrier in the Mach-Zehnder modulator is modulated by the input electrical signal x.

[0009] Step 3: After the modulated optical signal is transmitted through the optical fiber, it is completely received by the photodetector and converted into an electrical signal y.

[0010] Step 4: The electrical signal y output by the photodetector is sampled through the analog-to-digital conversion module and sent to the DSP;

[0011] Step 5: First, suppress the second-order distortion in DSP.

[0012] Step 6: Further suppress the third-order distortion in DSP.

[0013] Furthermore, step 5 is specifically as follows:

[0014] Step 5.1: Simply block the DC of the output signal y and ignore the terms higher than the third order to obtain Y and the quadratic Y 2 and the cubic Y 3 function.

[0015] Step 5.2: According to the frequency characteristics of the input electrical signal x, when the sub-octave condition is met, that is, f up <2f down When the passband range is [0,f up -f down ] and [2f down ,2f up ] dual-channel filter for Y 2 Perform filtering; when the multi-octave condition is met, that is, f up ≥2f down When no filtering is performed, the output result is f(Y 2 ).

[0016] Step 5.3: Output Y, quadratic Y 2 After processing, the output f(Y 2 ), cubic Y 3 Perform Fourier transform (FT) at the same point; then, according to Y and Y 3 The third-order distortion inverse FT value at the same frequency point is considered to be Y and Y 3 The frequency domain component of the third-order distortion is determined, and the frequency point position of the third-order distortion frequency domain component is determined, and FT(Y) and FT[f(Y 2 )] is reset to zero at the corresponding frequency point, so that Y and f(Y 2 ) in the frequency domain to remove the third-order distortion components; Finally, in the frequency domain, the stop band range is [f down ,f up ] further removes Y and f(Y 2 ) in the frequency domain components of the baseband signal x, and obtain Y and f(Y 2 ) in the second-order distortion frequency components D1 and D2.

[0017] Step 5.4: Calculate the optimal second-order distortion linearization coefficient based on equation (1);

[0018]

[0019] Step 5.5: Based on equation (2), the second-order distortion is suppressed.

[0020] r(Y)=Y+Re(c2)f(Y 2 ) (2)

[0021] Furthermore, step 6 is specifically as follows:

[0022] Step 6.1: Suppress the second-order distortion output r(Y) and the cubic r(Y) 3 Through the same number of points FT, then according to, r(Y) and r(Y) 3 The values of the third-order distortion inverse FT at the same frequency point are considered to be r(Y) and r(Y) 3 Finally, the data vectors N1 and N2 are obtained.

[0023] Step 6.2: Calculate the optimal third-order distortion linearization coefficient based on equation (3);

[0024]

[0025] Step 6.3: Based on the calculation of formula (4), the third-order distortion is suppressed;

[0026] I(Y)=r(Y)+real(c3)r(Y) 3 (4)

[0027] The beneficial technical effects of the present invention are:

[0028] 1. The present invention does not rely on the bias angle perception of the MZM, can effectively suppress the ND2s and ND3s of the MZM under different bias states, and enhance the spurious-free dynamic range (SFDR) of the MWP link.

[0029] 2. The present invention can be adaptively applied to MZM microwave photonic links of various input electrical signals. It only requires knowing the upper and lower cutoff frequencies of the input electrical signal bandwidth, without requiring other prior parameters of the link or baseband signal.

[0030] 3. The present invention has analytical non-iterative behavior, avoiding computationally intensive iterative search and tedious parameter (e.g., initial point, step size) adjustment, thereby reducing time / cost and improving ease of implementation and use.

[0031] 4. The present invention can flexibly adapt to changes in the MZM offset angle and improve the robustness of the MWP link. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 The present invention is a flow chart of the bias angle insensitive fast adaptive linearization method for microwave photonic links.

[0033] Figure 2 Schematic diagram of the intensity modulation direct detection microwave optical link based on Mach-Zehnder modulator of the present invention.

