A method for joint signal recovery of oversampling reception and quantization in random multiplexing systems

Abstract

This application relates to the field of communication technology, and in particular to a joint signal recovery method for oversampling reception and quantization in a random multiplexing system. The method includes: a transmitter performing random multiplexing modulation on a symbol vector using a random unitary matrix to obtain a time-domain signal, and transmitting the time-domain signal to a receiver; the receiver performing signal processing on the received time-domain signal to obtain a processed received signal; using an oversampling cross-domain message passing detector to recover the processed received signal, obtaining a recovered symbol vector; and predicting the asymptotic performance of the oversampling cross-domain message passing detector through state evolution analysis to ensure Bayesian optimality of signal recovery. This method can solve the technical problems of channel correlation caused by oversampling, nonlinear distortion introduced by low-resolution quantization, and the resulting limitations in detection performance.

Description

Technical Field

[0001] The embodiments of this application relate to the field of communication technology, and in particular to a method for joint signal recovery of oversampling reception and quantization for random multiplexing systems. Background Technology

[0002] With the continuous iteration and upgrading of communication technologies, multi-carrier modulation technology plays a crucial role in mobile communication systems. In existing 4G and 5G systems, Orthogonal Frequency Division Multiplexing (OFDM) technology has been widely used, effectively combating quasi-static multipath fading. However, as high-speed communication applications continue to expand, future mobile communication networks will face the dual challenges of complex scattering environments and high-speed mobile scenarios. Wireless channels exhibit complex multipath effects, rapid delay spread, and non-stationary characteristics such as Doppler shift, making existing OFDM technology inadequate. To address these challenges, numerous emerging multicarrier modulation systems have emerged, such as Interleave Frequency Division Multiplexing (IFDM), Orthogonal Time Frequency Space (OTFS), Affine Frequency Division Multiplexing (AFDM), Orthogonal Delay-Doppler Division Multiplexing (ODDM), and Orthogonal Chirp Division Multiplexing (OCDM), among others.

[0003] However, in practical transceivers, the unavoidable non-ideal characteristics of pulse shaping filters lead to out-of-band leakage, limiting the performance of these multi-carrier modulation systems. To mitigate the impact of out-of-band leakage, an effective strategy is to combine multi-carrier modulation with oversampling techniques. However, oversampling increases the correlation between channel responses and noise samples, which presents new challenges for signal detection design.

[0004] Existing multicarrier modulation techniques face significant challenges when combining oversampling reception and low-resolution quantization. On the one hand, oversampling significantly enhances the correlation between channel responses and noise samples, but existing multicarrier modulation techniques cannot fundamentally solve or effectively utilize this correlation, resulting in limited performance gains. On the other hand, under oversampling conditions, the computational cost of joint detection of all oversampling branches required to achieve optimal performance is extremely high, while independent detection of each oversampling branch is difficult to fully utilize channel information, typically failing to achieve optimal detection performance. Furthermore, under low-resolution quantization conditions, linearization-based methods often provide inaccurate modeling of quantization noise and are prone to generating high error planes at medium to high signal-to-noise ratios, thus limiting practical applications. Summary of the Invention

[0005] In view of this, embodiments of this application propose a joint signal recovery method for oversampling reception and quantization for random multiplexing systems, aiming to solve the technical problems of channel correlation caused by oversampling, nonlinear distortion introduced by low-resolution quantization, and the resulting limited detection performance.

[0006] To achieve the above objectives, embodiments of this application propose a method for joint signal recovery of oversampling reception and quantization in random multiplexing systems, the method comprising the following steps: The transmitter uses a random unitary matrix to perform random multiplexing modulation on the symbol vector to obtain a time-domain signal, and then sends the time-domain signal to the receiver. The random unitary matrix is ​​used to achieve randomness in the equivalent channel matrix to reduce channel correlation caused by oversampling. The receiving end performs signal processing on the received time-domain signal to obtain the processed received signal; the signal processing includes oversampling and quantization. The oversampled cross-domain message passing detector is used to recover the processed received signal and obtain the recovered symbol vector. The oversampled cross-domain message passing detector is used to perform iterative time-domain linear estimation and symbol-domain nonlinear estimation by taking advantage of the randomness of the random unitary matrix, and to exchange information through cross-domain operations to optimize noise covariance and signal estimation. By using state evolution analysis to predict the asymptotic performance of the oversampled cross-domain message passing detector, the Bayesian optimality of signal recovery is ensured.

