Constant modulus blind equalization-minimum mean square frequency domain equalization method for dual-mode switching

Abstract

The invention discloses a dual-mode switching constant modulus blind equalization-minimum mean square frequency domain equalization method, which specifically comprises the following steps that: a transmitting end modulates N paths of input electric signals # imgabs0 # onto N paths of Gaussian beams respectively, and outputs N paths of Gaussian beams carrying data information; enabling the N paths of Gaussian beams carrying data information obtained in the step 1 to pass through different spiral phase plates to generate N OAM beams carrying different topological charges; n OAM light beams with different topological charges are multiplexed into one path of OAM multiplexed light beam by using an OAM state multiplexer, and the OAM multiplexed light beam reaches a receiving end after passing through an atmospheric turbulence channel; the method comprises the following steps: processing an OAM multiplexing light beam received by a receiving end through an OAM state demultiplexer and a deconverter to obtain each path of user receiving signal # imgabs1 #; and processing each path of user receiving signal # imgabs2 # by using a frequency domain equalizer so as to continuously update a filter tap vector # imgabs3 #. According to the invention, the problems of signal attenuation and inter-mode crosstalk of a traditional OAM multiplexing system in the prior art are solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal processing of an orbital angular momentum multiplexing communication system, and relates to a dual-mode switching constant modulus blind equalization-minimum mean square frequency domain equalization method. Background Art

[0002] Wireless optical communications are rapidly developing due to their advantages, including large transmission bandwidth, lack of spectrum licensing, and excellent security and confidentiality. However, with the increasing demand for system transmission capacity, traditional optical communication technologies are gradually approaching their capacity limits. To overcome this limitation, orbital angular momentum (OAM) multiplexing optical communication technology has become a key technology.

[0003] However, conventional orbital angular momentum multiplexing (OAM) optical communication technology is susceptible to factors such as atmospheric turbulence, leading to channel attenuation and mode crosstalk, which significantly degrades communication system performance. To address this issue, applying multiple-input-output (MIMO) equalization technology to OAM multiplexing communication systems has become an important research direction. Summary of the Invention

[0004] The purpose of the present invention is to provide a dual-mode switching constant modulus blind equalization-minimum mean square frequency domain equalization method, which solves the signal attenuation and inter-mode crosstalk problems of traditional OAM multiplexing systems in the prior art.

[0005] The technical solution adopted by the present invention is a dual-mode switching constant modulus blind equalization-minimum mean square frequency domain equalization method, which specifically includes the following steps: Step 1: The transmitter inputs N electrical signals They are modulated onto N Gaussian beams respectively, and output N Gaussian beams carrying data information; Step 2: Pass the N data-carrying Gaussian beams obtained in step 1 through different spiral phase plates to generate N OAM beams carrying different topological charges. Step 3: Use an OAM state multiplexer to multiplex N OAM beams with different topological charges into one OAM multiplexed beam. The OAM multiplexed beam passes through the atmospheric turbulence channel and reaches the receiver. Step 4: The OAM multiplexed beam received by the receiving end is processed by the OAM state demultiplexer and deconverter to obtain the received signal for each user. ; Step 5: Use frequency domain equalizer to receive the signal from each user. Processing is performed to continuously update the filter tap vector .

[0006] The present invention is also characterized in that: In step 1, input the N-way electrical signal After passing through the optical modulator, it is modulated into a Gaussian beam and outputs N Gaussian beams carrying data information. The process is:

[0007]

[0008] in, is the amplitude of the N-way Gaussian beam at the beam waist position, is the radiation distance from the light beam to the transmission axis, is the waist radius.

[0009] In step 2, the N OAM beams carrying different topological charges are:

[0010] Where, is the nth input electrical signal, is the amplitude of the n-th Gaussian beam, is the spiral light phase added by the n-th Gaussian beam, is the topological charge value of the nth OAM beam, is the azimuth.

[0011] In step 3, N OAM beams with different topological charges are multiplexed into one channel through the OAM state multiplexer:

[0012] The OAM multiplexed beam passes through the atmospheric turbulence channel and becomes:

[0013] in, refers to the atmospheric turbulence phase factor, is the channel noise.

[0014] In step 4, the OAM multiplexed light beam received by the receiving end is processed by the OAM state demultiplexer and deconverter as follows: Where, The topological charge is The complex conjugate of the electric field at is the beam transmission distance.