[0034] Figure 3 This is the flow chart of the linearization algorithm. DETAILED DESCRIPTION

[0035] The present invention will be further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0036] The present invention first establishes an intensity modulation direct detection MWP link based on a Mach-Zehnder modulator (MZM). The devices in the link include a laser, a Mach-Zehnder modulator, an optical fiber, a photodetector, an analog-to-digital conversion module and a digital signal processing module.

[0037] The present invention is a bias angle insensitive fast adaptive linearization method for microwave photonic links. Figure 1 As shown, the specific steps include:

[0038] Step 1: If Figure 2 As shown, the continuous optical carrier output by the laser is injected into the Mach-Zehnder modulator.

[0039] Step 2: If Figure 2 As shown, the optical carrier in the Mach-Zehnder modulator is modulated by the input electrical signal x.

[0040] Step 3: If Figure 2 As shown, after the modulated optical signal is transmitted through the optical fiber, the photodetector completes the signal reception and converts it into an electrical signal y.

[0041] In general, the nonlinear transfer function of an MWP link can be explicitly expressed as:

[0042]

[0043] Where G represents the link gain; x represents the input electrical signal, and the upper and lower cutoff frequencies of its bandwidth are f up and f down ; V π Indicates the half-wave voltage of MZM.

[0044] Under weak nonlinear conditions, nonlinearities higher than the third order are usually ignored due to their small contribution, so the nonlinear transfer function can be approximated by a Taylor series around the bias point x0:

[0045] y=a0+a1(x-x0)+a2(x-x0) 2 +a3(x-x0) 3 (2)

[0046] Where a k (k=0,1,2,3) is the Taylor expansion coefficient defined by the following formula:

[0047]

[0048] Where θ=πx0 / V π is the bias angle of the MZM, a0 is the DC term, and a1, a2, and a3 control the amplitudes of the fundamental frequency signal, ND2s, and ND3s, respectively.

[0049] Step 4: If Figure 2 As shown, the electrical signal y output by the photodetector is sampled by the analog-to-digital conversion module and sent to the DSP;

[0050] Step 5: Figure 3 As shown, the suppression of second-order distortion is first completed in DSP.

[0051] Step 5.1: Simply block the DC of the output signal y and ignore the terms higher than the third order to obtain Y and the quadratic Y 2 and the cubic Y 3 function.

[0052] Y=a1(x-x0)+a2(x-x0) 2 +a3(x-x0) 3 (4)

[0053]

[0054] Step 5.2: Convert the time domain output to the quadratic Y 2 The Fourier transform (FT) is converted into its frequency domain counterpart to obtain the frequency domain data vector E1.

[0055] Step 5.3: Based on the frequency characteristics, perform dual-channel filtering on E1 when the sub-octave condition is met, and do not perform filtering on E1 when the multi-octave condition is met. The specific method is as follows:

[0056]

[0057] Among them H DCF is the data vector of the frequency response of the ideal dual-channel filter, whose passband range is [0,f up -f down ] and [2f down ,2f up ]. represents the Hadamard product.

[0058] Step 5.4: Perform inverse Fourier transform (IFT) on E2 to convert it into its time domain counterpart f(Y 2 ).

[0059]

[0060] Step 5.5: Output the time domain Y and the quadratic Y 2 After processing, the output f(Y 2 ), and its cube Y 3 The frequency domain data vectors A1, A2 and A3 are obtained by converting them into their frequency domain counterparts through Fourier transform (FT) with the same number of points.

[0061] Step 5.6: ND3s in A1 and A2 are removed by:

[0062]

[0063] in,

[0064]

[0065] x i Indicates an element that belongs to set A1 or A3. ⊙ is the exclusive OR operator.

[0066] Step 5.7: The fundamental frequency signals in B1 and B2 are filtered out by:

[0067]

[0068] Among them H BSF is the data vector of the frequency response of the ideal band-stop filter, and its stop band range is [f down ,f up ].

[0069] Step 5.8: Calculate the optimal second-order distortion linearization coefficient based on equation (12);

[0070]

[0071] Step 5.9: Calculate based on equation (13) to achieve suppression of second-order distortion;

[0072] r(Y)=Y+Re(c2)f(Y 2 ) (13)

[0073] Step 6: Figure 3 As shown, the suppression of third-order distortion is further completed in DSP.

