A spectrum constrained multi-harmonic wireless communication system and method

Abstract

This invention discloses a spectrum-constrained multi-harmonic wireless communication system and method. The system includes a single-tone continuous wave signal source, a programmable metasurface, a real-time control module, a complex state library, a control sequence generation module, and a receiving module. The metasurface has independent amplitude and phase control capabilities, converting the single-tone excitation into multiple orthogonal harmonic subcarriers under the action of time-varying complex transmission coefficients. Based on an experimentally established IQ-voltage complex state library, information is loaded onto the target harmonic through nearest-neighbor matching or joint complex coefficient construction. Time-domain windowing is introduced in multi-harmonic transmission to suppress spectral broadening caused by symbol switching and reduce residual out-of-band noise. Experiments show that the system achieves single-harmonic reference transmission and joint transmission of 8 harmonic subcarriers at a 4GHz carrier frequency. After windowing, the out-of-band noise is reduced by approximately 10dB, and the spectral contrast reaches approximately 30dB. This invention achieves multi-harmonic communication and out-of-band suppression uniformly at the physical layer of the transmitter, and is suitable for spectrum-constrained wireless communication and low-complexity RF front-ends.

Description

Technical Field

[0001] This invention relates to the fields of microwave radio frequency, reconfigurable smart surfaces, programmable metasurfaces, wireless communication and physical layer spectrum engineering, and more specifically, to a spectrum-constrained multi-harmonic wireless communication system and method based on a programmable metasurface with independent amplitude and phase control. Background Technology

[0002] As wireless communication systems evolve towards higher spectral efficiency, higher transmission capacity, and more flexible spectrum utilization, multi-carrier transmission and higher-order modulation have become important means to improve spectrum utilization capabilities. However, while increasing the information carrying capacity within the target frequency band, residual energy leakage outside the target frequency band can lead to interference from adjacent channels and a decrease in spectrum utilization quality. Therefore, how to construct the target spectrum structure at the transmitter and suppress energy leakage in non-target frequency bands has become a key issue in spectrum-constrained wireless communication.

[0003] Traditional spectrum shaping and out-of-band suppression typically rely on digital baseband processing, filters, digital predistortion, mixing links, and multi-stage RF front-ends. While these methods have been widely used in traditional communication architectures, the system hardware links are complex and power consumption is high. Furthermore, spectrum construction, modulation loading, and out-of-band suppression are often distributed across multiple functional modules, making it difficult to achieve low-complexity, real-time, programmable, and integrated spectrum engineering at the transmitter physical layer.

[0004] In recent years, programmable metasurfaces have attracted widespread attention in beam manipulation, wireless communication, and spectrum engineering due to their flexible control over the amplitude, phase, polarization, and propagation path of electromagnetic waves. In particular, time-varying programmable metasurfaces can map single-frequency excitation into multiple discrete harmonic components, providing a new physical platform for directly constructing multi-frequency, multi-harmonic, and multi-carrier wireless transmission systems. Compared with traditional mixing and multi-stage RF links, this type of platform promises to unify spectrum generation, harmonic modulation, and information loading within the same physical layer process.

[0005] However, existing time-varying metasurface communication technologies still have several shortcomings. First, some platforms can only perform single-parameter modulation, making it difficult to simultaneously shape the amplitude and phase of the target harmonic in the complex domain, thus limiting their ability to jointly construct multi-harmonic complex weights. Second, existing research often focuses on harmonic generation or single-harmonic modulation phenomena, with limited system-level verification of the joint construction, parallel transmission, and reception recovery of multiple orthogonal harmonic subcarriers. Third, at the spectral level, existing schemes mostly focus on the generation and manipulation of harmonic energy, lacking clear system implementation schemes for further suppressing residual out-of-band noise and improving the spectral contrast between the target subcarrier and non-target frequency bands based on existing orthogonal multi-carrier structures.

