CN110350980B - Radar detection method and device based on microwave photon-assisted de-skewed bandwidth synthesis - Google Patents

Abstract

The invention discloses a radar detection method based on microwave photon-assisted de-skewed bandwidth synthesis. Convert 2n intermediate frequency chirp electrical signals to n channels of orthogonal polarization states of different wavelengths in the optical domain for m frequency multiplication processing, and combine the n channels of optical signals into one channel and transmit it to the transmitting end; at the transmitting end, the One optical signal is separated into 2n channels, each signal is divided into two branches, one of which is photoelectrically converted and amplified and then radiated by the transmitting array element, and the other branch is used as an optical reference signal; The signal is converted to the optical domain for optical de-skew processing, and then undergoes photoelectric conversion for time domain synthesis processing to obtain the target detection result with an equivalent large bandwidth. The invention also discloses a radar detection device based on microwave photon-assisted de-skewed bandwidth synthesis. The invention effectively solves the mismatch problem of optical broadband bearing and electrical narrowband processing, and can realize real-time detection of equivalent large bandwidth and high distance resolution.

Description

Radar detection method and device based on microwave photon-assisted de-skewed bandwidth synthesis

technical field

The invention relates to a radar detection method, in particular to a microwave photon-assisted radar detection method and device.

Background technique

Radar is an important means for humans to detect and identify all-weather targets, and it has extremely important applications in both civilian and military fields. In order to achieve detection with high range resolution, chirp signals with large bandwidth are widely used in radar systems. However, with the increasingly high resolution requirements of radar systems, it is difficult for traditional radar technology to meet the needs of future applications. The application of microwave photonic technology with the characteristics of large bandwidth, low transmission loss, and anti-electromagnetic interference to radar systems can improve the technical performance of traditional radars (see [G.Serafino, F.Scotti, L.Lembo, B.Hussain, C. . Porzi, A. Malacarne, S. Maresca, D. Onori, P. Ghelfi, and A. Bogoni, “Toward a new generation of radar systems based on microwave photonic technologies,” J. Lightw. Technol. 37(2), 643 –650 (2019).]). However, the direct sampling and pulse compression of the ultra-large bandwidth chirp signal requires a high sampling rate and strong signal processing capability, and it is difficult to perform real-time processing.

Optical domain de-slope processing is a technical solution that can reduce the high sampling rate requirement of the radar system in the currently reported microwave photonic radar (see [F.Zhang, Q.Guo, Z.Wang, P.Zhou, G.Zhang, J. Sun, and S. Pan, "Photonics-based broadband radar for high-resolution and real-time inversesynthetic aperture imaging," Opt. Express 25(14), 16274(2017).]). However, in the case of long-distance detection, the de-slope signal frequency of the large-bandwidth chirp signal is still very high, so there is a high requirement for the sampling rate, high-frequency and large-bandwidth electronic devices are required, and it is difficult to process the data in real time. Therefore, it is very meaningful to study how to improve the range resolution of radar systems in the case of low sampling rate requirements, which is very meaningful for the improvement and improvement of target detection capabilities.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is to overcome the deficiencies of the prior art, and to provide a radar detection method based on microwave photon-assisted de-slope and bandwidth synthesis, which has the advantages of microwave photon technology and bandwidth synthesis radar technology at the same time, and can utilize low-cost low-speed The electronic device realizes the fast processing of the equivalent large-bandwidth signal, and realizes the purpose of real-time high-resolution detection.

The radar detection method based on the microwave photon-assisted de-skewed bandwidth synthesis proposed by the present invention includes:

Use 2n intermediate frequency chirp electrical signals with the same frequency modulation slope and the center frequency increase or decrease in turn to perform electro-optic modulation of m frequency doubling mode on the two orthogonal polarization states of n channels of optical signals with different wavelengths in one-to-one correspondence. , and combine the obtained n-channel polarization multiplexing modulated optical signals into one channel and send it to the transmitting end. The bandwidth B _i of the i-th IF chirp electrical signal is greater than or equal to the i+1-th and i-th IF chirp electrical signals. The frequency interval Δf _i between the center frequencies of the signal, m, n are both positive integers, i=1, 2, . . . , 2n-1;