[0007] To achieve the above objectives, embodiments of this application also propose an oversampling reception and quantization joint signal recovery apparatus for random multiplexing systems, the apparatus comprising: The signal modulation module is used by the transmitter to perform random multiplexing modulation on the symbol vector using a random unitary matrix to obtain a time-domain signal, and then transmit the time-domain signal to the receiver. The random unitary matrix is ​​used to achieve randomness in the equivalent channel matrix to reduce channel correlation caused by oversampling. The signal processing module is used by the receiving end to process the received time-domain signal to obtain the processed received signal; the signal processing includes oversampling and quantization. The signal recovery module is used to recover the processed received signal using an oversampled cross-domain message passing detector to obtain the recovered symbol vector. The oversampled cross-domain message passing detector is used to perform iterative time-domain linear estimation and symbol-domain nonlinear estimation by utilizing the randomness of the random unitary matrix, and to exchange information through cross-domain operations to optimize noise covariance and signal estimation. The analysis and prediction module is used to predict the asymptotic performance of the oversampled cross-domain message passing detector through state evolution analysis, ensuring the Bayesian optimality of signal recovery.

[0008] To achieve the above objectives, embodiments of this application also propose an electronic device, including: a processor and a memory, wherein the memory stores instructions executable by the processor, and the processor is configured to execute the instructions such that the electronic device can implement the oversampling reception and quantization joint signal recovery method for a random multiplexing system as described above.

[0009] To achieve the above objectives, embodiments of this application also propose a computer-readable storage medium storing a computer program that, when executed by a processor, enables the implementation of a method for joint oversampling reception and quantization signal recovery for a random multiplexing system as described above.

[0010] This application proposes a joint signal recovery method for oversampling reception and quantization in a stochastic multiplexing system. The transmitting end uses a stochastic unitary matrix to perform stochastic multiplexing modulation on the symbol vector to obtain a time-domain signal, which is then transmitted to the receiving end. The receiving end processes the received time-domain signal to obtain a processed received signal. An oversampling cross-domain message passing detector is used to recover the processed received signal, yielding the recovered symbol vector. State evolution analysis is used to predict the asymptotic performance of the oversampling cross-domain message passing detector, ensuring Bayesian optimality of the signal recovery. Because the stochastic unitary matrix is ​​used for stochastic multiplexing modulation of the symbol vector, the randomness of the equivalent channel matrix after sampling is ensured, thereby reducing channel correlation caused by oversampling. The oversampling cross-domain message passing detector utilizes the randomness of the stochastic unitary matrix to iteratively perform time-domain linear estimation and symbol-domain nonlinear estimation, and exchanges information through cross-domain operations to optimize... By incorporating noise covariance and signal estimation, the oversampled cross-domain message passing detector can fully utilize the sparsity of the time-domain channel and the randomness of the equivalent channel to achieve efficient signal detection. Furthermore, by predicting the asymptotic performance of the oversampled cross-domain message passing detector through state evolution analysis, its asymptotic optimality can be theoretically proven, and its final performance under different signal-to-noise ratio conditions can be accurately predicted without time-consuming Monte Carlo simulations. Based on this, this scheme can utilize the random characteristics of the random multiplexing modulation matrix to solve the channel correlation problem caused by oversampling, and leverage the sparsity of the time-domain channel and the randomness of the equivalent channel matrix to achieve Bayesian optimal detection performance with low complexity. Simultaneously, combined with an iterative interference cancellation mechanism, it significantly improves detection performance under low-resolution analog-to-digital converter conditions, thereby solving the technical problems of channel correlation caused by oversampling, nonlinear distortion introduced by low-resolution quantization, and the resulting limitations in detection performance. Attached Figure Description

[0011] To more clearly illustrate the technical solutions in the embodiments or related technologies of this application, the accompanying drawings used in the description of the embodiments or related technologies of this application will be briefly introduced below. Obviously, the following drawings are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. The drawings described herein are only used to explain this application and are not intended to limit this application.

