Delay-doppler transmission method, apparatus and device based on continuous domain mapping

Abstract

The application provides a delay-Doppler transmission method, device and equipment based on continuous domain mapping. Continuous amplitude modulation symbols generated by Shannon-Kotelnikov space filling mapping are sequentially filled into a delay-Doppler domain two-dimensional grid in a column priority rule, so that the geometric neighborhood relationship of continuous mapping is maintained in the delay-Doppler domain. The characteristics that each symbol in the domain experiences approximately uniform equivalent channel gain are utilized to avoid the destruction of the continuous mapping structure by double selected fading. Meanwhile, amplitude enhancement pilots are inserted in the grid and a guard band is set, and energy threshold adaptive adjustment based on a mapping scale parameter is combined to realize channel sparsity parameter estimation, so that the channel estimation and equalization process adapt to the continuous amplitude signal characteristics, thereby realizing the organic integration of analog joint source channel coding and orthogonal time-frequency-space modulation without relying on discrete constellation modulation.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and in particular to a delay-Doppler transmission method, apparatus, and device based on continuous domain mapping. Background Technology

[0002] Existing wireless communication systems generally adopt a separate source coding and channel coding architecture, which first quantizes and compresses the source information, and then performs channel coding and modulation. The performance of this separate design is heavily dependent on channel stability, and it is difficult to achieve both low latency and transmission robustness in scenarios where the channel's time-frequency characteristics change rapidly.

[0003] Analog Joint Source Channel Coding (AJSCC) bypasses quantization distortion by directly mapping continuous-valued source samples to continuous-amplitude modulation symbols and possesses asymptotic distortion characteristics as channel quality degrades, offering significant advantages in low-bandwidth and real-time transmission scenarios. However, existing AJSCC schemes are typically based on the assumption of an approximately flat channel or weak time-varying characteristics. When the channel simultaneously exhibits significant delay spread and Doppler spread (i.e., dual-select fading), multipath propagation causes the same symbol to arrive at the receiver at different times. The Doppler effect induces the superposition of different frequency shift components, both of which jointly disrupt the geometric proximity relationship of the continuous mapping curve, resulting in severe demapping errors and a significant deterioration in source recovery quality.

[0004] Orthogonal Time-Frequency Modulation (OTFS) is a novel modulation technique that maps information symbols to the delay-Doppler domain. It can equate rapidly changing channels in the time-frequency domain to a sparsely structured two-dimensional convolution, ensuring that each modulation symbol experiences a nearly uniform equivalent channel gain. This results in excellent energy focusing and anti-fading capabilities under high-speed movement and strong Doppler conditions. However, existing OTFS systems are primarily designed for discrete constellation modulation (such as QPSK and 16QAM) and digital channel coding. Their symbol mapping, pilot structures, and channel estimation methods are all optimized around discrete modulation, making them unsuitable for the efficient transmission of continuous-amplitude signals.

[0005] In view of the above, this application is hereby submitted. Summary of the Invention

[0006] This invention discloses a delay-Doppler transmission method, apparatus, and device based on continuous domain mapping, aiming to solve the problem that the continuous mapping structure of analog joint source channel coding is easily destroyed and the recovery performance is significantly reduced in a dual-select fading channel environment, while overcoming the defect that traditional orthogonal time-frequency control systems cannot directly support continuous amplitude signal transmission.

[0007] The first embodiment of the present invention provides a delay-Doppler transmission method based on continuous domain mapping, comprising:

[0008] Two independent zero-mean Gaussian distribution continuous value simulation source sequences are generated to form a two-dimensional continuous source sample pair. The Shannon-Kotelnikov space filling mapping is used to map each pair of the two-dimensional continuous source sample pairs to a continuous amplitude modulation symbol, and the power normalization processing is performed on the resulting continuous amplitude modulation symbol sequence.

[0009] The power-normalized continuous amplitude modulation symbol sequence is filled into the delay-Doppler domain two-dimensional grid in an orderly manner according to the generation order and column priority rule. Each grid carries a continuous amplitude modulation symbol, and amplitude-enhanced pilot symbols and guard bands are inserted at predetermined positions in the two-dimensional grid.

[0010] The inverse symplectic finite Fourier transform and Heisenberg transform are sequentially performed on the padded delay-Doppler domain two-dimensional grid to generate a time-domain transmitted signal, which is then transmitted through a dual-select fading channel.

[0011] The receiver sequentially performs Wigner transform and symplectic finite Fourier transform on the received time-domain signal to recover the delayed-Doppler domain received symbol matrix, extracts the pilot neighborhood spread component from the received symbol matrix, and uses adaptive energy threshold to detect effective channel paths and estimate channel sparsity parameters.

