Flexible hierarchical HACO-OFDM method and system based on IMDD

By using a flexible hierarchical HACO-OFDM method, the problem of insufficient subcarrier resource utilization in HACO-OFDM is solved, achieving higher spectral efficiency and lower reception complexity, and adapting to different channel conditions.

CN118921261BActive Publication Date: 2025-11-04BEIJING TOPSKY INFORMATION TECH CO LTD
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Patent Information

Application Number
CN202411260136.6
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-09-10
Publication Date
2025-11-04
Estimated Expiration
2044-09-10

AI Technical Summary

Technical Problem

Existing HACO-OFDM methods fail to fully utilize subcarrier resources, have significant room for improvement in spectral efficiency, and cannot flexibly adjust the number and sequence of subcarriers in each layer, making them particularly difficult to adapt to frequency-selective fading channels.

Method used

The flexible hierarchical HACO-OFDM method based on IMDD is adopted. QAM symbols are transmitted through odd number and subcarrier sets to generate two-layer frequency domain signals. A hybrid time domain signal is generated through frequency domain transformation, amplitude limiting and superposition. The number and sequence of subcarriers are adjusted by using an optimized parameter model to generate a non-negative FL-HACO-OFDM signal.

Benefits of technology

It achieves higher subcarrier utilization, reduces reception complexity and processing latency, while maintaining flexible subcarrier resource utilization to adapt to different channel conditions.

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Abstract

The application discloses a kind of flexible layered HACO-OFDM method and system based on IMDD, according to mixed time domain signal vector, construct optimization parameter model, solve optimal solution and in optimization parameter model, according to optimal solution and, construct reconstruction signal vector;Reconstruction signal in reconstruction signal vector is superimposed with mixed time domain signal, obtain non-negative FL-HACO-OFDM signal;Non-negative FL-HACO-OFDM signal is carried out digital-analog conversion, obtain transformed signal, utilize transformed signal and drive LED to emit light signal.The application can achieve higher subcarrier utilization compared with traditional HACO-OFDM method, while, keep the advantage that the receiving complexity of HACO-OFDM method is low.
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Description

TECHNICAL FIELD

[0001] The present application relates to a flexible layered HACO-OFDM method and system based on IMDD, belonging to the technical field of wireless optical communication. BACKGROUND

[0002] Wireless optical communication (OWC) is a communication technology that uses propagating light waves for data transmission. Unlike traditional radio wave communication, OWC uses a frequency band that does not require spectrum license and has abundant spectrum resources, enabling high-speed data transmission. With the advantages of high bandwidth, strong anti-interference ability and good confidentiality, OWC is expected to be widely used in many fields such as high-speed internet access, emergency communication, military communication and unmanned aerial vehicle communication.

[0003] Orthogonal frequency division multiplexing (OFDM) is a multi-carrier modulation technology that divides a data stream into multiple parallel sub-data streams, each of which is transmitted on a different sub-carrier. Each sub-carrier is orthogonal to each other, so they do not interfere with each other in the frequency spectrum. OFDM has the advantages of anti-multipath interference, high spectrum utilization, and easy equalization, and is widely used in various communication systems. In the field of OWC, OFDM has also become a mainstream modulation method for high-speed communication. However, OWC usually uses intensity modulation / direct detection (IM / DD), which modulates the intensity of the light source to transmit information, requiring the modulation signal to be a non-negative real number, thus giving rise to a variety of special optical-OFDM (O-OFDM) schemes. Traditional O-OFDM schemes include direct current bias O-OFDM (DCO-OFDM), asymmetric clipping O-OFDM (ACO-OFDM), etc., but DCO-OFDM has low power efficiency, and ACO-OFDM has low spectral efficiency.

[0004] In order to effectively improve the spectral efficiency while maintaining high power efficiency, a layered O-OFDM scheme is proposed, including hybrid ACO-OFDM (HACO-OFDM), layered ACO-OFDM (LACO-OFDM), and enhanced spectral discrete multi-tone (ASE-DMT). HACO-OFDM adopts ACO-OFDM and pulse amplitude modulation-discrete multi-tone (PAM-DMT) two-layer signal superposition transmission, which effectively improves the spectral efficiency compared with ACO-OFDM, but still only utilizes 3 / 4 of the subcarrier resources, and the spectral efficiency still has room for further improvement. LACO-OFDM and ASE-DMT adopt multi-layer signal hybrid transmission, which can fully utilize the subcarrier resources, but the complexity and processing delay of the receiving end also increase sharply with the number of layers. In addition, in these layered O-OFDM schemes, the number of subcarriers in each layer cannot be adjusted, and each layer needs to use a fixed subcarrier sequence number, which makes it difficult to flexibly use subcarrier resources, resulting in poor adaptation to different channel conditions.

