Low-storage high-reliability transceiver cooperative interleaving transformation method for random multiplexing communication system

Abstract

This invention discloses a low-storage, high-reliability transceiver cooperative interleaving transformation method for random multiplexing communication systems. The method includes: at the transmitter, mapping the bit stream to be transmitted into source domain information symbol vectors; interleaving and rearranging the symbol vectors using a low-storage interleaver; performing phase perturbation and multi-layer coupling transformation on the interleaved and rearranged transmitted signal to generate a high-reliability random multiplexing modulation signal and adding a cyclic prefix before sending it to the receiver; at the receiver, after receiving the signal, removing the cyclic prefix to obtain a time-domain observation signal vector; performing iterative signal detection using an HR-CD-MAMP detector matched to the transmitter's transformation to complete symbol estimation; and completing the interleaving and deinterleaving operations of the high-reliability transformation and inverse transformation in the iterative estimator using a low-storage interleaver corresponding to the synchronization parameters to recover the source domain symbol vectors; and recovering the binary bit stream from the obtained source domain symbol vectors through digital demapping.

Description

Technical Field

[0001] This invention relates to the field of multicarrier modulation, and more particularly to a low-storage, high-reliability transceiver cooperative interleaving transformation method for random multiplexing communication systems. Background Technology

[0002] With the deepening commercialization of 5G-A (5th Generation Mobile Communication Technology-Advanced) and the rapid evolution of 6G (6th Generation Mobile Communication Technology), wireless communication systems are facing emerging application scenarios such as integrated air-space-ground communication, highly mobile vehicle-to-everything (V2X) communication, and low-altitude economical communication. These scenarios place core demands on communication systems, including ultra-high reliability, low latency, high bandwidth, and strong robustness. Against this backdrop, complex time-varying multipath channels, Doppler shift caused by high-speed movement, and hardware resource constraints resulting from large-scale multiple-input multiple-output (MIMO) deployments have become the core challenges facing the physical layer design of next-generation communication systems.

[0003] Random Multiplexing (RM) technology, as a next-generation multi-carrier modulation scheme, introduces random unitary transforms at the transmitter to ensure that the equivalent channel matrix satisfies universal statistical characteristics. This modulation technique is perfectly compatible with the Memory Approximate Message Passing (MAMP) detection algorithm, achieving Bayesian optimal detection performance even under large system limits. Compared to traditional modulation schemes such as Orthogonal Frequency Division Multiplexing (OFDM), Orthogonal Time Frequency Space (OTFS), and Affine Frequency Division Multiplexing (AFDM), RM technology can achieve a bit error rate performance gain of over 8dB in high-speed mobile scenarios, making it one of the most promising core technologies for the 6G physical layer.

[0004] In the RM (Realistic Array) technology framework, the interleaving transform, as a core module, directly determines the statistical characteristics of the equivalent channel matrix in the RM system, the convergence performance of the MAMP detector, and the storage and computational overhead of the actual system in terms of hardware implementation. However, the interleaving transform design in existing RM systems suffers from the following two major bottlenecks:

[0005] First, traditional pseudo-random interleavers require storing the complete interleaving sequence, and their storage complexity increases linearly with the sequence length. This leads to severe hardware storage and access bottlenecks in large-scale applications. Interleaver design faces a trade-off between storage overhead and transmission performance, failing to balance low hardware implementation cost with the optimal requirements of random multiplexing systems. On one hand, traditional random interleavers require both the transmitting and receiving ends to store the complete interleaving index sequence, and their storage complexity increases linearly with the sequence length. This results in extremely high on-chip storage overhead in large-scale communication scenarios. Simultaneously, these interleavers rely on random table lookup memory access operations, resulting in bus overhead far exceeding that of sequential operations, leading to significant hardware implementation difficulties and power consumption burdens. On the other hand, traditional low-storage structured interleavers, represented by Quadratic Polynomial Permutation (QPP) interleavers, while reducing storage complexity to constant levels, exhibit strong structural correlation in the interleaving sequences generated by fixed polynomials, lacking sufficient pseudo-randomness and failing to meet the requirements of convergence characteristics and right-unitary invariance of the equivalent channel matrix spectrum in random multiplexing systems. In high-mobility, highly correlated channel environments, the symbol rearrangement patterns of this type of interleaver are prone to coupling with the time-varying characteristics of the channel, leading to a sharp decline in sequence decorrelation capability and a significant deterioration in the system's bit error rate performance. This makes it unsuitable for the Bayesian optimality design requirements of memory approximate message passing detectors.

[0006] Second, in complex wireless channels, the interleaving transformation in existing RM systems can cause residual coherence in the equivalent channel matrix, which in turn leads to instability in the iterative convergence process of the MAMP detector and the occurrence of error flattening. This phenomenon is significantly aggravated in small-scale system configurations, ultimately causing a sharp deterioration in the system's transmission performance.

[0007] Existing random multiplexing transform architectures lack robustness in complex channel environments, resulting in severe transmission performance degradation. The original random multiplexing transform relies solely on basic random interleaving and unitary transform for signal modulation. In scenarios with severely time-varying multipath channels and small-scale system configurations, it cannot adequately eliminate the inherent structural characteristics of the channel matrix, leading to significant residual coherence in the equivalent channel matrix. This residual coherence causes the iterative state evolution process of the memory-based approximate message-passing detector to deviate from the Gaussian assumption, leading to error propagation and iterative convergence instability. Ultimately, this problem causes the system to experience bit error rate flattening, resulting in a severe mismatch between the simulated bit error rate curve and the theoretical performance boundary, significantly reducing the system's transmission reliability.

[0008] To address the aforementioned issues, this invention proposes a low-storage, high-reliability transceiver collaborative interleaving transformation technology for random multiplexing communication systems. Starting from two dimensions—an efficient interleaver with low storage overhead and a high-reliability interleaving transformation algorithm—it achieves collaborative optimization between storage overhead and reliability at the transceiver end, providing technical support for the engineering implementation of RM technology in communication systems. Summary of the Invention

[0009] The purpose of this invention is to address the shortcomings of existing technologies by proposing a low-storage, high-reliability transceiver cooperative interleaving transformation method for random multiplexing communication systems.

[0010] The objective of this invention is achieved through the following technical solution: a low-storage, high-reliability transceiver cooperative interleaving transformation method for random multiplexing communication systems, comprising:

[0011] First, the interleaving transformation parameters at both the transmitting and receiving ends are synchronized;

[0012] The transmitting end maps the bit stream to be transmitted into source domain information symbol vectors, uses a low-storage interleaver to interleave and rearrange the symbol vectors, performs a high-reliability transformation based on phase perturbation on the interleaved and rearranged transmitted signal, generates a high-reliability random multiplexed modulated signal, adds a cyclic prefix and sends it to the receiving end.

[0013] After receiving the signal, the receiver removes the cyclic prefix to obtain the time-domain observation signal vector. Iterative signal detection is performed by an HR-CD-MAMP detector matched with the transmitter's transform to complete symbol estimation. The high-reliability transform and inverse transform in the iterative estimator are interleaved and deinterleaved by a low-storage interleaver corresponding to the synchronization parameter to recover the source domain symbol vector. The obtained source domain symbol vector is then restored to a binary bit stream through digital demapping.

[0014] Furthermore, the interleaving rearrangement using a low-memory interleaver is performed using a Logistic chaotic mapping interleaver, and the interleaving process includes:

[0015] Select initial value and chaos control parameters To ensure the mapping is in a chaotic state, the interleaving sequence length is set to... The number of subcarriers should be consistent with the number of subcarriers in the system.

[0016] Generate a length of [length] based on the Logistic mapping iterative formula. chaotic sequence Its iterative formula is expressed as:

[0017]

[0018] The generated chaotic sequence Sort in ascending order, record the original index of each element after sorting, forming a sequence of length [length missing]. Interleaved index sequences ,in, Indicates the sorted order of the first... The original positions corresponding to each element;

[0019] Based on the joint parameter selection criterion of interleaved displacement metric and discrete entropy measurement, the performance of the generated interleaved index sequence is verified to ensure that the sequence satisfies the properties of solution correlation and uniform distribution. Based on the generated interleaved index sequence, the input symbol sequence is... Rearrange the symbols to obtain the interleaved sequence: .