[0012] An equivalent channel matrix is ​​constructed based on the channel sparsity parameters. Equalization is performed on the data symbols in the received symbol matrix to obtain continuous amplitude symbol estimates. The original two-dimensional continuous source sample pairs are then recovered by Shannon-Kotelnikov inverse mapping.

[0013] Preferably, the column priority rule is as follows:

[0014] The power-normalized continuous amplitude modulation symbol sequence The data is filled sequentially along the lag dimension in the order of generation. After the lag dimension is filled, the data is filled incrementally along the Doppler dimension. The mapping relationship is as follows: ,in, M represents the number of grid cells in the delay direction, and N represents the number of grid cells in the Doppler direction. For the delay direction index, The Doppler direction index is used to ensure that the spatial proximity of continuous amplitude modulation symbols in the two-dimensional grid is consistent with their geometric proximity in the continuous mapping space.

[0015] Preferably, the amplitude of the pilot symbol is ,in The amount of boost from pilot power The linear gain factor obtained from the conversion, Let be the average power of the data symbols, where Represents the mathematical expectation. For data symbols;

[0016] The guard band extends in the time delay direction according to the maximum channel time delay. The corresponding discrete grid number is expanded unidirectionally, according to the maximum Doppler frequency shift of the channel in the Doppler direction. The corresponding discrete grid number is reset to zero before and after the pilot position to form a bidirectional guard band.

[0017] Preferably, the inverse symplectic finite Fourier transform is expressed as: ,in, For the delayed-Doppler domain symbol matrix, and These are the normalized discrete Fourier transform matrices, for The conjugate transpose of the matrix. The symbol matrix is ​​in the time-frequency domain;

[0018] The Heisenberg transform is specifically as follows: ,in Let S be the transmitter window matrix, and S be the discrete-time sampling matrix. for The conjugate transpose of .

[0019] Preferably, the time-varying impulse response of the dual-select fading channel is:

[0020]

[0021] Where P represents the number of effective propagation paths. , and They represent the first The path delay, Doppler shift, and complex path gain are considered, where t is a time variable. For time delay variables, The Dirac impulse function is used; the path gain is generated using an equal-power Rayleigh fading model, and its mathematical expression is:

[0022]

[0023] in, and Let them be mutually independent Gaussian random variables with zero mean and unit variance. Let p be the power allocation coefficient for the p-th path. It is the imaginary unit.

[0024] Preferably, the recovery delay-Doppler domain received symbol matrix is ​​specifically:

[0025] First, perform a Wigner transform on the received time-domain signal to obtain the time-frequency domain received symbol matrix. Then perform the symplectic finite Fourier transform: The delayed-Doppler domain received symbol matrix is ​​obtained. , Let represent the space of complex matrices with M rows and N columns.

[0026] Preferably, the adaptive energy threshold is ,in For noise variance, This is the threshold adjustment coefficient. Δ is the basic coefficient, and Δ is the scaling parameter of the Shannon-Kotelnikov mapping.

[0027] To satisfy The grid positions are determined as candidate path points, forming a path index set. And extract the corresponding Doppler index. Delay Index The normalized observations are used as path gain to form a complete set of sparse channel parameters. For adaptive energy threshold, For receiving symbol matrix The observation at position (k,l) in the mid-guide frequency neighborhood.

[0028] Preferably, the equilibrium adopts the minimum mean square error criterion, the expression of which is:

[0029] ;in: This represents the equalized delay-Doppler domain symbol matrix. The sparse block cyclic channel matrix is ​​constructed based on the estimated path. for The conjugate transpose of ; for identity matrix This represents noise power.

[0030] A second embodiment of the present invention provides a delay-Doppler transmission device based on continuous domain mapping, comprising:

[0031] The source mapping unit is used to generate two independent zero-mean Gaussian distribution continuous value analog source sequences to form a two-dimensional continuous source sample pair. The Shannon-Kotelnikov space filling mapping is used to map each pair of the two-dimensional continuous source sample pairs to a continuous amplitude modulation symbol, and the power normalization processing is performed on the obtained continuous amplitude modulation symbol sequence.

[0032] The grid filling and pilot insertion unit is used to fill the power-normalized continuous amplitude modulation symbol sequence into the delay-Doppler domain two-dimensional grid in an orderly manner according to the generation order and column priority rule. Each grid carries a continuous amplitude modulation symbol, and amplitude-enhanced pilot symbols and guard bands are inserted at predetermined positions in the two-dimensional grid.

