CN112865875A - High-linearity multichannel radio-over-fiber communication link system and linearity optimization method - Google Patents
High-linearity multichannel radio-over-fiber communication link system and linearity optimization method Download PDFInfo
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Abstract
The invention relates to a high-linearity multichannel radio-over-fiber communication link system and a linearity optimization method, wherein a microwave photon technology is combined with a Lagrange multiplier optimization technology, the inherent advantages of large bandwidth, high frequency and electromagnetic interference resistance of the microwave photon technology are utilized to carry out modeling optimization on parameters influencing the linearity of the system, the optimal working point of the system is solved, the nonlinear distortion of the link is reduced, and the purposes of improving the spurious-free dynamic range and bandwidth of the system are achieved.
Description
Technical Field
The invention relates to the technical field of communication links, in particular to a high-linearity multi-channel radio-over-fiber communication link system and a linearity optimization method.
Background
The wireless communication technology utilizes optical fiber to transmit and distribute radio frequency signals, can overcome the electronic bottlenecks of high loss, low frequency and narrow bandwidth of the traditional microwave system, and becomes a new key enabling technology. In recent years, with the continuous increase of broadband wireless services and intelligent terminal equipment, the radio over fiber technology has been widely applied in Distributed Antenna Systems (DAS) by virtue of its outstanding advantages of low loss, large bandwidth, high transmission rate, strong anti-electromagnetic interference capability, etc., and has become an ideal and effective solution for replacing microwave cable links. However, with the use of advanced data modulation formats, such as Orthogonal Frequency Division Multiplexing (OFDM) signals, signal distortion tends to be easily caused due to high peak power ratio (PAPR), which puts strict requirements on linearity and bandwidth of an over-the-optical wireless communication link. Therefore, linearization of wireless communication links over optical carriers has become the greatest challenge facing researchers in the field of microwave photonics today. The Mach-Zehnder modulator (MZM) is a key device in an optical carrier wireless communication link, the main function of the Mach-Zehnder modulator is to perform electro-optical conversion, but the inherent nonlinear characteristic of the electro-optical conversion will generate serious third-order intermodulation distortion (IMD3) and second-order harmonic distortion (HD2), deteriorate the spurious-free dynamic range (SFDR) and the bandwidth of a system, and become a main obstacle for the application and development of the optical carrier wireless communication link in a DAS system. Therefore, how to suppress IMD3 and HD2 simultaneously in an over-the-air wireless communication link, realizing high-linearity multi-channel signal transmission and distribution has become a hot point of research in the field of microwave photonics, and has urgent needs in scenes with many mobile device connections and many broadband applications, such as conference centers, ground drop tunnels, airports, and the like.
Disclosure of Invention
In view of the above situation, currently, the proposed linearization scheme based on the microwave photon technology can only suppress third-order intermodulation distortion or second-order harmonic distortion, or has the disadvantages of high implementation difficulty, complex structure, high practical application limitation, and the like. In order to solve the problems, the microwave photon technology is combined with an optimization theory, the optimal working point of the system is solved through a Lagrange multiplier method, so that the third-order intermodulation distortion can be further inhibited, the third-order spurious-free dynamic range and the linearity of the system are improved, after the system is optimized, the simultaneous inhibition of the third-order intermodulation distortion and the second-order harmonic distortion can be realized only by adjusting a polarization controller positioned on a far-end antenna unit, the method can overcome some defects in the prior art, and has the advantages of high linearity, large bandwidth and simple structure, so the invention aims to provide a high-linearity multi-channel radio-over-fiber communication link system and a linearity optimization method to solve the problems.