[0012] Figure 1 This is a flowchart of a method for joint signal recovery of oversampling reception and quantization for random multiplexing systems provided in one embodiment of this application; Figure 2 This is a schematic diagram of a MIMO-RM system with oversampling reception provided in one embodiment of this application; Figure 3 This is a schematic diagram of an oversampling cross-domain message passing detector for a MIMO-RM system provided in one embodiment of this application; Figure 4 This is a schematic diagram of an enhanced oversampling cross-domain message passing detector for a MIMO-RM system provided in one embodiment of this application; Figure 5 This is a schematic diagram of the bit error rate between the oversampling cross-domain message passing detector of this application and the detector of related technologies in a SISO system, provided in one embodiment of this application; Figure 6 This is a schematic diagram illustrating the bit error rate between the oversampling cross-domain message passing detector of this application and detectors of related technologies in a MIMO system, provided in one embodiment of this application; Figure 7 This is a schematic diagram illustrating the performance of a cross-domain message passing detector with enhanced oversampling under low-resolution quantization provided in one embodiment of this application; Figure 8 This is a schematic diagram of the structure of a joint signal recovery device for oversampling reception and quantization for a random multiplexing system provided in another embodiment of this application; Figure 9 This is a schematic diagram of the structure of an electronic device provided in another embodiment of this application. Detailed Implementation

[0013] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the various embodiments of this application will be described in detail below with reference to the accompanying drawings. Those skilled in the art will understand that many technical details have been presented in the embodiments of this application to facilitate better understanding. However, the technical solutions claimed in this application can be implemented even without these technical details and various variations and modifications based on the following embodiments. The division of the following embodiments is for ease of description and should not constitute any limitation on the specific implementation of this application. The following embodiments can be combined with and referenced by each other without contradiction.

[0014] The existing technology provides the following solutions: For oversampled OTFS modulation systems, the paper "Receiver design for OTFS with afractionally spaced sampling approach" studies a Turbo Message Passing (TMP) receiver, applying a Gaussian message passing detector to each oversampled branch and iteratively estimating the signal based on the Turbo principle. To mitigate the noise correlation introduced by oversampling, the papers "Low complexity MRC detection for OTFS receiver with oversampling" and "Low-complexity oversampled OTFS receivers with reduced overhead" propose a low-complexity maximum ratio combining (MRC) receiver with noise whitening. Furthermore, for oversampled AFDM systems, the paper "Joint channelestimation and data detection for AFDM receivers with oversampling" proposes an oversampled parametric bilinear Gaussian trust propagation algorithm for jointly estimating the channel matrix and detecting symbols. Furthermore, the paper "Oversampled receiver for coded OTFS with different D / A reconstruction filters" studies the coded oversampled OTFS system and analyzes the impact of different roll-off factors of the transceiver filters on the MRC receiver at different code rates. However, combining OTFS and AFDM with well-designed detection algorithms cannot fundamentally eliminate the correlation between oversampled channels, thus limiting system performance.

[0015] In multi-carrier modulation systems, especially when combined with MIMO technology, low-resolution ADCs are often required at the receiver due to hardware cost constraints. However, low-resolution quantization introduces significant nonlinear distortion, posing new challenges to signal detection. Existing low-resolution ADC detectors can be divided into two categories based on their dequantization methods: detectors based on minimum mean-square error (MMSE) and detectors based on linearization.

[0016] MMSE-based detectors: For quantized OTFS systems, the paper "Symbol detection for coarsely quantized OTFS" studies a Generalized Expectation-Consistent Signal Recovery (GEC-SR) algorithm, which performs iterative detection between MMSE dequantization, linear MMSE (LMMSE) estimation, and signal demodulation. In LMMSE estimation, the sparse banded structure of the equivalent channel is utilized, and the computational complexity is greatly reduced by fast banded matrix inversion based on upper and lower bound decomposition. Considering the combined effects of oversampling and low-resolution quantization, the paper "Bayesian channel estimation and data detection in oversampled OFDM receiver with low-resolution ADC" proposes a variational Bayesian-based algorithm for joint channel estimation and signal detection in oversampled OFDM systems, iteratively estimating signal, channel parameters, and noise covariance during the variational process. For oversampled OTSM systems with low-resolution ADCs, the paper "Data detection for oversampled OTSM system with low-bit ADCs" redefines the detection problem in a three-layer generative random network and proposes an improved time-domain multilayer VAMP detector by utilizing the principles of noise whitening and Vector Approximate Message Passing (VAMP) to improve signal detection performance.

