Orthogonal Chirp multiplexing system of variable-length symbol pilot frequency structure based on constant sampling rate and channel estimation method of orthogonal Chirp multiplexing system

Abstract

The invention relates to an orthogonal multiplexing system of a variable-length symbol pilot frequency structure based on a constant sampling rate and a channel estimation method of the orthogonal multiplexing system, and belongs to the technical field of wireless communication. The system comprises a sending part and a receiving part, the sending part comprises a data block modulation module, a resource mapping module and a module, and the receiving part comprises a module, a module and a data block demodulation module. The method divides transmission data into data symbols and pilot symbols. The pilot frequency design adopts block-shaped pilot frequency, data symbols and pilot frequency symbols are realized by adopting different Fresnel transform points, and the pilot frequency signal design is realized by adopting a signal with a lower peak-to-average ratio of the pilot frequency in a time domain and a Fourier transform domain; a time domain signal received at a receiving end is firstly demodulated and then is subjected to fast Fourier transform, and finally channel estimation and equalization are completed in a Fourier transform domain. According to the invention, pilot overhead compression is realized by using a variable-length symbol structure, and the complexity of the system and estimation is reduced by combining a constant-amplitude sequence and domain transformation.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of wireless communication, and relates to channel estimation and equalization technology of wireless communication physical layer, in particular to an orthogonal Chirp multiplexing system based on constant sampling rate variable length symbol pilot structure and a channel estimation method thereof. BACKGROUND

[0002] In low earth orbit (LEO) satellites, high-speed railways, and high-speed vehicle networking, the channel presents significant frequency-selective and time-selective dual characteristics: frequency-selective fading is caused by multipath time delay spread, and Doppler shift and its dynamic change are caused by rapid relative motion. In such scenarios, the physical layer receiver needs to achieve high-precision and low-complexity estimation and equalization of the time-frequency two-dimensional and time-drifting channel response under the premise of limited pilot overhead, and then guarantee the reliability and spectral efficiency of the communication link.

[0003] Orthogonal frequency division multiplexing (OFDM) technology is maturely applied in wideband communication systems. Its typical channel estimation scheme is to use frequency-domain comb-shaped pilots or block-shaped pilots, to obtain the channel response at the pilot position by least squares (LS) or linear minimum mean square error (LMMSE) algorithm, and then to complete full-grid channel reconstruction by time-frequency two-dimensional interpolation. However, in the case of strong time variation and high Doppler, in order to maintain the interpolation accuracy, the pilot density in the time and frequency dimensions needs to be increased synchronously, which will significantly increase the pilot overhead. If the pilot density is limited, two-dimensional interpolation may have extrapolation errors, trajectory lag, or smoothing distortion, and cannot effectively track high-speed time-varying components. In addition, the inter-carrier interference (ICI) caused by frequency offset and the inter-block interference (IBI) caused by insufficient cyclic prefix (CP) length will introduce estimation bias and noise amplification effects at the pilot position, further degrading the estimation performance of LS or LMMSE algorithm. Although existing adaptive or iterative interpolation methods can improve the local fitting effect, their complexity and parameter selection sensitivity bring a heavy burden to engineering implementation.

[0004] In the design of pilot sequence, the QAM pilot with random bit mapping has the problem of large energy fluctuation and high peak-to-average power ratio (PAPR), which not only requires the transmit link power amplifier to reserve a large backoff margin and reduce energy efficiency, but also easily triggers nonlinear distortion and out-of-band signal regeneration in nonlinear devices and power-limited platforms, weakening the reference stability and correlation detection performance of the pilot. The Zadoff-Chu (ZC) sequence widely used in communication standards has excellent synchronization and estimation robustness due to its constant envelope zero cyclic autocorrelation (CAZAC) characteristics, but how to efficiently apply it in the pilot sparsification, block structure design, and two-dimensional reconstruction framework in high-speed time-varying scenarios still needs to be designed in combination with the specific system structure.

[0005] OCDM technology realizes the domain representation of signals in time-frequency domain through discrete Fresnel transform (DFnT). The current technical solutions are mostly developed around OFDM system, and the special channel estimation process and pilot configuration optimization research for the structure characteristics of OCDM / DFnT are relatively scarce, which is embodied in the following three core problems: First, in the OCDM system, how to reasonably configure the time-frequency block density of the pilot, so as to realize the balance between estimation accuracy and pilot overhead under the condition of complex channel with strong time-varying and frequency-selective; Second, under the dual-domain mapping relationship between DFnT and FFT, how to build the separable relationship between the pilot and the channel impulse response, so as to simplify the observation model at the pilot into the product form, and provide convenience for the parallelization and low complexity implementation of LS / LMMSE algorithm; Third, how to organically couple the ZC sequence with low PAPR and low cross-correlation characteristics with the above pilot block design, not only to reduce the risk of non-linear distortion at the transmitting end, but also to improve the stability of pilot observation under strong noise and large frequency offset conditions.

[0006] At the engineering implementation level, the transceiver under high-speed mobile scenario also faces multiple real constraints: the scarcity of spectrum resources puts strict restrictions on the pilot occupation ratio; the computing power and power consumption budget of terminal equipment are limited, which restricts the application of complex matrix operation and large-scale two-dimensional filtering; the radio frequency linearity and dynamic range of satellite-ground link or vehicle-mounted equipment are difficult to be greatly improved, making them more sensitive to the PAPR and transmission power efficiency of the pilot; at the same time, the system needs to be compatible with the existing OFDM receiving link components as much as possible to reduce the cost of technical transformation and deployment.

[0007] These constraints collectively point to a core technical requirement: under the premise of not significantly increasing the pilot overhead and implementation complexity, fully tap the time-frequency domain structure advantages of OCDM / DFnT, and build a pilot design and estimation algorithm system that matches it. Through optimized design, the pilot observation model is closer to the ideal product form, reducing the interpolation dimension and amplitude, and reducing the estimation bias and variance; at the same time, with the help of low PAPR ZC pilot sequence, the stability and synchronization performance of the transmitting link are further improved.

[0008] In view of the physical layer receiving requirements of high-speed mobile broadband communication, the existing OFDM pilot and two-dimensional interpolation scheme exposes the problems of pilot overhead and estimation accuracy being difficult to balance, high PAPR causing nonlinear distortion of the transmission chain, etc. under high Doppler and high frequency selective channel; although the OCDM technology has the potential to reconstruct the channel estimation relationship through the DFnT structure, it currently lacks a systematic solution that organically integrates the time-frequency domain mapping characteristics, block sparse pilot and low PAPR ZC sequence, and simultaneously meets the requirements of low complexity and high accuracy. Therefore, a design based on time-frequency domain structure and block ZC pilot is proposed to realize low complexity LS or LMMSE estimation and the supporting two-dimensional reconstruction technical scheme, which has clear engineering practice value and application necessity. SUMMARY

[0009] Therefore, the purpose of the present application is to provide an orthogonal Chirp multiplexing system based on a constant sampling rate variable length symbol pilot structure and a channel estimation method thereof.

[0010] To achieve the above-mentioned purpose, the present application provides the following technical scheme: On the one hand, an orthogonal Chirp multiplexing system based on a constant sampling rate variable length symbol pilot structure is provided, which comprises a sending part and a receiving part. The sending part comprises a data block modulation module, an OCDM resource mapping module and a FastInvDFnT module. The receiving part comprises a FastDFnT module, a ChanEst module and a data block demodulation module, wherein: The data block modulation module is used to map the original information bits to be transmitted through channel coding and modulation, and convert them into a complex modulation symbol set that meets the requirements of subsequent resource mapping and transformation; The OCDM resource mapping module maps the modulated data symbols and block pilot reference signals to the corresponding resource grid in the time-frequency domain according to the established time-frequency double-dimensional density strategy under the unified sampling rate framework; The FastInvDFnT module is used to map the constructed data and pilot frequency domain resources to time domain symbol sequences respectively; wherein the data and the pilot use different Fresnel transform lengths to complete the low complexity transformation from time-frequency structure to transmission time domain; The FastDFnT module is located in the receiving link and is used to map the time domain symbol block that has been transmitted through the channel and has completed synchronization and de-prefix processing to recover the time-frequency domain representation corresponding to the resource grid structure of the sending end; The ChanEst module is used to extract pilot observations in the receiving resource grid, construct a frequency domain approximate product model, and perform least squares and separated linear minimum mean square error estimation algorithm to recover the full grid channel response; After obtaining the full-grid channel estimation results, the data block demodulation module performs frequency domain equalization, soft and hard decision-making, and channel decoding operations on the data resource elements to complete the bit-level information recovery.