[0015] The specific process of step 5 is: Step 5.1, assume that the received signal of each user obtained in step 4 is Length is , and after serial-to-parallel conversion, it is divided into data blocks of length M, represents the subscript of the block, then The relationship between time and block is:

[0016] At this time, the user receives the signal The output in the frequency domain is expressed as:

[0017] Wherein, FFT stands for Fast Fourier Transform; Step 5.2, initialize the frequency domain filter tap coefficients:

[0018] Where, is the time domain filter tap vector, is an M×1-dimensional zero vector; Step 5.3: Use the frequency domain equalizer to process the frequency domain input signal to obtain the frequency domain output signal. After the inverse fast Fourier transform (IFFT), the time domain output signal is obtained. :

[0019] in, represents the frequency domain filter tap vector, Indicates taking the last M elements of the vector in the brackets; Step 5.4, using constant modulus blind equalization, i.e. CMA algorithm, to perform iterative equalization and update the filter tap vector; Step 5.5: Determine the error signal variation using the CMA algorithm. , according to the change of error signal The relationship between the preset threshold and the CMA algorithm is used to switch between the CMA algorithm and the LMS algorithm. Specifically:

[0020] Where, For the The error value when executing the CMA algorithm for the first time, For the k -1 error value when executing the CMA algorithm, is the preset threshold, when When , continue to use the frequency domain CMA algorithm, and update the number of iterations of the CMA equalization stage, repeat step 5.4, when When , it switches to the LMS algorithm to continue iterative equalization; Step 5.6, using the least mean square frequency domain equalization, i.e., LMS algorithm, to perform iterative equalization and update the filter tap vector; Step 5.7, by continuously updating the filter tap vector, reduce the received signal N-way input electrical signal The error between .

[0021] The specific process of step 5.4 is as follows: Step 5.4.1: According to the principle of CMA algorithm, calculate the time domain error signal of CMA equalization stage:

[0022] in, is the modulus value, which is a constant and is expressed as: , is the original time domain signal at the transmitter; Step 5.4.2, the time domain error signal of the CMA stage Perform zero padding and perform FFT again to obtain the frequency domain error signal of the corresponding CMA equalization stage :

[0023] Step 5.4.3, use the frequency domain error signal obtained in the CMA stage With the frequency domain input signal Perform the operation to obtain the gradient vector of the corresponding CMA stage:

[0024] in, is the gradient vector of the CMA algorithm equalization stage, represents conjugation, Indicates taking the first M elements; Step 5.4.4, use the corresponding gradient vector And the corresponding step size to update the filter tap vector:

[0025] Where, is the step size of the CMA algorithm, is a 1×M-dimensional zero vector.

[0026] The specific process of step 5.6 is: In step 5.6.1, according to the principle of LMS algorithm, the time domain error signal of the LMS equalization stage is calculated:

[0027] Where, is the original time domain signal at the transmitter, y( k ) is the time domain output signal; Step 5.6.2, the time domain error signal of the LMS stage Perform zero padding and perform FFT again to obtain the frequency domain error signal of the corresponding LMS stage :

[0028] Step 5.6.3, use the frequency domain error signal obtained in the LMS phase With the frequency domain input signal Perform the operation to obtain the gradient vector of the corresponding LMS stage;

[0029] in, is the gradient vector of the LMS algorithm equalization stage, represents conjugation, Indicates taking the first M elements; Step 5.6.4, use the corresponding gradient vector And the corresponding step size to update the filter tap vector, the specific formula is:

[0030] Where, is the step size of the LMS algorithm, is a 1×M-dimensional zero vector; Step 5.6.5, judge Is it ,like , then the iteration ends; if ,but , repeat steps 5.6.1 to 5.6.4.

[0031] The beneficial effects of the present invention are as follows: The dual-mode switching constant modulus blind equalization-minimum mean square frequency domain equalization method of the present invention effectively reduces the system bit error rate, suppresses system crosstalk, significantly reduces the system calculation complexity, and accelerates the convergence speed of the algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1a is the constellation diagram corresponding to different users at the receiving end when not affected by turbulence; Figure 1b This is a constellation diagram corresponding to different users at the receiving end when the embodiment 6 of the constant modulus blind equalization-minimum mean square frequency domain equalization method of the present invention is affected by turbulence and is not used; Figure 1c is a constellation diagram corresponding to different users at the receiving end when affected by turbulence and using embodiment 6 of the present invention; Figure 2 is a graph showing the average bit error rate obtained by using Example 6 of the present invention and the change of the atmospheric turbulence structure constant; Figure 3 is a graph showing the variation of the average bit error rate with the signal-to-noise ratio obtained by using Example 6 of the present invention; Figure 4 It is an iterative convergence curve diagram in Example 6 of the present invention. DETAILED DESCRIPTION

[0033] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0034] The technical solution adopted by the present invention is a dual-mode switching constant modulus blind equalization-minimum mean square frequency domain equalization method, which specifically includes the following steps: Step 1: The transmitter inputs N electrical signals They are modulated onto N Gaussian beams respectively, and output N Gaussian beams carrying data information; In step 1, input the N-way electrical signal After passing through the optical modulator, it is modulated into a Gaussian beam and outputs N Gaussian beams carrying data information. The process is:

[0035]

[0036] in, is the amplitude of the N-way Gaussian beam at the beam waist position, is the radiation distance from the light beam to the transmission axis, is the waist radius.

[0037] Step 2: Pass the N data-carrying Gaussian beams obtained in step 1 through different spiral phase plates to generate N OAM beams carrying different topological charges. In step 2, the N OAM beams carrying different topological charges are:

[0038] Where, is the nth input electrical signal, is the amplitude of the n-th Gaussian beam, is the spiral light phase added by the n-th Gaussian beam, is the topological charge value of the nth OAM beam, is the azimuth.