At the transmitting end, wavelength demultiplexing and polarization demultiplexing are performed on the combined optical signal, and the separated 2n channels of modulated optical signals are divided into two channels, and one channel is photoelectrically converted into an m-multiplied chirp signal. It is radiated by the transmitting array element, and the other channel is used as the optical reference signal received by the optical domain de-skew;

At the receiving end, the 2n optical reference signals are used to perform optical domain de-slope processing on the echo signals collected by the 2n receiving array elements respectively, and then 2n low-frequency de-slope signals carrying target information are obtained through photoelectric conversion; The 2n low-frequency de-slope signals are subjected to analog-to-digital conversion, and phase and amplitude compensation is performed in the digital domain, and then the 2n low-frequency de-slope signals are respectively delayed by 0, Δf ₁ /k,..., (Δf ₁ +Δf ₂ +…+Δf _2n-1 )/k, remove the overlapping part to synthesize an equivalent bandwidth m[Δf ₁ +Δf ₂ +…+Δf _2n-1 +(B ₁ +B _2n )/2], where k is the slope of the IF chirp electrical signal.

Preferably, the n paths of polarization multiplexing modulated optical signals are obtained by n polarization division multiplexing modulators, and each polarization division multiplexing modulator modulates two intermediate frequency linear frequency modulation electrical signals respectively on two positive lines of one path optical signal. in the cross-polarized state.

Further preferably, the polarization division multiplexing modulator is a polarization division multiplexing dual-parallel Mach-Zehnder modulator.

Preferably, the optical domain de-skew processing is implemented by a Mach-Zehnder modulator operating at a quadrature bias point.

According to the same inventive idea, the following technical solutions can also be obtained:

A radar detection device based on microwave photon-assisted de-skewed bandwidth synthesis, including:

The optical domain signal frequency multiplication and multiplexing module is used to use the 2n intermediate frequency linear frequency modulation electrical signals with the same frequency modulation slope and the center frequency increase or decrease in turn. The electro-optical modulation of the m frequency doubling mode is respectively performed on the polarization state, and the obtained n channels of polarization multiplexing modulated optical signals are combined into one channel and sent to the transmitting end. The bandwidth B _i of the ith IF chirp electrical signal is greater than or equal to the th The frequency interval Δf _i between i+1 and the center frequency of the i-th IF chirp electrical signal, m, n are both positive integers, i=1, 2, . . . , 2n-1;

The optical domain demultiplexing module, which is located at the transmitting end, is used to perform wavelength demultiplexing and polarization demultiplexing on the combined optical signal, and divide the separated 2n channels of modulated optical signals into two channels, one channel of optoelectronic After being converted into an m-multiplied chirp signal, it is radiated by the transmitting array element, and the other channel is used as the optical reference signal received by the optical domain de-skew;

The optical domain de-skew receiving module, which is located at the receiving end, is used to perform optical domain de-skew processing on the echo signals collected by the 2n receiving array elements by using the 2n optical reference signals, and then obtain 2n carrying targets through photoelectric conversion. low frequency de-slope signal of information;

The digital bandwidth synthesis module is used to perform analog-to-digital conversion on the 2n low-frequency de-slope signals, and perform phase and amplitude compensation in the digital domain, and then extend the 2n low-frequency de-slope signals according to the sequence of numbers from low to high. When 0, Δf ₁ /k,...,(Δf ₁ +Δf ₂ +...+Δf _2n-1 )/k, the overlapping part is removed to synthesize an equivalent bandwidth m[Δf ₁ +Δf ₂ +...+Δf _2n-1 +(B ₁ +B _2n )/2], where k is the slope of the intermediate frequency chirp electrical signal.

Preferably, the optical domain signal frequency doubling and multiplexing module includes n polarization division multiplexing modulators, and each polarization division multiplexing modulator modulates two intermediate frequency linear frequency modulation electrical signals on two positive signals of one optical signal respectively. in the cross-polarized state.

Further preferably, the polarization division multiplexing modulator is a polarization division multiplexing dual-parallel Mach-Zehnder modulator.

Preferably, the optical domain de-skew receiving module includes 2n Mach-Zehnder modulators operating at quadrature bias points.

Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

1. The present invention utilizes low-speed electronic devices to quickly synthesize and process the de-slope signal, realize the processing of equivalent large-bandwidth signals, reduce the system's demand for sampling rate, and can effectively solve the problem of mismatch between optical broadband carrying and electrical narrowband processing, thereby obtaining Real-time high-resolution detection results; 2. The present invention simultaneously uses optical wavelength division multiplexing and partial division multiplexing technology to transmit and process multiple signals, thereby realizing a relatively compact structure and reducing system costs.

Description of drawings

Fig. 1 is the schematic diagram of the structure principle of the radar detection device of the present invention based on the microwave photon-assisted de-skewed bandwidth synthesis;

FIG. 2 is a schematic structural diagram of a preferred embodiment of the radar detection device of the present invention.

Fig. 3 is the principle schematic diagram of bandwidth synthesis;

FIG. 4 is a schematic diagram showing the comparison of effects before and after bandwidth synthesis.

Detailed ways

Aiming at the deficiencies of the prior art, the idea of the present invention is to use the characteristics of microwave photonic technology such as large bandwidth, low loss, and multiple degrees of freedom of parallel processing combined with the characteristics of chirp waves to synthesize and process the de-slope signal with low-cost and low-speed electronic devices, In order to solve the working bandwidth bottleneck of traditional radar, real-time high-resolution detection can be realized.

The radar detection method based on the microwave photon-assisted de-skewed bandwidth synthesis proposed by the present invention includes:

Use 2n intermediate frequency chirp electrical signals with the same frequency modulation slope and the center frequency increase or decrease in turn to perform electro-optic modulation of m frequency doubling mode on the two orthogonal polarization states of n channels of optical signals with different wavelengths in one-to-one correspondence. , and combine the obtained n-channel polarization multiplexing modulated optical signals into one channel and send it to the transmitting end. The bandwidth B _i of the i-th IF chirp electrical signal is greater than or equal to the i+1-th and i-th IF chirp electrical signals. The frequency interval Δf _i between the center frequencies of the signal, m, n are both positive integers, i=1, 2, . . . , 2n-1;

At the transmitting end, wavelength demultiplexing and polarization demultiplexing are performed on the combined optical signal, and the separated 2n channels of modulated optical signals are divided into two channels, and one channel is photoelectrically converted into an m-multiplied chirp signal. It is radiated by the transmitting array element, and the other channel is used as the optical reference signal received by the optical domain de-skew;

At the receiving end, the 2n optical reference signals are used to perform optical domain de-slope processing on the echo signals collected by the 2n receiving array elements respectively, and then 2n low-frequency de-slope signals carrying target information are obtained through photoelectric conversion; The 2n low-frequency de-slope signals are subjected to analog-to-digital conversion, and phase and amplitude compensation is performed in the digital domain, and then the 2n low-frequency de-slope signals are respectively delayed by 0, Δf ₁ /k,..., (Δf ₁ +Δf ₂ +…+Δf _2n-1 )/k, remove the overlapping part to synthesize an equivalent bandwidth m[Δf ₁ +Δf ₂ +…+Δf _2n-1 +(B ₁ +B _2n )/2], where k is the slope of the IF chirp electrical signal.

Fig. 1 shows the basic structure of the radar detection device of the present invention. The dotted line in the figure represents the electrical signal, and the solid line represents the optical signal. As shown in Figure 1, the radar detection device of the present invention includes:

The optical domain signal frequency multiplication and multiplexing module is used to use the 2n intermediate frequency linear frequency modulation electrical signals with the same frequency modulation slope and the center frequency increase or decrease in turn. The electro-optical modulation of the m frequency doubling mode is respectively performed on the polarization state, and the obtained n channels of polarization multiplexing modulated optical signals are combined into one channel and sent to the transmitting end. The bandwidth B _i of the ith IF chirp electrical signal is greater than or equal to the th The frequency interval Δf _i between i+1 and the center frequency of the i-th IF chirp electrical signal, m, n are both positive integers, i=1, 2, . . . , 2n-1;

The optical domain demultiplexing module, which is located at the transmitting end, is used to perform wavelength demultiplexing and polarization demultiplexing on the combined optical signal, and divide the separated 2n channels of modulated optical signals into two channels, one channel of optoelectronic After being converted into an m-multiplied chirp signal, it is radiated by the transmitting array element, and the other channel is used as the optical reference signal received by the optical domain de-skew;