[0011] Furthermore, the overall execution process of this system can be represented as follows: Let the Fresnel transform function be DFnT, and the corresponding inverse transform be denoted as IDFnT. Then the time-domain waveform signal of the transmitting end is represented as:

[0012] The signal received by the channel receiver is denoted as Perform on the signal Transformed to a time-frequency grid, it is represented as:

[0013] Based on the properties of circular convolution using Fresnel transform, we can conclude that:

[0014] Add an FFT module to perform an FFT transformation on the entire received symbol set, resulting in:

[0015] in, Satisfying the product property, the locally synchronized DMRS sequence is transformed by FFT and then compared with the received sequence. The channel impulse response at the DMRS location in the time-frequency resource grid was calculated; Interpolation is performed on both the time and frequency axes based on the density parameters to obtain a complete time-frequency channel estimation map, which is then used to construct a complete time-frequency resource grid mapping at the receiver.

[0016] On the other hand, a channel estimation method for the aforementioned orthogonal Chirp multiplexing system based on a constant sampling rate variable-length symbol pilot structure is also provided, the method comprising the following steps: S1. Obtain the original information bit stream to be transmitted and perform channel coding on it to generate data blocks Data; at the same time, design block pilot DMRS based on constant amplitude ZC sequence; S2. Perform fast discrete inverse Fresnel transform with different numbers of points on the data block Data and the pilot block DMRS respectively to obtain the time-domain data symbol and the time-domain pilot symbol. S3. Add a cyclic prefix to the time-domain data symbols and time-domain pilot symbols, and introduce two independent control parameters, time density and frequency density, to construct a pilot and data variable-length symbol structure based on a constant sampling frequency, which serves as the transmission frame; S4. The receiving end extracts the corresponding number of pilot blocks and data blocks from the received time-domain transmission frame, uses fast Fresnel transform to convert them from time-domain waveforms to time-frequency domain, and rearranges them into a receive resource grid according to column index. S5. Perform a fast Fourier transform on the output time-frequency domain pilot components to transform the convolution approximation into a frequency domain product form, and use the least squares method for initial estimation. S6. The linear least mean square error (LMMSE) smoothing algorithm is used to smooth and interpolate the initial least squares estimation results to obtain the complete channel response matrix. S7. Combine the data frequency domain observations and the channel response matrix to perform frequency domain equalization processing, restore it to the demodulation domain through inverse mapping, and recover the original bit information stream after soft and hard decision and channel decoding.

[0017] Furthermore, step S1 includes a parameter initialization setting process, which at least configures the data symbols to use a long transform point count. Data cycle prefix length Number of subcarriers occupied by data The length of the time-domain symbol is gridDataSymbolNum, and the pilot symbol uses a short transform point. Pilot symbol cyclic prefix length Sparse frequency index set DmrsSubChirpSpaceIndex, pilot time-domain symbol length gridDmrsSymbolNum, time-domain density Frequency domain density Simultaneously, a centrally continuous distribution strategy is adopted, initializing the starting frequency index startSubCarrierSpace and the actual center occupied range index gridOcdmDataSubChirpSpaceIndex; Step S1 includes a data block generation process, which generates data blocks Data based on the bit stream to be transmitted: performing channel coding based on the bit stream to be transmitted, and then using 16QAM modulation mapping to distribute the generated complex modulation symbols according to... The corresponding subcarrier width is mapped to The corresponding frequency domain resource index set is filled with zeros in the middle, and the rest of the positions are padded with zeros; Step S1 also includes a pilot block generation process, which uses the ZC sequence as the demodulation reference signal and generates a pilot block DMRS based on the ZC sequence: according to Generate a ZC sequence based on the length of the target length; if the target length is even, use... The strategy of truncating after generating a +1 length is used to maintain approximate CAZAC characteristics; the root sequence parameter is controlled by dmrs.zcRoot, which defaults to 1; if cyclic shift is required, the field dmrs.zcCyclicShift is used to set it, with a default value of 0; after normalization, the generated sequence forms dmrs symbols DmrsModSymbol in column vector form, and then is copied to the time domain positions corresponding to all DMRS according to the time index gridDmrsSymbolIndex; in the final frequency domain resource grid txOcdmGrid, the pilot column is filled with the corresponding row subset according to the sparse row index, the data column is filled with the center continuous subcarrier, and the remaining positions are padded with zeros.

[0018] Furthermore, in step S2, the data frequency domain block is executed. The fast discrete Fresnel inverse transform of points, through the combination of phase factor matrix weighting and IFFT, realizes the mapping from the time-frequency domain to the time domain, and obtains the time-domain data symbol txOcdmDataWaveform; Execute on pilot frequency domain block The fast discrete Fresnel inverse transform of the point yields the time-domain pilot symbol txOcdmDmrsWaveform.

[0019] Furthermore, in step S3, the last part of the data time-domain waveform and the pilot time-domain waveform are respectively truncated. , Each sampling point is pre-stitched onto the time-domain waveform to form a CP extension block, denoted as txOcdmDmrsCpWaveform and txOcdmDataCpWaveform; Time domain density That is, every time in the time domain Inserting one DMRS symbol into each DATA symbol forms a periodic structure of one DMRS plus N-1 DATA symbols; frequency domain density In other words, the subcarrier spacing used by the DMRS symbol is M times that of the DATA symbol subcarrier spacing, and each block DMRS symbol occupies the entire transmission bandwidth allocated to its corresponding OCDM symbol time in the frequency domain. Based on the above density strategy, the DMRS symbol is sequentially concatenated with N-1 data symbols following the timing logic to form a continuous time-domain transmission frame txOcdmWaveform; finally, after processing by a pulse shaping filter, it is transmitted through the radio frequency link.

[0020] Furthermore, in step S4, the receiving end first performs frame synchronization and cyclic prefix removal operations; for the received time-domain symbol stream, according to the known symbol structure, it divides it into gridDmrsSymbolNum pilot blocks and gridDataSymbolNum data blocks; Each block calls the FastDFnT function to convert the time-domain waveform back to the time-frequency domain, denoted as rxDmrsOcdmSymbol and rxDataOcdmSymbol; the obtained pilot and data time-frequency domain representations are rearranged by column index to construct a receiving resource grid, denoted as rxOcdmGrid.

[0021] Further, in step S5, the receiver first performs FastDFnT on the time-domain symbol block containing data and pilot signals. The resulting time-frequency domain representation is essentially a discrete convolution of the DMRS sequence and the channel impulse response h(t). Subsequently, an FFT mapping is performed on the time-frequency domain pilot component to approximately transform the convolution into a frequency-domain product form. The product is then normalized using the full-amplitude average to form frequency-domain observations rxDmrsOcdmSymbol and rxDataOcdmSymbol. The Fresnel transform convolution satisfies the following relationship:

[0022] in for and Linear convolution, express The Fresnel transform result; Indicates signal The Fresnel transform result; These are the domain coordinates of the corresponding time-domain variable t after Fresnel transformation; After obtaining approximate product observations at the pilot frequency domain location, an initial estimation is performed using the least squares algorithm: based on the aforementioned product model, the frequency domain index where the pilot exists is directly indexed. Perform a division operation to obtain the channel estimate of the pilot position. , denoted as ocdmChannEst_hls, is used for subsequent LMMSE smoothing; the estimation process satisfies:

[0023] in, Pilot observation term , It is the result of the local pilot sequence after FFT transformation, corresponding to .