[0006] Therefore, there is an urgent need in this field for a new transmitter physical layer wireless transmission system that can directly construct orthogonal multi-harmonic subcarriers using a programmable metasurface with independent amplitude and phase modulation capabilities, and complete complex symbol loading, multi-harmonic joint transmission, receiver joint recovery, and spectrum constraint enhancement on the same platform, thereby reducing the complexity of traditional radio frequency links and improving spectrum-constrained wireless transmission capabilities. Summary of the Invention

[0007] Technical issues:

[0008] This invention aims to solve the problem that spectrum construction, information loading, and out-of-band suppression are difficult to achieve uniformly at the physical layer of the transmitter in existing wireless transmission architectures and time-varying metasurface communication platforms; at the same time, it solves the technical problems that single-parameter time-varying modulation is difficult to jointly shape multiple harmonic complex coefficients in the complex domain, multiple harmonic subcarriers are difficult to jointly construct through a unified control sequence, and spectrum broadening and residual out-of-band noise caused by symbol switching are difficult to effectively suppress.

[0009] Technical solution:

[0010] To address the aforementioned technical problems, this invention proposes a spectrum-constrained multi-harmonic wireless communication system and method based on a programmable metasurface with independent amplitude and phase control.

[0011] I. System Solution

[0012] The system includes:

[0013] A single-tone continuous wave signal source is used to generate a frequency of The single-tone continuous wave incident signal.

[0014] Programmable metasurface with amplitude response and phase response Its independent control capability, its instantaneous complex transmission coefficient is expressed as ,in This refers to the time-varying control voltage sequence applied to the programmable metasurface.

[0015] The real-time control module and the multi-channel drive module are used to generate multiple bias voltages based on the time-varying control voltage sequence and apply them to the programmable metasurface.

[0016] The complex state library construction module is used to establish a complex transmission response library containing the real part of the complex transmission coefficient by scanning different combinations of control voltages and measuring the corresponding complex transmission responses. virtual part A library of experimental complex states corresponding to the control voltage. Each valid state includes the real part of the aforementioned state. virtual part and the corresponding three control voltages , , The correspondence is established. The complex state library construction module also normalizes the measured data and selects a square region with a side length of 1.5 centered at the origin in the normalized IQ plane as the state space.

[0017] The control sequence generation module is used to generate the time-varying control voltage sequence based on the digital information to be transmitted. The single-tone continuous wave incident signal is thus rendered in Under the influence of the time-varying control voltage sequence, it is converted into a set of orthogonal harmonic subcarriers. Specifically, when the time-varying control voltage sequence... Having a periodicity At that time, the instantaneous complex transmission coefficient This can be expanded into a Fourier series:

[0018]

[0019] Frequency is The single-tone incident signal is converted to a frequency located at Discrete harmonic subcarriers at different harmonic indices The corresponding basis function in one modulation period The internal properties satisfy orthogonality. The control sequence generation module performs symbol loading on one or more target harmonic subcarriers.

[0020] In the multi-harmonic joint transmission mode, the control sequence generation module uses a target vector composed of multiple target harmonic complex coefficients. As input, the same time-varying control voltage sequence is jointly generated based on the experimental complex state library. The actual harmonic complex coefficient vector generated by this sequence Approximating the target vector This allows for the simultaneous determination of the complex coefficients of multiple target harmonic subcarriers.

[0021] In the single-harmonic reference transmission mode, the control sequence generation module maps the target complex symbol to the target complex coefficient on the specified harmonic subcarrier, and uses the IQ-voltage correspondence in the experimental complex state library to perform nearest neighbor matching, thereby generating the time-varying control voltage sequence.

[0022] The control sequence generation module also applies windowing processing to the time-domain symbols in the multi-harmonic joint transmission mode and uses overlapping between adjacent symbols for smooth transition. By smoothing the time-domain abrupt changes during symbol switching, it suppresses the spectral broadening caused by time-domain abrupt changes and reduces the residual out-of-band spectral noise floor around the target subcarrier. The windowing processing is a Hann window, and the overlap ratio is 25%.

[0023] The receiving and recovery module is used to acquire, separate harmonics, and recover digital information from the transmitted signal after propagation in free space. The receiving and recovery module performs synchronization, framing, cyclic prefix removal, fast Fourier transform, target harmonic extraction, amplitude normalization, and common phase correction on the received signal, and recovers the corresponding digital information based on the complex values ​​of one or more extracted target harmonic subcarriers.

[0024] In a preferred embodiment, the programmable metasurface is a transmissive array, operating at a microwave frequency; the real-time control module employs a programmable logic control platform, and the reception recovery module adopts a software-defined radio architecture; wireless transmission occurs between the transmitter and receiver. The multi-harmonic joint transmission mode uses a 64-point discrete multi-subcarrier frame structure with a cyclic prefix length of 16, a sampling rate of 64 kHz, and selects eight effective harmonic subcarriers for information loading, with frequency offsets of ±1 kHz, ±3 kHz, ±5 kHz, and ±7 kHz, respectively.