The optical domain de-skew receiving module, which is located at the receiving end, is used to perform optical domain de-skew processing on the echo signals collected by the 2n receiving array elements by using the 2n optical reference signals, and then obtain 2n carrying targets through photoelectric conversion. low frequency de-slope signal of information;

The digital bandwidth synthesis module is used to perform analog-to-digital conversion on the 2n low-frequency de-slope signals, and perform phase and amplitude compensation in the digital domain, and then extend the 2n low-frequency de-slope signals according to the sequence of numbers from low to high. When 0, Δf ₁ /k,...,(Δf ₁ +Δf ₂ +...+Δf _2n-1 )/k, the overlapping part is removed to synthesize an equivalent bandwidth m[Δf ₁ +Δf ₂ +...+Δf _2n-1 +(B ₁ +B _2n )/2], where k is the slope of the intermediate frequency chirp electrical signal.

Wherein, the optical domain signal frequency multiplication and multiplexing module includes n partial division multiplexing modulators, and each partial division multiplexing modulator modulates two intermediate frequency linear frequency modulation electrical signals into two orthogonal optical signals of one optical signal respectively. on the polarization state. By adjusting the bias point of the partial multiplexing modulator, the working mode of the modulator can be controlled, and then the frequency multiplication times m can be adjusted. The polarization multiplexing modulator may be a polarization division multiplexing dual-parallel Mach-Zehnder modulator or a polarization-division multiplexing Mach-Zehnder modulator, etc. The present invention preferably adopts a polarization-division multiplexing dual-parallel Mach-Zehnder modulator.

For the convenience of public understanding, the technical solution of the present invention is further described in detail below through a specific embodiment:

The specific structure of this embodiment is shown in Figure 2, which consists of an optical domain signal frequency doubling and multiplexing module (including a laser, a polarization-division multiplexing double-parallel Mach-Zehnder modulator, and an optical wavelength division multiplexer), an optical-domain demultiplexer Application module (including optical wavelength division multiplexer, polarization beam splitter, coupler, photodetector), optical domain de-skew receiving module (including Mach-Zehnder modulator, photodetector), digital bandwidth synthesis module, optical amplifier, It consists of a power amplifier, a low noise amplifier, and a transceiver array element. The chirp signal in Figure 2 is generated by an electrical signal generator.

First, the optical carriers of different wavelengths generated by n lasers are input to the polarization division multiplexing double parallel Mach-Zehnder modulator. The 2n intermediate frequency chirp signals generated by the electrical signal generator are used as driving signals, which can be expressed as:

Among them, 1≤i≤2n, -T _i /2≤t≤T _i /2, V _s , f _ci , _{ki , and T i are} the amplitude, center frequency, FM slope and pulse width of the signal, respectively; the bandwidth of the signal B _i =k _i T _i , the center frequency interval Δf _i =f _ci+1 -f _ci ; every two electrical intermediate frequency chirps modulate two polarization states of one wavelength, thereby converting 2n electrical intermediate frequency signals into n channels of optical signals, input the n channels of optical signals to the optical wavelength division multiplexer and combine them into one channel of optical modulation signal. The combined optical signal is amplified by the optical amplifier and then input to the optical domain demultiplexing module. By controlling the bias voltage of the modulator, the modulator can generate different sidebands, that is, work in different frequency doubling modes:

1 frequency doubling mode (m=1): the two sub-modulators and their synthesis arms in each polarization state are biased at the orthogonal point, and the two modulator ports are respectively connected to the electric intermediate frequency chirp signal and pass through a 90° microwave Two signals with a phase difference of 90° generated after the bridge; only the carrier and +1 or -1 order sidebands are retained at this time;

Frequency doubling mode (m=2): the two sub-modulators in each polarization state are biased at the minimum point, the synthesis arm is biased at the maximum point, and the two modulator ports are respectively connected to the electrical IF chirp signal ; At this time, only the +1 and -1 order sidebands are retained;

Frequency doubling mode (m=4): the two sub-modulators in each polarization state are biased at the maximum operating point, the synthesis arm is biased at the minimum point, and the two modulator ports are respectively connected to the electrical IF chirp After the signal passes through a 90° microwave bridge, two signals with a phase difference of 90° are generated; at this time, only the +2 and -2 order sidebands are retained.

In this embodiment, the quadruple frequency mode is taken as an example.