[0017] Linearization-based detectors: The paper "The Bussgang decomposition of nonlinear systems: Basic theory and MIMO extensions [lecture notes]" uses Bussgang decomposition to approximate nonlinear quantized systems as linear models and combines this with existing detection algorithms. For example, in the paper "Oversampling in one-bit quantized massive MIMO systems and performance analysis," a Bussgang-based linear zero-forcing receiver is proposed for oversampled OFDM systems. However, equivalent quantization noise is usually modeled as Gaussian white noise, which becomes inaccurate under oversampling, thus limiting signal recovery performance. To address this issue, the paper "MIMO detection with spatial..." ADCs: AvariationalBayesian approach," and "Millimeter-wave receiver design using low-precision quantization and parallel architecture,” adopted Quantization, with its feedback mechanism, makes the statistical properties of noise easy to model. However, when quantization noise is correlated with the input signal, The accuracy of noise approximation decreases, and this degradation is particularly noticeable in oversampling situations.

[0018] Existing multicarrier modulation techniques face significant challenges when combining oversampling reception and low-resolution quantization. On the one hand, oversampling significantly enhances the correlation between channel responses and noise samples, but existing multicarrier modulation techniques cannot fundamentally solve or effectively utilize this correlation, resulting in limited performance gains. On the other hand, under oversampling conditions, the computational cost of joint detection of all oversampling branches required to achieve optimal performance is extremely high, while independent detection of each oversampling branch is difficult to fully utilize channel information, typically failing to achieve optimal detection performance. Furthermore, under low-resolution quantization conditions, linearization-based methods often provide inaccurate modeling of quantization noise and are prone to generating high error planes at medium to high signal-to-noise ratios, thus limiting practical applications.

[0019] In view of this, embodiments of this application propose a joint signal recovery method for oversampling reception and quantization for random multiplexing systems, aiming to solve the technical problems of channel correlation caused by oversampling, nonlinear distortion introduced by low-resolution quantization, and the resulting limited detection performance.

[0020] Specifically, the embodiments of this application first propose an oversampling random multiplexing (RM) system and an oversampling cross-domain memory approximate message passing (OS-CD-MAMP) detector, which possesses low complexity and Bayesian optimality. This RM system can utilize the randomness of the RM modulation matrix to eliminate correlations between oversampling channels. Simultaneously, the OS-CD-MAMP detector further utilizes the sparsity of the time-domain channel and the randomness of the equivalent channel matrix to achieve Bayesian optimal detection performance with low complexity. Furthermore, for oversampling RM systems employing low-resolution analog-to-digital converters (ADCs), an iterative interference cancellation mechanism is introduced into the OS-CD-MAMP detector, further improving detection performance by iteratively estimating the noise covariance matrix.

[0021] The technical problems to be solved by the embodiments of this application include: First, regardless of whether a carefully designed or conventional transceiver pulse shaping filter is used, its non-ideal characteristics inevitably lead to out-of-band leakage, thus limiting detection performance. To alleviate this problem, oversampling techniques can be employed, acquiring out-of-band observation signals of the filter at a rate higher than the conventional Nyquist sampling rate, thereby effectively mitigating out-of-band leakage of the transceiver filter and improving system detection performance. However, for existing multi-carrier modulation techniques (such as Orthogonal Time Frequency Space (OTFS) modulation and Affine Frequency-Division Multiplexing (AFDM), since their modulation matrices are unitary, they cannot fundamentally eliminate the correlation between oversampled channel responses and noise samples, thus limiting the improvement in system performance.

[0022] Secondly, in multi-carrier modulation systems, especially when combined with Multiple-Input Multiple-Output (MIMO) technology, low-resolution ADCs are often required at the receiver due to hardware cost constraints. However, low-resolution quantization introduces significant nonlinear distortion, posing new challenges to signal detection. Existing low-resolution ADC detectors can be divided into two categories based on their dequantization methods: detectors based on Minimum Mean-Squared Error (MMSE) and detectors based on linearization. MMSE-based detectors estimate the sign and equivalent noise covariance based on the quantization system model under the Bayesian criterion, but their computational complexity is high. In contrast, linearization-based detectors mostly utilize methods such as Bussgang decomposition to convert the nonlinear quantization process into a linear model and add equivalent noise, thus allowing the direct use of existing detection algorithms and reducing computational complexity. However, the equivalent noise is difficult to model accurately, limiting detection performance. Furthermore, both existing detectors tend to exhibit high error planes under medium-to-high signal-to-noise ratio (SNR) conditions, limiting practical applications.