[0020] Furthermore, the performance verification of the generated interleaved index sequence includes:

[0021] Set the weighting coefficients for interleaved displacement measurement and discrete entropy measurement. and ,satisfy ,

[0022] Calculate the interlacing displacement metric Quantify the symbol dispersion of interleaved sequences: ,

[0023] Calculate discrete entropy measurement Quantifying the uniform distribution characteristics of chaotic sequences: The range of values ​​is divided into A series of equal-width intervals, Then count the number of chaotic sequence elements in each interval. Calculate empirical probability The normalized discrete entropy is defined as: ,

[0024] Calculate the parameter evaluation score: measure the interlaced displacement. and discrete entropy measurement By performing normalized weighted combination, a formula for parameter evaluation score is constructed: If the evaluation score meets the system's preset threshold, then the current parameter and the interleaving index sequence are confirmed to be usable; otherwise, a new initial value is selected. With chaotic control parameters Repeat the interleaving process until a satisfactory interleaving index sequence is generated.

[0025] Furthermore, addressing the engineering shortcomings of Logistic chaotic map interleavers, such as high computational complexity, poor parallelism, and sensitivity to finite precision, this invention proposes a two-stage high-order permutation polynomial interleaver as a preferred alternative. This achieves lower computational latency and higher hardware parallelism while maintaining equivalent storage complexity and error rate performance. The interleaving and rearrangement using a low-storage interleaver is performed using a two-stage high-order permutation polynomial interleaver, and the interleaving process includes:

[0026] Set the interleaving sequence length To maintain consistency with the number of system subcarriers, set the order of the permutation polynomial. , Then adjust the sequence length Perform prime factorization to obtain the set of its prime power factors;

[0027] basis permutation function Defined in the ring of integers On The permutation polynomial of order 1 is expressed as follows: Based on the Chinese Remainder Theorem, the polynomial coefficients are... Set the following number theory constraints:

[0028] Invertibility of linear terms: linear coefficients and Coprime,

[0029] Divisibility of higher-order terms: for all odd prime factors Must meet The polynomial modulo each odd prime number The subdegenerates into a first-order polynomial, ensuring that the mapping constitutes a complete permutation in the corresponding modulus.

[0030] Parity: When When the coefficients of even-degree terms and odd-degree terms of a polynomial are equal, they must simultaneously satisfy the following: , ;

[0031] A two-stage polynomial cascade structure is adopted, and row and column reshaping operators are inserted between the two stages. The overall mapping process corresponds to the following expression:

[0032]

[0033] in, This represents the composition operation of functions in the matrix space, that is, for any two mappings , ,have: ;No. Permutation polynomial Defined as: , No. Rank-level column reshaping operator , refers to input sequence First fill in the rows The matrix is ​​then read and reconstructed column by column. The specific mapping steps are as follows:

[0034] First-stage permutation: Input the original symbol sequence, and pass it through a first-stage permutation polynomial. Complete the first symbol rearrangement;

[0035] First-stage row and column reshaping: The sequence output from the first-stage permutation is then reshaped using the row and column reshaping operator. Complete matrix reshaping and sequence reconstruction to eliminate structural dependencies caused by single-level polynomials;

[0036] Second-stage permutation: The reshaped sequence of rows and columns is then permuted using a second-stage permutation polynomial. Complete the second symbol rearrangement.

[0037] Second-stage row and column reshaping: The sequence output from the second-stage permutation is then reshaped using row and column reshaping operators. Complete the quadratic matrix reshaping and sequence reconstruction, and output the final interleaved symbol sequence.

[0038] Furthermore, the high-reliability transformation based on phase perturbation of the interleaved rearranged transmitted signal includes interleaved phase perturbation transformation, specifically as follows:

[0039] First, define the diagonalized phase perturbation matrix. Its specific expression is:

[0040]

[0041] in, This represents the phase perturbation matrix acting in the transform domain. This represents the phase perturbation matrix acting on the source domain. It follows an independent uniform distribution, and satisfies the following when the quantization accuracy of the phase is sufficient. To achieve decorrelation between columns;

[0042] For different application scenarios, implement double-sided interleaved phase perturbation transformation, inner-sided interleaved phase perturbation transformation, or outer-sided interleaved phase perturbation transformation;

[0043] The bi-sided interleaved phase perturbation transform introduces phase randomness both before and after the modulation transform, constructing a composite modulation transform matrix: ,in, This is a diagonal phase perturbation matrix, whose elements all conform to... Uniform distribution; This is the permutation matrix corresponding to the low-storage interleaver. This is the normalized unitary transformation matrix;

[0044] The inner interleaved phase perturbation transform applies a phase perturbation to the input symbol vector only before modulation, constructing the transform matrix: ,in, For direct action on the source domain information symbol vector The corresponding diagonal phase perturbation matrix;

[0045] The outer interleaved phase perturbation transform places the phase perturbation after the modulation transform, constructing the transform matrix: ,in, It operates on the transform domain after modulation transformation to suppress residual inter-symbol interference.

[0046] Furthermore, the high-reliability transformation also includes a multi-layer coupled transformation, specifically extending the phase perturbation to... Cascaded structures of layer-coupled transformations;

[0047] The expression for the transformation matrix is:

[0048]

[0049] in, To change the number of layers, Alternating coupling between the transformation matrix and its corresponding transpose matrix, if the number of layers is odd. The transformation used is Then even-numbered layers Let its corresponding transpose transformation matrix be: This ensures the unitary invariance of the transformation as a whole; This is an optional diagonal phase perturbation matrix. If there is no additional phase perturbation requirement, it will... The value is the identity matrix. ; This is the permutation matrix corresponding to the low-storage interleaver;

[0050] The high-reliability multicarrier modulation conversion process at the transmitting end is as follows:

[0051]

[0052] Source domain information symbol vector High-reliability interleaving transformation and modulation are performed using the HR transformation matrix to generate the time-domain signal vector to be transmitted. .

[0053] Furthermore, the HR-CD-MAMP detector performs iterative signal detection including:

[0054] Initial iteration count and maximum iteration count Initialize the nonlinear estimator to 0, and the variance of the nonlinear estimator... ;

[0055] The detector performs the following operations in a single iteration:

[0056] The memory linear detection iterative formula is:

[0057]

[0058] in, This is the set of estimates from all previous iterations; For normalization parameters, For orthogonalization parameters, For the optimized convergence acceleration parameters, the matrix Defined as ,in, , and Represented as The minimum and maximum eigenvalues;

[0059] High-reliability cross-domain inverse transform transforms the memory linear detection output of the high-reliability transform domain signal. Mapping back to the source domain, the transformation formula is:

[0060]

[0061] The inverse matrix of the unitary transformation is equivalent to the Hermitian transpose matrix;

[0062] Nonlinear detection utilizes the prior distribution characteristics of the symbols to optimize the accuracy of signal estimation. The iterative formula is as follows:

[0063]

[0064] in, These are the normalization parameters and orthogonality parameters of the source domain, respectively. Indicates based on estimated signal The posterior mean estimate is obtained by solving the conditional expectation of the sign.

[0065] High-reliability cross-domain transformation module

[0066] The source domain signal output by nonlinear detection Remapping back to the high-reliability transform domain generates the input signal estimate required for the next iteration of periodic memory linear detection. The transform formula is as follows:

[0067]

[0068] This transformation is strictly dual to the modulation at the transmitting end;

[0069] Update the iteration count and repeat the iteration process until the maximum number of iterations is reached or the bit error rate meets the system's preset threshold. Then stop the iteration and output the final signal estimation result.

[0070] Furthermore, the deinterleaving operation includes: strictly synchronizing the initial values ​​between the receiver and the transmitter. Chaos control parameters With sequence length A completely consistent interleaved index sequence is regenerated, and the deinterleaving operation is completed through inverse mapping to restore the original symbol sequence.

[0071] Furthermore, the deinterleaving operation includes: strictly synchronizing the coefficient set and sequence length of the two-stage permutation polynomial between the receiver and transmitter. By combining the parameters of the row and column reshaping operator with the inverse polynomial mapping and inverse row and column reshaping operation, the deinterleaving is completed, and the original symbol sequence is restored.

[0072] Furthermore, the inverse transformation includes: the receiver performs a symmetrical inverse phase perturbation transformation according to the transformation structure adopted by the transmitter, the inverse matrix of the phase perturbation matrix is ​​its conjugate transpose matrix, and the inverse transformation of the received signal is completed by combining the deinterleaving operation of the interleaver and the inverse transformation of the unitary transformation, and the signal sequence adapted to the detector is output.