[0005] In OWC, the existing HACO-OFDM method fails to fully utilize the subcarrier resources, and the spectral efficiency still has a large room for improvement. Although LACO-OFDM and ASE-DMT can fully utilize the subcarrier resources, the multiple layered superposition results in high receiving complexity and processing delay. More importantly, these layered O-OFDM methods cannot adjust the number of subcarriers in each layer, and each layer needs to use a fixed subcarrier sequence number, which makes it difficult to flexibly use subcarrier resources, especially for frequency-selective fading channels.

[0006] In order to solve these problems, the existing HACO-OFDM method needs to be improved. SUMMARY

[0007] Objective: In order to overcome the deficiencies in the prior art, the present application provides a flexible layered HACO-OFDM method based on IMDD, which adopts two-layer transmission to maintain low receiving complexity and processing delay. More importantly, the second layer adopts a flexible layered manner, and the number and sequence of subcarriers used in the layered manner can be flexibly adjusted, which can fully and flexibly utilize the subcarrier resources.

[0008] Technical scheme: In order to solve the above technical problems, the technical scheme adopted by the present application is:

[0009] In a first aspect, a flexible layered HACO-OFDM method based on IMDD is provided, which specifically includes:

[0010] Step 1: QAM symbol transmission is performed using odd subcarriers to obtain the frequency domain signal of the first layer .

[0011] Step 2: QAM symbol transmission is performed on the subcarriers to obtain the frequency-domain signal of the second layer .

[0012] Step 3: The frequency-domain signal and the frequency-domain signal are respectively subjected to frequency-domain transformation to generate the first-layer time-domain signal and the second-layer time-domain signal , The first-layer time-domain signal is sequentially subjected to amplitude limiting and parallel-to-serial conversion to generate a non-negative signal . The second-layer time-domain signal is subjected to parallel-to-serial conversion to generate a converted time-domain signal . The non-negative signal is superimposed with the converted time-domain signal to generate a mixed time-domain signal .

[0013] Step 4: The value of is substituted into the expression of the mixed time-domain signal to obtain , and is obtained to generate a mixed time-domain signal vector of one FL-HACO-OFDM symbol time , z = [ z 0 , z 1 , ⋯ , z N − 1 ] T .

[0014] Step 5: An optimization parameter model is constructed according to the mixed time-domain signal vector , and the optimal solution and of the optimization parameter model are solved, wherein represents the optimal solution of the first column vector of to-be-optimized parameters for generating the real and imaginary parts of the reconstructed signal, represents the optimal solution of the second column vector of to-be-optimized parameters for generating the real and imaginary parts of the reconstructed signal.

[0015] Step 6: A reconstructed signal vector is constructed according to the optimal solution and .

[0016] Step 7: The reconstructed signal in the reconstructed signal vector is superimposed with the mixed time-domain signal to obtain a non-negative FL-HACO-OFDM signal , and the reconstructed signal represents the reconstructed signal vector The first element. The first element.

[0017] Step 8: Digital-to-analog conversion is performed on the non-negative FL-HACO-OFDM signal to obtain a converted signal, and the converted signal is used to drive the LED to emit an optical signal.

[0018] As a preferred solution, it also includes:

[0019] Step 9: The optical signal is converted into an electrical signal, after analog-to-digital conversion, serial-to-parallel conversion, and frequency domain conversion, a frequency domain received signal is generated, the signal is extracted from the odd subcarriers of the frequency domain received signal and QAM symbol detection is performed, and the QAM detection symbol of the odd subcarriers is output.

[0020] Step 10: The QAM detection symbol of the odd subcarriers is generated after inverse frequency domain conversion, amplitude limiting operation, and frequency domain conversion, and the amplitude limiting noise is generated.

[0021] Step 11: The amplitude limiting noise is removed from the even subcarriers of the frequency domain received signal, and the QAM symbol detection of the even subcarriers is output.

[0022] As a preferred solution, the expression of the frequency domain signal of the first layer is as follows:

[0023]

[0024] In the formula: denotes the QAM symbol of the first element of the subcarriers in the first layer, denotes the QAM symbol of the first element of the subcarriers in the first layer, denotes the conjugate operation, denotes the total number of subcarriers, .