The technical scheme adopted by the invention for solving the technical problems is as follows: the high-linearity multichannel radio-over-fiber communication link system is characterized by comprising a laser, a radio frequency front end, a second-order harmonic distortion suppression unit, an optical fiber, a third-order intermodulation distortion suppression unit, a photoelectric detector and an antenna;
the output port of the laser is connected with the input port of the second-order harmonic distortion suppression unit, the radio frequency front end is connected with the second-order harmonic distortion suppression unit, the output port of the second-order harmonic distortion suppression unit is connected with the input ports of a plurality of groups of third-order intermodulation distortion suppression units through optical fibers, the output port of the third-order intermodulation distortion suppression unit is connected with the input port of the photoelectric detector, and the output port of the photoelectric detector is connected with the antenna for signal transmission;
the second-order harmonic distortion suppression unit comprises a polarization multiplexing Mach modulator, the polarization multiplexing Mach modulator comprises two sub-modulators MZMX and MZMY, two paths of double-tone signals generated by a radio frequency front end are respectively fed into two radio frequency ports of the PDM-MZM, and direct current bias voltages of the two sub-modulators MZMX and MZMY of the PDM-MZM are adjusted to respectively work at orthogonal bias points with opposite slopes, so that second-order harmonic distortion suppression is realized;
the third-order intermodulation distortion suppression unit is composed of a polarization controller and a polarizer, the polarization controller is connected with an output port of the second-order harmonic distortion suppression unit, the polarization controller adjusts the polarization state of the orthogonal polarized light signal output by the second-order harmonic distortion suppression unit, the orthogonal polarized light signal is mapped to the polarizer at a certain polarization incidence angle, a complementary third-order intermodulation distortion component is generated, and therefore third-order intermodulation distortion suppression is achieved, and the output end of the polarizer is connected with an input port of the photoelectric detector.
Preferably, the polarization multiplexing maser modulator further comprises an optical coupler, one end of the optical coupler is connected with the output end of the laser, the other end of the optical coupler is connected with the input ends of the two sub-modulators MZMX and MZMY, the polarization multiplexing maser further comprises a polarization beam combiner, the input end of the polarization beam combiner is connected with the output ends of the two sub-modulators MZMX and MZMY, and the input end of the polarization beam combiner is connected with the optical fiber.
Preferably, a 90 ° polarization rotator is connected between the sub-modulator MZMY and the polarization beam combiner.
The linearity optimization method adopting the high-linearity multichannel radio-over-fiber communication link system is characterized in that an output port of the second-order harmonic distortion suppression unit is marked as a point a, an output port of the third-order intermodulation distortion suppression unit is marked as a point b, an output port of the photoelectric detector is marked as a point c, and the linearity optimization method comprises the following steps:
step 1: the linearly polarized light output by the laser is represented as:
the two-tone signals with power ratio gamma generated by the RF front end can be respectively expressed as
And
wherein E iscAnd ωcRespectively the electric field strength and the angular frequency, omega, of the optical carrier1And ω2Is the angular frequency of the diphone signal;
step 2: after the two-tone signal is electro-optically modulated by the second-order harmonic distortion suppression unit, the optical signal at the point a of the output port is represented as:
wherein E isXAnd EYRespectively representing the two polarization states of the optical signal,φ1and phi2Respectively representing the DC bias angles of the sub-modulators MZMX and MZMY, the bias angles being controlled by a DC bias voltage, VπRepresenting the half-wave voltage of the modulator, the DC offset angle phi for suppressing second-order harmonic distortion1And phi2Set as the two orthogonal points with opposite slopes-pi/2 and pi/2, respectively.