[0073] The beneficial effects of this invention are:

[0074] (1) Traditional random interleavers require both the transmitting and receiving ends to store the complete interleaving index sequence, and their storage complexity increases linearly with the sequence length. Although the existing mainstream QPP interleavers can generate interleaving sequences with a small number of parameters and do not require pre-storing the full-length index, their corresponding sequences have inherent structural correlations, which will exacerbate the column coherence of the equivalent channel matrix in a random multiplexing system, causing deterioration of the iterative convergence of the receiver's MAMP detector and a significant loss in bit error rate performance. The LCM and DPP low-storage interleaver proposed in this invention also only requires the transmitting and receiving ends to agree on a small number of fixed parameters to dynamically generate the full permutation interleaving sequence, maintaining constant-level storage complexity. At the same time, through targeted decorrelation design, the inherent structural correlations are completely eliminated, the equivalent channel coherence is greatly reduced, and the convergence performance of the MAMP detector and the system bit error rate performance are guaranteed.

[0075] (2) Existing random multiplexing systems are prone to problems such as high coherence of the equivalent channel matrix and insufficient diversity gain under complex time-varying channels, which leads to the deterioration of the performance of the receiver's MAMP detection algorithm. The high-reliability interleaving transform of IPPT and IMCT designed in this invention can effectively reduce the coherence of the channel matrix and improve the diversity gain. The transform maintains unitary invariance throughout the process and can be demodulated in coordination with the MAMP detector, significantly improving the transmission reliability and algorithm convergence stability under complex time-varying channels.

[0076] (3) Existing interleaving and transformation schemes in random multiplexing communication systems cannot simultaneously achieve low storage overhead and high reliable transmission performance, making them difficult to implement in resource-constrained communication terminals. In contrast, this invention deeply integrates low-storage, high-efficiency interleavers with high-reliability interleaving transformations, designing a complete system scheme for transceiver collaboration. This significantly reduces storage overhead while achieving a substantial improvement in transmission performance. Compared to mainstream modulation schemes such as OFDM, OTFS, and AFDM, it has a clear advantage in bit error rate performance and is more feasible in engineering. Attached Figure Description

[0077] Figure 1 This is a diagram of a MIMO multicarrier modulation system based on RM-MAMP.

[0078] Figure 2 This is a schematic diagram of the high-reliability modulation conversion at the transmitter of the HR-RM-MAMP system.

[0079] Figure 3 This is a structural diagram of the HR-CD-MAMP detector.

[0080] Figure 4 A comparison of the empirical spectral distributions of the original random interleaver, LCM interleaver, and DPP interleaver.

[0081] Figure 5 A comparison of the bit error rates of the HR-RM-MAMP system corresponding to the storage-efficient interleaver for the TDL-A channel under different conditions.

[0082] Figure 6 A comparison chart showing the equivalent total storage and computation overhead of different interleavers under different sequence lengths.

[0083] Figure 7 This is a comparison chart of the bit error rates of different high-reliability transformation schemes under small-scale TDL-A channels.

[0084] Figure 8 This is a comparison of the bit error rates of different interleavers in RM-MAMP and HR-RM-MAMP systems under the TDL-A channel.

[0085] Figure 9 A comparison of the bit error rates of RM-MAMP and HR-RM-MAMP systems under different channel settings.

[0086] Figure 10 This is a comparison of the bit error rates of detection algorithms for low-storage, high-reliability RM modulation and mainstream modulation schemes under TDL-A channels. Detailed Implementation

[0087] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0088] This invention addresses the design of a multi-carrier multiple-input multiple-output (MIMO) communication system based on random multiplexing (RM) modulation and a memory approximate message passing (MAMP) detector. First, the generalized linear model for transmission in this system is defined as follows:

[0089]

[0090] in, Represented as the time-domain observation vector at the receiving end, It is the time-domain impulse response matrix of the wireless channel, covering complex channel characteristics such as time-varying multipath, Doppler frequency shift, and antenna spatial correlation. This is the core interleaving transform matrix for performing RM modulation at the transmitter. Let be the information symbol vector after digital mapping from the source domain, where each symbol follows the prior property of being independent and identically distributed. The representative example is Gaussian additive white noise.

[0091] In the RM modulation architecture, the core interleaving transform matrix This can be specifically expressed as: ,in, Represented as a random permutation interleaving matrix, This is represented as a normalized Inverse Fast Fourier Transform (IFFT) matrix. At the receiver, this invention employs a Cross-Domain MAMP (CD-MAMP) detector, primarily comprising a Memory Linear Detector (MLD) module, a Non-Linear Detector (NLD) module, and corresponding interleaving transformation modules. This detector fully utilizes the decoupling characteristics after the RM cross-domain transformation and significantly reduces the detection complexity of the algorithm by leveraging the ultra-sparse structure of the channel. Furthermore, by introducing a long-memory matched filter structure, this detector achieves orthogonality throughout the process while maintaining low complexity, thus balancing convergence, stability, and applicability. Based on the above system model, this invention rewrites it as a generalized large-scale noisy linear system model with two constraints:

[0092]

[0093] The MLD module and NLD module are used to solve the following problems respectively. The problem model corresponding to the two constraints. The goal of the system model considered in this invention is to address the known... and Under the premise, according to Two constraints are addressed by designing the transformation matrix. And the corresponding signal recovery algorithm to obtain the target The minimum mean square error (MMSE) is estimated. The iterative process of the CD-MAMP detector used at the receiver can then be described as four steps: MLD, Inverse Cross-Domain Transform (ICDT), NLD, and Cross-Domain Transform (CDT), explained in detail below:

[0094]

[0095]

[0096]

[0097]

[0098] In the formula, the output vector By maximum likelihood estimator This estimator is generated primarily based on the channel matrix. and all previous estimates The subsequent step is ICDT, which estimates the output vector of the MLD module in the source domain. A cross-domain inverse transform is performed to map the signal to the time domain, and then the data is sent to the NLD module for signal estimation. Subsequently, a nonlinear symbol-by-symbol estimator... according to Generate the next symbol estimation. Finally, the symbols of the source domain. In the CDT step, the RM modulation matrix is ​​used. Mapped to the time domain Then it is input into the MLD module for iterative estimation in this way.

[0099] Based on the above-mentioned RM-MAMP system model, this invention designs an interleaving conversion modulation module that combines low storage overhead and high reliability, and designs a receiver cooperative detector that matches the transmitter. The specific implementation of this invention will be described in detail below through multiple embodiments.

[0100] This embodiment describes the implementation process of a complete transceiver collaborative system integrating a low-storage, high-efficiency interleaver and a high-reliability interleaver transformation algorithm. It achieves synergistic optimization of low storage overhead and high-reliability transmission, specifically divided into three core components: the transmitter, channel transmission, and the receiver. The steps are as follows:

[0101] S1. Synchronization of transmit and receive parameters

[0102] The transmitting and receiving ends complete strict synchronization of core parameters through system signaling, including: all generation parameters of LCM interleaver or DPP interleaver, structural configuration and phase parameters of IPPT or IMCT high-reliability transform, number of system subcarriers, modulation method, and iterative detection related parameters, to ensure strict duality between the transform and inverse transform at the transmitting and receiving ends.

[0103] S2, Transmitter signal modulation and transmission

[0104] (1) Source symbol mapping: The binary bit stream to be transmitted is mapped into a source domain information symbol vector through digital modulation methods such as Quadrature Phase Shift Keying (QPSK). .

[0105] (2) Low storage interleaving operation: The source domain symbols or transform domain symbols are interleaved and rearranged by the LCM interleaver or DPP interleaver corresponding to the synchronization parameters.

[0106] (3) High reliability interleaving transformation: Through IPPT or IMCT high reliability transformation, the phase perturbation and multi-layer coupling transformation of the transmitted signal are completed, the statistical characteristics of the equivalent channel are reconstructed, and the HR-RM modulated signal is generated.

[0107] (4) Signal transmission: After adding a cyclic prefix, the modulated time-domain signal is transmitted to the wireless channel through the radio frequency front end.

[0108] S3, Channel Transmission

[0109] The transmitted signal is transmitted through typical time-varying multipath channels such as TDL-A, TDL-C, and TDL-D as defined by the 3GPP TR 38.901 standard. At the same time, it is affected by Doppler frequency shift caused by high-speed movement, antenna spatial correlation, and Gaussian additive white noise before reaching the receiving end.

[0110] S4. Receiver-side collaborative demodulation and signal recovery

[0111] (1) Cyclic prefix removal: After synchronizing the received signal, the receiver removes the cyclic prefix to obtain the time-domain observation signal vector. .