[0025] As a preferred solution, the expression of the frequency domain signal of the second layer is as follows:

[0026]

[0027] In the formula, denotes the QAM symbol of the first element of the subcarriers in the second layer, denotes the QAM symbol of the first element of the subcarriers in the second layer, denotes the set of subcarriers used for QAM symbol transmission in the second layer, .

[0028] wherein, , Represents the set of subcarriers The sequence number of the neutron carrier. Represents the set of subcarriers The Middle One element, Represents the set of subcarriers The number of elements in the middle.

[0029] As a preferred option, hybrid time-domain signals The expression is as follows:

[0030]

[0031] As a preferred option, the optimized parameter model expression is as follows:

[0032]

[0033] In the formula: Denotes the first parameter matrix. Denotes the second parameter matrix. This represents the first column vector of parameters to be optimized, used to generate the real and imaginary parts of the reconstructed signal. This represents the column vector of second parameters to be optimized, used to generate the real and imaginary parts of the reconstructed signal. This represents the L1 norm.

[0034] As the preferred solution For length is column vectors, For length is column vectors, For having lines and A matrix of columns, For having lines and A matrix of columns.

[0035] As the preferred solution The expression for the element in the middle is as follows:

[0036]

[0037] In the formula, Indicates the first OK Column elements, Represents pi (π). This represents the total number of subcarriers. Represents the set of subcarriers middle of , Represents the set of subcarriers the sequence number of the subcarrier in the subcarrier set denotes a subcarrier set which is not used for QAM symbol transmission in the second layer.

[0038] As a preferred solution, the expression of the reconstructed signal vector is as follows:

[0039]

[0040] wherein, denotes the total number of subcarriers, denotes the sequence number of the subcarrier in the subcarrier set denotes a subcarrier set which is not used for QAM symbol transmission in the second layer. denotes the sequence number of the subcarrier in the subcarrier set denotes a subcarrier set which is not used for QAM symbol transmission in the second layer. denotes the sequence number of the subcarrier in the subcarrier set denotes a subcarrier set which is not used for QAM symbol transmission in the second layer. denotes a subcarrier set which is not used for QAM symbol transmission in the second layer. denotes a subcarrier set which is not used for QAM symbol transmission in the second layer. denotes a subcarrier set which is not used for QAM symbol transmission in the second layer. denotes a subcarrier set which is not used for QAM symbol transmission in the second layer. denotes a subcarrier set which is not used for QAM symbol transmission in the second layer.

[0041] As a preferred solution, the expression of the reconstructed signal vector is as follows:

[0042]

[0043] wherein, v = [ v 0 , v 1 , ⋯ , v N − 1 ] .

[0044] As a preferred solution, the expression of the non-negative FL-HACO-OFDM signal is as follows:

[0045] .

[0046] In a second aspect, a flexible hierarchical HACO-OFDM system based on IMDD comprises: an optical signal sending end and an optical signal receiving end.

[0047] The optical signal sending end is configured to implement the method of steps 1 to 8.

[0048] The optical signal receiving end is configured to implement the method of steps 9 to 11.

[0049] Beneficial effects: the flexible hierarchical HACO-OFDM method and system based on IMDD provided by the present application can achieve higher subcarrier utilization compared with the traditional HACO-OFDM method, while maintaining the advantage of low receiving complexity of the HACO-OFDM method.

[0050] Further, compared with LACO-OFDM and ASE-DMT based on multi-layer signal superposition, the method of the application only adopts a two-layer signal superposition transmission structure, effectively reduces the receiving complexity and processing delay, but can realize the same subcarrier utilization rate as LACO-OFDM and ASE-DMT.

[0051] Further, compared with the fixed hierarchical mode in the traditional method, the second layer of the method of the application adopts a flexible hierarchical mode, and the number and sequence number of subcarriers used for hierarchical layer can be flexibly adjusted, so that the subcarrier resources can be fully and flexibly utilized. BRIEF DESCRIPTION OF DRAWINGS

[0052] Figure 1 It is a flexible hierarchical HACO-OFDM transmitter diagram based on IM / DD.

[0053] Figure 2 It is a flexible hierarchical HACO-OFDM receiver diagram based on IM / DD.

[0054] Figure 3 It is a simulation result diagram of the complementary cumulative distribution function of the peak-to-average power ratio (PAPR) of the method of the application.