[0025] II. Methodology and Scheme

[0026] The method includes the following steps:

[0027] S1. Using a single-tone continuous wave signal source to generate a frequency of... The single-tone continuous wave incident signal is irradiated onto a programmable metasurface with independent amplitude and phase control capabilities;

[0028] S2. Scan different combinations of control voltages, measure the complex transmission response of the programmable metasurface, and establish a model including the real part of the complex transmission coefficient. virtual part An experimental complex state library corresponding to the control voltage;

[0029] S3. Map the digital information to be transmitted to target complex coefficients on one or more target harmonic subcarriers, wherein the target harmonic subcarriers are located at frequency Place, For modulation frequency, The period of the time-varying control voltage sequence to be generated. For harmonic indexing;

[0030] S4. Generate a time-varying control voltage sequence based on the experimental complex state library. The transient complex transmission coefficient of the programmable metasurface is then loaded onto the programmable metasurface via a multi-channel drive module. As time changes, the single-tone continuous wave incident signal in Under the action of the target harmonic subcarrier carrying information, the target vector composed of multiple target harmonic complex coefficients is used as input, and the same time-varying control voltage sequence is jointly generated based on the experimental complex state library, so that the actual harmonic complex coefficient vector generated by the sequence approximates the target vector.

[0031] III. Application

[0032] The system or method described in this invention can be applied to spectrum-limited wireless transmission, reconfigurable smart surface communication, physical layer spectrum engineering, low-complexity radio frequency front-end, and multi-harmonic multi-carrier wireless communication.

[0033] Beneficial effects:

[0034] 1. This invention utilizes a programmable metasurface with independent amplitude and phase control capabilities. Through an experimentally established IQ-voltage complex state library, the target multiharmonic complex coefficient vector is directly mapped to the same time-varying control voltage sequence. This allows for the simultaneous construction of multiple orthogonal harmonic subcarriers in the same physical process, achieving the integration of physical layer spectrum construction and multiharmonic information loading at the transmitter.

[0035] 2. This invention models the joint transmission of multiple harmonics as a joint complex coefficient construction problem driven by a unified control sequence, avoiding the limitation of simply treating multiple harmonics as independent single harmonic links. It can simultaneously determine, load in parallel and jointly recover the complex coefficients of multiple target harmonic subcarriers based on the IQ-voltage complex state library.

[0036] 3. This invention introduces time-domain windowing and overlapping smooth transition in multi-harmonic joint transmission, further enhancing the spectrum constraint capability on the orthogonal multi-carrier transmission baseline, effectively suppressing spectrum broadening caused by symbol switching, reducing residual out-of-band noise, and improving the spectrum contrast between target subcarriers and non-target frequency bands.

[0037] 4. This invention combines single-tone continuous wave excitation with a programmable metasurface, eliminating the need for traditional multi-stage mixing, filtering, and digital predistortion links. This significantly reduces the complexity of the transmitter's RF front-end and provides a low-complexity, real-time programmable implementation path for spectrum-constrained wireless communication, reconfigurable smart surface transmitters, and physical layer programmable spectrum engineering.

[0038] 5. This invention verifies the spectrum constraint enhancement effect of single harmonic reference transmission, joint wireless transmission of 8 orthogonal harmonic subcarriers, and time-domain windowing through free-space experiments. After windowing, the out-of-band noise floor is reduced by about 10 dB, the spectrum contrast reaches about 30 dB, and the bit error rate shows a clear downward trend with the increase of transmission power. It has strong engineering feasibility and scalability. Attached Figure Description

[0039] Figure 1The diagram shows the experimental platform and complex state characterization in this invention; (a) is a block diagram of the free space real-time experimental platform, (b) is a physical diagram of the experimental platform, and (c) is a distribution diagram of the experimentally achievable complex transmission state of the programmable metasurface in the IQ plane.

[0040] Figure 2 The diagram shows the results of single-harmonic reference verification and multi-harmonic joint transmission in this invention; where (a) is the measured spectrum of single-harmonic reference transmission, (b) is the 16QAM constellation diagram corresponding to single-harmonic reference transmission, (c) is the measured spectrum of 8 harmonic subcarriers working simultaneously, and (d) is the total recovered constellation diagram under the condition of joint transmission of 8 harmonic subcarriers.