[0024] Furthermore, in step S6, a split Wiener filter structure is used to perform two-stage smoothing of the LS estimation results in both the time and frequency domains; the mathematical model for this smoothing process is as follows:

[0025] In the formula, Indicates the noise variance; The pilot matrix is ​​composed of pilot symbols; To obtain a separable approximate correlation matrix using channel correlation ,in The frequency domain channel correlation matrix, The time-domain channel correlation matrix, ; The two-dimensional LMMSE estimation is decomposed into two one-dimensional filtering processes: constructing time-dimensional weights. Smooth the LS results along the time axis; construct frequency-dimensional weights. The time-domain smoothed result is further filtered along the frequency axis; the specific forms of the two one-dimensional filter weights mentioned above are as follows:

[0026]

[0027] Finally, using linear interpolation or spline interpolation algorithms, the sparse smooth estimates are extended to a full-time-frequency grid to obtain the complete channel response matrix. Used for subsequent balancing processing, denoted as .

[0028] Furthermore, in step S7, the received data frequency domain observation values ​​are... Divide point by channel estimate This completes frequency domain equalization, and the output result is denoted as eqDataModSymbol. The equalized symbols are restored to the demodulation domain by IFFT, and then soft / hard decision and channel decoding are performed sequentially to recover the original bit stream.

[0029] The beneficial effects of this invention are as follows: First, this invention, through the joint design of variable-length symbols and a two-dimensional density controllable mechanism, significantly reduces the time-frequency resource overhead of pilots while ensuring the same channel tracking accuracy, thereby achieving a dual improvement in resource utilization efficiency and effective data throughput.

[0030] Second, by leveraging the convolutional properties of DFnT and the domain mapping capability of FFT, this invention transforms the originally complex problem of estimating long convolutional channels in the time domain into a low-complexity frequency domain multiplication operation. At the same time, by combining the split LMMSE algorithm, the two-dimensional estimation process is decomposed into two independent one-dimensional filtering steps, which significantly reduces the amount of matrix inversion computation and provides convenience for engineering implementation.

[0031] Third, this invention introduces a constant amplitude ZC pilot, which effectively enhances link robustness and reduces the system peak-to-average power ratio (PAPR). This design not only improves the linearity and power efficiency of the transmit link, but also completely eliminates the noise amplification risk in least squares estimation (LS) and LMMSE estimation, and significantly suppresses the error plane phenomenon under high signal-to-noise ratio conditions.

[0032] Fourth, this invention achieves variable-length symbol design while maintaining a constant sampling rate, possessing excellent compatibility and scalability. It can maximize the reuse of existing OFDM system's FFT / IFFT hardware accelerators, significantly reducing the implementation cost and migration difficulty of evolving from OFDM to OCDM technology.

[0033] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0034] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein: Figure 1 This is a schematic diagram of the framework structure of an orthogonal Chirp multiplexing system based on a constant sampling rate variable-length symbol pilot structure according to an embodiment of the present invention; Figure 2 This is a detailed flowchart illustrating the channel estimation method for an orthogonal Chirp multiplexing system based on a constant sampling rate and variable-length symbol pilot structure, according to an embodiment of the present invention. Figure 3 This is a schematic diagram of subcarrier allocation for data block Data according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the variable-length symbol structure for pilots and data in an embodiment of the present invention; Figure 5 This is a schematic diagram of the time-frequency resource grid structure for pilots and data according to an embodiment of the present invention; Figure 6 This is a schematic diagram of the frequency domain resource grid amplitude distribution within a complete frame of the OCDM system according to an embodiment of the present invention. Figure 6 (a) is a schematic diagram of the frequency domain resource grid amplitude distribution at the transmitter. Figure 6 (b) is a schematic diagram of the frequency domain resource grid amplitude distribution after channel and noise are applied; Figure 7 This is a schematic diagram illustrating the changes in block error rate and corresponding throughput as a function of Eb / N0 for LS channel estimation in a TDL-B scenario according to an embodiment of the present invention. Figure 7 (a) shows the curve of block error rate. Figure 7 (b) shows the throughput variation curve; Figure 8This is a schematic diagram illustrating the block error rate and corresponding throughput of the LMMSE channel estimation in the TDL-B scenario under an embodiment of the present invention, as a function of Eb / N0. Figure 8 (a) shows the curve of block error rate. Figure 8 (b) shows the throughput variation curve; Figure 9 This is a schematic diagram illustrating the block error rate and corresponding throughput of the LS channel estimation in the RA scenario under an embodiment of the present invention, as a function of Eb / N0. Figure 9 (a) shows the curve of block error rate. Figure 9 (b) shows the throughput variation curve; Figure 10 This is a schematic diagram illustrating the block error rate and corresponding throughput of the LMMSE channel estimation in the RA scenario under an embodiment of the present invention, as a function of Eb / N0. Figure 10 (a) shows the curve of block error rate. Figure 10 (b) shows the throughput variation curve; Detailed Implementation The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0035] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0036] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0037] Please see Figures 1-10 This paper presents an orthogonal Chirp multiplexing system based on a constant sampling rate variable-length symbol pilot structure and its channel estimation method.

[0038] Example 1 This embodiment provides an orthogonal Chirp multiplexing system based on a variable-length symbol pilot structure with a constant sampling rate, such as... Figure 1 As shown, it includes a transmitting section and a receiving section. The transmitting section includes a data block modulation module, an OCDM resource mapping module, and a FastInvDFnT module; the receiving section includes a FastDFnT module, a ChanEst module, and a data block demodulation module, wherein: The data block modulation module converts the raw information bits to be transmitted into a set of complex modulation symbols that meet the requirements of subsequent resource mapping and transformation through channel coding and modulation mapping. Internally, it first generates a coded bit stream according to a preset coding strategy, and then performs normalized constellation mapping according to the modulation method to ensure that the average symbol power conforms to a unit or specified energy reference. The output provides a structured symbol matrix, carrying derived parameters related to time-frequency resource occupancy, such as length, modulation order, and coding ratio, providing strictly size-matched inputs for subsequent OCDM resource mapping and domain transformation modules.

[0039] Under a unified sampling rate framework, the OCDM resource mapping module maps modulated data symbols and pilot reference signals to the corresponding resource grid in the discrete time-frequency domain according to a predetermined two-dimensional density (time density, frequency density) strategy. Based on the transform length, occupied bandwidth, center guard band, and frequency sparsity interval of the data and pilots, this module fills the data symbols into a continuous set of center subcarriers and arranges pilots (DMRS) with different subcarrier occupied bandwidths. Simultaneously, short-time pilot symbols are inserted in a block-like cyclical manner in the time dimension to achieve Doppler tracking and power overhead balance. The dual-length Zadoff-Chu constant envelope sequence is generated and normalized at this stage and seamlessly spliced ​​with the data resources to form a frequency domain complex matrix.

[0040] The FastInvDFnT module maps constructed frequency-domain resources (data and pilots) to time-domain symbol sequences, performing a low-complexity transformation from the time-frequency domain to the transmit time domain. Its core functionality combines quadratic phase pre-addition (chirp) with an inverse fast Fourier transform (IFFT) (chirp×IFFT×chirp) to achieve amplitude and phase transformations equivalent to the standard discrete inverse Fresnel transform, reducing algorithm complexity. This module uses separate transform lengths for data and pilots, appending a cyclic prefix to the output time-domain blocks. Pilot and data OFDM symbols use the same cyclic prefix length. Subsequently, pilot blocks followed by several data blocks are concatenated to form a complete frame of time-domain waveform. This design ensures adaptive configuration of pilot symbol duration and frequency-domain resolution while maintaining a uniform sampling rate and high reusability of hardware resources compared to traditional OFDM systems.