[0112] (2) HR-CD-MAMP Iterative Detection: The iterative signal detection is performed by the HR-CD-MAMP detector matched with the transmitter transform, symbol estimation is completed, and the interleaving and deinterleaving operations of the high reliability transform and inverse transform in the iterative estimator are completed by the low storage interleaver corresponding to the synchronization parameter, so as to recover the source domain symbol vector.

[0113] (3) Symbol demapping: The estimated source domain symbol vector is restored to a binary bit stream through digital demapping to complete the entire signal transmission process.

[0114] Example 1: The interleaver adopts a specific implementation of a Logistic Chaotic Mapping-based (LCM) interleaver. The Logistic map exhibits excellent randomness, with the iterative sequence showing a near-uniform distribution within the parameter range. Its decorrelation effect is close to that of an ideal random sequence, and it can dynamically generate near-random sequences from a small number of parameters, making it suitable for low-storage interleaver designs. Furthermore, this map has low computational complexity, requiring only basic arithmetic operations and no complex function calculations. Therefore, this invention selects the Logistic map as the generation module of the LCM interleaver. Its core idea is to dynamically generate pseudo-random sequences through the Logistic map, and then obtain the interleaving index through sorting to achieve symbol rearrangement.

[0115] This embodiment demonstrates the complete implementation flow of the LCM interleaver. This interleaver dynamically generates pseudo-random sequences through a Logistic mapping, and then obtains the interleaving index through sorting to achieve symbol rearrangement. It requires only a small number of parameters to complete the interleaving operation, reducing storage complexity from linear to that of traditional random interleavers. Reduced to constant level The specific implementation steps are as follows:

[0116] S1, Parameter Initialization

[0117] Select initial value and chaos control parameters This ensures the mapping is in a chaotic state, guaranteeing the iterative sequence possesses strong ergodicity and a uniformly distributed class. Simultaneously, the length of the interleaved sequence is set to... This is consistent with the number of system subcarriers. Subsequently, the weighting coefficients for the interleaving displacement metric and the discrete entropy measurement are set. and ,satisfy This embodiment uses equal weight settings. This allows for a balance between the global dispersion of the permutation sequence and the uniformity of the chaotic sample distribution.

[0118] S2, Chaotic Sequence Generation

[0119] Generate a length of [length] based on the Logistic mapping iterative formula. chaotic sequence Its iterative formula is expressed as:

[0120]

[0121] In the above iterative process, each sample value depends only on the calculation result of the previous sample, thus completing the generation of the full-length sequence in sequence.

[0122] S3, Generation of Interleaved Index Sequences

[0123] The chaotic sequence generated in step S2 Sort in ascending order, record the original index of each element after sorting, forming a sequence of length [length missing]. Interleaved index sequences ,in, Indicates the sorted order of the first... The original positions corresponding to each element are given by an index sequence that is a bijective permutation sequence, ensuring no sign loss or duplication.

[0124] S4. Joint parameter optimization verification

[0125] Based on the joint parameter selection criterion of interleaved displacement metric and discrete entropy measurement, the performance of the generated interleaved index sequence is verified to ensure that the sequence satisfies the properties of solution correlation and uniform distribution. The specific calculation process is as follows:

[0126] (1) Calculate the interlacing displacement measure Quantify the symbol dispersion of interleaved sequences: ,in, The larger the value, the more thorough the symbol rearrangement and the better the discorrelation effect. This indicates that there is absolutely no interweaving.

[0127] (2) Calculate discrete entropy measurement Quantifying the uniform distribution characteristics of chaotic sequences: The range of values ​​is divided into A series of equal-width intervals, Then, count the number of chaotic sequence elements within each interval. Calculate empirical probability At this point, the normalized discrete entropy is defined as: ,in, This indicates that the sequence is completely uniformly distributed (ideal random). This indicates that the sequence has no randomness.

[0128] (3) Calculate the parameter evaluation score: measure the interlacing displacement. and discrete entropy measurement By performing normalized weighted combination, a formula for parameter evaluation score is constructed: If the evaluation score meets the system's preset threshold, the current parameter and interleaving index sequence are confirmed to be usable; otherwise, a new initial value is selected. With chaotic control parameters Repeat steps S2 to S4 until a satisfactory interleaved index sequence is generated.

[0129] S5, Symbol Interleaving Operation

[0130] Based on the interleaving index sequence generated in step S3, the input symbol sequence Rearrange the symbols to obtain the interleaved sequence: .

[0131] S6, Deinterlacing operation

[0132] The receiver and transmitter must be strictly synchronized with the initial values. Chaos control parameters With sequence length Following steps S2 to S3, a completely consistent interleaved index sequence is regenerated, and the deinterleaving operation is completed through inverse mapping to restore the original symbol sequence.

[0133] The technical principle of this embodiment is: the LCM interleaver does not require both the sender and receiver to store a length of... The complete interleaved index sequence only requires synchronizing two core parameters to dynamically generate a fully permuted interleaved sequence that meets the requirements, compressing the storage complexity to constant level. Simultaneously, through a joint parameter optimization criterion, it solves the problems of traditional Logistic mapping parameter selection relying on experience and the instability of the random characteristics of the interleaved sequence, ensuring that the generated interleaved sequence possesses excellent solution correlation and uniform distribution characteristics, meeting the requirements of the RM-MAMP system for the convergence characteristics and right unitary invariance of the equivalent channel matrix spectrum. However, its engineering implementation still has significant limitations. Firstly, the computational complexity is high. The generated length is... The interleaved permutation sequence needs to be iteratively generated into a chaotic sequence through logical mapping, which requires execution. Each iteration involves parameter multiplication and subtraction. The computational complexity of the subsequent global sorting is O(n log n). As the sequence length increases, the computational load rises sharply, significantly increasing the computational burden and hindering resource-constrained devices. Secondly, its parallel adaptability is weak. Chaotic sequence generation exhibits a serial dependency; the first... Each sample depends on the calculation results of the preceding samples, making it impossible to generate multiple sets of samples in parallel. Global sorting requires all data to be generated and cannot be effectively split, limiting hardware parallelism and throughput. Furthermore, this interleaver is highly sensitive to finite precision; when implemented with low bit width fixed-point, chaotic trajectories are prone to random degradation, which weakens hardware efficiency and introduces engineering risks.

[0134] Example 2: Detailed Implementation of a Dual-stage High-order Permutation Polynomial (DPP) Interleaver

[0135] This embodiment represents a preferred implementation of a low-storage interleaver, specifically optimizing it to address the engineering shortcomings of the aforementioned LCM interleaver. Specifically, to solve the problems of high computational complexity, large latency, weak parallelism, and high accuracy risk associated with the LCM interleaver, this invention proposes a DPP interleaver structure. This embodiment presents the complete implementation flow of the DPP interleaver. This interleaver achieves sign rearrangement through two cascaded high-order permutation polynomials and matrix reshaping operations, eliminating sorting operations, completing the mapping in a single cycle, supporting fully parallel hardware implementation, requiring only the storage of two sets of polynomial coefficients, and achieving constant-level storage complexity. This approach simultaneously addresses the issues of strong structural correlation and insufficient pseudo-randomness in traditional Quadratic Polynomial Permutation (QPP) interleavers. The specific implementation steps are as follows:

[0136] S1, Parameter Initialization

[0137] Set the interleaving sequence length to This is consistent with the number of system subcarriers. Subsequently, the order of the permutation polynomial is set. , Then adjust the sequence length. Prime factorization is performed to obtain the set of its prime power factors, providing a number theory basis for the subsequent design of polynomial coefficients.

[0138] S2, Higher-order permutation polynomial full permutation constraint configuration

[0139] In this embodiment, the basis permutation function Defined in the ring of integers On The permutation polynomial of order 1 is expressed as follows: Based on the Chinese Remainder Theorem (CRT), to guarantee... exist The mapping on is a bijective mapping with full permutations, for polynomial coefficients Set the following number theory constraints:

[0140] (1) Invertibility of linear terms: linear coefficients and Coprime, that is: This ensures the uniqueness of the mapping and avoids many-to-one mappings.

[0141] (2) Divisibility of higher-order terms: for all odd prime factors Must meet The polynomial modulo each odd prime number The subdegenerates into a first-order polynomial, ensuring that the mapping constitutes a complete permutation in the corresponding modulus domain.

[0142] (3) Parity consistency: when When the coefficients of even-degree terms and odd-degree terms of a polynomial are equal, they must simultaneously satisfy the following: , To avoid polynomials in or Mapping conflicts occur, ensuring the permutation property.