And step 3: the orthogonal polarization multiplexing signal output by the second-order harmonic distortion suppression unit is transmitted by an optical fiber and then input to an input port of a third-order intermodulation distortion suppression unit, a polarization controller is used for controlling a main shaft of an orthogonal polarization optical signal to form a certain included angle with a main shaft of a polarizer, the included angle is defined as a polarization incident angle and is expressed by alpha, and a point b output optical signal is as follows:
EPol.(t)＝EX(t)cos(α)+[EY(t)sin(α)]ejφ (2)
where φ represents the phase difference between two orthogonal polarization states; due to the square-law characteristic of photoelectric detection, TE and TM mode optical signals generate cross terms after passing through the PD, so that nonlinear distortion and computational complexity are increased. To solve this problem, phi is set to pi/2, and the generated cross terms can cancel each other;
and 4, step 4: the optical signal output by the third-order intermodulation distortion suppression unit is injected into a photoelectric detector for photoelectric conversion, and the output photocurrent of the point c is as follows:
where f (γ, α) and g (γ, α) are functions of the rf output power and the third-order conditional intermodulation distortion power with respect to the rf power ratio γ and the polarization incidence angle α, respectively, and can be expressed as:
and 5: in order to eliminate third-order intermodulation distortion, conditions g (γ, α) of 0 and f (γ, α) of 0 must be satisfied. As can be seen from the expression of the function f (γ, α), the suppression of third-order intermodulation distortion inevitably causes a loss of rf output power. In order to maximize the radio frequency output power on the basis of eliminating third-order intermodulation distortion, an optimization model under an equality constraint condition is established according to the Lagrange multiplier theory, and the result is expressed as follows:
L(γ,α,λ)＝f(γ,α)-λg(γ,α) (5)
where λ represents the lagrange multiplier, and f (γ, α) and g (γ, α) are the objective function and the constraint function of the optimization model. Taking the first partial derivative of equation (5) and let the gradient vector
At 0, the following expression can be obtained:
solving equation (6) can yield:
therefore, from the lagrangian optimization results, when the radio frequency power ratio is an arbitrary value, and the polarization incidence angle is 0.34 radians, the radio frequency output power can reach the maximum value.
The invention has the advantages that the invention can effectively realize the radio over fiber communication link with high linearity and large bandwidth, and the proposal not only can realize the maximized link linearity, but also has the advantages of simple operation and compact structure. The method combines the microwave photon technology with the Lagrange multiplier optimization technology to obtain the optimal values of the radio frequency output power, the polarization incident angle and the radio frequency power ratio. Therefore, under orthogonal polarization, the suppression of third-order intermodulation distortion and second-order harmonic distortion can be realized simultaneously only by changing the polarization incidence angle, the nonlinear distortion of a link is obviously reduced, and the spurious-free dynamic range and the bandwidth of a system are improved. In addition, the method can also realize the functions of multi-channel radio frequency transmission and distribution, and the suppression of the third-order intermodulation distortion of each channel can be realized by a polarization controller positioned in a far-end antenna unit respectively. Therefore, the method can effectively meet the application of the distributable antenna system and has wide application prospect.
Drawings
FIG. 1: the invention is used for a high-linearity and large-bandwidth multichannel radio-over-fiber communication link schematic diagram of a distributed antenna system;
FIG. 2: electric spectrum of two-tone signal: (a) IMD3 electric spectrum of the proposed inventive method; (b) IMD3 electric spectrum of the comparative method; (c) HD2 electric spectrum of the proposed inventive method;
FIG. 3: spurious free dynamic range: (a) the second and third order spurious-free dynamic ranges of the proposed method; (b) comparing the second-order and third-order spurious-free dynamic ranges of the method;
FIG. 4 optimization validation: the relationship of normalized radio frequency output power and radio frequency power ratio of simulation (triangle line) and measurement (circle line);
FIG. 5(a) a contour plot of an objective function; (b) a constraint function contour map. :
Detailed Description
The following description will explain embodiments of the present invention in detail by taking an embodiment as an example and referring to the accompanying drawings.
First, it should be noted that: in the invention:
1) a laser: for outputting linearly polarized light;
2) a radio frequency front end: the power ratio adjustable dual-tone radio frequency signal is generated;
3) second order harmonic distortion suppression unit: the direct-current bias voltage of the polarization multiplexing Mach modulator is adjusted to enable MZMX and MZMY to work at working points with opposite slopes, and therefore second-order harmonic distortion is suppressed;
4) optical fiber: for transmitting the modulated optical signal;
5) third-order intermodulation distortion suppression unit: third-order intermodulation distortion suppression is realized by controlling the polarization controller;
6) a photoelectric detector: the device is used for realizing photoelectric conversion and generating a distortion-free radio frequency signal.