[0041] The FastDFnT module, located in the receive link, performs domain mapping recovery on time-domain symbol blocks transmitted through the channel and after synchronization and deprecation processing, obtaining a time-frequency domain representation corresponding to the transmitter's resource grid structure. This module calls the fast transform structure (chirp×FFT×chirp) paired with the transmit signal according to symbol type, processing pilot and data blocks of different lengths respectively, ensuring that time-domain splicing does not introduce cross-block spectral pollution. By performing a uniform amplitude normalization operation after the transform, the energy scaling differences caused by different symbol lengths are offset, providing a numerical consistency basis for the stable establishment of the subsequent pilot product model. The obtained frequency-domain pilot and data columns are reconstructed into a receive resource grid using an index, clearly distinguishing the pilot and data positions.

[0042] The ChanEst module's channel estimation module extracts pilot observations from the received resource grid and constructs a frequency-domain approximate product model. This model then performs least squares and separable linear minimum mean square error estimation to recover the full-grid channel response. First, it directly obtains the initial least squares estimate by utilizing the approximate relationship established between the FFT transform of the frequency-domain reference of the transmitter's constant-amplitude pilot and the frequency-domain observations of the received pilot. Subsequently, it constructs a one-dimensional Wiener filter weight based on autocorrelation statistics or hypothetical models in the time and frequency dimensions, smoothing the sparse estimate sequentially in the time and frequency dimensions. Finally, it extends the smoothed result to the complete two-dimensional grid using interpolation or extrapolation techniques.

[0043] After obtaining the full-grid channel estimate, the data block demodulation module performs frequency domain equalization, soft and hard decision processing, and channel decoding on the data resource elements to complete bit-level recovery. This module cancels channel amplitude and phase distortion using point-by-point division or a modified MMSE equalization method, projects the equalized symbols back to the modulation constellation, and generates soft metrics or hard decisions. Decoding is then performed according to the encoding method, outputting the original information bitstream. Through collaboration with the aforementioned estimation module, this demodulation unit achieves robust data recovery in highly time-varying scenarios with low complexity.

[0044] Let the Fresnel transform function be DFnT, and the corresponding inverse transform be denoted as IDFnT. Therefore, the time-domain waveform signal at the transmitting end is denoted as... The signal received by the channel receiver is denoted as , to perform on the signal Transform to a time-frequency grid, denoted as .

[0045]

[0046] Based on the property of circular convolution using Fresnel transform, the time-domain convolution of two signals is equal to the convolution of the Fresnel transform of one signal with the original signal. Therefore:

[0047] Therefore, the Fresnel transform is a transparent process for the entire transmit / receive link. Unlike the Fourier transform, where time-domain convolution equals frequency-domain multiplication, the received signal cannot be directly used to calculate channel estimation in the frequency domain. Therefore, an FFT module is added to perform an FFT transform on the entire received symbol set. The result is:

[0048] At this point, the product property is satisfied. The locally synchronized DMRS sequence is then transformed using an FFT and compared with the received sequence. The channel impulse response at the DMRS location in the time-frequency resource grid was calculated.

[0049] To construct a complete time-frequency resource grid mapping at the receiver, interpolation is performed on both the time and frequency axes based on the density parameters to obtain a complete time-frequency channel estimation map.

[0050] Example 2 This embodiment provides a detailed implementation process of a channel estimation method for an orthogonal Chirp multiplexing system based on a constant sampling rate and a variable-length symbol pilot structure. This method is an OCDM physical layer transmission scheme for high-speed mobile scenarios. Its core lies in utilizing a variable-length symbol structure to achieve pilot overhead compression, and combining constant-amplitude ZC sequences with DFnT domain transformation to reduce the system PAPR and estimation complexity. Figure 2 As shown, it includes at least the following steps: S1. Obtain the original information bit stream to be transmitted and perform channel coding on it to generate data blocks Data; at the same time, design block pilot DMRS based on constant amplitude ZC sequence; S2. Perform fast discrete inverse Fresnel transform with different numbers of points on the data block Data and the pilot block DMRS respectively to obtain the time-domain data symbol and the time-domain pilot symbol. S3. Add a cyclic prefix to the time-domain data symbols and time-domain pilot symbols, and introduce two independent control parameters, time density and frequency density, to construct a pilot and data variable-length symbol structure based on a constant sampling frequency, which serves as the transmission frame; S4. The receiving end extracts the corresponding number of pilot blocks and data blocks from the received time-domain transmission frame, uses fast Fresnel transform to convert them from time-domain waveforms to time-frequency domain, and rearranges them into a receive resource grid according to column index. S5. Perform a fast Fourier transform on the output time-frequency domain pilot components to transform the convolution approximation into a frequency domain product form, and use the least squares method for initial estimation. S6. The linear least mean square error (LMMSE) smoothing algorithm is used to smooth and interpolate the initial least squares estimation results to obtain the complete channel response matrix. S7. Combine the data frequency domain observations and the channel response matrix to perform frequency domain equalization processing, restore it to the demodulation domain through inverse mapping, and recover the original bit information stream after soft and hard decision and channel decoding.

[0051] In step S1 of this embodiment, the system parameters first need to be initialized, including: The data symbols use a long transform point count of data.DFnTlen=2048, corresponding to a fine frequency resolution, denoted as ; The data loop prefix length, data.cpLen=878, is denoted as... ; The number of data-occupied subcarriers, occupScsNum = 1536, is denoted as... ; The length of the time-domain symbol is gridDataSymbolNum = 16; The subcarriers are continuously distributed in the center, with 256 subcarriers reserved on each side of the frequency band as guard intervals to suppress out-of-band leakage; The starting frequency index is startSubCarrierSpace=256, and the actual center occupied range index is gridOcdmDataSubChirpSpaceIndex=[257,1792]; Pilot symbols use a short transform point count of dmrs.DFnTLen=512, denoted as ; Pilot symbol cyclic prefix length drms.DFnTLen=128, denoted as ; Pilot time-domain symbol length gridDataSymbolNum = 48; Sparse frequency index set DmrsSubChirpSpaceIndex=1:4:2048; Time domain density That is, in the time domain, one DMRS symbol is inserted every three DATA symbols to form a structure of one DMRS and three DATA symbols; Frequency domain density That is, the subcarrier spacing used by the DMRS symbol is 4 times that of the DATA symbol subcarrier spacing, and each DMRS symbol occupies the entire transmission bandwidth allocated to its corresponding OCDM symbol time in the frequency domain; Data symbols use channelCode.codeType= modulation. Using a root value of 1 Constant amplitude sequence.

[0052] In this embodiment, the key parameters and initial values ​​of the system are shown in Table 1 below: Table 1

[0053] Then, data blocks (Data) are generated based on the bitstream to be transmitted. Channel coding is performed based on the bitstream to be transmitted. In this embodiment, multiple coding schemes are selected, including no coding, Turbo coding, LDPC coding, and Viterbi coding. Then, 16QAM modulation mapping is performed. The generated complex modulation symbols are then... Width mapped to The frequency domain resource index set is padded with zeros in the middle, and the remaining positions are padded with zeros. For example... Figure 3 As shown.

[0054] Finally, pilot block DMRS is generated based on the ZC sequence: according to The ZC sequence is generated based on the length of the target sequence. If the target length is even, an N+1 length generation and truncation strategy is used to maintain approximate CAZAC characteristics. The root value is controlled by dmrs.zcRoot, which defaults to 1. Cyclic shift is set using the field dmrs.zcCyclicShift, which defaults to 0. After normalization, the generated sequence forms a column vector dmrs symbols DmrsModSymbol, which is then copied to all DMRS time columns according to the time index gridDmrsSymbolIndex=1:4:64. In the final frequency domain resource grid txOcdmGrid, the pilots are filled with the row subset corresponding to the 512-point sequence according to the sparse row index, the data columns are filled with the central 1536 subcarriers, and the remaining positions are kept zero.