[0039] Step 3: Use an OAM state multiplexer to multiplex N OAM beams with different topological charges into one OAM multiplexed beam. The OAM multiplexed beam passes through the atmospheric turbulence channel and reaches the receiver. In step 3, N OAM beams with different topological charges are multiplexed into one channel through the OAM state multiplexer:

[0040] The OAM multiplexed beam passes through the atmospheric turbulence channel and becomes:

[0041] in, refers to the atmospheric turbulence phase factor, is the channel noise.

[0042] Step 4: The OAM multiplexed beam received by the receiving end is processed by the OAM state demultiplexer and deconverter to obtain the received signal for each user. ; In step 4, the OAM multiplexed light beam received by the receiving end is processed by the OAM state demultiplexer and deconverter as follows: Where, The topological charge is The complex conjugate of the electric field at is the beam transmission distance.

[0043] Step 5: Use frequency domain equalizer to receive the signal from each user. Processing is performed to continuously update the filter tap vector .

[0044] The specific process of step 5 is: Step 5.1, assume that the received signal of each user obtained in step 4 is Length is , and after serial-to-parallel conversion, it is divided into data blocks of length M, represents the subscript of the block, then The relationship between time and block is:

[0045] At this time, the user receives the signal The output in the frequency domain is expressed as:

[0046] Wherein, FFT stands for Fast Fourier Transform; Step 5.2, initialize the frequency domain filter tap coefficients:

[0047] Where, is the time domain filter tap vector, is an M×1-dimensional zero vector; Step 5.3: Use the frequency domain equalizer to process the frequency domain input signal to obtain the frequency domain output signal. After the inverse fast Fourier transform (IFFT), the time domain output signal is obtained. :

[0048] in, represents the frequency domain filter tap vector, Indicates taking the last M elements of the vector in the brackets; Step 5.4, using constant modulus blind equalization, i.e. CMA algorithm, to perform iterative equalization and update the filter tap vector; The specific process of step 5.4 is as follows: Step 5.4.1: According to the principle of CMA algorithm, calculate the time domain error signal of CMA equalization stage:

[0049] in, is the modulus value, which is a constant and is expressed as: , is the original time domain signal at the transmitter; Step 5.4.2, the time domain error signal of the CMA stage Perform zero padding and perform FFT again to obtain the frequency domain error signal of the corresponding CMA equalization stage :

[0050] Step 5.4.3, use the frequency domain error signal obtained in the CMA stage With the frequency domain input signal Perform the operation to obtain the gradient vector of the corresponding CMA stage:

[0051] in, is the gradient vector of the CMA algorithm equalization stage, represents conjugation, Indicates taking the first M elements; Step 5.4.4, use the corresponding gradient vector And the corresponding step size to update the filter tap vector:

[0052] Where, is the step size of the CMA algorithm, is a 1×M-dimensional zero vector.

[0053] Step 5.5: Determine the error signal variation using the CMA algorithm. , according to the change of error signal The relationship between the preset threshold and the CMA algorithm is used to switch between the CMA algorithm and the LMS algorithm. Specifically:

[0054] Where, For the The error value when executing the CMA algorithm for the first time, For the k -1 error value when executing the CMA algorithm, is the preset threshold, when When , continue to use the frequency domain CMA algorithm, and update the number of iterations of the CMA equalization stage, repeat step 5.4, when When , it switches to the LMS algorithm to continue iterative equalization; Step 5.6, using the least mean square frequency domain equalization, i.e., LMS algorithm, to perform iterative equalization and update the filter tap vector; The specific process of step 5.6 is: In step 5.6.1, according to the principle of LMS algorithm, the time domain error signal of the LMS equalization stage is calculated:

[0055] Where, is the original time domain signal at the transmitter, y( k ) is the time domain output signal; Step 5.6.2, the time domain error signal of the LMS stage Perform zero padding and perform FFT again to obtain the frequency domain error signal of the corresponding LMS stage :

[0056] Step 5.6.3, use the frequency domain error signal obtained in the LMS phase With the frequency domain input signal Perform the operation to obtain the gradient vector of the corresponding LMS stage;

[0057] in, is the gradient vector of the LMS algorithm equalization stage, represents conjugation, Indicates taking the first M elements; Step 5.6.4, use the corresponding gradient vector And the corresponding step size to update the filter tap vector, the specific formula is:

[0058] Where, is the step size of the LMS algorithm, is a 1×M-dimensional zero vector; Step 5.6.5, judge Is it ,like , then the iteration ends; if ,but , repeat steps 5.6.1 to 5.6.4.

[0059] Step 5.7, by continuously updating the filter tap vector, reduce the received signal N-way input electrical signal The error between .

[0060] Solve problems such as signal fading and mode crosstalk caused by factors such as atmospheric turbulence - reduce bit error rate, suppress system crosstalk, and improve system communication quality.