[0033] The modulation transmission unit is used to sequentially perform inverse symplectic finite Fourier transform and Heisenberg transform on the padded delay-Doppler domain two-dimensional grid to generate a time-domain transmission signal and transmit it through a dual-select fading channel;

[0034] The demodulation and channel estimation unit is used to perform Wigner transform and symplectic finite Fourier transform on the received time-domain signal at the receiver, recover the delayed-Doppler domain received symbol matrix, extract the pilot neighborhood spread component from the received symbol matrix, and use adaptive energy threshold to detect effective channel paths and estimate channel sparsity parameters.

[0035] The equalization and source recovery unit is used to construct an equivalent channel matrix based on the channel sparsity parameters, perform equalization on the data symbols in the received symbol matrix to obtain continuous amplitude symbol estimates, and recover the original two-dimensional continuous source sample pairs through Shannon-Kotelnikov inverse mapping.

[0036] The third embodiment of the present invention provides a delay-Doppler transmission device based on continuous domain mapping, characterized in that it includes a memory and a processor, wherein the memory stores a computer program, and the computer program can be executed by the processor to implement a delay-Doppler transmission method based on continuous domain mapping as described in any of the above embodiments.

[0037] Based on the delay-Doppler transmission method, apparatus, and device disclosed in this invention, continuous amplitude modulation symbols generated by Shannon-Kotelnikov space-filling mapping are ordered and filled into a two-dimensional grid in the delay-Doppler domain according to a column-priority rule. This preserves the geometric proximity of the continuous mapping in the delay-Doppler domain. By utilizing the characteristic that each symbol in this domain experiences approximately uniform equivalent channel gain, the destruction of the continuous mapping structure by dual-select fading is avoided. Simultaneously, amplitude enhancement pilots are inserted into the grid and guard bands are set. Combined with an energy threshold adaptively adjusted based on the mapping scale parameter, channel sparsity parameter estimation is achieved. This adapts the channel estimation and equalization process to the characteristics of continuous amplitude signals, thereby achieving the organic integration of analog joint source channel coding and orthogonal time-frequency control without relying on discrete constellation modulation. Attached Figure Description

[0038] Figure 1 This is a flowchart illustrating a delay-Doppler transmission method based on continuous domain mapping provided in the first embodiment of the present invention;

[0039] Figure 2 This is a schematic diagram of the OTFS modulation channel estimation transmission scheme based on joint source channel coding provided by the present invention;

[0040] Figure 3 This is a schematic diagram of the ordered filling method of continuous mapping symbols in the delayed-Doppler domain;

[0041] Figure 4 This is a schematic diagram of the pilot insertion and channel estimation structure based on OTFS;

[0042] Figure 5 This is a schematic diagram of a delay-Doppler transmission device based on continuous domain mapping provided in the second embodiment of the present invention. Detailed Implementation

[0043] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0044] To better understand the technical solution of the present invention, the embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0045] This invention discloses a delay-Doppler transmission method, apparatus, and device based on continuous domain mapping, aiming to solve the problem that the continuous mapping structure of analog joint source channel coding is easily destroyed and the recovery performance is significantly reduced in a dual-select fading channel environment, while overcoming the defect that traditional orthogonal time-frequency control systems cannot directly support continuous amplitude signal transmission.

[0046] Please see Figure 1 and Figure 2 The first embodiment of the present invention provides a delay-Doppler transmission method based on continuous domain mapping, comprising:

[0047] S101, generate two independent zero-mean Gaussian distribution continuous value simulation source sequences to form a two-dimensional continuous source sample pair. Use Shannon-Kotelnikov space filling mapping to map each pair of the two-dimensional continuous source sample pairs to a continuous amplitude modulation symbol, and perform power normalization processing on the obtained continuous amplitude modulation symbol sequence.

[0048] In this embodiment, the transmitter generates two independent continuous-value analog source sequences. Where n = 1, 2, ..., 10000, each source sample follows a Gaussian distribution with zero mean and unit variance. A simulated joint source-channel coding method based on the Shannon-Kotelnikov space-filling curve is used to continuously map the above two-dimensional simulated sources, transforming each pair of source samples... Mapped to a continuous amplitude modulation symbol The mapping scale parameter Δ has a value range of [0,3] and a step size of 0.1. The mapping resolution of the space-filling curve can be controlled by adjusting the value of Δ. The smaller Δ is, the smaller the minimum distance between adjacent mapping points and the higher the mapping accuracy. The larger Δ is, the lower the mapping resolution.

[0049] The continuous amplitude modulation symbol sequence obtained by mapping Power normalization is performed, and the specific calculation method is as follows:

[0050]

[0051] First, the average power of all L=10000 symbols is calculated, which is the mean of the squares of the magnitudes of all symbols. Then, each symbol is divided by the square root of this average power to obtain the normalized symbol sequence. After power normalization, the average power of the symbol sequence is constrained to unit power, ensuring that each symbol has a uniform power reference when subsequently filled into the delay-Doppler domain grid. This provides a reliable reference for setting the pilot power boost and constructing the energy threshold in channel estimation.