[0023] The following is a detailed description of a method for joint signal recovery of oversampling reception and quantization in an directional random multiplexing system proposed in the embodiments of this application.

[0024] One embodiment of this application proposes a method for joint oversampling reception and quantization signal recovery for random multiplexing systems, applied to an electronic device, wherein the electronic device can be a terminal or a server. This embodiment and the following embodiments will use a server as an example for illustration. The implementation details of the proposed method for joint oversampling reception and quantization signal recovery for random multiplexing systems are described below. The following implementation details are provided for ease of understanding and are not essential for implementing this solution.

[0025] The specific process of the oversampling reception and quantization joint signal recovery method for random multiplexing systems proposed in this embodiment can be described as follows: Figure 1 As shown, it includes steps 101 to 104.

[0026] Step 101: The transmitting end performs random multiplexing modulation on the symbol vector using a random unitary matrix to obtain a time-domain signal, and then sends the time-domain signal to the receiving end.

[0027] The random unitary matrix is ​​used to achieve randomness in the equivalent channel matrix, thereby reducing channel correlation caused by oversampling.

[0028] In one possible embodiment, step 101 is specifically implemented as follows: Transmitted time-domain signal Represented as: ; in, , represents the random unitary matrix corresponding to random multiplexing modulation, and ; Represents the identity matrix; , Represents a random matrix. Represents the fast transformation matrix; , representing a symbol vector, where each element is independently derived from the constellation set. Extract from, Indicates the length of the symbol vector.

[0029] For example, a collection of constellations It can be a constellation diagram such as Quadrature Phase Shift Keying (QPSK) or Quadrature Amplitude Modulation (QAMs), and this application does not impose specific limitations on it.

[0030] For example, a random multiplexing system can be described by the following formula: ; in, Represents the channel matrix, This is the noise vector.

[0031] In the following situations, it is possible to Called a signal Random reuse: (1) It is a random unitary matrix that satisfies And independent of

[0032] (2) Equivalent channel matrix Belongs to the universal category ,Right now .

[0033] Among them, the universal category The coverage area includes: Initial range (real number field): initially defined on the real number field. Ensuring that the error vectors in OAMP and VAMP are asymptotically independent and identically distributed (IID) Gaussian guarantees the accuracy of SE.

[0034] Extended range (complex field): In the embodiments of this application, It is extended to the complex field. This extension involves replacing the concept of the real field with the concept of the complex field, such as replacing the transpose with the Hermitian transpose, and replacing orthogonal matrices with random unitary matrices, etc.

[0035] Step 102: The receiving end performs signal processing on the received time-domain signal to obtain the processed received signal.

[0036] Signal processing includes oversampling and quantization.

[0037] For example, oversampling refers to sampling the signal at the receiving end at a rate higher than the conventional Nyquist sampling rate to obtain richer observation information. Quantization refers to converting a continuous analog signal into a discrete digital signal using an analog-to-digital converter. However, in low-resolution analog-to-digital converters, quantization introduces nonlinear distortion. Specific solutions can be found in the following embodiments, which will not be elaborated here.

[0038] Understandably, oversampling and quantization can improve signal detection performance, especially in high-mobility scenarios where out-of-band leakage and low-resolution analog-to-digital converters are a concern.

[0039] Specifically, oversampling can capture out-of-band signal components by sampling the signal at a higher sampling rate than the conventional Nyquist rate (e.g., a sampling multiple G), thereby mitigating out-of-band leakage caused by the non-ideal characteristics of the pulse shaping filter. Oversampling increases the dimensionality of the observed data, but also introduces correlations between channel responses and noise samples. Embodiments of this application utilize the randomness of the random multiplexing modulation matrix to fundamentally eliminate this correlation.

[0040] Specifically, quantization processing converts continuous analog signals into discrete digital signals using an ADC. With low-resolution ADCs (such as 1-bit or ΣΔ quantization), quantization introduces nonlinear distortion. Embodiments of this application employ ΣΔ quantization technology, using a feedback mechanism to process quantization noise, making its statistical characteristics easier to model, thereby reducing performance loss.