[0061] Example 1 The dual-mode switching constant modulus blind equalization-minimum mean square frequency domain equalization method proposed in this embodiment specifically includes the following steps: Step 1: The transmitter inputs N electrical signals They are modulated onto N Gaussian beams respectively, and output N Gaussian beams carrying data information; Step 2: Pass the N data-carrying Gaussian beams obtained in step 1 through different spiral phase plates to generate N OAM beams carrying different topological charges. Step 3: Use an OAM state multiplexer to multiplex N OAM beams with different topological charges into one OAM multiplexed beam. The OAM multiplexed beam passes through the atmospheric turbulence channel and reaches the receiver. Step 4: The OAM multiplexed beam received by the receiving end is processed by the OAM state demultiplexer and deconverter to obtain the received signal for each user. ; Step 5: Use frequency domain equalizer to receive the signal from each user. Processing is performed to continuously update the filter tap vector .

[0062] Example 2 The dual-mode switching constant modulus blind equalization-minimum mean square frequency domain equalization method proposed in this embodiment specifically includes the following steps: Step 1: The transmitter inputs N electrical signals They are modulated onto N Gaussian beams respectively, and output N Gaussian beams carrying data information; In step 1, input the N-way electrical signal After passing through the optical modulator, it is modulated into a Gaussian beam and outputs N Gaussian beams carrying data information. The process is:

[0063]

[0064] in, is the amplitude of the N-way Gaussian beam at the beam waist position, is the radiation distance from the light beam to the transmission axis, is the waist radius.

[0065] Step 2: Pass the N data-carrying Gaussian beams obtained in step 1 through different spiral phase plates to generate N OAM beams carrying different topological charges. In step 2, the N OAM beams carrying different topological charges are:

[0066] Where, is the nth input electrical signal, is the amplitude of the n-th Gaussian beam, is the spiral light phase added by the n-th Gaussian beam, is the topological charge value of the nth OAM beam, is the azimuth.

[0067] Step 3: Use an OAM state multiplexer to multiplex N OAM beams with different topological charges into one OAM multiplexed beam. The OAM multiplexed beam passes through the atmospheric turbulence channel and reaches the receiver. Step 4: The OAM multiplexed beam received by the receiving end is processed by the OAM state demultiplexer and deconverter to obtain the received signal for each user. ; Step 5: Use frequency domain equalizer to receive the signal from each user. Processing is performed to continuously update the filter tap vector .

[0068] Example 3 The dual-mode switching constant modulus blind equalization-minimum mean square frequency domain equalization method proposed in this embodiment specifically includes the following steps: Step 1: The transmitter inputs N electrical signals They are modulated onto N Gaussian beams respectively, and output N Gaussian beams carrying data information; In step 1, input the N-way electrical signal After passing through the optical modulator, it is modulated into a Gaussian beam and outputs N Gaussian beams carrying data information. The process is:

[0069]

[0070] in, is the amplitude of the N-way Gaussian beam at the beam waist position, is the radiation distance from the light beam to the transmission axis, is the waist radius.

[0071] Step 2: Pass the N data-carrying Gaussian beams obtained in step 1 through different spiral phase plates to generate N OAM beams carrying different topological charges. In step 2, the N OAM beams carrying different topological charges are:

[0072] Where, is the nth input electrical signal, is the amplitude of the n-th Gaussian beam, is the spiral light phase added by the n-th Gaussian beam, is the topological charge value of the nth OAM beam, is the azimuth.

[0073] Step 3: Use an OAM state multiplexer to multiplex N OAM beams with different topological charges into one OAM multiplexed beam. The OAM multiplexed beam passes through the atmospheric turbulence channel and reaches the receiver. In step 3, N OAM beams with different topological charges are multiplexed into one channel through the OAM state multiplexer:

[0074] The OAM multiplexed beam passes through the atmospheric turbulence channel and becomes:

[0075] in, refers to the atmospheric turbulence phase factor, is the channel noise.

[0076] Step 4: The OAM multiplexed beam received by the receiving end is processed by the OAM state demultiplexer and deconverter to obtain the received signal for each user. ; Step 5: Use frequency domain equalizer to receive the signal from each user. Processing is performed to continuously update the filter tap vector .

[0077] Example 4 The dual-mode switching constant modulus blind equalization-minimum mean square frequency domain equalization method proposed in this embodiment specifically includes the following steps: Step 1: The transmitter inputs N electrical signals They are modulated onto N Gaussian beams respectively, and output N Gaussian beams carrying data information; In step 1, input the N-way electrical signal After passing through the optical modulator, it is modulated into a Gaussian beam and outputs N Gaussian beams carrying data information. The process is:

[0078]

[0079] in, is the amplitude of the N-way Gaussian beam at the beam waist position, is the radiation distance from the light beam to the transmission axis, is the waist radius.

[0080] Step 2: Pass the N data-carrying Gaussian beams obtained in step 1 through different spiral phase plates to generate N OAM beams carrying different topological charges. In step 2, the N OAM beams carrying different topological charges are:

[0081] Where, is the nth input electrical signal, is the amplitude of the n-th Gaussian beam, is the spiral light phase added by the n-th Gaussian beam, is the topological charge value of the nth OAM beam, is the azimuth.