[0143] S3, Two-stage Cascaded Interleaving Mapping Implementation

[0144] By employing a two-stage polynomial cascade structure and inserting row and column reshaping operators between the two stages, the overall mapping process corresponds to the following expression:

[0145]

[0146] in, This represents the composition operation of functions in the matrix space, that is, for any two mappings , ,have: . No. Permutation polynomial Defined as: . No. Rank-level column reshaping operator , refers to input sequence First fill in the rows The matrix is ​​then read and reconstructed column by column. The specific mapping steps are as follows:

[0147] (1) First-stage permutation: Input the original symbol sequence, and pass it through a first-stage permutation polynomial. Complete the first symbol rearrangement.

[0148] (2) First stage row and column reshaping: The sequence output from the first stage permutation is reshaped by the row and column reshaping operator. Complete matrix reshaping and sequence reconstruction to eliminate structural dependencies caused by single-level polynomials.

[0149] (3) Second-stage permutation: The sequence after the rows and columns are reshaped is permuted by a second-stage permutation polynomial. Complete the second symbol rearrangement.

[0150] (4) Second-stage row and column reshaping: The sequence output from the second-stage permutation is reshaped using the row and column reshaping operator. Complete the quadratic matrix reshaping and sequence reconstruction, and output the final interleaved symbol sequence.

[0151] S4, Deinterlacing operation

[0152] The receiver and transmitter are strictly synchronized. This involves the set of coefficients and the sequence length of the two-stage permutation polynomial. By combining the parameters of the row and column reshaping operator with the inverse polynomial mapping and inverse row and column reshaping operation, the deinterleaving is completed, and the original symbol sequence is restored.

[0153] The technical principle of this embodiment is as follows: The DPP interleaver only needs to store two sets of polynomial coefficients. Through polynomial calculation and reshaping operations, it can quickly reconstruct a permutation sequence with randomness equivalent to that of traditional pseudo-random interleaving. There is no sorting operation, and the computational complexity is much lower than that of the LCM interleaver. It also supports fully parallel hardware implementation. At the same time, the DPP interleaver completely eliminates the inherent structural correlation of the traditional QPP interleaver through two-stage concatenation and row and column reshaping operations, ensuring that the interleaved sequence meets the universal requirements of the RM-MAMP system and is suitable for high-mobility, highly correlated channel environments.

[0154] Example 3: Interleaved Phase Perturbation Transform (IPPT). This invention addresses the performance degradation problem of RM-MAMP systems in complex wireless channels, especially in severely time-varying multipath channels in small-scale system configurations. In highly mobile and other time-varying communication scenarios, severe channel state jitter leads to a decrease in the accuracy of receiver signal estimation, causing significant bit errors. The limited diversity resources of small-scale systems further amplify the negative impact of rapid time variations. Therefore, this invention, based on efficient storage design, urgently needs to enhance the robustness of the RM-MAMP system to cope with the performance degradation challenges under complex channels. To this end, this invention proposes a high-reliability transformation framework. By reconstructing the modulation / demodulation and iterative detection process of the RM-MAMP system, it comprehensively strengthens the unitary invariant properties of the transformation matrix, improves the randomness and incoherence of the equivalent channel matrix, and enhances the reliability of signal recovery in harsh scenarios.

[0155] This embodiment describes the specific implementation process of IPPT transformation. This transformation, by introducing controllable random phase rotation into the modulation and detection transformation link, reshapes the statistical characteristics of the equivalent channel matrix and weakens the column coherence of the equivalent channel matrix. This solves the performance degradation problem of RM-MAMP systems under complex time-varying channels and small-scale system configurations. This embodiment details three configurable IPPT transformation structures, with specific implementation methods as follows:

[0156] S1, Phase perturbation matrix initialization

[0157] First, define the diagonalized phase perturbation matrix. Its specific expression is:

[0158]

[0159] in, This represents the phase perturbation matrix acting in the transform domain. This represents the phase perturbation matrix acting on the source domain. It follows an independent uniform distribution, and satisfies the following when the quantization accuracy of the phase is sufficient. This effectively suppresses the statistical mean of off-diagonal elements, achieving decorrelation between columns. Strict synchronization of phase sequence parameters between the transmitting and receiving ends ensures that the receiving end can perform a symmetrical inverse transform.

[0160] S2. Implementation of Interleaved Phase Perturbation Transform-DualSide (IPPT-DUAL)

[0161] By introducing phase randomness both before and after the modulation transformation, a composite modulation transformation matrix is ​​constructed: ,in, This is a diagonal phase perturbation matrix, whose elements all conform to... Uniformly distributed. This is the permutation matrix corresponding to the low-storage interleaver designed in Example 1 or Example 2. To obtain the normalized unitary transform matrix, a discrete Fourier transform matrix, a Walsh-Hadamard transform matrix, or similar matrix can be selected. This scheme, through joint randomization of the source and transform domains, completely eliminates the residual deterministic structure of the equivalent channel matrix, achieving theoretically optimal diversity gain. It is suitable for high-speed mobile scenarios with stringent error rate performance requirements, such as vehicle-mounted communication and low-altitude aircraft data links.

[0162] S3, Interleaved Phase Perturbation Transform-Inner Side (IPPT-IN) Implementation

[0163] The transformation matrix is ​​constructed by applying a phase perturbation to the input symbol vector only before modulation: ,in, For direct action on the source domain information symbol vector The corresponding diagonal phase perturbation matrix. This scheme introduces only one phase parameter, and the number of complex multiplication operations is halved compared to the IPPT-DUAL scheme, making it suitable for application scenarios where the source domain symbol phase is concentrated and has structured characteristics.

[0164] S4. Implementation of Interleaved Phase Perturbation Transform-Outer Side (IPPT-OUT)

[0165] The phase perturbation is placed after the modulation transform, and the transform matrix is ​​constructed as follows: ,in, This method operates on the transform domain after modulation transformation, suppressing residual inter-symbol interference. By introducing only one phase parameter and requiring only a single complex multiplication overhead, this scheme effectively reduces the coherence between signal trains, making the statistical characteristics of the equivalent channel matrix closer to the right-unitary invariance required by the MAMP algorithm. It achieves an optimal balance between performance and complexity, making it the preferred high-reliability modulation scheme of this invention.

[0166] S5, Inverse Transformation Implementation at the Receiver End

[0167] The receiver performs a symmetrical inverse phase perturbation transformation based on the IPPT transformation structure used by the transmitter. The inverse of the phase perturbation matrix is ​​its conjugate transpose. Combined with the deinterleaving operation of the interleaver and the inverse transformation of the unitary transform, the receiver completes the inverse transformation of the received signal and outputs a signal sequence that is compatible with the detector.

[0168] Example 4: Detailed Implementation of Interleaved Multi-Layer Coupled Transform (IMCT) and Highly Reliable CD-MAMP (HR-CD-MAMP) Detector

[0169] This embodiment presents the complete implementation flow of the IMCT transform and its matching HR-CD-MAMP detector. The IMCT transform uses a multi-layer transform cascade coupling interleaving strategy to diffuse the energy of each transmitted symbol into multiple approximately independent channel observations, further improving the transmission reliability of the system under extreme ill-conditioned channel conditions. Simultaneously, an HR-CD-MAMP detector, strictly dual to the transmitter transform, is designed to ensure the iterative convergence stability of the algorithm under complex time-varying channels. The specific implementation steps are as follows:

[0170] S1, IMCT Transform Structure Initialization

[0171] Promote the IPPT solution to The cascaded structure of layer-coupled transforms, where each layer integrates basic interleaving, alternating cross-domain transforms, and optional external phase perturbations, has the IMCT transform matrix expressed as follows:

[0172]

[0173] in, To change the number of layers, for typical complex wireless channel scenarios, Setting it to 2 will satisfy the system reliability requirements. Alternating coupling between the transformation matrix and its corresponding transpose matrix, if the number of layers is odd. The transformation used is Then even-numbered layers Let its corresponding transpose transformation matrix be: This ensures the unitary invariance of the entire transformation. The diagonal phase perturbation matrix is ​​optional. If no additional phase perturbation is required, it can be... The value is the identity matrix. . This is the permutation matrix corresponding to the low-storage interleaver designed in Example 1 or Example 2.