Example (b):
the high-linearity multichannel radio-over-fiber communication link system is characterized by comprising a laser, a radio frequency front end, a second-order harmonic distortion suppression unit, an optical fiber, a third-order intermodulation distortion suppression unit, a photoelectric detector and an antenna;
the output port of the laser is connected with the input port of the second-order harmonic distortion suppression unit, the radio frequency front end is connected with the second-order harmonic distortion suppression unit, the output port of the second-order harmonic distortion suppression unit is connected with the input ports of a plurality of groups of third-order intermodulation distortion suppression units through optical fibers, the output port of the third-order intermodulation distortion suppression unit is connected with the input port of the photoelectric detector, and the output port of the photoelectric detector is connected with the antenna for signal transmission;
the second-order harmonic distortion suppression unit comprises a Polarization multiplexing Mach-Zehnder modulator (PDM-MZM), the Polarization multiplexing Mach modulator comprises two sub-modulators MZMX and MZMY, two paths of double-tone signals generated by a radio frequency front end are respectively fed into two radio frequency ports of the PDM-MZM, the power ratio of the two paths of double-tone signals can be adjusted, and the direct current bias voltages of the two sub-modulators MZMX and MZMY of the PDM-MZM are adjusted to respectively work at orthogonal bias points with opposite slopes, so that second-order harmonic distortion suppression is achieved; the polarization multiplexing Mach modulator also comprises an optical coupler, one end of the optical coupler is connected with the output end of the laser, the other end of the optical coupler is connected with the input ends of the two sub-modulators MZMX and MZMY, the polarization multiplexing Mach modulator also comprises a polarization beam combiner, the input end of the polarization beam combiner is connected with the output ends of the two sub-modulators MZMX and MZMY, the input end of the polarization beam combiner is connected with an optical fiber, and a 90-degree polarization rotator is connected between the sub-modulators MZMY and the polarization beam combiner;
the third-order intermodulation distortion suppression unit is composed of a polarization controller and a polarizer, the polarization controller is connected with an output port of the second-order harmonic distortion suppression unit, and the polarization controller is mainly used for carrying out polarization state adjustment on orthogonal polarized light signals output by the second-order harmonic distortion suppression unit, so that the orthogonal polarized light signals are mapped to a main shaft of the polarizer at a certain polarization incidence angle to generate complementary third-order intermodulation distortion components, and therefore third-order intermodulation distortion suppression is achieved, and the output end of the polarizer is connected with an input port of a photoelectric detector.
The linearity optimization method adopting the high-linearity multichannel radio-over-fiber communication link system is characterized in that an output port of the second-order harmonic distortion suppression unit is marked as a point a, an output port of the third-order intermodulation distortion suppression unit is marked as a point b, an output port of the photoelectric detector is marked as a point c, and the linearity optimization method comprises the following steps:
step 1: the linearly polarized light output by the laser is represented as:
the two-tone signals with power ratio gamma generated by the RF front end can be respectively expressed as
And
wherein E iscAnd ωcRespectively the electric field strength and the angular frequency, omega, of the optical carrier1And ω2Is the angular frequency of the diphone signal;
step 2: after the two-tone signal is electro-optically modulated by the second-order harmonic distortion suppression unit, the optical signal at the point a of the output port is represented as:
wherein E isXAnd EYRespectively representing two polarization states, phi, of the optical signal1And phi2Respectively representing the DC bias angles of the sub-modulators MZMX and MZMY, the bias angles being controlled by a DC bias voltage, VπRepresenting the half-wave voltage of the modulator, the DC offset angle phi for suppressing second-order harmonic distortion1And phi2Set as the two orthogonal points with opposite slopes-pi/2 and pi/2, respectively.