[0082] Step 3: Use an OAM state multiplexer to multiplex N OAM beams with different topological charges into one OAM multiplexed beam. The OAM multiplexed beam passes through the atmospheric turbulence channel and reaches the receiver. In step 3, N OAM beams with different topological charges are multiplexed into one channel through the OAM state multiplexer:

[0083] The OAM multiplexed beam passes through the atmospheric turbulence channel and becomes:

[0084] in, refers to the atmospheric turbulence phase factor, is the channel noise.

[0085] Step 4: The OAM multiplexed beam received by the receiving end is processed by the OAM state demultiplexer and deconverter to obtain the received signal for each user. ; In step 4, the OAM multiplexed light beam received by the receiving end is processed by the OAM state demultiplexer and deconverter as follows: Where, The topological charge is The complex conjugate of the electric field at is the beam transmission distance.

[0086] Step 5: Use frequency domain equalizer to receive the signal from each user. Processing is performed to continuously update the filter tap vector .

[0087] Example 5 The dual-mode switching constant modulus blind equalization-minimum mean square frequency domain equalization method proposed in this embodiment specifically includes the following steps: Step 1: The transmitter inputs N electrical signals They are modulated onto N Gaussian beams respectively, and output N Gaussian beams carrying data information; In step 1, input the N-way electrical signal After passing through the optical modulator, it is modulated into a Gaussian beam and outputs N Gaussian beams carrying data information. The process is:

[0088]

[0089] in, is the amplitude of the N-way Gaussian beam at the beam waist position, is the radiation distance from the light beam to the transmission axis, is the waist radius.

[0090] Step 2: Pass the N data-carrying Gaussian beams obtained in step 1 through different spiral phase plates to generate N OAM beams carrying different topological charges. In step 2, the N OAM beams carrying different topological charges are:

[0091] Where, is the nth input electrical signal, is the amplitude of the n-th Gaussian beam, is the spiral light phase added by the n-th Gaussian beam, is the topological charge value of the nth OAM beam, is the azimuth.

[0092] Step 3: Use an OAM state multiplexer to multiplex N OAM beams with different topological charges into one OAM multiplexed beam. The OAM multiplexed beam passes through the atmospheric turbulence channel and reaches the receiver. In step 3, N OAM beams with different topological charges are multiplexed into one channel through the OAM state multiplexer:

[0093] The OAM multiplexed beam passes through the atmospheric turbulence channel and becomes:

[0094] in, refers to the atmospheric turbulence phase factor, is the channel noise.

[0095] Step 4: The OAM multiplexed beam received by the receiving end is processed by the OAM state demultiplexer and deconverter to obtain the received signal for each user. ; In step 4, the OAM multiplexed light beam received by the receiving end is processed by the OAM state demultiplexer and deconverter as follows: Where, The topological charge is The complex conjugate of the electric field at is the beam transmission distance.

[0096] Step 5: Use frequency domain equalizer to receive the signal from each user. Processing is performed to continuously update the filter tap vector .

[0097] The specific process of step 5 is: Step 5.1, assume that the received signal of each user obtained in step 4 is Length is , and after serial-to-parallel conversion, it is divided into data blocks of length M, represents the subscript of the block, then The relationship between time and block is:

[0098] At this time, the user receives the signal The output in the frequency domain is expressed as:

[0099] Wherein, FFT stands for Fast Fourier Transform; Step 5.2, initialize the frequency domain filter tap coefficients:

[0100] Where, is the time domain filter tap vector, is an M×1-dimensional zero vector; Step 5.3: Use the frequency domain equalizer to process the frequency domain input signal to obtain the frequency domain output signal. After the inverse fast Fourier transform (IFFT), the time domain output signal is obtained. :

[0101] in, represents the frequency domain filter tap vector, Indicates taking the last M elements of the vector in the brackets; Step 5.4, using constant modulus blind equalization, i.e. CMA algorithm, to perform iterative equalization and update the filter tap vector; The specific process of step 5.4 is: Step 5.4.1: According to the principle of CMA algorithm, calculate the time domain error signal of CMA equalization stage:

[0102] in, is the modulus value, which is a constant and is expressed as: , is the original time domain signal at the transmitter; Step 5.4.2, the time domain error signal of the CMA stage Perform zero padding and perform FFT again to obtain the frequency domain error signal of the corresponding CMA equalization stage :

[0103] Step 5.4.3, use the frequency domain error signal obtained in the CMA stage With the frequency domain input signal Perform the operation to obtain the gradient vector of the corresponding CMA stage:

[0104] in, is the gradient vector of the CMA algorithm equalization stage, represents conjugation, Indicates taking the first M elements; Step 5.4.4, use the corresponding gradient vector And the corresponding step size to update the filter tap vector:

[0105] Where, is the step size of the CMA algorithm, is a 1×M-dimensional zero vector.