[0174] when At this time, IMCT degenerates into an IPPT-OUT structure. Therefore, this invention incorporates IPPT-OUT and IMCT into a unified Highly Reliable (HR) transformation framework, defining... The HR transform matrix corresponds to Highly Reliable Random Multiplexing (HR-RM) modulation, and its expression is:

[0175]

[0176] S2, Transmitter HR-RM modulation implementation

[0177] Based on the HR transform matrix designed in step S1, the high-reliability multicarrier modulation transformation process at the transmitter is as follows:

[0178]

[0179] Source domain information symbol vector By performing high-reliability interleaving transformation and modulation using the HR transformation matrix, the time-domain signal vector to be transmitted can be generated. .

[0180] S3, HR-CD-MAMP detector iterative initialization

[0181] Initialize the number of iterations Maximum number of iterations Initialize the nonlinear estimator to 0, and the variance of the nonlinear estimator... Strict synchronization of HR transformation matrix between transmitting and receiving ends All parameters are configured to ensure that the receiver can perform a symmetrical inverse transform.

[0182] S4, HR-CD-MAMP detector iterative execution

[0183] A single iteration of the detector consists of four core modules, which perform the following operations in sequence:

[0184] (1) Memory Linear Detection (MLD) Module

[0185] Leveraging the high reliability and sparsity of the channel's transform domain, low-complexity signal estimation is achieved while ensuring iterative orthogonality. The iterative formula is as follows:

[0186]

[0187] in, This is the set of estimates from all previous iterations; For normalization parameters, The orthogonalization parameter ensures that the input and output estimation errors are orthogonal during the iteration process. These are optimized convergence acceleration parameters, used to improve the iterative convergence speed and stability. Matrix Defined as ,in, , and Represented as The minimum and maximum eigenvalues ​​are obtained, and this matrix is ​​designed to adapt to the spectral characteristics of the channel.

[0188] (2) High Reliability Cross-Domain Inverse Transform (HR-ICDT) Module

[0189] High-reliability transform domain signal output by MLD Mapping back to the source domain provides a suitable signal form for subsequent nonlinear estimation; the transformation formula is as follows:

[0190]

[0191] The inverse matrix of the unitary transformation is equivalent to the Hermitian transpose matrix, i.e.: This transformation fully preserves the variance and independent identically distributed Gaussianity of the estimation error, ensuring the accuracy of subsequent detection.

[0192] (3) Nonlinear detection (NLD) module

[0193] The accuracy of signal estimation is optimized by utilizing the prior distribution characteristics of the symbols. The iterative formula is as follows:

[0194]

[0195] in, These are the normalization parameter and orthogonality parameter of the source domain, respectively, and their effects are related to the MLD stage. Consistency is used to ensure the orthogonality of the source domain iteration process. Indicates based on estimated signal The posterior mean estimate is obtained by solving the conditional expectation of the sign.

[0196] (4) High Reliability Cross-Domain Transform (HR-CDT) Module

[0197] The source domain signal output by the NLD module Remap back to the high-reliability transform domain to generate the input signal estimate required by the MLD module in the next iteration cycle. The transform formula is as follows:

[0198]

[0199] This transformation is strictly dual to the modulation at the transmitting end, ensuring the consistency of error propagation, and forming a closed-loop transformation mechanism with HR-ICDT.

[0200] S5. Iterative Convergence Judgment

[0201] Update iteration count Repeat step S4 iteratively until the maximum number of iterations is reached. If the bit error rate meets the system's preset threshold, the iteration stops and the final signal estimation result is output.

[0202] The technical principle of this embodiment is as follows: The IMCT transform, through multi-layered cascaded unitary transforms and interleaving operations, distributes the energy of each transmitted symbol to more approximately independent channel observations, fully utilizing the channel diversity characteristics, while effectively reducing the column correlation of the equivalent channel matrix and alleviating the iterative convergence instability problem under ill-conditioned channels. This transform strictly preserves unitary invariance throughout, ensuring that the theoretical convergence basis of the MAMP detection algorithm remains unaffected. Furthermore, the accompanying HR-CD-MAMP detector is strictly coupled and dual with the transmitter transform, fully preserving the Gaussianity and orthogonality of the estimation error during iteration, achieving highly reliable signal recovery of the RM-MAMP system under complex time-varying channels.

[0203] Based on the above solution, the embodiment also provides a simulation scenario:

[0204] The carrier frequency in this simulation was set to 4 GHz, with a subcarrier spacing of 2 to verify the algorithm's scenario scalability. The number of subcarriers covered a range of 32, 64, 128, 256, 512, and 1024, balancing performance verification in both small-scale systems and high-bandwidth scenarios. QPSK was used as the digital modulation scheme as a benchmark. A CD-MAMP detector was employed at the receiver for iterative signal estimation. Both the transmitter and receiver used root-raised cosine pulse-shaping filters with a roll-off factor of 0.4. Multiple baseline simulations were set up, including a benchmark system with a traditional random interleaver and the original RM transform, and a comparison system with a QPP interleaver and the original RM transform. OFDM, OTFS, and AFDM, three mainstream waveforms, and their corresponding detection schemes were also introduced as performance references.

[0205] All simulation channel models adopt the Tap Delay Line (TDL) channel model defined by the 3GPP TR 38.901 standard, covering three typical channel scenarios: TDL-A, TDL-C, and TDL-D. The TDL-A channel uses 23 multipath paths to simulate typical urban propagation environments, while the TDL-C and TDL-D channels correspond to complex propagation scenarios with different delay spreads, comprehensively verifying the algorithm's universality under different multipath environments. Moving speeds of 100km / h, 300km / h, and 500km / h are covered, and the Jakes model is used to accurately simulate the Doppler shift effect caused by high-speed movement, verifying the algorithm's robustness in high-dynamic scenarios. Regarding the spatial correlation between MIMO antennas, the industry-standard exponential spatial correlation model is used, setting the correlation level between the transmitting and receiving antennas to be consistent, covering strongly correlated channel scenarios with different correlation coefficients, verifying the algorithm's performance stability under non-ideal antenna array configurations.

[0206] This simulation uses bit error rate as the core performance evaluation index, focusing on comparing the bit error rate curve trends of each scheme under different signal-to-noise ratios. At the same time, it verifies the matching degree between the simulation performance and the State Evolution (SE) theory during the MAMP detector iteration process, and completes the algorithm convergence analysis.

[0207] like Figure 4The figure shows a comparison of the empirical spectral distributions of the original random interleaver (ORI), LCM interleaver, and DPP interleaver. Curve explanations: ① The black dashed line represents the Marchenko-Pastur (MP) distribution theoretical curve, which is the ideal spectral distribution required for the general class of RM systems; ② The red solid line represents the empirical spectral distribution curve of the original random interleaver (ORI); ③ The green solid line represents the empirical spectral distribution curve of the LCM interleaver; ④ The yellow solid line represents the empirical spectral distribution curve of the DPP interleaver. This figure verifies that the empirical spectral distributions of the equivalent channel matrices corresponding to the LCM and DPP interleavers are highly consistent with the MP theoretical distribution, and the spectral distribution deviations among the three types of interleavers are all less than 10⁻⁻⁶. 8 This demonstrates that the low-storage interleaver of the present invention can meet the spectral convergence requirements of the universal class of RM systems, thus providing a guarantee for the Bayesian optimality of the MAMP detector.

[0208] like Figure 5 The figure shows a comparison of the bit error rate (BER) of the TDL-A channel under different conditions for the storage-efficient interleaver corresponding to the HR-RM-MAMP system. The simulation data on the left is MIMO 2×2, 100km / h, 512 subcarriers, while the simulation data on the right is MIMO 4×4, 500km / h, 1024 subcarriers. The curves are explained as follows: ① The orange asterisk curve represents the BER curve of the original random interleaver (ORI) corresponding to the HR-RM-MAMP system; ② The yellow circle curve represents the BER curve of the DPP interleaver of this invention corresponding to the HR-RM-MAMP system; ③ The green triangle curve represents the BER curve of the LCM interleaver of this invention corresponding to the HR-RM-MAMP system; ④ The blue diamond curve represents the BER curve of the traditional QPP interleaver corresponding to the HR-RM-MAMP system. This figure verifies that the LCM and DPP low-storage interleavers of this invention can achieve almost the same BER performance as the original random interleaver, while the traditional QPP interleaver exhibits significant BER performance loss.