[0055] This invention employs the Zadoff-Chu (ZC) sequence instead of traditional random QAM symbols as the demodulation reference signal, constructing a highly robust pilot scheme tailored to the unique time-frequency domain transformation characteristics of OCDM systems. This design leverages the inherent constant envelope characteristic of the ZC sequence; after DFnT or IFFT transformation, its peak-to-average power ratio distribution in the time domain is significantly lower than that of the random QAM sequence. This characteristic not only effectively reduces the back-off requirement of the transmitter power amplifier and improves transmit efficiency, but more importantly, it mitigates in-band distortion and out-of-band radiation caused by PA nonlinearity at the source, reducing the basis interference of nonlinear distortion on channel estimation accuracy.

[0056] The constant amplitude characteristic of the ZC sequence in the frequency domain significantly improves the numerical stability of LS / LMMSE channel estimation. During division at the receiver, the constant amplitude pilot acts as the denominator, fundamentally avoiding the noise amplification effect caused by the small amplitude of random QAM symbols. This significantly improves the signal-to-noise ratio of the initial LS estimate, providing a more reliable benchmark for subsequent LMMSE interpolation. Simultaneously, utilizing the excellent zero cyclic autocorrelation (ZAC) characteristic of the ZC sequence, the system can achieve extremely high timing synchronization accuracy and multipath resolution. Its good cross-correlation characteristics also support lightweight orthogonal differentiation of multi-user or multi-layer signals through parameterized configuration of different root values ​​and cyclic shifts, without the need to introduce complex orthogonal overlay codes.

[0057] In step S2 of this embodiment, a 2048-point Fast Discrete Fresnel Inverse Transform is performed on the data frequency domain block. A combination of phase factor matrix weighting and IFFT is used to achieve the mapping from the time frequency domain to the time domain, resulting in the time-domain data symbol txOcdmDataWaveform. A 512-point Fast Discrete Fresnel Inverse Transform is performed on the pilot frequency domain block, resulting in the time-domain pilot symbol txOcdmDmrsWaveform.

[0058] In step S3 of this embodiment, cyclic prefix addition and timing concatenation are performed. The last 878 and 128 sampling points of the data time-domain waveform and pilot time-domain waveform, respectively, are pre-concatenated to form a cp extension block, denoted as txOcdmDmrsCpWaveform and txOcdmDataCpWaveform. (Time-domain density) That is, in the time domain, one DMRS symbol is inserted every three DATA symbols, forming a structure of one DMRS and three DATA symbols; frequency domain density That is, the subcarrier spacing used by the DMRS symbol is 4 times that of the DATA symbol subcarrier spacing, and each DMRS symbol occupies the entire transmission bandwidth allocated to its corresponding OCDM symbol time in the frequency domain; based on the above density strategy, the DMRS symbol is serially spliced ​​with N-1 data symbols following the timing logic to form a continuous time domain transmission frame txOcdmWaveform; finally, after being processed by a pulse shaping filter, it is transmitted by the radio frequency link.

[0059] In resource grid design, two independently controllable parameters, dmrsTimeDensity and dmrsFrequencyDensity, are introduced to construct a variable-length symbol pilot structure based on a constant sampling rate. This design breaks away from the traditional OFDM system limitation that pilot and data symbols must use the same transform length. While maintaining a constant global sampling rate, data symbols use a long transform number to achieve fine frequency resolution, while pilot symbols use a short transform number to save resource overhead. Figure 4 As shown.

[0060] The subcarrier spacing extension of DMRS naturally creates a uniform and sparse distribution in the frequency domain. This not only directly reduces frequency domain resource consumption but also avoids the high PAPR problem caused by zero-interpolation in long symbols in traditional comb pilots. Due to the reduced number of transform points, the physical duration of DMRS symbols is proportionally shortened. The system inserts short DMRS symbols into the long data symbol stream at intervals corresponding to the pilot time density, forming a hybrid frame structure of short pilots and long data. By shortening the physical duration of pilot symbols, time-domain resources are directly freed up for data transmission, significantly improving system throughput compared to traditional full-length block pilots. Figure 5 As shown.

[0061] In scenarios with rapidly changing Doppler frequencies, the time density parameter can be reduced to increase the pilot frequency, leveraging the low overhead of short symbols to achieve high-frequency channel tracking. In frequency-selective fading scenarios, the frequency density parameter can be adjusted to balance the frequency domain resolution. Although the symbol length is variable, the constant sampling rate eliminates the need for clock frequency switching between the transmitter DAC and receiver ADC; only the number of FFT / DFnT points needs to be switched in the digital baseband processing, maintaining high engineering feasibility.

[0062] By adjusting the two density parameters mentioned above, this design can dynamically balance pilot overhead and channel estimation accuracy under different moving speeds, bandwidths, and multipath delays.

[0063] In step S4 of this embodiment, after channel transmission, the receiver first performs frame synchronization and removes the cyclic prefix. For the received time-domain symbol stream, it is divided into 16 pilot blocks and 48 data blocks according to the known symbol structure. Each block calls the FastDFnT function to convert the time-domain waveform back to the time-frequency domain, denoted as rxDmrsOcdmSymbol and rxDataOcdmSymbol. This step transforms symbols of different lengths independently, without performing a uniform-length FFT on the entire frame, ensuring that the variable-length symbol structure does not produce cross-symbol spectral aliasing. The obtained pilot and data time-frequency domain representations are reconstructed into a receive grid by column index, denoted as rxOcdmGrid.

[0064] In step S5, an FFT is performed on each DFnT output column, and the results are normalized to the full-amplitude average to form frequency domain observations rxDmrsOcdmSymbol and rxDataOcdmSymbol. The receiver first performs FastDFnT on the time-domain symbol block containing data and pilot signals. The resulting time-frequency domain representation is essentially a discrete convolution of the DMRS sequence and the channel impulse response h(t). Subsequently, an FFT mapping is performed on the time-frequency domain pilot component, making the convolution approximately transform into a frequency-domain product. The theoretical basis is the cyclic property of the Fresnel transform. Unlike the Fourier transform's convolution-to-product property, the Fresnel transform convolution is equal to the convolution of one signal with the Fresnel transform of another signal.

[0065] in for and Linear convolution, express The Fresnel transform result; Indicates signal The Fresnel transform result; This represents the coordinates of the corresponding time-domain variable t after domain transformation.

[0066] Approximate product observations are obtained at the pilot frequency domain location, allowing direct estimation using least squares (LS) and linear minimum mean square error (LMMSE). This two-stage DFnT to FFT structure avoids directly processing the high-dimensional deconvolution problem of long convolution kernels in the original time domain, reducing the cascading amplification of noise and interpolation errors. Finally, after frequency domain equalization is completed across the entire grid, the data block is recovered through an equivalent backoff transformation using IFFT and then proceeds to the subsequent demodulation and channel decoding process. The pilot frequency domain observations and the Fast Fourier Transform of the transmitter reference pilot satisfy an approximate product relationship. Due to the constant pilot amplitude, this model does not face noise enhancement caused by the denominator approaching zero in the least squares operation.

[0067] The initial estimation process of the least squares (LS) method is as follows: Based on the above product model, a division operation is directly performed on the frequency domain index k where the pilot exists to obtain the channel estimate of the pilot position. , denoted as ocdmChannEst_hls, is used in the subsequent LMMSE smoothing function.

[0068]

[0069] in, Pilot observation term , It is obtained by performing an FFT on the local pilot sequence. .

[0070] In step S6 of this embodiment, a split Wiener filter structure is used to perform two-stage smoothing of the LS estimate in both the time and frequency domains. The principle formula is as follows:

[0071] In the formula, Indicates the noise variance. The pilot matrix is ​​composed of pilot symbols; This represents the time correlation matrix and frequency estimation matrix obtained by using the separable approximation of channel correlation. ,in, and These represent the channel correlation matrix in the frequency domain and the channel correlation matrix in the time domain, respectively. Constructing one-dimensional filter weights:

[0072]

[0073] At this point, the high-dimensional two-dimensional LMMSE estimation is decomposed into two one-dimensional filtering processes. Time-dimensional weights are then constructed. Smooth the LS results along the time axis. Construct frequency-dimensional weights. The time-domain smoothed result is further filtered along the frequency axis. Using linear interpolation or spline interpolation algorithms, the sparse smoothed estimates are extended to the entire time-frequency grid to obtain the complete channel response matrix. For use in balancing purposes, denoted as .