[0106] Step 5.5: Determine the error signal variation using the CMA algorithm. , according to the change of error signal The relationship between the preset threshold and the CMA algorithm is used to switch between the CMA algorithm and the LMS algorithm. Specifically:

[0107] Where, For the The error value when executing the CMA algorithm for the first time, For the k -1 error value when executing the CMA algorithm, is the preset threshold, when When , continue to use the frequency domain CMA algorithm, and update the number of iterations of the CMA equalization stage, repeat step 5.4, when When , it switches to the LMS algorithm to continue iterative equalization; Step 5.6, using the least mean square frequency domain equalization, i.e., LMS algorithm, to perform iterative equalization and update the filter tap vector; Step 5.7, by continuously updating the filter tap vector, reduce the received signal N-way input electrical signal The error between .

[0108] Example 6 The dual-mode switching constant modulus blind equalization-minimum mean square frequency domain equalization method proposed in this embodiment specifically includes the following steps: Step 1: The transmitter inputs N electrical signals They are modulated onto N Gaussian beams respectively, and output N Gaussian beams carrying data information; In step 1, input the N-way electrical signal After passing through the optical modulator, it is modulated into a Gaussian beam and outputs N Gaussian beams carrying data information. The process is:

[0109]

[0110] in, is the amplitude of the N-way Gaussian beam at the beam waist position, is the radiation distance from the light beam to the transmission axis, is the waist radius.

[0111] Step 2: Pass the N data-carrying Gaussian beams obtained in step 1 through different spiral phase plates to generate N OAM beams carrying different topological charges. In step 2, the N OAM beams carrying different topological charges are:

[0112] Where, is the nth input electrical signal, is the amplitude of the n-th Gaussian beam, is the spiral light phase added by the n-th Gaussian beam, is the topological charge value of the nth OAM beam, is the azimuth.

[0113] Step 3: Use an OAM state multiplexer to multiplex N OAM beams with different topological charges into one OAM multiplexed beam. The OAM multiplexed beam passes through the atmospheric turbulence channel and reaches the receiver. In step 3, N OAM beams with different topological charges are multiplexed into one channel through the OAM state multiplexer:

[0114] The OAM multiplexed beam passes through the atmospheric turbulence channel and becomes:

[0115] in, refers to the atmospheric turbulence phase factor, is the channel noise.

[0116] Step 4: The OAM multiplexed beam received by the receiving end is processed by the OAM state demultiplexer and deconverter to obtain the received signal for each user. ; In step 4, the OAM multiplexed light beam received by the receiving end is processed by the OAM state demultiplexer and deconverter as follows: Where, The topological charge is The complex conjugate of the electric field at is the beam transmission distance.

[0117] Step 5: Use frequency domain equalizer to receive the signal from each user. Processing is performed to continuously update the filter tap vector .

[0118] The specific process of step 5 is: Step 5.1, assume that the received signal of each user obtained in step 4 is Length is , and after serial-to-parallel conversion, it is divided into data blocks of length M, represents the subscript of the block, then The relationship between time and block is:

[0119] At this time, the user receives the signal The output in the frequency domain is expressed as:

[0120] Wherein, FFT stands for Fast Fourier Transform; Step 5.2, initialize the frequency domain filter tap coefficients:

[0121] Where, is the time domain filter tap vector, is an M×1-dimensional zero vector; Step 5.3: Use the frequency domain equalizer to process the frequency domain input signal to obtain the frequency domain output signal. After the inverse fast Fourier transform (IFFT), the time domain output signal is obtained. :

[0122] in, represents the frequency domain filter tap vector, Indicates taking the last M elements of the vector in the brackets; Step 5.4, using constant modulus blind equalization, i.e. CMA algorithm, to perform iterative equalization and update the filter tap vector; The specific process of step 5.4 is: Step 5.4.1: According to the principle of CMA algorithm, calculate the time domain error signal of CMA equalization stage:

[0123] in, is the modulus value, which is a constant and is expressed as: , is the original time domain signal at the transmitter; Step 5.4.2, the time domain error signal of the CMA stage Perform zero padding and perform FFT again to obtain the frequency domain error signal of the corresponding CMA equalization stage :

[0124] Step 5.4.3, use the frequency domain error signal obtained in the CMA stage With the frequency domain input signal Perform the operation to obtain the gradient vector of the corresponding CMA stage:

[0125] in, is the gradient vector of the CMA algorithm equalization stage, represents conjugation, Indicates taking the first M elements; Step 5.4.4, use the corresponding gradient vector And the corresponding step size to update the filter tap vector:

[0126] Where, is the step size of the CMA algorithm, is a 1×M-dimensional zero vector.