[0041] Figure 3 This is a graph showing the bit error rate as a function of transmit power in the multi-harmonic joint transmission of this invention.

[0042] Figure 4 The figures show the experimental results of the time-domain windowing method used in this invention to enhance the spectral constraint capability; (a) is the measured spectrum of the joint transmission of 8 harmonic subcarriers without windowing, (b) is the measured spectrum of the joint transmission of 8 harmonic subcarriers with windowing, (c) is a local comparison of the out-of-band region before and after windowing, and (d) is a comparison of the spectrum between the target subcarrier and the adjacent non-target frequency band after windowing. Detailed Implementation

[0043] To fully disclose the purpose, technical solution, and beneficial effects of this invention, the invention will be further described below in conjunction with the accompanying drawings and embodiments. It should be understood that the following embodiments are for illustrative purposes only and are not intended to limit the scope of protection of this invention; without departing from the concept of this invention, those skilled in the art can make equivalent substitutions or adaptive adjustments to specific device models, array size, operating frequency, sampling rate, number of subcarriers, and receiving processing methods.

[0044] like Figure 1 As shown, this embodiment constructs a free space real-time experimental platform. Figure 1 Figure (a) shows the block diagram of the free-space real-time experimental platform: the transmitter consists of a 4 GHz single-tone continuous wave signal source, a PXIe real-time control system, a multi-channel driver board, and a 15×15 programmable metasurface; the receiver uses a USRP-2974 software radio receiver to collect the transmitted field. The free-space transmission distance between the transmitter and receiver is 3 m, and both the transmitter and receiver use 2-6 GHz horn antennas. The single-tone excitation signal is generated by a RIGOL DSG3060 signal source and illuminates the programmable metasurface; the PXIe real-time control platform uses an NI PXIe-1092 chassis and a PXIe-8881 embedded controller, and works with a PXIe-6674T synchronization module and a multi-channel driver board to achieve time-varying control signal output. Figure 1 (b) is a physical image of the experimental platform, showing the actual layout of each piece of equipment.

[0045] Figure 1 Image (c) shows the distribution of experimentally attainable complex transmission states of the programmable metasurface in the IQ plane. During the construction of the complex state library, different bias voltage combinations were first scanned near the operating frequency, and the corresponding transmission responses were recorded using a receiver. The measured complex transmission responses were represented as discrete state points in the IQ plane, thus establishing an experimental state library between the complex transmission responses and the control voltage. Each effective state can be represented as a correspondence between I, Q, V1, V2, and V3. In the experimental setup of this embodiment, a total of 196,000 complex transmission state samples were obtained. This number of state samples represents the sampling scale and resolution of the current experimental characterization and does not limit the theoretical number of states of the programmable metasurface.

[0046] To improve the stability of subsequent lookup table mapping and sequence generation, the measured IQ data can be normalized, and a square region with a side length of 1.5 centered at the origin can be selected in the normalized IQ plane as the lookup table state space. This process ensures a good matching relationship between the target resampling points and the experimentally reachable states, while reducing mapping errors caused by sparse edge state points.

[0047] like Figure 2 As shown, the single-harmonic reference transmission is first verified. Figure 2 In Figure (a), the measured spectrum of single-harmonic reference transmission is shown. Based on the experimental complex state library and IQ-voltage lookup table, the system maps the target complex symbol to a single target harmonic subcarrier. Stable target harmonic components can be observed in the measured spectrum. Figure 2 Figure (b) shows the corresponding 16QAM constellation diagram. The 16QAM constellation points recovered by the receiver exhibit clear clustering characteristics. This result demonstrates that the present invention can support complex symbol loading and wireless transmission of a single harmonic subcarrier.

[0048] Based on single-harmonic verification, the system is extended to joint transmission of eight orthogonal harmonic subcarriers. Figure 2 (c) shows the measured spectrum of eight harmonic subcarriers operating simultaneously. Multiple target harmonic components can be constructed simultaneously on the same programmable metasurface platform and form clearly identifiable discrete spectral peaks at the target frequency positions. Figure 2 In the middle (d), the total recovered constellation diagram under the condition of joint transmission of 8 harmonic subcarriers is shown. The receiver separates and jointly recovers the 8 target harmonic subcarriers. The resulting total recovered constellation diagram still maintains good clustering characteristics, indicating that the present invention can realize multi-harmonic multi-carrier wireless transmission under the drive of a unified control sequence.