[0209] like Figure 6 The graph shows a comparison of the total equivalent storage and computation overhead of different interleavers under different sequence lengths. Bar explanations: ① Green bars represent the total equivalent overhead of the original random interleaver; ② Blue bars represent the total equivalent overhead of the LCM interleaver of this invention; ③ Purple bars represent the total equivalent overhead of the DPP interleaver of this invention. This graph quantifies the hardware implementation advantages of the low-memory interleaver of this invention. Under different sequence lengths, the equivalent overhead of the original random interleaver is significantly higher than that of the LCM and DPP interleavers, and this gap widens with increasing sequence length. Furthermore, the interleaver of this invention has no random memory access operations, thus solving the hardware bus overhead bottleneck of traditional interleavers.

[0210] like Figure 7The figure shows a comparison of the bit error rate (BER) of different high-reliability transformation schemes under a small-scale TDL-A channel. Curve explanations: ① The purple square curve represents the BER curve of the original RM-MAMP system; ② The blue diamond curve represents the BER curve of the IPPT-IN scheme of this invention; ③ The green triangle curve represents the BER curve of the IPPT-OUT scheme of this invention; ④ The yellow circle curve represents the BER curve of the IPPT-DUAL scheme of this invention; ⑤ The orange asterisk curve represents the BER curve of the IMCT dual-layer coupling scheme of this invention. This figure verifies the performance gain of the high-reliability transformation scheme of this invention. In a small-scale system with 32 subcarriers and a mobile scenario of 100 km / h, the IPPT-OUT, IPPT-DUAL, and IMCT schemes achieve a BER performance gain of more than 5 dB compared to the original RM system, effectively eliminating the bit error rate leveling problem of the original system, while the IPPT-IN scheme shows no significant performance improvement.

[0211] like Figure 8 The graph shows a comparison of the bit error rate (BER) of different interleavers in RM-MAMP and HR-RM-MAMP systems under a TDL-A channel. Curve explanations: ① The solid green circle represents the BER curve of the traditional QPP interleaver paired with the original RM-MAMP system; ② The solid purple diamond represents the BER curve of the traditional QPP interleaver paired with HR-RM-MAMP. ( and ) BER curves; ③ The green circle dashed line and dotted line correspond to the BER curves of the DPP and LCM interleavers of this invention paired with the original RM-MAMP system, respectively; ④ In the magnified area, the blue asterisk solid line is the BER curve of the IPPT system of the traditional QPP interleaver paired with HR-RM-MAMP; ⑤ In the magnified area, the purple diamond dashed line is the BER curve of the DPP interleaver of this invention paired with HR-RM-MAMP. The BER curve of the system; ⑥ In the magnified area, the blue asterisked dashed line represents the BER curve of the IPPT system using the LCM interleaver of this invention in conjunction with HR-RM-MAMP. This figure verifies the performance advantages of the LCM and DPP low-memory interleaver of this invention in the original RM system and the high-reliability HR-RM system, as well as the synergistic gain effect of combining it with the high-reliability transform. In the original RM-MAMP benchmark system, the BER performance of the DPP and LCM interleaver of this invention is significantly better than that of the traditional QPP interleaver, and the bit error rate performance of the two is almost identical; when introducing In HR-RM systems with phase-configured high-reliability transitions, QPP interleavers still suffer from significant BER performance degradation. However, the DPP and LCM interleavers of this invention can fully leverage the performance gains of the high-reliability transition, effectively compensating for the performance loss of the original system. In HR-RM-MAMP systems incorporating IPPT, although the phase perturbation mechanism narrows the performance gap, QPP interleavers still exhibit quantifiable BER performance loss. This figure fully demonstrates the necessity of combining low-memory interleavers with high-reliability interleaver transitions. Their synergy enables MAMP detector-based communication systems to achieve robust and efficient transmission performance under complex and harsh channel conditions.

[0212] like Figure 9 The figure shows a comparison of the bit error rate (BER) of the RM-MAMP and HR-RM-MAMP systems under different channel settings. Curve explanations: ① The blue circle represents the theoretical performance boundary of the MAMP state evolution; ② The green solid line represents the BER simulation curve of the HR-RM-MAMP system (DPP interleaver + IPPT-OUT transform) of this invention; ③ The purple dashed line represents the BER simulation curve of the original RM-MAMP system. This figure verifies the robustness of the high-reliability transform of this invention under different channel settings, covering three 3GPP standardized TDL channel models: TDL-A, TDL-C, and TDL-D channels, and also includes two different mobility scenarios: 100km / h and 500km / h. Based on this, the experiment set up four different system scales to further evaluate the effectiveness of the proposed algorithm, with the number of subcarriers being 32, 64, 128, and 256, respectively. In different scenarios, the BER simulation curves of the present invention are in perfect agreement with the SE theoretical boundary, while the BER curves of the original RM system are seriously mismatched with the theoretical boundary and the performance is significantly degraded. This proves that the present invention can guarantee the iterative convergence stability of the MAMP detector under complex time-varying channels.

[0213] like Figure 10The graph shows a comparison of the bit error rate (BER) of low-storage, high-reliability RM modulation and corresponding detection algorithms for mainstream modulation schemes under TDL-A channels. Curve explanations: ① The purple solid square line represents the BER curve of the OFDM system using the MAMP detector; ② The yellow solid asterisk line represents the BER curve of the AFDM system using the MAMP detector; ③ The green inverted triangle line represents the BER curve of the AFDM system using the Orthogonal Approximate Message Passing (OAMP) detector; ④ The blue diamond solid line represents the BER curve of the OTFS system using the OAMP detector; ⑤ The orange solid asterisk line represents the BER curve of the RM-MAMP baseline system; ⑥ Within the magnified area, the red polygonal solid line represents the BER curve of the HR-RM-MAMP system corresponding to the Original Random Interleaver (ORI) interleaver, the green triangular solid line represents the BER curve of the LCM interleaver, and the yellow circle solid line represents the BER curve of the DPP interleaver; these three curves almost completely overlap. This figure verifies the comprehensive performance advantages of the complete solution of the present invention. In a mobile scenario of 4×4 MIMO and 100km / h TDL-A channel, the solution of the present invention achieves a performance gain of 4.5dB compared with the original RM system and a performance gain of more than 8dB compared with other mainstream modulation and detection schemes, while having the advantages of low storage and high reliability.

[0214] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the disclosure herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of this application are indicated by the claims.

[0215] It should be understood that the foregoing general description and the following detailed description are exemplary and explanatory only, and are not intended to limit this application. This application is not limited to the precise structures described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of this application is limited only by the appended claims.

Claims

1. A low-storage, high-reliability transceiver cooperative interleaving transformation method for random multiplexing communication systems, characterized in that, include: First, the interleaving transformation parameters at both the transmitting and receiving ends are synchronized; The transmitting end maps the bit stream to be transmitted into source domain information symbol vectors, uses a low-storage interleaver to interleave and rearrange the symbol vectors, performs a high-reliability transformation based on phase perturbation on the interleaved and rearranged transmitted signal, generates a high-reliability random multiplexed modulated signal, adds a cyclic prefix and sends it to the receiving end. After receiving the signal, the receiver removes the cyclic prefix to obtain the time-domain observation signal vector. Iterative signal detection is performed by an HR-CD-MAMP detector matched with the transmitter's transform to complete symbol estimation. The high-reliability transform and inverse transform in the iterative estimator are interleaved and deinterleaved by a low-storage interleaver corresponding to the synchronization parameter to recover the source domain symbol vector. The obtained source domain symbol vector is then recovered into a binary bit stream through digital demapping.

2. The low-storage, high-reliability transceiver cooperative interleaving transformation method for random multiplexing communication systems according to claim 1, characterized in that, The interleaving rearrangement using a low-storage interleaver is an interleaving rearrangement using a Logistic chaotic mapping interleaver, and the interleaving process includes: Select initial value and chaos control parameters To ensure the mapping is in a chaotic state, the interleaving sequence length is set to... The number of subcarriers should be consistent with the number of subcarriers in the system. Generate a length of [length] based on the Logistic mapping iterative formula. chaotic sequence Its iterative formula is expressed as: The generated chaotic sequence Sort in ascending order, record the original index of each element after sorting, forming a sequence of length [length missing]. Interleaved index sequences ,in, Indicates the sorted order of the first... The original positions corresponding to each element; Based on the joint parameter selection criterion of interleaved displacement metric and discrete entropy measurement, the performance of the generated interleaved index sequence is verified to ensure that the sequence satisfies the properties of solution correlation and uniform distribution. Based on the generated interleaved index sequence, the input symbol sequence is... Rearrange the symbols to obtain the interleaved sequence: .