[0127] Step 5.5: Determine the error signal variation using the CMA algorithm. , according to the change of error signal The relationship between the preset threshold and the CMA algorithm is used to switch between the CMA algorithm and the LMS algorithm. Specifically:

[0128] Where, For the The error value when executing the CMA algorithm for the first time, For the k -1 error value when executing the CMA algorithm, is the preset threshold, when When , continue to use the frequency domain CMA algorithm, and update the number of iterations of the CMA equalization stage, repeat step 5.4, when When , it switches to the LMS algorithm to continue iterative equalization; Step 5.6, using the least mean square frequency domain equalization, i.e., LMS algorithm, to perform iterative equalization and update the filter tap vector; The specific process of step 5.6 is: In step 5.6.1, according to the principle of LMS algorithm, the time domain error signal of the LMS equalization stage is calculated:

[0129] Where, is the original time domain signal at the transmitter, y( k ) is the time domain output signal; Step 5.6.2, the time domain error signal of the LMS stage Perform zero padding and perform FFT again to obtain the frequency domain error signal of the corresponding LMS stage :

[0130] Step 5.6.3, use the frequency domain error signal obtained in the LMS phase With the frequency domain input signal Perform the operation to obtain the gradient vector of the corresponding LMS stage;

[0131] in, is the gradient vector of the LMS algorithm equalization stage, represents conjugation, Indicates taking the first M elements; Step 5.6.4, use the corresponding gradient vector And the corresponding step size to update the filter tap vector, the specific formula is:

[0132] Where, is the step size of the LMS algorithm, is a 1×M-dimensional zero vector; Step 5.6.5, judge Is it ,like , then the iteration ends; if ,but , repeat steps 5.6.1 to 5.6.4.

[0133] Step 5.7, by continuously updating the filter tap vector, reduce the received signal N-way input electrical signal The error between .

[0134] After steps 1 to 5, Figures 1 to 4 are obtained through simulation experiments. Figure 1 shows the constellation diagrams corresponding to different users before and after equalization. The Error Vector Magnitude (EVM) is defined as the difference between the actual measured signal and the ideal signal vector, which can fully reflect the quality of the received signal. The larger the EVM value, the greater the interference to the signal, and vice versa. The atmospheric turbulence structure constant is set to , the signal-to-noise ratio is 10dB, and User1~User4 correspond to four user signals. Figure 1a As shown), the constellation diagram of QPSK signal affected by atmospheric turbulence ( Figure 1bThe constellation points are scattered and deviate from the original positions, and the signal transmission quality is significantly reduced. The EVM values ​​of User1 to User4 are 41.86%, 52.07%, 61.13% and 66.67% respectively. After using the constant modulus blind equalization-minimum mean square frequency domain equalization method ( Figure 1c The EVM values ​​for the 100-μm CMOS (as shown in the figure) were 13.60%, 13.68%, 14.05%, and 15.18%, respectively. This result demonstrates that this method can more effectively recover signals and reduce errors when dealing with atmospheric turbulence interference, demonstrating better equalization results. Figure 2 The graph of the average bit error rate of the system after using this method changes with the atmospheric turbulence structure constant, where the signal-to-noise ratio is fixed at 20dB and the atmospheric turbulence structure constant varies within a range of arrive This result shows that the average bit error rate of the OAM multiplexing communication system increases with the increase of the atmospheric turbulence structure constant, while the system average bit error rate decreases with the introduction of the equalization algorithm; Figure 3 The curve of the average bit error rate of the system changing with the signal-to-noise ratio after using this method. At this time, the atmospheric turbulence structure constant value is fixed. for , the system signal-to-noise ratio range is 5 to 20dB. The results show that when the system signal-to-noise ratio changes from 5dB to 20dB, the average bit error rate of the system before equalization is basically After using this method, the average bit error rate of the system is reduced to It can be seen that this method has a significant effect on correcting the average bit error rate of the system; Figure 4 The following graph shows the algorithm's iterative convergence after using this method. It shows that the algorithm completes switching after 70 iterations, and after 90 iterations, the system's mean square error reaches a minimum and stabilizes within a range of 0.02-0.03. This demonstrates the significant advantages of this method in terms of convergence speed and final error performance. This verification confirms the correctness of this dual-mode switching constant modulus blind equalization-minimum mean square frequency domain equalization method.

Claims

1. Dual-mode switching constant modulus blind equalization-minimum mean square frequency domain equalization method, characterized by: The specific steps include: Step 1: The transmitter inputs N electrical signals They are modulated onto N Gaussian beams respectively, and output N Gaussian beams carrying data information; Step 2: Pass the N data-carrying Gaussian beams obtained in step 1 through different spiral phase plates to generate N OAM beams carrying different topological charges. Step 3: Use an OAM state multiplexer to multiplex N OAM beams with different topological charges into one OAM multiplexed beam. The OAM multiplexed beam passes through the atmospheric turbulence channel and reaches the receiver. Step 4: The OAM multiplexed beam received by the receiving end is processed by the OAM state demultiplexer and deconverter to obtain the received signal for each user. ; Step 5: Use frequency domain equalizer to receive the signal from each user. Processing is performed to continuously update the filter tap vector .

2. The dual-mode switching constant modulus blind equalization-minimum mean square frequency domain equalization method according to claim 1, characterized in that: In step 1, N circuits of input electrical signals are After passing through the optical modulator, it is modulated into a Gaussian beam and outputs N Gaussian beams carrying data information. The process is: in, is the amplitude of the N-way Gaussian beam at the beam waist position, is the radiation distance from the light beam to the transmission axis, is the waist radius.