[0049] like Figure 3As shown, in order to evaluate the system's communication performance, this embodiment gradually adjusts the transmission power while keeping other parameters unchanged, and calculates the corresponding bit error rate. Figure 3 The figure shows the bit error rate (BER) curve of multi-harmonic joint transmission as a function of transmit power, with the transmit power scanning range from -55 dBm to -35 dBm. Test results show that the BER continuously decreases with increasing transmit power, demonstrating that multi-harmonic joint transmission based on an experimental complex state library and a unified time-varying control sequence has an achievable trend of improved communication performance.

[0050] like Figure 4 As shown, in order to verify the effect of time-domain windowing on the spectrum constraint capability, this embodiment compares the measured spectrum of 8-harmonic multicarrier under two working modes: no window and windowed. Figure 4 In the middle (a), the measured spectrum is under the condition of no windowing. The system has been able to form a multi-carrier spectrum framework by relying on the orthogonal harmonic subcarrier structure. However, due to the time domain abrupt change during the symbol switching process, there are still residual spectrum skirts and out-of-band noise around the target subcarrier. Figure 4 In (b), the measured spectrum is under windowing conditions. After introducing time-domain windowing, the symbol transition is smoothed, the spectral energy is more concentrated near the target harmonic, and the residual energy in the non-target frequency band is further suppressed.

[0051] Figure 4 Image (c) shows a local comparison of the out-of-band region before and after windowing. Compared to the unwindowed case, the residual out-of-band spectral noise floor around the target subcarrier is further reduced by approximately 10 dB after windowing. This value represents the additional improvement brought by time-domain windowing compared to the unwindowed orthogonal multicarrier baseline. Figure 4 Image (d) shows a spectrum comparison between the target subcarrier and adjacent non-target frequency bands after windowing. In the final windowed state, the target subcarrier maintains a spectral contrast of approximately 30 dB relative to the surrounding non-target frequency bands. This result demonstrates that the present invention can not only construct multi-harmonic communication links but also enhance spectral constraint capabilities at the transmitter physical layer.

[0052] In summary, the system disclosed in this embodiment unifies independent amplitude and phase control, joint construction of orthogonal multi-harmonic subcarriers, experimental complex state library mapping, time-domain windowed spectrum constraints, and receiver joint recovery within a single programmable metasurface wireless communication platform. This system enables multi-harmonic wireless transmission and spectrum leakage suppression with lower RF link complexity, providing a new implementation path for spectrum-constrained wireless communication, reconfigurable smart surface transmitters, and physical layer programmable spectrum engineering.

Claims

1. A spectrum-constrained multi-harmonic wireless communication system, characterized in that, include: A single-tone continuous wave signal source is used to generate a frequency of The single-tone continuous wave incident signal; Programmable metasurfaces that respond to the amplitude of electromagnetic waves. and phase response Its independent control capability, its instantaneous complex transmission coefficient is expressed as ,in A time-varying control voltage sequence applied to the programmable metasurface; The complex state library construction module is used to build an experimental complex state library containing the correspondence between the real part I and the imaginary part Q of the complex transmission coefficient and the control voltage, thereby realizing the IQ-voltage complex state library mapping. The control sequence generation module is used to generate the time-varying control voltage sequence based on the digital information to be transmitted. In the multi-harmonic joint transmission mode, the control sequence generation module uses a target vector composed of multiple target harmonic complex coefficients. As input, the same time-varying control voltage sequence is jointly generated based on the experimental complex state library. When this sequence is applied to the programmable metasurface with independent amplitude and phase control capabilities, the resulting actual harmonic complex coefficient vector... Approximating the target vector Thus, the complex coefficients of multiple target harmonic subcarriers are jointly constructed using the same control sequence; The real-time control module and the multi-channel drive module are used to generate multiple bias voltages according to the time-varying control voltage sequence and apply them to the programmable metasurface. The receiver recovery module is used to acquire, separate harmonics, and recover digital information from transmitted signals that have propagated through free space.

2. The system according to claim 1, characterized in that, Each valid state established by the complex state library construction module includes the real part. virtual part and the corresponding three control voltages , , The correspondence is established; and the complex state library construction module normalizes the measured data and selects a square region with the origin as the center and a side length of 1.5 as the state space in the normalized IQ plane; and the complex state library is obtained through experimental measurement, simulation modeling or a combination of both.