In the optical domain demultiplexing module, the optical signals of n different wavelengths in the optical modulation signal are separated into n optical signals by the optical wavelength division multiplexer, and each optical signal passes through a polarization beam splitter, so that the two positive The cross polarization state is separated into two polarization state branches, and finally 2n optical signals are separated. Each optical signal is then divided into two branches through an optical coupler, one of which is provided to the optical domain de-skew receiving module as an optical reference signal, and the other branch is converted into an electrical signal with a frequency of 4 through a photodetector. , the signal after frequency multiplication can be expressed as:

I _i (t)∝cos[2π(4f _ci t+2k _i t ² )] (2)

The signal after 4 times of frequency is fed into the transmitting array element and radiated into the environment containing the detection target after passing through the power amplifier.

The echo signal reflected by the target is received by the receiving array element and enters the low noise amplifier for amplification. The amplified echo signal modulates the reference optical signal through the Mach-Zehnder modulator in the optical domain de-skew receiving module. Here Mach The Zender modulator operates at the quadrature bias point. The output optical signal of the Mach-Zehnder modulator enters the low-frequency photodetector to complete the photoelectric conversion, thereby completing the de-slope. Assuming that the delay of the echo signal is τ, the de-slope signal can be expressed as:

r _i (t)cos{2π[4f _ci τ-2k _i τ ² +4k _i τt]} (3)

For ease of understanding, take two signals (i=1, 2) as an example, and represent them as:

r ₁ (t)=cos{2π[4f _c1 τ-2k ₁ τ ² +4k ₁ τt]} (4)

Let the two signals have the same frequency modulation slope, that is, k ₁ =k ₂ , delay the signal r ₂ (t) by T=Δf ₁ /k, and obtain:

r ₂ (tT)=cos{2π[4f _c1 τ-2k ₁ τ ² +4k ₁ τt]} (6)

It can be seen that the expressions of (4) and (6) are exactly the same, and the two signals can be spliced together at this time. Similarly, the 2n-way de-slope signals can be spliced into one signal after corresponding delay.

After analog-to-digital conversion of 2n signals in the digital bandwidth synthesis module, the 1st to 2nth signals are respectively delayed by 0, Δf ₁ /k, ..., (Δf ₁ +Δf ₂ +...+Δf through digital signal processing. _2n-1 )/k, and remove the overlap to synthesize a chirp signal with an equivalent bandwidth of m[Δf ₁ +Δf ₂ +…+Δf _2n-1 +(B ₁ +B _2n )/2] De-oblique results. FIG. 3 is a schematic diagram of the basic principle of bandwidth synthesis after microwave photon de-slope processing, and the waveform of the de-slope signal is represented in the dotted box in the figure. Figure 4 is a schematic diagram of the power spectrum comparison before and after de-slope signal synthesis. It is obvious that the main lobe of the signal power spectrum after synthesis is much narrower than that before synthesis, which indicates that the resolution after synthesis has been greatly improved. The distance, speed, image and other information of the detected target can be extracted from the synthesized de-slope processing result through the existing radar algorithm.

Claims (8)

1. The radar detection method based on bandwidth synthesis after microwave photon-assisted deskew is characterized by comprising the following steps:

2n intermediate frequency linear frequency modulation electric signals with equal frequency modulation slope and sequentially increased or decreased center frequency are used for respectively carrying out electro-optical modulation in m frequency multiplication mode on two orthogonal polarization states of n paths of optical signals with different wavelengths in a one-to-one correspondence mode, the obtained n paths of polarization multiplexing modulation optical signals are combined into a path of combined optical signal and then sent to a transmitting end, and the bandwidth B of the ith intermediate frequency linear frequency modulation electric signal is_iFrequency interval delta f between the central frequency of the (i + 1) th intermediate frequency linear frequency modulation electric signal and the central frequency of the (i) th intermediate frequency linear frequency modulation electric signal_iM and n are positive integers, i is 1,2, …,2 n-1;

at the transmitting end, wavelength demultiplexing and polarization demultiplexing are carried out on the combined optical signal, the 2n paths of separated modulated optical signals are divided into two paths, one path of modulated optical signals is subjected to photoelectric conversion to m frequency-doubled linear frequency modulation signals and then is radiated by a transmitting array element, and the other path of modulated optical signals is used as optical domain deskew received optical reference signals;