3. The dual-mode switching constant modulus blind equalization-minimum mean square frequency domain equalization method according to claim 2, characterized in that: In step 2, the N OAM beams carrying different topological charges are: Where, is the nth input electrical signal, is the amplitude of the n-th Gaussian beam, is the spiral light phase added by the n-th Gaussian beam, is the topological charge value of the nth OAM beam, is the azimuth.

4. The dual-mode switching constant modulus blind equalization-minimum mean square frequency domain equalization method according to claim 3, characterized in that: In step 3, N OAM beams with different topological charges are multiplexed into one channel through the OAM state multiplexer: The OAM multiplexed beam passes through the atmospheric turbulence channel and becomes: in, refers to the atmospheric turbulence phase factor, is the channel noise.

5. The dual-mode switching constant modulus blind equalization-minimum mean square frequency domain equalization method according to claim 4, characterized in that: In step 4, the OAM multiplexed light beam received by the receiving end is processed by the OAM state demultiplexer and deconverter as follows: Where, The topological charge is The complex conjugate of the electric field at is the beam transmission distance.

6. The dual-mode switching constant modulus blind equalization-minimum mean square frequency domain equalization method according to claim 5, characterized in that: The specific process of step 5 is as follows: Step 5.1, assume that the received signal of each user obtained in step 4 is Length is , and after serial-to-parallel conversion, it is divided into data blocks of length M, represents the subscript of the block, then The relationship between time and block is: At this time, the user receives the signal The output in the frequency domain is expressed as: Wherein, FFT stands for Fast Fourier Transform; Step 5.2, initialize the frequency domain filter tap coefficients: Where, is the time domain filter tap vector, is an M×1-dimensional zero vector; Step 5.3: Use the frequency domain equalizer to process the frequency domain input signal to obtain the frequency domain output signal. After the inverse fast Fourier transform (IFFT), the time domain output signal is obtained. : in, represents the frequency domain filter tap vector, Indicates taking the last M elements of the vector in the brackets; Step 5.4, using constant modulus blind equalization, i.e. CMA algorithm, to perform iterative equalization and update the filter tap vector; Step 5.5: Determine the error signal variation using the CMA algorithm. , according to the change of error signal The relationship between the preset threshold and the CMA algorithm is used to switch between the CMA algorithm and the LMS algorithm. Specifically: Where, For the The error value when executing the CMA algorithm for the first time, For the k -1 error value when executing the CMA algorithm, is the preset threshold, when When , continue to use the frequency domain CMA algorithm, and update the number of iterations of the CMA equalization stage, repeat step 5.4, when When , it switches to the LMS algorithm to continue iterative equalization; Step 5.6, using the least mean square frequency domain equalization, i.e., LMS algorithm, to perform iterative equalization and update the filter tap vector; Step 5.7, by continuously updating the filter tap vector, reduce the received signal N-way input electrical signal The error between .

7. The dual-mode switching constant modulus blind equalization-minimum mean square frequency domain equalization method according to claim 6, characterized in that: The specific process of step 5.4 is as follows: Step 5.4.1: According to the principle of CMA algorithm, calculate the time domain error signal of CMA equalization stage: in, is the modulus value, which is a constant and is expressed as: , is the original time domain signal at the transmitter; Step 5.4.2, the time domain error signal of the CMA stage Perform zero padding and perform FFT again to obtain the frequency domain error signal of the corresponding CMA equalization stage : Step 5.4.3, use the frequency domain error signal obtained in the CMA stage With the frequency domain input signal Perform the operation to obtain the gradient vector of the corresponding CMA stage: in, is the gradient vector of the CMA algorithm equalization phase, represents conjugation, Indicates taking the first M elements; Step 5.4.4, use the corresponding gradient vector And the corresponding step size to update the filter tap vector: Where, is the step size of the CMA algorithm, is a 1×M-dimensional zero vector.

8. The dual-mode switching constant modulus blind equalization-minimum mean square frequency domain equalization method according to claim 7, characterized in that: The specific process of step 5.6 is as follows: In step 5.6.1, according to the principle of LMS algorithm, the time domain error signal of the LMS equalization stage is calculated: Where, is the original time domain signal at the transmitter, y( k ) is the time domain output signal; Step 5.6.2, the time domain error signal of the LMS stage Perform zero padding and perform FFT again to obtain the frequency domain error signal of the corresponding LMS stage : Step 5.6.3, use the frequency domain error signal obtained in the LMS phase With the frequency domain input signal Perform the operation to obtain the gradient vector of the corresponding LMS stage; in, is the gradient vector of the LMS algorithm equalization stage, represents conjugation, Indicates taking the first M elements; Step 5.6.4, use the corresponding gradient vector And the corresponding step size to update the filter tap vector, the specific formula is: Where, is the step size of the LMS algorithm, is a 1×M-dimensional zero vector; Step 5.6.5, judge Is it ,like , then the iteration ends; if ,but , repeat steps 5.6.1 to 5.6.4.

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