[0052] S102, the power-normalized continuous amplitude modulation symbol sequence is filled into the delay-Doppler domain two-dimensional grid in an orderly manner according to the generation order and column priority rule. Each grid carries a continuous amplitude modulation symbol, and amplitude-enhanced pilot symbols and guard bands are inserted at predetermined positions in the two-dimensional grid.

[0053] Please combine Figure 3 and Figure 4 The delay-Doppler grid size of the OTFS system is set to M×N=50×50. The continuous amplitude modulation symbol sequence after analog joint source channel coding and power normalization is... According to their generation order, the two-dimensional mesh in the delay-Doppler domain is filled using a column-first mapping rule. middle.

[0054] After filling is complete, select the center position in the grid. As pilot positions, amplitude-enhanced pilot symbols are inserted. In this embodiment, the number of channel taps is 4, and the corresponding discrete delay index is {1,1,2,3}, where the maximum delay index is 3. Therefore, a unidirectional guard band of 3 grid lengths is set in the delay direction. The maximum Doppler index is 3, and a bidirectional zeroing method is adopted in the Doppler direction, that is, 3 Doppler grids are zeroed before and after the pilot position to form a bidirectional guard band, ensuring that the extended component of the pilot symbol does not interfere with the data symbol.

[0055] The specific mapping relationship is as follows: The continuous amplitude modulation (MAM) symbol sequence is first filled sequentially along the delay dimension. The first column of M grids is filled sequentially along the delay dimension. Once the column is full, the Doppler index is incremented by one, and the process continues until all M and N symbols are filled. This ordered filling method ensures that adjacent symbols in the simulated joint source channel coding output sequence also occupy adjacent positions in the delay-Doppler domain two-dimensional grid. This maintains the geometric proximity of continuously mapped symbols under dual-select fading channel conditions, reduces inter-symbol interference caused by channel delay spread and Doppler spread, and provides structured constraints for subsequent channel estimation and equalization.

[0056] The amplitude setting process for pilot symbols is as follows: First, determine the dB value of the pilot power boost p, and then convert it into a linear gain factor. Then calculate the average power of the data symbol block. Set the pilot amplitude to In this embodiment, the pilot symbol amplitude This enhancement ensures that the pilot symbol retains sufficient energy after channel spreading at the receiver, which improves the reliability of channel estimation. The guard band design is determined based on the channel's maximum time delay and maximum Doppler parameters: the time delay direction extends from the pilot position in the positive direction, and the extension length covers 0 to... The corresponding three grids; the Doppler direction extends from the pilot position in both positive and negative directions respectively. The three corresponding grids form a bidirectional protection zone symmetrical about the pilot position. All grids within the protection zone are set to zero and do not carry any data symbols, thus completely isolating the pilot spread region from the data region in space. This ensures that the receiver can extract a clean channel spread component from the pilot neighborhood for channel parameter estimation.

[0057] S103, perform inverse symplectic finite Fourier transform and Heisenberg transform sequentially on the filled delay-Doppler domain two-dimensional grid to generate a time-domain transmitted signal and transmit it through a dual-select fading channel;

[0058] The delay-Doppler domain symbol matrix after inserting pilot and guard bands The input to the OTFS modulation module first performs an inverse symplectic finite Fourier transform to obtain the time-frequency domain symbol matrix. The Heisenberg transform is then performed on the time-frequency domain symbol matrix to map it into a time-domain transmitted signal. This time-domain transmitted signal is transmitted through a dual-select fading channel, which simultaneously includes delay spread caused by multipath propagation, Doppler shift, and additive white Gaussian noise. In this embodiment, the channel is represented using a delay-Doppler model, with an effective propagation path number P=4. The discrete delay index of each path is {1,1,2,3}. The complex channel coefficients of each path are generated using an equal-power Rayleigh fading model, and each path uses an equal-power allocation method, i.e., the power allocation coefficient for each path is... .

[0059] The specific execution process of the inverse symplectic finite Fourier transform is as follows: taking the delay-Doppler domain symbol matrix as input, its expression is: The time-frequency domain discrete symbol matrix is ​​obtained. This transformation converts the two-dimensional symbol distribution in the delay-Doppler domain to a time-frequency domain representation, preparing for the subsequent generation of a time-domain signal. Based on this, the Heisenberg transform is performed, and its expression is: This yields the time-domain sampling matrix S, which maps the discrete time-frequency symbols to a continuous time-domain transmitted signal. Through these two transformations, the signal modulation process from the delay-Doppler domain to the time domain is completed.