at a receiving end, the 2n optical reference signals are utilized to respectively perform optical domain deskew processing on echo signals collected by the 2n receiving array elements, and then 2n low-frequency deskew signals carrying target information are obtained through photoelectric conversion; performing analog-to-digital conversion on the 2n low-frequency deskew signals, performing phase and amplitude compensation in a digital domain, and delaying the 2n low-frequency deskew signals by 0, delta f and delta f respectively according to the sequence of numbers from low to high₁/k，…，(Δf₁+Δf₂+…+Δf_2n-1) K, removing the overlapping part to synthesize an equivalent bandwidth of m [ Delta f ]₁+Δf₂+…+Δf_2n-1+(B₁+B_2n)/2]Wherein k is the slope of the intermediate frequency chirp signal, B_2nIs the bandwidth of the 2 nth intermediate frequency chirp signal.

2. The radar detection method of claim 1, wherein the n polarization-multiplexed modulated optical signals are obtained by n polarization-division-multiplexed modulators, each polarization-division-multiplexed modulator modulating two intermediate-frequency chirp signals onto two orthogonal polarization states of one optical signal, respectively.

3. The radar detection method of claim 2 wherein the partial division multiplexed modulator is a partial division multiplexed dual parallel mach-zehnder modulator.

4. The radar detection method of claim 1 wherein the optical domain deskew is performed by a mach-zehnder modulator operating at a quadrature bias point.

5. Radar detection device based on bandwidth synthesis after supplementary declivity of microwave photon, its characterized in that includes:

an optical domain signal frequency doubling and multiplexing module, which is used for performing electro-optical modulation of m frequency doubling modes on two orthogonal polarization states of n paths of optical signals with different wavelengths by using 2n intermediate frequency linear frequency modulation electric signals with equal frequency modulation slopes and sequentially increased or decreased center frequencies, combining the obtained n paths of polarization multiplexing modulation optical signals into a path of combined optical signal and then transmitting the combined optical signal to a transmitting end, wherein the bandwidth B of the ith intermediate frequency linear frequency modulation electric signal is_iFrequency interval delta f between the central frequency of the (i + 1) th intermediate frequency linear frequency modulation electric signal and the central frequency of the (i) th intermediate frequency linear frequency modulation electric signal_iM and n are positive integers, i is 1,2, …,2 n-1;

the optical domain demultiplexing module is positioned at the transmitting end and used for carrying out wavelength demultiplexing and polarization demultiplexing on the combined optical signal, dividing the 2n paths of separated modulated optical signals into two paths, carrying out photoelectric conversion on one path of modulated optical signals into m frequency-doubled linear frequency signals, radiating the m frequency-doubled linear frequency signals by a transmitting array element, and taking the other path of modulated optical signals as optical domain deskew received optical reference signals;

the optical domain deskew receiving module is positioned at a receiving end and used for respectively carrying out optical domain deskew processing on echo signals collected by the 2n receiving array elements by utilizing the 2n optical reference signals and then obtaining 2n low-frequency deskew signals carrying target information through photoelectric conversion;

a digital bandwidth synthesis module for performing analog-to-digital conversion on the 2n low-frequency deskew signals, performing phase and amplitude compensation in a digital domain, and delaying the 2n low-frequency deskew signals by 0, delta f according to the sequence of numbers from low to high₁/k，…，(Δf₁+Δf₂+…+Δf_2n-1) K, removing the overlapping part to synthesize an equivalent bandwidth of m [ Delta f ]₁+Δf₂+…+Δf_2n-1+(B₁+B_2n)/2]Wherein k is the slope of the intermediate frequency chirp signal, B_2nIs the bandwidth of the 2 nth intermediate frequency chirp signal.

6. The radar detection device of claim 5, wherein the optical domain signal frequency doubling and multiplexing module includes n polarization division multiplexing modulators, each polarization division multiplexing modulator modulating two intermediate frequency chirp signals onto two orthogonal polarization states of one optical signal, respectively.

7. The radar detection device of claim 6 wherein the partial division multiplexed modulator is a partial division multiplexed dual parallel mach-zehnder modulator.

8. The radar detection device of claim 5 wherein the optical domain deskew receiving module comprises 2n mach-zehnder modulators operating at quadrature bias points.

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