And step 3: the orthogonal polarization multiplexing signal output by the second-order harmonic distortion suppression unit is transmitted by an optical fiber and then input to an input port of a third-order intermodulation distortion suppression unit, a polarization controller is used for controlling a main shaft of an orthogonal polarization optical signal to form a certain included angle with a main shaft of a polarizer, the included angle is defined as a polarization incident angle and is expressed by alpha, and a point b output optical signal is as follows:
EPol.(t)＝EX(t)cos(α)+[EY(t)sin(α)]ejφ (2)
where φ represents the phase difference between two orthogonal polarization states; due to the square-law characteristic of photoelectric detection, TE and TM mode optical signals generate cross terms after passing through the PD, so that nonlinear distortion and computational complexity are increased. To solve this problem, phi is set to pi/2, and the generated cross terms can cancel each other;
and 4, step 4: the optical signal output by the third-order intermodulation distortion suppression unit is injected into a photoelectric detector for photoelectric conversion, and the output photocurrent of the point c is as follows:
where f (γ, α) and g (γ, α) are functions of the rf output power and the third-order conditional intermodulation distortion power with respect to the rf power ratio γ and the polarization incidence angle α, respectively, and can be expressed as:
and 5: in order to eliminate third-order intermodulation distortion, conditions g (γ, α) of 0 and f (γ, α) of 0 must be satisfied. As can be seen from the expression of the function f (γ, α), the suppression of third-order intermodulation distortion inevitably causes a loss of rf output power. In order to maximize the radio frequency output power on the basis of eliminating third-order intermodulation distortion, an optimization model under an equality constraint condition is established according to the Lagrange multiplier theory, and the result is expressed as follows:
L(γ,α,λ)＝f(γ,α)-λg(γ,α) (5)
wherein λ represents LagThe Langerian multipliers, f (γ, α) and g (γ, α) are the objective and constraint functions of the optimization model. Taking the first partial derivative of equation (5) and let the gradient vector
At 0, the following expression can be obtained:
solving equation (6) can yield:
therefore, from the lagrangian optimization results, when the rf power ratio is an arbitrary value, the rf power is 6dB here, and the polarization incident angle is 0.34 radians, the rf output power can reach the maximum value.
In the experimental verification, the high-linearity and large-bandwidth multi-channel radio-over-fiber communication link based on the polarization multiplexing Mach modulator can be verified by building an experimental platform, and an experimental schematic diagram refers to FIG. 1.
The devices required in the experiments included: radio frequency front end (MSG, Agilent E8257D and HP 83640A), laser (KG-DFB-40), polarization controller (Thorlabs, FPC032), polarizer (ILP-1550), PDM-MZM (Fujitsu FTM7981) and photodetector (Finisar, BPDV2150 RM). The main experimental parameters of the system are configured as follows:
the two-tone signal: the center frequency is 10GHz and 10.1GHz, and the power is tunable;
distributed feedback laser: the output wavelength is 1550.12nm, and the power is 14 dBm;
PDM-MZM: the half-wave voltage is 3.5V, the 3dB bandwidth is 30GHz, the insertion loss is 14dB, and the extinction ratio is 20 dB;
polarization controller: wavelength range 1260 and 1625 nm;
photodetector: the bandwidth is 43 GHz.