[0060] The time-domain transmitted signal is transmitted through a dual-select fading channel. The channel is represented using a delay-Doppler model, and its time-varying impulse response can be expressed as:

[0061]

[0062] in Indicates the number of effective transmission paths; , and They represent the first The path delay, Doppler shift, and complex path gain are calculated. Based on the channel tap number, Doppler shift, and delay index, the complex channel coefficients for each path are generated using an equal-power Rayleigh fading model, with the mathematical expression as follows:

[0063]

[0064] in, and Let them represent mutually independent Gaussian random variables with zero mean and unit variance, respectively. The imaginary unit; Indicates the first The power allocation coefficient of each propagation path.

[0065] S104, the receiver sequentially performs Wigner transform and symmetric finite Fourier transform on the received time-domain signal to recover the delayed-Doppler domain received symbol matrix, extracts the pilot neighborhood spread component from the received symbol matrix, and uses adaptive energy threshold to detect the effective channel path and estimate the channel sparsity parameters.

[0066] At the receiving end, the received time-domain signal is first subjected to a Wigner transform to map it from the time domain to the time-frequency domain, resulting in a time-frequency domain received symbol matrix. Subsequently, a symplectic finite Fourier transform is performed on the time-frequency domain received symbol matrix, i.e. ,in The normalized discrete Fourier transform matrix of order 50 The conjugate transpose of . The normalized discrete Fourier transform matrix is ​​50th order, which is used to recover the time-frequency domain signal to the delay-Doppler domain, thus obtaining the received symbol matrix.

[0067] From the received symbol matrix Extracting pilot positions The extended components of the pilot signal and its neighborhood constitute the received pilot observation matrix. Because the pilot symbols transmitted through the dual-select fading channel undergo expansion in the delay-Doppler domain, the observed values ​​at each grid position within the pilot neighborhood... It includes the product of the corresponding channel path gain and the pilot symbol, as well as the superposition of additive noise. Therefore, the effective propagation path can be identified by detecting the energy of the pilot neighborhood observations.

[0068] An adaptive energy threshold is constructed based on noise variance and continuous mapping parameters. ,in For noise variance. Threshold adjustment coefficient. The adaptive strategy is related to the Shannon-Kotelnikov mapping scale parameter Δ: first, the basic coefficients are set. Then, adjust dynamically based on the Δ value. The specific formula is as follows: The physical meaning of this adaptive strategy is that when Δ is small, the continuous mapping resolution is high and the spacing between adjacent mapping points is small. In this case, the residual energy leakage of data symbols is low, and the threshold can be lowered accordingly to detect weak paths. When Δ is large, the mapping resolution decreases and the symbol energy distribution becomes more dispersed, requiring an appropriate increase in the threshold to avoid false alarms. In this embodiment, when Δ=0.5, noise variance estimate Then the energy threshold .

[0069] Calculate the observed power for each grid position within the pilot neighborhood. to the threshold Compare. For those that satisfy... The grid position is used to determine if there is a valid channel propagation path corresponding to that position, and its Doppler index is recorded. and delay index The normalized observation value at that location is used as the complex gain estimate for the corresponding path. For locations that do not meet the threshold condition, it is determined that there is no valid propagation path at that location. All detected candidate paths are aggregated into a path index set. Each element in the set contains three parameters: delay index, Doppler index, and path gain, thus obtaining a complete sparse parameter representation of the channel in the delay-Doppler domain, providing a basis for subsequent construction of the equivalent channel matrix and equalization processing only for the location of data symbols.

[0070] S105, construct an equivalent channel matrix based on the channel sparsity parameters, perform equalization on the data symbols in the received symbol matrix to obtain continuous amplitude symbol estimates, and recover the original two-dimensional continuous source sample pairs through Shannon-Kotelnikov inverse mapping.

[0071] Based on the sparse parameter set of the channel The delay-Doppler domain equivalent channel matrix is ​​constructed using the delay index, Doppler index, and complex path gain of each path. The matrix has a sparse block cyclic structure, where the positions and values ​​of its non-zero elements are determined by the estimated path parameters. The block cyclic characteristic of the matrix originates from the periodic structure of the channel convolution relationship in the delay-Doppler domain. In this embodiment, the grid size is M×N=50×50, therefore the equivalent channel matrix has a dimension of 2500×2500, containing only a small number of non-zero blocks corresponding to the number of detected effective paths, fully demonstrating the sparsity of the dual-select fading channel in the delay-Doppler domain.

[0072] Based on the construction of the equivalent channel matrix, the minimum mean square error criterion is used to analyze the received symbol matrix in the delay-Doppler domain. The data symbols in the code undergo linear equalization, and its expression is: ,in Equivalent channel matrix The conjugate transpose of . Let I represent the noise power, and I be a 2500×2500 identity matrix. This equalization operation, by jointly considering the channel response and noise power, performs optimal linear filtering on the received signal while minimizing the mean square error. This effectively suppresses inter-symbol interference caused by multipath delay and Doppler spread, yielding the equalized delay-Doppler domain symbol matrix. Each element corresponds to an estimate of a continuous amplitude modulation symbol.