[0055] Figure 4 It is a simulation result diagram of the complementary cumulative distribution function of the peak-to-average power ratio (PAPR) of the method of the application. Below, the bit error rate performance diagram of the method of the application. DETAILED DESCRIPTION

[0056] The technical solutions in the embodiments of the application will be clearly and completely described below with reference to the drawings in the embodiments of the application. Obviously, the described embodiments are only part of the embodiments of the application, rather than all the embodiments of the application. Based on the embodiments of the application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the application.

[0057] The application will be further described below with reference to specific embodiments.

[0058] Embodiment 1:

[0059] This embodiment introduces a flexible hierarchical HACO-OFDM method based on IMDD, as shown in Figure 1 As can be seen from the figure, similar to HACO-OFDM, the application adopts a two-layer signal superposition transmission structure, and compared with the traditional LACO-OFDM and ASE-DMT based on multi-layer signal superposition, the implementation complexity of the transmitter is reduced. The method comprises:

[0060] Step 1: QAM symbol transmission is performed by using odd subcarriers to obtain the frequency domain signal of the first layer .

[0061] wherein the expression of the frequency-domain signal of the first layer is as follows:

[0062]

[0063] wherein: denotes the QAM symbol of the th subcarrier in the first layer, denotes the QAM symbol of the th subcarrier in the first layer, denotes the conjugate operation, denotes the total number of subcarriers, .

[0064] Step 2: QAM symbol transmission is performed on the subcarriers in the subcarrier set to obtain the frequency-domain signal of the second layer .

[0065] wherein the expression of the frequency-domain signal of the second layer is as follows:

[0066]

[0067] wherein: denotes the QAM symbol of the th subcarrier in the second layer, denotes the QAM symbol of the th subcarrier in the second layer, denotes the subcarrier set used for QAM symbol transmission in the second layer, .

[0068] wherein: , denotes the serial number of the subcarriers in the subcarrier set denotes the th element in the subcarrier set denotes the number of elements in the subcarrier set . Step 3: after performing frequency-domain transformation (IFFT) operation on the frequency-domain signals and

[0069] respectively, the first-layer time-domain signal and the second-layer time-domain signal are generated, . after the first-layer time-domain signal is sequentially subjected to amplitude limiting operation and parallel-to-serial conversion, the non-negative signal ​The second layer time domain signal After parallel-serial conversion, the converted time domain signal is generated. The non-negative signal is superimposed with the converted time domain signal to generate a mixed time domain signal .

[0070] The expression of the mixed time domain signal is as follows:

[0071]

[0072] Step 4: respectively substituting the values of into the expression of the mixed time domain signal , obtaining , according to obtaining a mixed time domain signal vector of an FL-HACO-OFDM (Flexible Layered-Hybrid ACO-OFDM) symbol time z = [ z 0 , z 1 , ⋯ , z N − 1 ] T .

[0073] Step 5: constructing an optimization parameter model according to the mixed time domain signal vector , solving the optimal solutions and in the optimization parameter model to generate a reconstructed signal for ensuring non-negativity, wherein represents the optimal solution of the first to-be-optimized parameter column vector for generating the real and imaginary parts of the reconstructed signal, represents the optimal solution of the second to-be-optimized parameter column vector for generating the real and imaginary parts of the reconstructed signal.

[0074] The expression of the optimization parameter model is as follows:

[0075]

[0076] In the formula: represents the first parameter matrix, represents the second parameter matrix, represents the first to-be-optimized parameter column vector for generating the real and imaginary parts of the reconstructed signal, represents the second to-be-optimized parameter column vector for generating the real and imaginary parts of the reconstructed signal, represents the L1 norm.

[0077] Further, is a column vector with a length of , and is a column vector with a length of . is a matrix with rows and columns, is a matrix with rows and columns.

[0078] Further, the expression of the element in is as follows:

[0079]

[0080] In the formula, denotes the element in the row column, denotes the constant pi, denotes the total number of subcarriers, denotes the subcarrier set in , , denotes the serial number of the subcarrier in the subcarrier set , and the subcarrier set denotes the subcarrier set not used for QAM symbol transmission in the second layer.

[0081] Further, the expression of the element in is as follows:

[0082]

[0083] In the formula, denotes the element in the row column, denotes the constant pi, denotes the total number of subcarriers, denotes the subcarrier set in , , denotes the serial number of the subcarrier in the subcarrier set , and the subcarrier set denotes the subcarrier set not used for QAM symbol transmission in the second layer.