The method comprises the following operation steps:
step 1: the laser is connected with the light input port of the PDM-MZM, and two paths of double-tone signals with the power ratio of gamma are output by the radio frequency front end;
step 2: two paths of double-tone signals are respectively input into two radio frequency ports of a second-order harmonic distortion suppression unit, and the direct current bias angles phi of two sub-modulators MZMX and MZMY1And phi2Set as two orthogonal points with opposite slopes-pi/2 and pi/2 respectively;
and step 3: in the third-order intermodulation distortion suppression unit, a polarization controller is used for adjusting the polarization incidence angle, so that the third-order intermodulation distortion is completely suppressed;
and 4, step 4: measuring the photocurrent output by the photodetector with a spectrum analyzer, the output spectrum being shown in fig. 2;
and 5: adjusting the power of the two-tone signal, recording the power of radio frequency, third-order intermodulation distortion and second-order harmonic distortion in the frequency spectrum, and drawing third-order and second-order spurious-free dynamic ranges as shown in figure 3;
step 6: the power ratio of the two paths of the two-tone signals output by the radio frequency front end is changed, and the obtained radio frequency output power-radio frequency power ratio curve is shown in fig. 4;
and 7: the simulation was performed according to the lagrangian multiplier optimization model shown in formula (5), and the result is shown in fig. 5.
The invention combines the microwave photon technology with the Lagrange multiplier optimization technology, utilizes the inherent advantages of the microwave photon technology such as large bandwidth, high frequency and anti-electromagnetic interference to carry out modeling optimization on parameters influencing the linearity of the system, solves the optimal working point of the system, and achieves the purposes of reducing the nonlinear distortion of a link and improving the spurious-free dynamic range and bandwidth of the system. The method can realize the suppression of third-order intermodulation distortion and second-order harmonic distortion by utilizing devices such as a laser, a polarization multiplexing Mach modulator, a polarization controller, a polarizer, a photoelectric detector and the like and only changing a polarization incidence angle by using the polarization controller, and has the advantages of high linearity, large bandwidth, compact structure and simple operation.
The above-described embodiments are only examples of the present invention and are not intended to limit the scope of the present invention, it should be noted that those skilled in the art can make several equivalent variations and substitutions on the disclosure of the present invention, and the frequency and power of the two-tone signal, the laser wavelength and power, etc. can be changed. Such equivalent modifications and substitutions, as well as adjustments to the frequency range, should also be considered to be within the scope of the present invention.
Claims (4)
1. The high-linearity multichannel radio-over-fiber communication link system is characterized by comprising a laser, a radio frequency front end, a second-order harmonic distortion suppression unit, an optical fiber, a third-order intermodulation distortion suppression unit, a photoelectric detector and an antenna;
the output port of the laser is connected with the input port of the second-order harmonic distortion suppression unit, the radio frequency front end is connected with the second-order harmonic distortion suppression unit, the output port of the second-order harmonic distortion suppression unit is connected with the input ports of a plurality of groups of third-order intermodulation distortion suppression units through optical fibers, the output port of the third-order intermodulation distortion suppression unit is connected with the input port of the photoelectric detector, and the output port of the photoelectric detector is connected with the antenna for signal transmission;
the second-order harmonic distortion suppression unit comprises a polarization multiplexing Mach modulator, the polarization multiplexing Mach modulator comprises two sub-modulators MZMX and MZMY, two paths of double-tone signals generated by a radio frequency front end are respectively fed into two radio frequency ports of the PDM-MZM, and direct current bias voltages of the two sub-modulators MZMX and MZMY of the PDM-MZM are adjusted to respectively work at orthogonal bias points with opposite slopes, so that second-order harmonic distortion suppression is realized;
the third-order intermodulation distortion suppression unit is composed of a polarization controller and a polarizer, the polarization controller is connected with an output port of the second-order harmonic distortion suppression unit, the polarization controller adjusts the polarization state of the orthogonal polarized light signal output by the second-order harmonic distortion suppression unit, the orthogonal polarized light signal is mapped to the polarizer at a certain polarization incidence angle, a complementary third-order intermodulation distortion component is generated, and therefore third-order intermodulation distortion suppression is achieved, and the output end of the polarizer is connected with an input port of the photoelectric detector.