[0073] The equalized continuous amplitude symbol estimates are input to the inverse mapping module of the simulated joint source channel coding. This inverse mapping module performs a reverse mapping operation on each continuous amplitude modulation symbol, based on the Shannon-Kotelnikov mapping rule and space-filling curve structure identical to those at the transmitter, to restore it to its corresponding two-dimensional simulated source estimate. Specifically, the inverse mapping process proceeds in the reverse direction of the space-filling curve, locating the nearest mapping point on the mapping curve based on the received continuous amplitude symbol, thereby determining the original two-dimensional source coordinates corresponding to that symbol. This restores each equalized symbol to a pair of source sample estimates. Through this inverse mapping process, the joint recovery from the OTFS equalized symbol to the original continuous source is achieved, completing the signal reconstruction at the receiver of the AJSCC-OTFS system.

[0074] It should be noted that in the signal transmission method based on continuous domain mapping and delay-Doppler modulation described in this embodiment, when system parameters change, such as the delay-Doppler domain grid size, pilot power configuration, guard band length setting, and specific parameter selection of the continuous domain mapping function, the above parameters should be adjusted accordingly based on the channel delay spread, Doppler spread range, and signal-to-noise ratio conditions, so as to obtain better transmission performance and source recovery effect under different dual-select fading scenarios.

[0075] Please see Figure 5 The second embodiment of the present invention provides a delay-Doppler transmission device based on continuous domain mapping, comprising:

[0076] The source mapping unit 201 is used to generate two independent zero-mean Gaussian distribution continuous value analog source sequences to form a two-dimensional continuous source sample pair. The Shannon-Kotelnikov space filling mapping is used to map each pair of the two-dimensional continuous source sample pairs to a continuous amplitude modulation symbol, and the power normalization processing is performed on the obtained continuous amplitude modulation symbol sequence.

[0077] The grid filling and pilot insertion unit 202 is used to fill the power-normalized continuous amplitude modulation symbol sequence into the delay-Doppler domain two-dimensional grid in an orderly manner according to the generation order and column priority rule. Each grid carries a continuous amplitude modulation symbol, and amplitude-enhanced pilot symbols and guard bands are inserted at predetermined positions in the two-dimensional grid.

[0078] The modulation transmission unit 203 is used to sequentially perform inverse symplectic finite Fourier transform and Heisenberg transform on the padded delay-Doppler domain two-dimensional grid to generate a time-domain transmission signal and transmit it through a dual-select fading channel.

[0079] The demodulation and channel estimation unit 204 is used to perform Wigner transform and symplectic finite Fourier transform on the received time-domain signal at the receiver, recover the delayed-Doppler domain received symbol matrix, extract the pilot neighborhood spread component from the received symbol matrix, and use adaptive energy threshold to detect effective channel paths and estimate channel sparsity parameters.

[0080] The equalization and source recovery unit 205 is used to construct an equivalent channel matrix based on the channel sparsity parameters, perform equalization on the data symbols in the received symbol matrix to obtain continuous amplitude symbol estimates, and recover the original two-dimensional continuous source sample pairs through Shannon-Kotelnikov inverse mapping.

[0081] The third embodiment of the present invention provides a delay-Doppler transmission device based on continuous domain mapping, characterized in that it includes a memory and a processor, wherein the memory stores a computer program, and the computer program can be executed by the processor to implement a delay-Doppler transmission method based on continuous domain mapping as described in any of the above embodiments.

[0082] The fourth embodiment of the present invention provides a computer-readable storage medium storing a computer program, which can be executed by a processor of the device in which the computer-readable storage medium is located, to implement a delay-Doppler transmission method based on continuous domain mapping as described in any of the above claims.

[0083] Based on the delay-Doppler transmission method, apparatus, and device disclosed in this invention, continuous amplitude modulation symbols generated by Shannon-Kotelnikov space-filling mapping are ordered and filled into a two-dimensional grid in the delay-Doppler domain according to a column-priority rule. This preserves the geometric proximity of the continuous mapping in the delay-Doppler domain. By utilizing the characteristic that each symbol in this domain experiences approximately uniform equivalent channel gain, the destruction of the continuous mapping structure by dual-select fading is avoided. Simultaneously, amplitude enhancement pilots are inserted into the grid and guard bands are set. Combined with an energy threshold adaptively adjusted based on the mapping scale parameter, channel sparsity parameter estimation is achieved. This adapts the channel estimation and equalization process to the characteristics of continuous amplitude signals, thereby achieving the organic integration of analog joint source channel coding and orthogonal time-frequency control without relying on discrete constellation modulation.