[0074] Step 6.1: Time domain output r(Y) and its cubic r(Y) after suppressing ND2s 3 The frequency domain data vectors M1 and M2 are obtained by converting them into their frequency domain counterparts through Fourier transform (FT) with the same number of points.

[0075] Step 6.2: ND3s (N1, N2) in M1 and M2 are identified by:

[0076]

[0077] where sign(x i ) is defined in the same way as in (10), where x i Represents elements belonging to sets M1 and M2. is the exclusive OR operator.

[0078] Step 6.3: Calculate the optimal third-order distortion linearization coefficient based on equation (15);

[0079]

[0080] Step 6.4: Calculate based on equation (16) to achieve suppression of third-order distortion;

[0081] I(Y)=r(Y)+real(c3)r(Y) 3 (16)

[0082] What has been stated above is merely a preferred embodiment of the present invention. It should be noted that, without departing from the essence of the method of the present invention, several changes and modifications may be made in actual implementation and should also be included in the scope of protection of the present invention.

Claims

1. A bias-angle-insensitive fast adaptive linearization method for microwave photonic links, characterized by: The following steps are involved: Step 1: The continuous optical carrier output by the laser is injected into the Mach-Zehnder modulator; Step 2: The optical carrier in the Mach-Zehnder modulator is modulated by the input electrical signal x; Step 3: After the modulated optical signal is transmitted through the optical fiber, it is completely received by the photodetector and converted into an electrical signal y; Step 4: The electrical signal y output by the photodetector is sampled through the analog-to-digital conversion module and sent to the DSP; Step 5: First, suppress the second-order distortion in DSP; Step 6: Further suppress the third-order distortion in DSP.

2. The bias-angle-insensitive fast adaptive linearization method for microwave photonic links according to claim 1, characterized in that: The step 5 is specifically as follows: Step 5.1: Simply block the DC of the output signal y and ignore the terms higher than the third order to obtain Y and the quadratic Y 2 and the cubic Y 3 function; Step 5.2: According to the frequency characteristics of the input electrical signal x, when the sub-octave condition is met, that is, f up <2f down When the passband range is [0,f up -f down ] and [2f down ,2f up ] dual-channel filter for Y 2 Perform filtering; when the multi-octave condition is met, that is, f up ≥2f down When no filtering is performed, the output result is f9Y 2 ); Step 5.3: Output Y, quadratic Y 2 After processing, the output f9Y 2 ), cubic Y 3 Perform Fourier transform (FT) at the same point; then, according to Y and Y 3 The third-order distortion inverse FT value at the same frequency point is considered to be Y and Y 3 The frequency domain component of the third-order distortion is determined, and the frequency point position of the third-order distortion frequency domain component is determined, and FT9Y) and FT[f(Y 2 )] is reset to zero at the corresponding frequency point, so that Y and f(Y 2 ) in the frequency domain to remove the third-order distortion components; Finally, in the frequency domain, the stop band range is [f down ,f up ] further removes Y and f(Y 2 ) in the frequency domain components of the baseband signal x, and obtain Y and f(Y 2 ) in the second-order distortion frequency components D1 and D2; Step 5.4: Calculate the optimal second-order distortion linearization coefficient based on equation (1); Step 5.5: Based on the calculation of formula (2), the second-order distortion is suppressed. r(Y)=Y+Re(c2)f(Y 2 ) (2)。 3. The bias-angle-insensitive fast adaptive linearization method for microwave photonic links according to claim 1, characterized in that: The step 6 is specifically as follows: Step 6.1: Suppress the second-order distortion output r(Y) and the cubic r(Y) 3 Through the same number of points FT, then according to, r(Y) and r(Y) 3 The values of the third-order distortion inverse FT at the same frequency point are considered to be r(Y) and r(Y) 3 Finally, we get the data vectors N1 and N2. Step 6.2: Calculate the optimal third-order distortion linearization coefficient based on equation (3); Step 6.3: Based on the calculation of formula (4), the third-order distortion is suppressed; I(Y)=r(Y)+real(c3)r(Y) 3 (4)。

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