[0074] In step S7 of this embodiment, the received data frequency domain observation value is... Divide point by channel estimate Equalization is completed, and the output is denoted as rx.eqDataModSymbol. The equalized symbol is then restored to the demodulation domain via IFFT (or equivalent inverse mapping), where soft / hard decision-making and channel decoding are performed to recover the original bit stream.

[0075] Example 3 This embodiment demonstrates the performance of the system in Embodiment 1 and the method in Embodiment 2 under various channel coding conditions.

[0076] Scenario 1: Performance curves of various channel coding methods under the TDL-B channel model of OCDM system Figure 6 This demonstrates the frequency domain resource grid amplitude distribution of the OCDM system within a complete frame. Figure 6 (a) is the txOcdmGrid at the transmitting end. Figure 6 (b) is the rxOcdmGrid after channel and noise. The horizontal axis corresponds to the order of the 64 time-domain symbols, and the vertical axis is the 1536 sub-Chirp indices. The color mapping represents the amplitude, with yellow areas indicating higher amplitude and blue areas indicating lower amplitude.

[0077] In txOcdmGrid, the structure is very regular. High-amplitude stripes spanning the entire frequency band appear at fixed intervals of symbol columns; these are DMRS resource blocks. Because the pre-mapped Zadoff-Chu sequence is approximately uniform in amplitude in the frequency domain, it appears as uniform yellow vertical bars. Data symbol-filled blocks follow immediately, with colors concentrated between 0.8 and 1.2, indicating a relatively concentrated amplitude distribution after normalized QAM mapping, with minimal differences between subcarriers. Furthermore, vertically, the frequency domain segmentation of DMRS and data is consistent, indicating correct resource mapping and density parameter configuration, with no holes or out-of-bounds errors.

[0078] The rxOcdmGrid retains the same resource distribution shape, indicating that the demodulation and grid reconstruction process at the receiver is correct; however, the color distribution changes significantly, especially with a large blue-green trough in the symbol index region of approximately 20–45, followed by a rebound in the last few columns. This amplitude fluctuation along the time axis reflects selective fading and gain fluctuations in the channel. Despite overall power attenuation, the DMRS column maintains a high amplitude, indicating that the pilots remain prominent and can provide relatively accurate information for the channel estimation module. The data column shows reduced amplitude and frequency-dependent fluctuations, with alternating colors in the vertical stripes, indicating that the signal-to-noise ratio on different subcarriers has widened, which will affect subsequent equalization and decoding performance. The pilot column is easily distinguishable, thus aiding in fast channel estimation. The data column is controlled within a narrow amplitude range at the transmitter, ensuring PAPR performance of the transmit link. Although the receiver is affected by fading, the overall structure can still be recovered.

[0079] Figure 7The curves on the left (Block Error Rate (BLER) versus Eb / N0) and the right (corresponding throughput versus Eb / N0) constitute the data. The red curve family represents the OCDM system, and the blue curve family represents the OFDM system. Each family contains four channel coding configurations: None, Viterbi, Turbo, and LDPC, with a code rate set to 1 / 2. Under fixed pilot overhead, this embodiment systematically demonstrates the threshold characteristics and convergence of different coding schemes and modulation schemes in terms of block-level reliability and effective rate through a two-dimensional sparse reference signal design and channel estimation equalization process.

[0080] Figure 7 (a) The curves exhibit a typical waterfall pattern, meaning that the BLER approaches 1 in the low Eb / N0 range, drops rapidly after crossing their respective thresholds, and approaches 0 in the higher Eb / N0 range. Under the same reference signal density and estimation process, the OCDM family's overall threshold shifts to the left compared to the OFDM family. In OCDM, the Viterbi and Turbo curves show a significant cliff-like drop at lower Eb / N0, while the LDPC's drop starts in the middle decibel range further to the right, requiring a further increase in Eb / N0 before entering the drop phase; the corresponding tails are essentially zero at higher Eb / N0. In OFDM, the waterfall starting points for all four coding systems shift to the right. Viterbi and Turbo require a higher Eb / N0 than OCDM to trigger a rapid drop; the drop segments of LDPC and the uncoded curves shift further back, and the drop slope is gentler. In the Viterbi and Turbo configurations, the curve drops sharply after threshold triggering, indicating that with improved reference signal design and estimation support, the failure probability dominated by residual error rapidly decreases after the decoder enters the error correction threshold. The Viterbi and no-coding curves drop more gradually, reflecting the higher sensitivity to estimation bias and frequency-selective fading when there is low or no redundancy. However, OCDM still maintains a relatively faster convergence and forward shift compared to OFDM. These differences reflect that, under the same overhead and complexity, the two-dimensional sparse reference signal layout combined with the Discrete Fresnel Transform (DFnT) coupling structure of OCDM can improve the accuracy of channel estimation, reduce residual mismatch and noise propagation, thereby achieving a forward shift of the threshold and accelerated convergence in the waterfall region under various coding configurations.

[0081] Figure 7(b) The throughput curve is a mirror image of BLER. At low Eb / N0, the throughput approaches zero, then rises rapidly after crossing their respective thresholds and tends to plateau. Under the same reference signal overhead, the throughput of the OCDM family generally climbs earlier than that of the OFDM family, and approaches the high-level plateau even faster in the Viterbi / Turbo configuration. This phenomenon holds true in all four coding schemes and two modulation schemes, demonstrating the universality of the reference signal design and channel estimation process. That is, regardless of changes in error correction capability and redundancy level, the leftward shift of the threshold and the earlier convergence of throughput of OCDM relative to OFDM can be maintained. Under typical TDL-B multipath fading conditions, the two-dimensional sparse reference signal and the DFnT structure of OCDM, combined with channel estimation and equalization, can achieve near-plateau throughput at medium Eb / N0, reducing transmit power and link budget requirements; in the absence of coding, the threshold shifts to the right overall, but OCDM still maintains an advantage over OFDM, demonstrating the robustness of the method to estimation errors and frequency-selective fading.

[0082] Figure 8 While maintaining consistent channel and resource configuration, the channel estimator was replaced by a two-dimensional correlation-separated LMMSE, yielding the corresponding block error rate and throughput curves. Compared to the LS method, the entire family of curves shifts to the left towards lower Eb / N0: under the OCDM system, the waterfall starting point of Viterbi and Turbo is advanced by approximately 2–3 dB, and the thresholds for Viterbi and uncoded methods also shift forward accordingly. This means that OCDM essentially enters a high-throughput plateau around 18–20 dB, while OFDM requires a higher Eb / N0 to achieve the same convergence. The curve steepness is further enhanced under Turbo, and the transition region where the block error rate drops rapidly from near 1 to near 0 becomes narrower, indicating that after the estimation error variance decreases, the decoder enters the SNR range of the error correction threshold more concentratedly. The throughput curve mirrors the BLER decline: under LMMSE, the Eb / N0 required for throughput of the same target is significantly lower than that under LS, with the most significant early convergence for strongly coded methods; while the improvement for uncoded and LDPC is slightly smaller, it still reflects the trend of a unified leftward shift in the system threshold. The relative gap between OCDM and OFDM narrows slightly in the high SNR plateau region, while OCDM still leads in the low-to-medium SNR region. This indicates that LMMSE provides a gain for both systems but does not eliminate the inherent advantage of time-frequency coupling brought by OCDM.