[0084] Step 6: according to the optimal solution and , construct the reconstructed signal vector for ensuring non-negativity.

[0085] In the formula, the expression of the reconstructed signal vector for ensuring non-negativity is as follows:

[0086]

[0087] In the formula, v = [ v 0 , v 1 , ⋯ , v N − 1 ] .

[0088] Step 7: superimpose the reconstructed signal vector for ensuring non-negativity in the reconstructed signal with the mixed time domain signal to obtain a non-negative FL-HACO-OFDM signal , the reconstructed signal represents the element of the reconstructed signal vector .

[0089] wherein the expression of the non-negative FL-HACO-OFDM signal is as follows:

[0090]

[0091] Step 8: perform digital-analog conversion on the non-negative FL-HACO-OFDM signal to obtain a converted signal, and utilize the converted signal to drive the LED to emit a light signal.

[0092] Further, the method further comprises:

[0093] Step 9: the receiving end of the proposed scheme adopts the same receiver structure as the traditional HACO-OFDM, that is, after the optical signal passes through the photoelectric device, it is converted into an electrical signal, after analog-digital conversion, serial-parallel conversion and fast Fourier transform, a frequency domain receiving signal is generated, the signal is extracted from the odd subcarriers of the frequency domain receiving signal and QAM symbol detection is performed, and the QAM detection symbol of the odd subcarriers is output.

[0094] Step 10: the QAM detection symbol of the odd subcarriers is generated after inverse frequency domain conversion, amplitude limiting operation and frequency domain conversion, and the amplitude limiting noise is generated.

[0095] Step 11: the amplitude limiting noise is removed from the even subcarriers of the frequency domain receiving signal, and the QAM symbol detection of the even subcarriers is output.

[0096] As shown in Figure 2 , it can be seen from the figure that the method proposed in the application adopts the same receiver structure as HACO-OFDM, and compared with LACO-OFDM and ASE-DMT, the complexity and processing delay of the receiving end are effectively reduced.

[0097] Embodiment 2

[0098] This embodiment introduces a flexible layered HACO-OFDM system based on IMDD, which comprises an optical signal sending end and an optical signal receiving end. ​

[0099] The optical signal transmitting end is used to implement the methods of steps 1 to 8.

[0100] The optical signal receiving end is used to implement the methods of steps 9 to 11.

[0101] Example 3:

[0102] During the simulation process, such as Figure 3 As shown, using the division of the first few digits (excluding the one with the index zero) QAM symbol transmission is performed using an even number of subcarriers; simulation parameters Setting it to 30, 40, or 50 indicates that the number and sequence number of subcarriers in the second layer of the method of this invention can be flexibly adjusted. As can be seen from the figure, with... With the increase of [the required value], the method of the present invention has a lower PAPR.

[0103] like Figure 4 As shown, when simulation parameters When the subcarriers are set to 30, 40, and 50, the subcarrier utilization rates are 73.44%, 81.25%, and 89.06%, respectively, indicating that... When the value is large enough, a subcarrier utilization rate higher than that of HACO-OFDM can be achieved. As can be seen from the figure, under a certain signal-to-noise ratio, different... The methods described in this invention can all achieve good bit error rate performance.

[0104] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A flexible hierarchical HACO-OFDM method based on IMDD, characterized in that: Specifically, it includes: Step 1: Use odd-numbered subcarriers for QAM symbol transmission to obtain the first-layer frequency domain signal. ; Step 2: Use subcarrier sets The neutron carrier performs QAM symbol transmission to obtain the second-layer frequency domain signal. ; Step 3: Convert the frequency domain signal and frequency domain signals After performing frequency domain transformation operations, the first-level time domain signal is generated. Second-level time-domain signal , The first-level time-domain signal After sequentially performing amplitude limiting and parallel-to-serial conversion, a non-negative signal is generated. ; the second-layer time-domain signal After parallel-to-serial conversion, the converted time-domain signal is generated. ; non-negative signals With the transformed time-domain signal Superposition to generate mixed time-domain signals ; Step 4: Separately Substituting the values ​​into the mixed time-domain signal The expression yields ,according to A hybrid time-domain signal vector of FL-HACO-OFDM symbol time is obtained. , ; Step 5: Based on the mixed time-domain signal vector Construct an optimization parameter model and solve for the optimal solution in the optimization parameter model. and ,in, Let represent the optimal solution for the first column vector of parameters to be optimized, used to generate the real and imaginary parts of the reconstructed signal. This represents the optimal solution for the second column vector of parameters to be optimized, which is used to generate the real and imaginary parts of the reconstructed signal; Step 6: Based on the optimal solution and Constructing the reconstructed signal vector ; Step 7: Reconstruct the signal vector Reconstructed signal With mixed time domain signals Superimposed, a nonnegative FL-HACO-OFDM signal is obtained. Reconstructed signal Represents the reconstructed signal vector The Middle One element; Step 8: Convert the non-negative FL-HACO-OFDM signal A digital-to-analog conversion is performed to obtain a converted signal, which is then used to drive an LED to emit a light signal.