3. The system according to claim 1, characterized in that, In the single-harmonic reference transmission mode, the control sequence generation module maps the target complex symbol to the target complex coefficient on the specified harmonic subcarrier, and uses the IQ-voltage correspondence in the experimental complex state library to perform nearest neighbor matching, thereby generating the time-varying control voltage sequence.

4. The system according to claim 1, characterized in that, The plurality of target harmonic subcarriers are determined by the time-varying complex transmission coefficient. The Fourier series expansion is generated; when Having a periodicity hour, The frequency is The single-tone incident signal is converted into a signal located at Discrete harmonic subcarriers at different harmonic indices The corresponding basis function in one modulation period The interior satisfies orthogonality.

5. The system according to claim 1, characterized in that, The control sequence generation module also applies windowing processing to the time-domain symbols in the multi-harmonic joint transmission mode and uses overlapping smooth transition between adjacent symbols; by smoothing the time-domain abrupt changes during the symbol switching process, it suppresses the spectral broadening caused by the time-domain abrupt changes and reduces the residual out-of-band spectral noise around the target subcarrier.

6. The system according to claim 5, characterized in that, The windowing process is a Hann window, and the overlap ratio is 25%. The multi-harmonic joint transmission mode adopts a 64-point discrete multi-subcarrier frame structure, with a cyclic prefix length of 16, a sampling rate of 64 kHz, and selects 8 effective harmonic subcarriers for information loading, with frequency offsets of ±1 kHz, ±3 kHz, ±5 kHz, and ±7 kHz, respectively.

7. The system according to claim 1, characterized in that, The receiving recovery module performs synchronization, framing, cyclic prefix removal, fast Fourier transform, target harmonic extraction, amplitude normalization, and common phase correction on the received signal, and recovers the corresponding digital information based on the complex values ​​of one or more extracted target harmonic subcarriers.

8. The system according to claim 1, characterized in that, The programmable metasurface is a transmissive array, operating at a microwave frequency; the real-time control module uses a programmable logic control platform, and the receiving and recovery module uses a software radio architecture; the transmission between the transmitter and receiver is wireless.

9. A spectrum-constrained multiharmonic wireless communication method based on a programmable metasurface with independent amplitude and phase control, characterized in that, The steps include: S1, generating a frequency of [frequency value missing] using a single-tone continuous wave signal source. A single-tone continuous wave incident signal is irradiated onto a programmable metasurface capable of independent amplitude and phase modulation; S2, different combinations of control voltages are scanned, and the complex transmission response of the programmable metasurface is measured to establish a model containing the real part of the complex transmission coefficient. virtual part An experimental complex state library corresponding to the control voltage; S3, mapping the digital information to be transmitted to target complex coefficients on one or more target harmonic subcarriers, wherein the target harmonic subcarriers are located at frequency Place, For modulation frequency, The period of the time-varying control voltage sequence to be generated. For harmonic indexing; S4, generate time-varying control voltage sequence based on the experimental complex state library. The transient complex transmission coefficient of the programmable metasurface is then loaded onto the programmable metasurface via a multi-channel drive module. As time changes, the single-tone continuous wave incident signal in Under the action of the signal, the signal is converted into a target harmonic subcarrier carrying information. In the multi-harmonic joint transmission mode, the target vector composed of multiple target harmonic complex coefficients is used as input. Based on the experimental complex state library, the same time-varying control voltage sequence is jointly generated so that the actual harmonic complex coefficient vector generated by the sequence approximates the target vector. S5. In the multi-harmonic joint transmission, windowing and overlapping smoothing processing are applied to the time domain symbol to smooth the time domain abrupt change during the symbol switching process, suppress spectrum broadening, and reduce the residual out-of-band noise around the target subcarrier. S6. The transmitted signal is acquired, synchronized, and subjected to fast Fourier transform by the receiving recovery module. The complex values ​​of each target harmonic subcarrier are separated and extracted. After amplitude normalization and phase correction, the original digital information is recovered.

10. An application of the system as described in any one of claims 1 to 8 or the method as described in claim 9 in spectrum-constrained wireless transmission, reconfigurable smart surface communication, physical layer spectrum engineering, or low-complexity radio frequency front-ends.

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