2. The high linearity multi-channel radio over fiber communication link system of claim 1, wherein the polarization multiplexing Mach modulator further comprises an optical coupler, one end of the optical coupler is connected to the output end of the laser, the other end of the optical coupler is connected to the input ends of the two sub-modulators MZMX and MZMY, the polarization multiplexing device further comprises a polarization beam combiner, the input end of the polarization beam combiner is connected to the output ends of the two sub-modulators MZMX and MZMY, and the input end of the polarization beam combiner is connected to the optical fiber.
3. The system of claim 2, wherein a 90 ° polarization rotator is connected between the sub-modulator MZMY and the polarization combiner.
4. The linearity optimization method adopting the high-linearity multichannel radio-over-fiber communication link system is characterized in that an output port of the second-order harmonic distortion suppression unit is marked as a point a, an output port of the third-order intermodulation distortion suppression unit is marked as a point b, an output port of the photoelectric detector is marked as a point c, and the linearity optimization method comprises the following steps:
step 1: the linearly polarized light output by the laser is represented as:
the two-tone signals with power ratio gamma generated by the RF front end can be respectively expressed as
And
wherein E iscAnd ωcRespectively the electric field strength and the angular frequency, omega, of the optical carrier1And ω2Is the angular frequency of the diphone signal;
step 2: after the two-tone signal is electro-optically modulated by the second-order harmonic distortion suppression unit, the optical signal at the point a of the output port is represented as:
wherein E isXAnd EYRespectively representing two polarization states, phi, of the optical signal1And phi2Respectively representing the DC bias angles of the sub-modulators MZMX and MZMY, the bias angles being controlled by a DC bias voltage, VπRepresenting the half-wave voltage of the modulator, the DC offset angle phi for suppressing second-order harmonic distortion1And phi2Set as the two orthogonal points with opposite slopes-pi/2 and pi/2, respectively.
And step 3: the orthogonal polarization multiplexing signal output by the second-order harmonic distortion suppression unit is transmitted by an optical fiber and then input to an input port of a third-order intermodulation distortion suppression unit, a polarization controller is used for controlling a main shaft of an orthogonal polarization optical signal to form a certain included angle with a main shaft of a polarizer, the included angle is defined as a polarization incident angle and is expressed by alpha, and a point b output optical signal is as follows:
EPol.(t)＝EX(t)cos(α)+[EY(t)sin(α)]ejφ (2)
where φ represents the phase difference between two orthogonal polarization states; due to the square-law characteristic of photoelectric detection, TE and TM mode optical signals generate cross terms after passing through the PD, so that nonlinear distortion and computational complexity are increased. To solve this problem, phi is set to pi/2, and the generated cross terms can cancel each other;
and 4, step 4: the optical signal output by the third-order intermodulation distortion suppression unit is injected into a photoelectric detector for photoelectric conversion, and the output photocurrent of the point c is as follows:
where f (γ, α) and g (γ, α) are functions of the rf output power and the third-order conditional intermodulation distortion power with respect to the rf power ratio γ and the polarization incidence angle α, respectively, and can be expressed as:
and 5: in order to eliminate third-order intermodulation distortion, conditions g (γ, α) of 0 and f (γ, α) of 0 must be satisfied. As can be seen from the expression of the function f (γ, α), the suppression of third-order intermodulation distortion inevitably causes a loss of rf output power. In order to maximize the radio frequency output power on the basis of eliminating third-order intermodulation distortion, an optimization model under an equality constraint condition is established according to the Lagrange multiplier theory, and the result is expressed as follows:
L(γ,α,λ)＝f(γ,α)-λg(γ,α) (5)
where λ represents the lagrange multiplier, and f (γ, α) and g (γ, α) are the objective function and the constraint function of the optimization model. Taking the first partial derivative of equation (5) and letting L be 0, the following expression can be obtained:
solving equation (6) can yield:
therefore, from the lagrangian optimization results, when the radio frequency power ratio is an arbitrary value, and the polarization incidence angle is 0.34 radians, the radio frequency output power can reach the maximum value.
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