3. The low-storage, high-reliability transceiver cooperative interleaving transformation method for random multiplexing communication systems according to claim 2, characterized in that, The performance verification of the generated interleaved index sequence includes: Set the weighting coefficients for interleaved displacement measurement and discrete entropy measurement. and ,satisfy , Calculate the interlacing displacement metric Quantify the symbol dispersion of interleaved sequences: , Calculate discrete entropy measurement Quantifying the uniform distribution characteristics of chaotic sequences: The range of values ​​is divided into A series of equal-width intervals, Then count the number of chaotic sequence elements in each interval. Calculate empirical probability The normalized discrete entropy is defined as: , Calculate the parameter evaluation score: measure the interlaced displacement. and discrete entropy measurement By performing normalized weighted combination, a formula for parameter evaluation score is constructed: If the evaluation score meets the system's preset threshold, then the current parameter and the interleaving index sequence are confirmed to be usable; otherwise, a new initial value is selected. With chaotic control parameters Repeat the interleaving process until a satisfactory interleaving index sequence is generated.

4. The low-storage, high-reliability transceiver cooperative interleaving transformation method for random multiplexing communication systems according to claim 1, characterized in that, The interleaving rearrangement using a low-memory interleaver is performed using a two-stage high-order permutation polynomial interleaver, and the interleaving process includes: Set the interleaving sequence length To maintain consistency with the number of system subcarriers, set the order of the permutation polynomial. , Then adjust the sequence length Perform prime factorization to obtain the set of its prime power factors; basis permutation function Defined in the ring of integers On The permutation polynomial of order 1 is expressed as follows: Based on the Chinese Remainder Theorem, the polynomial coefficients are... Set the following number theory constraints: Invertibility of linear terms: linear coefficients and Coprime, Divisibility of higher-order terms: for all odd prime factors Must meet The polynomial modulo each odd prime number The subdegenerates into a first-order polynomial, ensuring that the mapping constitutes a complete permutation in the corresponding modulus. Parity: When When the coefficients of even-degree terms and odd-degree terms of a polynomial are equal, they must simultaneously satisfy the following: , ; A two-stage polynomial cascade structure is adopted, and row and column reshaping operators are inserted between the two stages. The overall mapping process corresponds to the following expression: in, This represents the composition operation of functions in the matrix space, that is, for any two mappings , ,have: ;No. Permutation polynomial Defined as: , No. Rank-level column reshaping operator , refers to input sequence First fill in the rows The matrix is ​​then read and reconstructed column by column. The specific mapping steps are as follows: First-stage permutation: Input the original symbol sequence, and pass it through a first-stage permutation polynomial. Complete the first symbol rearrangement; First-stage row and column reshaping: The sequence output from the first-stage permutation is then reshaped using the row and column reshaping operator. Complete matrix reshaping and sequence reconstruction to eliminate structural dependencies caused by single-level polynomials; Second-stage permutation: The reshaped sequence of rows and columns is then permuted using a second-stage permutation polynomial. Complete the second symbol rearrangement; Second-stage row and column reshaping: The sequence output from the second-stage permutation is then reshaped using row and column reshaping operators. Complete the quadratic matrix reshaping and sequence reconstruction, and output the final interleaved symbol sequence.

5. The low-storage, high-reliability transceiver cooperative interleaving transformation method for random multiplexing communication systems according to claim 1, characterized in that, The high-reliability transformation based on phase perturbation of the interleaved rearranged transmitted signal includes interleaved phase perturbation transformation, specifically: First, define the diagonalized phase perturbation matrix. Its specific expression is: in, This represents the phase perturbation matrix acting in the transform domain. This represents the phase perturbation matrix acting on the source domain. It follows an independent uniform distribution, and satisfies the following when the quantization accuracy of the phase is sufficient. To achieve decorrelation between columns; For different application scenarios, implement double-sided interleaved phase perturbation transformation, inner-sided interleaved phase perturbation transformation, or outer-sided interleaved phase perturbation transformation; The bi-sided interleaved phase perturbation transform introduces phase randomness both before and after the modulation transform, constructing a composite modulation transform matrix: ,in, This is a diagonal phase perturbation matrix, whose elements all conform to... Uniform distribution; This is the permutation matrix corresponding to the low-storage interleaver. This is the normalized unitary transformation matrix; The inner interleaved phase perturbation transform applies a phase perturbation to the input symbol vector only before modulation, constructing the transform matrix: ,in, For direct action on the source domain information symbol vector The corresponding diagonal phase perturbation matrix; The outer interleaved phase perturbation transform places the phase perturbation after the modulation transform, constructing the transform matrix: ,in, It operates on the transform domain after modulation transformation to suppress residual inter-symbol interference.

6. The low-storage, high-reliability transceiver cooperative interleaving transformation method for random multiplexing communication systems according to claim 5, characterized in that, The high-reliability transformation also includes a multi-layer coupled transformation, specifically extending the phase perturbation to... Cascaded structures of layer-coupled transformations; The expression for the transformation matrix is: in, To change the number of layers, Alternating coupling between the transformation matrix and its corresponding transpose matrix, if the number of layers is odd. The transformation used is Then even-numbered layers Let its corresponding transpose transformation matrix be: This ensures the unitary invariance of the transformation as a whole; For the diagonal phase perturbation matrix, if there is no additional phase perturbation requirement, The value is the identity matrix. ; This is the permutation matrix corresponding to the low-storage interleaver; The high-reliability multicarrier modulation conversion process at the transmitting end is as follows: Source domain information symbol vector High-reliability interleaving transformation and modulation are performed using the HR transformation matrix to generate the time-domain signal vector to be transmitted. .

7. The low-storage, high-reliability transceiver cooperative interleaving transformation method for random multiplexing communication systems according to claim 1, characterized in that, The HR-CD-MAMP detector performs iterative signal detection including: Initial iteration count and maximum iteration count Initialize the nonlinear estimator to 0, and the variance of the nonlinear estimator... ; The detector performs the following operations in a single iteration: The memory linear detection iterative formula is: in, This is the set of estimates from all previous iterations; For normalization parameters, For orthogonalization parameters, For the optimized convergence acceleration parameters, the matrix Defined as ,in, , and Represented as The minimum and maximum eigenvalues; High-reliability cross-domain inverse transform transforms the memory linear detection output of the high-reliability transform domain signal. Mapping back to the source domain, the transformation formula is: The inverse matrix of the unitary transformation is equivalent to the Hermitian transpose matrix; Nonlinear detection utilizes the prior distribution characteristics of the symbols to optimize the accuracy of signal estimation. The iterative formula is as follows: in, These are the normalization parameters and orthogonality parameters of the source domain, respectively. Indicates based on estimated signal The posterior mean estimate is obtained by solving the conditional expectation of the sign. Highly reliable cross-domain transformation converts the source domain signal of the nonlinear detection output. Remapping back to the high-reliability transform domain generates the input signal estimate required for the next iteration of periodic memory linear detection. The transform formula is as follows: This transformation is strictly dual to the modulation at the transmitting end; Update the iteration count and repeat the iteration process until the maximum number of iterations is reached or the bit error rate meets the system's preset threshold. Then stop the iteration and output the final signal estimation result.

8. The low-storage, high-reliability transceiver cooperative interleaving transformation method for random multiplexing communication systems according to claim 2, characterized in that, The deinterleaving operation includes: strictly synchronizing the initial values ​​between the receiver and the transmitter. Chaos control parameters With sequence length A completely consistent interleaved index sequence is regenerated, and the deinterleaving operation is completed through inverse mapping to restore the original symbol sequence.

9. A low-storage, high-reliability transceiver cooperative interleaving transformation method for random multiplexing communication systems according to claim 4, characterized in that, The deinterleaving operation includes: strictly synchronizing the coefficient set and sequence length of the two-stage permutation polynomial between the receiver and transmitter. By combining the parameters of the row and column reshaping operator with the inverse polynomial mapping and inverse row and column reshaping operation, the deinterleaving is completed, and the original symbol sequence is restored.

10. A low-storage, high-reliability transceiver cooperative interleaving transformation method for random multiplexing communication systems according to claim 5, characterized in that, The inverse transformation includes: the receiver performs a symmetrical inverse phase perturbation transformation according to the transformation structure adopted by the transmitter. The inverse matrix of the phase perturbation matrix is ​​its conjugate transpose matrix. Combined with the deinterleaving operation of the interleaver and the inverse transformation of the unitary transformation, the inverse transformation of the received signal is completed, and the signal sequence adapted to the detector is output.

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