[0084] Exemplary examples show that the computer program described in the third and fourth embodiments of the present invention can be divided into one or more modules, which are stored in the memory and executed by the processor to complete the present invention. The one or more modules can be a series of computer program instruction segments capable of performing specific functions, which describe the execution process of the computer program in implementing a delay-Doppler transmission device based on continuous domain mapping. For example, the apparatus described in the second embodiment of the present invention.

[0085] The processor referred to can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor. This processor is the control center of the aforementioned delay-Doppler transmission method based on continuous domain mapping, connecting various parts of the entire implementation of the delay-Doppler transmission method based on continuous domain mapping through various interfaces and lines.

[0086] The memory can be used to store the computer program and / or modules. The processor, by running or executing the computer program and / or modules stored in the memory, and by calling the data stored in the memory, implements various functions of a delay-Doppler transmission method based on continuous domain mapping. The memory may mainly include a program storage area and a data storage area. The program storage area may store the operating system, at least one application program required for a function (such as sound playback function, text conversion function, etc.), etc.; the data storage area may store data created according to the use of the mobile phone (such as audio data, text message data, etc.). In addition, the memory may include high-speed random access memory, and may also include non-volatile memory, such as hard disk, memory, plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, at least one disk storage device, flash memory device, or other volatile solid-state storage device.

[0087] If the implemented module is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the above embodiments of the present invention can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electrical carrier signals and telecommunication signals.

[0088] It should be noted that the device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Furthermore, in the accompanying drawings of the device embodiments provided by this invention, the connection relationships between modules indicate that they have communication connections, which can be specifically implemented as one or more communication buses or signal lines. Those skilled in the art can understand and implement this without any creative effort.

[0089] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A delay-Doppler transmission method based on continuous domain mapping, characterized in that, include: Two independent zero-mean Gaussian distribution continuous value simulation source sequences are generated to form a two-dimensional continuous source sample pair. The Shannon-Kotelnikov space filling mapping is used to map each pair of the two-dimensional continuous source sample pairs to a continuous amplitude modulation symbol, and the power normalization processing is performed on the resulting continuous amplitude modulation symbol sequence. The power-normalized continuous amplitude modulation (LMM) symbol sequence is sequentially filled into a two-dimensional grid in the delay-Doppler domain according to the generation order and a column-priority rule. Each grid cell carries one LLM symbol. Amplitude-enhanced pilot symbols and guard bands are inserted at predetermined positions in the two-dimensional grid. Specifically, the column-priority rule is as follows: the power-normalized LLM symbol sequence... The data is filled sequentially along the lag dimension in the order of generation. After the lag dimension is filled, the data is filled incrementally along the Doppler dimension. The mapping relationship is as follows: ,in, M represents the number of grid cells in the delay direction, and N represents the number of grid cells in the Doppler direction. For the delay direction index, The Doppler direction index is used to ensure that the spatial proximity of continuous amplitude modulation symbols in the two-dimensional grid is consistent with their geometric proximity in the continuous mapping space; The inverse symplectic finite Fourier transform and Heisenberg transform are sequentially performed on the padded delay-Doppler domain two-dimensional grid to generate a time-domain transmitted signal, which is then transmitted through a dual-select fading channel. The receiver sequentially performs Wigner transform and symplectic finite Fourier transform on the received time-domain signal to recover the delayed-Doppler domain received symbol matrix, extracts the pilot neighborhood spread component from the received symbol matrix, and uses adaptive energy threshold to detect effective channel paths and estimate channel sparsity parameters. An equivalent channel matrix is ​​constructed based on the channel sparsity parameters. Equalization is performed on the data symbols in the received symbol matrix to obtain continuous amplitude symbol estimates. The original two-dimensional continuous source sample pairs are then recovered by Shannon-Kotelnikov inverse mapping.

2. The delay-Doppler transmission method based on continuous domain mapping according to claim 1, characterized in that, The amplitude of the pilot symbol is ,in The amount of boost from pilot power The linear gain factor obtained from the conversion, Let be the average power of the data symbols, where Represents the mathematical expectation. For data symbols; The guard band extends in the time delay direction according to the maximum channel time delay. The corresponding discrete grid number is expanded unidirectionally, according to the maximum Doppler frequency shift of the channel in the Doppler direction. The corresponding discrete grid number is reset to zero before and after the pilot position to form a bidirectional guard band.