2. The flexible hierarchical HACO-OFDM method based on IMDD according to claim 1, characterized in that: Also includes: Step 9: Convert the optical signal into an electrical signal. After analog-to-digital conversion, serial-to-parallel conversion and frequency domain transformation, generate a frequency domain received signal. Extract the signal from the odd subcarriers of the frequency domain received signal and perform QAM symbol detection. Output the QAM detection symbols of the odd subcarriers. Step 10: Generate amplitude-limited noise by performing inverse frequency domain transformation, amplitude limiting operation, and frequency domain transformation on the QAM detection symbols of the odd-numbered subcarriers; Step 11: Remove the amplitude limiting noise from the even subcarriers of the received signal in the frequency domain and output the QAM symbol detection of the even subcarriers.

3. A flexible hierarchical HACO-OFDM method based on IMDD according to claim 1 or 2, characterized in that: The frequency domain signal of the first layer The expression is as follows: ; In the formula: Indicates the first layer QAM symbols for each subcarrier, Indicates the first layer QAM symbols for each subcarrier, This indicates the conjugate operation. Indicates the total number of subcarriers. .

4. A flexible hierarchical HACO-OFDM method based on IMDD according to claim 1 or 2, characterized in that: The second layer of frequency domain signals The expression is as follows: ; In the formula, Indicates the second layer QAM symbols for each subcarrier, Indicates the second layer QAM symbols for each subcarrier, This represents the set of subcarriers used for QAM symbol transmission in the second layer. ; in, , Represents the set of subcarriers The sequence number of the neutron carrier. Represents the set of subcarriers The Middle One element, Represents the set of subcarriers The number of elements in the middle.

5. A flexible hierarchical HACO-OFDM method based on IMDD according to claim 1 or 2, characterized in that: Mixed time domain signals The expression is as follows: 。 6. A flexible hierarchical HACO-OFDM method based on IMDD according to claim 1 or 2, characterized in that: The optimized parameter model expression is as follows: ; In the formula: Denotes the first parameter matrix. Denotes the second parameter matrix. This represents the first column vector of parameters to be optimized, used to generate the real and imaginary parts of the reconstructed signal. This represents the column vector of second parameters to be optimized, used to generate the real and imaginary parts of the reconstructed signal. This represents the L1 norm.

7. The flexible hierarchical HACO-OFDM method based on IMDD according to claim 6, characterized in that: For length is column vectors, For length is column vectors, For having lines and A matrix of columns, For having lines and A matrix of columns; The expression for the element in the middle is as follows: ; In the formula, Indicates the first OK Column elements, Represents pi (π). Indicates the total number of subcarriers. Represents the set of subcarriers middle of , Represents the set of subcarriers Subcarrier index, subcarrier set This represents the set of subcarriers in the second layer that were not used for QAM symbol transmission; The expression for the element in the middle is as follows: ; In the formula, Indicates the first OK Column elements, Represents pi (π). Indicates the total number of subcarriers. Represents the set of subcarriers middle of , Represents the set of subcarriers Subcarrier index, subcarrier set This represents the set of subcarriers in the second layer that were not used for QAM symbol transmission.

8. A flexible hierarchical HACO-OFDM method based on IMDD according to claim 1 or 2, characterized in that: Used to reconstruct signal vectors The expression is as follows: ; In the formula, .

9. A flexible hierarchical HACO-OFDM method based on IMDD according to claim 1 or 2, characterized in that: Non-negative FL-HACO-OFDM signal The expression is as follows: 。 10. A flexible hierarchical HACO-OFDM system based on IMDD, characterized in that: include: Optical signal transmitter, optical signal receiver; The optical signal transmitting end is used to implement the methods of steps 1 to 8; The optical signal receiving end is used to implement the methods of steps 9 to 11.

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