[0083] Scenario 2: Performance curves of various channel coding in the Rician channel (RA) scenario Figure 9 This section presents performance curves for LS channel estimation in a RA scenario. Compared to previous TDL... Unlike the pure multipath fading and strong frequency selectivity of the B channel, the Rician channel has a stable direct component, which significantly reduces the probability of frequency selectivity and deep fading. The block error waterfall region is concentrated overall and shifts to the left towards lower Eb / N0. The red OCDM curve family and the blue OFDM curve family remain separated, but their relative spacing is greater than that of TDL. The narrowing of scenario B indicates that when the channel's selectivity is smoothed by LoS, the additional time-frequency gain of OCDM is weakened, but a identifiable lead is still retained at the threshold position.

[0084] The coding order remains unchanged. Under RicianLS, the Viterbi and Turbo curves of OCDM rapidly drop out of the high BLER region at 5–7 dB, LDPC enters the rapid decline region at around 10–12 dB, and uncoded curves only begin to decline rapidly at around 15–17 dB. The waterfall starting point for the same coding scheme in the OFDM family shifts to the right by approximately 2–3 dB: Viterbi / Turbo at 7–10 dB, LDPC at 12–14 dB, and uncoded curves at 18–20 dB. Due to the stable direct path, the waterfall transition band narrows significantly, highlighting that the estimation error's obstacle to decoding reaching the error correction threshold is further reduced under non-strong frequency selectivity conditions. The throughput curves mirror the BLER decline: Turbo and Viterbi approach the 90 Mbps platform at 8–10 dB, LDPC enters the stable region at 14–16 dB, and uncoded curves only gradually approach it after 20 dB; OFDM requires a higher Eb / N0 to reach the same platform level. The plateau value almost matches the theoretical throughput, with residual differences consisting of statistical jitter due to fixed pilot / CP overhead and extremely low residual error rate. Overall, when the channel has a significant Loss of Speed ​​(LoS) component, the system reliability threshold is shifted to the left by the channel conditions themselves, and OCDM still contributes additional advance margin, allowing the strong coding scheme to release its error correction gain at extremely low Eb / N0.

[0085] Maintaining the same channel and resource configuration, only transitioning the estimator from LS to LMMSE with two-dimensional correlation separation, the entire family of curves shifts to the left again, and the waterfall narrows further, demonstrating the combined effect of a dual reduction in estimation noise variance and interpolation error. The red OCDM strongly coded curve enters the low BLER region (close to zero) at around 4–5 dB; the Turbo curve almost overlaps with the Viterbi curve, indicating that the difference in error correction redundancy between the two is no longer sensitive to block error rate under the given channel smoothness and estimation accuracy. LDPC enters the rapid descent region at around 8–10 dB, while uncoded curves only rapidly decline after around 12–14 dB, about 3 dB earlier than LS. Correspondingly, the OFDM family, with Viterbi / Turbo at 6–8dB, LDPC at 10–12dB, and uncoded at 15–16dB, reaches its waterfall inflection point, still lagging behind OCDM by about 2–3dB. However, both systems converge further than the LS scenario, indicating that under the combined conditions of non-strong frequency selectivity and high-precision estimation, the structural advantage of OCDM is mainly reflected in the final few dB optimization of the threshold. The throughput curves climb faster: OCDM Viterbi / Turbo almost reaches the theoretical plateau just after crossing the waterfall inflection point, and Viterbi also quickly catches up. OFDM experiences a brief transition but achieves high available rates at low to medium Eb / N0. All curves in the plateau region perfectly match the theoretical throughput, with the residual gap approaching zero, indicating that under this channel and estimator configuration, the effective data rate loss beyond pilot and CP overhead is negligible, and the link has reached an almost optimal operating point outside of capacity.

[0086] contrast Figure 10 The differences between the two figures can be summarized as follows: the superposition effect and marginal variation law of the three-layer gain mechanism in the Rician channel. First, when the channel model is switched from TDL-B to Rician, the line-of-sight (LoS) component effectively eliminates some frequency selectivity and deep fading events, causing the starting point of the block error rate waterfall curve to shift forward as a whole, and the curve width to shrink significantly.

[0087] Second, while the structural gain of OCDM over OFDM still exists, its marginal advantage diminishes in LMMSE estimation scenarios. This phenomenon indicates that when both channel estimation error and frequency selectivity are reduced, the contribution of the absolute performance difference between the two systems weakens.

[0088] Third, the leftward shift in the performance threshold resulting from the transition of the estimator from LS to LMMSE exhibits a clear compression limit characteristic under strong coding configurations—the performance curves of LDPC and Turbo coding almost merge into a single optimal curve. This result indicates that the decoding performance has approached the saturation state supported by channel conditions and estimation accuracy, and further increasing coding redundancy can only bring about a very small improvement in the threshold.

[0089] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. An orthogonal Chirp multiplexing system based on a constant sampling rate variable-length symbol pilot structure, characterized in that: The system includes a transmitting section and a receiving section. The transmitting section includes a data block modulation module, an OCDM resource mapping module, and a FastInvDFnT module. The receiving section includes a FastDFnT module, a ChanEst module, and a data block demodulation module, wherein: The data block modulation module is used to convert the raw information bits to be transmitted into a set of complex modulation symbols that meet the requirements of subsequent resource mapping and transformation through channel coding and modulation mapping. Under the unified sampling rate framework, the OCDM resource mapping module maps the modulated data symbols and block pilot reference signals to the corresponding resource grid in the time and frequency domain according to a predetermined time-frequency dual-dimensional density strategy. The FastInvDFnT module is used to map the constructed data and pilot frequency domain resources to time domain symbol sequences respectively; the data and pilot use different Fresnel transform lengths to complete the low-complexity transformation from time-frequency structure to the transmission time domain. The FastDFnT module is located in the receiving link and is used to perform domain mapping recovery on the time-domain symbol blocks that have been transmitted through the channel and have completed synchronization and deprecation processing, so as to obtain the time-frequency domain representation corresponding to the resource grid structure of the transmitting end. The ChanEst module is used to extract pilot observations from the received resource grid, construct a frequency domain approximate product model, and execute the least squares and separable linear minimum mean square error estimation algorithm to recover the full grid channel response. After obtaining the full-grid channel estimation results, the data block demodulation module performs frequency domain equalization, soft and hard decision-making, and channel decoding operations on the data resource elements to complete the bit-level information recovery.

2. The orthogonal Chirp multiplexing system based on a constant sampling rate variable-length symbol pilot structure according to claim 1, characterized in that: The overall execution process of the system is represented as follows: Let the Fresnel transform function be DFnT, and the corresponding inverse transform be denoted as IDFnT. Then the time-domain waveform signal of the transmitting end is represented as: The signal received by the channel receiver is denoted as Perform on the signal Transformed to a time-frequency grid, it is represented as: Based on the property of circular convolution using Fresnel transform, the time-domain convolution of two signals is equal to the convolution of the Fresnel transform of one signal with the original signal. Therefore: Add an FFT module to perform an FFT transformation on the entire received symbol set, resulting in: in, Satisfying the product property, the locally synchronized DMRS sequence is transformed by FFT and then compared with the received sequence. The channel impulse response at the DMRS location in the time-frequency resource grid was calculated; Then, interpolation is performed on both the time and frequency axes to obtain a complete time-frequency channel estimation map, which is then used to construct a complete time-frequency resource grid mapping at the receiver.