3. The delay-Doppler transmission method based on continuous domain mapping according to claim 1, characterized in that, The inverse symplectic finite Fourier transform is expressed as: ,in, For the delayed-Doppler domain symbol matrix, and These are the normalized discrete Fourier transform matrices, for The conjugate transpose of the matrix. It is a time-frequency domain symbol matrix; The Heisenberg transform is specifically as follows: ,in Let S be the transmitter window matrix, and S be the discrete-time sampling matrix. for The conjugate transpose of .

4. The delay-Doppler transmission method based on continuous domain mapping according to claim 1, characterized in that, The time-varying impulse response of the dual-select fading channel is: Where P represents the number of effective propagation paths. , and They represent the first The path delay, Doppler shift, and complex path gain are considered, where t is a time variable. For time delay variables, The Dirac impulse function is used; the path gain is generated using an equal-power Rayleigh fading model, and its mathematical expression is: in, and Let them be mutually independent Gaussian random variables with zero mean and unit variance. Let p be the power allocation coefficient for the p-th path. It is the imaginary unit.

5. The delay-Doppler transmission method based on continuous domain mapping according to claim 3, characterized in that, The recovery delay-Doppler domain received symbol matrix is ​​specifically as follows: First, perform a Wigner transform on the received time-domain signal to obtain the time-frequency domain received symbol matrix. Then perform the symplectic finite Fourier transform: The delayed-Doppler domain received symbol matrix is ​​obtained. , Let represent the space of complex matrices with M rows and N columns.

6. The delay-Doppler transmission method based on continuous domain mapping according to claim 1, characterized in that, The adaptive energy threshold is ,in For noise variance, This is the threshold adjustment coefficient. Δ is the basic coefficient, and Δ is the scaling parameter of the Shannon-Kotelnikov mapping. To satisfy The grid positions are determined as candidate path points, forming a path index set. And extract the corresponding Doppler index. Delay Index The normalized observations are used as path gain to form a complete set of sparse channel parameters. For adaptive energy threshold, For receiving symbol matrix The observation at position (k,l) in the mid-guide frequency neighborhood.

7. The delay-Doppler transmission method based on continuous domain mapping according to claim 5, characterized in that, The equilibrium adopts the minimum mean square error criterion, the expression of which is: ;in: This represents the equalized delay-Doppler domain symbol matrix. The sparse block cyclic channel matrix is ​​constructed based on the estimated path. for The conjugate transpose of ; for identity matrix This represents noise power.

8. A delay-Doppler transmission device based on continuous domain mapping, characterized in that, include: The source mapping unit is used to generate two independent zero-mean Gaussian distribution continuous value analog source sequences to form a two-dimensional continuous source sample pair. The Shannon-Kotelnikov space filling mapping is used to map each pair of the two-dimensional continuous source sample pairs to a continuous amplitude modulation symbol, and the power normalization processing is performed on the obtained continuous amplitude modulation symbol sequence. The grid filling and pilot insertion unit is used to fill the power-normalized continuous amplitude modulation symbol sequence into a two-dimensional grid in the delay-Doppler domain according to the generation order and a column priority rule. Each grid carries one continuous amplitude modulation symbol, and amplitude-enhancing pilot symbols and guard bands are inserted at predetermined positions in the two-dimensional grid. Specifically, the column priority rule is: the power-normalized continuous amplitude modulation symbol sequence... The data is filled sequentially along the lag dimension in the order of generation. After the lag dimension is filled, the data is filled incrementally along the Doppler dimension. The mapping relationship is as follows: ,in, M represents the number of grid cells in the delay direction, and N represents the number of grid cells in the Doppler direction. For the delay direction index, The Doppler direction index is used to ensure that the spatial proximity of continuous amplitude modulation symbols in the two-dimensional grid is consistent with their geometric proximity in the continuous mapping space; The modulation transmission unit is used to sequentially perform inverse symplectic finite Fourier transform and Heisenberg transform on the padded delay-Doppler domain two-dimensional grid to generate a time-domain transmission signal and transmit it through a dual-select fading channel; The demodulation and channel estimation unit is used to perform Wigner transform and symplectic finite Fourier transform on the received time-domain signal at the receiver, recover the delayed-Doppler domain received symbol matrix, extract the pilot neighborhood spread component from the received symbol matrix, and use adaptive energy threshold to detect effective channel paths and estimate channel sparsity parameters. The equalization and source recovery unit is used to construct an equivalent channel matrix based on the channel sparsity parameters, perform equalization on the data symbols in the received symbol matrix to obtain continuous amplitude symbol estimates, and recover the original two-dimensional continuous source sample pairs through Shannon-Kotelnikov inverse mapping.

9. A delay-Doppler transmission device based on continuous domain mapping, characterized in that, The system includes a memory and a processor, wherein the memory stores a computer program that can be executed by the processor to implement a delay-Doppler transmission method based on continuous domain mapping as described in any one of claims 1 to 7.

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