3. A channel estimation method for an orthogonal Chirp multiplexing system based on a constant sampling rate variable-length symbol pilot structure as described in claim 1 or 2, characterized in that: The method includes the following steps: S1. Obtain the original information bit stream to be transmitted and perform channel coding on it to generate data blocks Data; at the same time, design block pilot DMRS based on constant amplitude ZC sequence; S2. Perform fast discrete inverse Fresnel transform with different numbers of points on the data block Data and the pilot block DMRS respectively to obtain the time-domain data symbol and the time-domain pilot symbol. S3. Add a cyclic prefix to the time-domain data symbols and time-domain pilot symbols, and introduce two independent control parameters, time density and frequency density, to construct a pilot and data variable-length symbol structure based on a constant sampling frequency, which serves as the transmission frame; S4. The receiving end extracts the corresponding number of pilot blocks and data blocks from the received time-domain transmission frame, uses fast Fresnel transform to convert them from time-domain waveforms to time-frequency domain, and rearranges them into a receive resource grid according to column index. S5. Perform a fast Fourier transform on the output time-frequency domain pilot components to transform the convolution approximation into a frequency domain product form, and use the least squares method for initial estimation. S6. The LMSE (Linear Minimum Mean Square Error) smoothing algorithm is used to smooth and interpolate the initial least squares estimation results to obtain the complete channel response matrix. S7. Combine the data frequency domain observations and the channel response matrix to perform frequency domain equalization processing, restore it to the demodulation domain through inverse mapping, and recover the original bit information stream after soft and hard decision and channel decoding.

4. The channel estimation method for an orthogonal Chirp multiplexing system based on a constant sampling rate and variable-length symbol pilot structure according to claim 3, characterized in that: Step S1 includes a parameter initialization setting process, which at least configures: Data symbols use long transform points Data cycle prefix length Number of subcarriers occupied by data The length of the time-domain symbol is gridDataSymbolNum, and the pilot symbol uses a short transform point. Pilot symbol cyclic prefix length Sparse frequency index set DmrsSubChirpSpaceIndex, pilot time-domain symbol length gridDmrsSymbolNum, time-domain density Frequency domain density Simultaneously, a centrally continuous distribution strategy is adopted, initializing the starting frequency index startSubCarrierSpace and the actual center occupied range index gridOcdmDataSubChirpSpaceIndex; Step S1 includes a data block generation process, which generates data blocks Data based on the bit stream to be transmitted: performing channel coding based on the bit stream to be transmitted, and then using 16QAM modulation mapping to distribute the generated complex modulation symbols according to... The corresponding subcarrier width is mapped to The corresponding frequency domain resource index set is filled with zeros in the middle, and the rest of the positions are padded with zeros; Step S1 also includes a pilot block generation process, which uses the ZC sequence as the demodulation reference signal and generates a pilot block DMRS based on the ZC sequence: according to Generate a ZC sequence based on the length of the target length; if the target length is even, use... The strategy of truncating after generating a +1 length is used to maintain approximate CAZAC characteristics; the root sequence parameter is controlled by dmrs.zcRoot, which defaults to 1; if cyclic shift is required, the field dmrs.zcCyclicShift is used to set it, with a default value of 0; after normalization, the generated sequence forms dmrs symbols DmrsModSymbol in column vector form, and then is copied to the time domain positions corresponding to all DMRS according to the time index gridDmrsSymbolIndex; in the final frequency domain resource grid txOcdmGrid, the pilot column is filled with the corresponding row subset according to the sparse row index, the data column is filled with the center continuous subcarrier, and the remaining positions are padded with zeros.

5. The channel estimation method for an orthogonal Chirp multiplexing system based on a constant sampling rate and variable-length symbol pilot structure according to claim 4, characterized in that: In step S2, the data frequency domain block is executed. The fast discrete Fresnel inverse transform of points, through the combination of phase factor matrix weighting and IFFT, realizes the mapping from the time-frequency domain to the time domain, and obtains the time-domain data symbol txOcdmDataWaveform; Execute on pilot frequency domain block The fast discrete Fresnel inverse transform of the point yields the time-domain pilot symbol txOcdmDmrsWaveform.

6. The channel estimation method for an orthogonal Chirp multiplexing system based on a constant sampling rate and variable-length symbol pilot structure according to claim 5, characterized in that: In step S3, the last part of the data time-domain waveform and the pilot time-domain waveform are respectively truncated. , Each sampling point is pre-stitched onto the time-domain waveform to form a CP extension block, denoted as txOcdmDmrsCpWaveform and txOcdmDataCpWaveform; Time domain density That is, every time in the time domain Inserting one DMRS symbol into each DATA symbol forms a periodic structure of one DMRS plus N-1 DATA symbols; frequency domain density That is, the subcarrier spacing used by the DMRS symbol is M times the subcarrier spacing of the DATA symbol, and each block DMRS symbol occupies the entire transmission bandwidth allocated to its corresponding OCDM symbol time in the frequency domain; based on the above density strategy, the DMRS symbol is serially spliced ​​according to the timing logic of N-1 data symbols following one DMRS symbol to form a continuous time domain transmission frame txOcdmWaveform; finally, after being processed by a pulse shaping filter, it is transmitted by the radio frequency link.

7. The channel estimation method for an orthogonal Chirp multiplexing system based on a constant sampling rate and variable-length symbol pilot structure according to claim 6, characterized in that: In step S4, the receiving end first performs frame synchronization and cyclic prefix removal operations; for the received time-domain symbol stream, according to the known symbol structure, it divides gridDmrsSymbolNum pilot blocks and gridDataSymbolNum data blocks. Each block calls the FastDFnT function to convert the time-domain waveform back to the time-frequency domain, denoted as rxDmrsOcdmSymbol and rxDataOcdmSymbol; the obtained pilot and data time-frequency domain representations are rearranged by column index to construct a receiving resource grid, denoted as rxOcdmGrid.

8. The channel estimation method for an orthogonal Chirp multiplexing system based on a constant sampling rate and variable-length symbol pilot structure according to claim 7, characterized in that: In step S5, the receiver first performs FastDFnT on the time-domain symbol block containing data and pilot signals. The resulting time-frequency domain representation is essentially a discrete convolution of the DMRS sequence and the channel impulse response h(t). Subsequently, an FFT mapping is performed on the time-frequency domain pilot component to approximately transform the convolution into a frequency-domain product form. The product is then normalized using the full-amplitude average to form frequency-domain observations rxDmrsOcdmSymbol and rxDataOcdmSymbol. The Fresnel transform convolution satisfies the following relationship: in for and Linear convolution, express The Fresnel transform result; Indicates signal The Fresnel transform result; These are the domain coordinates of the corresponding time-domain variable t after Fresnel transformation; After obtaining approximate product observations at the pilot frequency domain location, an initial estimation is performed using the least squares algorithm: based on the aforementioned product model, the frequency domain index where the pilot exists is directly indexed. Perform a division operation to obtain the channel estimate of the pilot position. , denoted as ocdmChannEst_hls, is used for subsequent LMMSE smoothing; the estimation process satisfies: in, Pilot observation term , It is the result of the local pilot sequence after FFT transformation, corresponding to .

9. The channel estimation method for an orthogonal Chirp multiplexing system based on a constant sampling rate and variable-length symbol pilot structure according to claim 8, characterized in that: In step S6, a split Wiener filter structure is used to perform two-stage smoothing of the LS estimation results in both the time and frequency domains; the mathematical model of the smoothing process is as follows: In the formula, Indicates the noise variance; The pilot matrix is ​​composed of pilot symbols; To obtain a separable approximate correlation matrix using channel correlation ,in The frequency domain channel correlation matrix, The time-domain channel correlation matrix, ; The two-dimensional LMMSE estimation is decomposed into two one-dimensional filtering processes: constructing time-dimensional weights. Smooth the LS results along the time axis; construct frequency-dimensional weights. The time-domain smoothed result is further filtered along the frequency axis; the specific forms of the two one-dimensional filter weights mentioned above are as follows: Finally, using linear interpolation or spline interpolation algorithms, the sparse smooth estimates are extended to a full-time-frequency grid to obtain the complete channel response matrix. Used for subsequent balancing processing, denoted as .

10. The channel estimation method for an orthogonal Chirp multiplexing system based on a constant sampling rate and variable-length symbol pilot structure according to claim 9, characterized in that: In step S7, the received data frequency domain observation values ​​are... Divide point by channel estimate This completes frequency domain equalization, and the output result is denoted as eqDataModSymbol. The equalized symbols are restored to the demodulation domain by IFFT, and then soft / hard decision and channel decoding are performed sequentially to recover the original bit stream.

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