[0041] In one possible embodiment, the received signal This can be expressed by the following formula: ; The length of the data segment transmitted by each antenna is 1. And in the SISO scenario, ,but ; ,express The Segment data, , indicating the first Road sampling branch road The received signal vector of each receiving antenna; , indicating the first Road sampling branch road Noise vector of each receiving antenna; , indicating the first Road sampling branch road The first transmitting antenna and the first The time-domain channel matrix between the receiving antennas , , Indicates the length of each data segment; Indicates the number of receiving antennas; This represents the oversampling factor, reflecting the sampling rate as a multiple of the Nyquist rate.

[0042] like Figure 2 As shown, Figure 2 This is a schematic diagram of a MIMO-RM system with oversampling reception provided for an embodiment of this application. Figure 2 This paper illustrates the overall architecture of the oversampling random multiplexing system proposed in this application under a multiple-input multiple-output (MIMO) scenario, aiming to address the out-of-band leakage problem caused by the non-ideal characteristics of pulse shaping filters in traditional multi-carrier modulation techniques. At the transmitter, the symbol vector is modulated using a random modulation matrix to generate a time-domain signal. The signal passes through a multipath channel, adding a noise vector. Oversampling is employed to acquire the received signal at a sampling rate higher than the Nyquist rate. The received signal is quantized by an analog-to-digital converter (ADC); under full-precision ADCs, the quantization error is negligible, while under low-resolution ADCs, nonlinear quantization effects are introduced. This figure highlights the core innovation of the RM system: utilizing the randomness of the random modulation matrix to ensure decorrelation of the channel response after oversampling, laying the foundation for subsequent low-complexity detector design.

[0043] Step 103: Use the oversampled cross-domain message passing detector to recover the processed received signal and obtain the recovered symbol vector.

[0044] Among them, the oversampling cross-domain message passing detector is used to utilize the randomness of the random unitary matrix to iteratively perform time-domain linear estimation and symbol-domain nonlinear estimation, and exchange information through cross-domain operations to optimize noise covariance and signal estimation.

[0045] For example, an oversampled cross-domain message passing detector is used to iteratively recover the processed received signal. This detector, based on the randomness of the random unitary matrix, achieves low-complexity, Bayesian-optimal detection by exchanging information through cross-domain operations (i.e., the time domain and the symbolic domain).

[0046] In one possible embodiment, the oversampled cross-domain message passing detector includes: a time-domain linear estimation module, an inverse random transformation (RT) module, a symbol-domain nonlinear estimation module, and a random transformation (RT) module. The time-domain linear estimation module estimates the time-domain signal based on the processed received signal and prior information through noise whitening, memory matched filtering, and orthogonalization operations. The inverse random transformation module converts the time-domain signal to a symbol-domain signal. The symbol-domain nonlinear estimation module updates the symbol estimate based on the symbol-domain signal through minimum mean square error demodulation and posterior probability decoding. The random transformation module converts the symbol-domain signal back to the time-domain signal and iteratively optimizes signal recovery.

[0047] For example, an oversampled cross-domain message passing detector can be an oversampled cross-domain memory approximation message passing detector; for instance, an oversampled cross-domain memory approximation message passing detector can be an oversampled cross-domain memory approximation message passing detector under a full-precision ADC, or it can be an enhanced oversampled cross-domain memory approximation message passing detector under a low-resolution ADC. These two detectors are described below as examples.

[0048] In one possible embodiment, such as Figure 3 As shown, Figure 3 A schematic diagram of an OS-CD-MAMP detector for a MIMO-RM system is provided for embodiments of this application. The OS-CD-MAMP detector is shown for a full-precision ADC. If the oversampling cross-domain message passing detector uses a full-precision analog-to-digital converter, the processed received signal is This can be expressed by the following formula: ; Let the time-domain linear estimation module be... And the time-domain linear estimation module Includes: Noise whitening module A memory matched filter Orthogonalization module and damping operation module; let the symbolic domain nonlinear estimation module be denoted as . And the symbolic domain nonlinear estimation module Includes: demodulator and orthogonalization modules; The oversampled cross-domain message passing detector is used to recover the processed received signal, resulting in a recovered symbol vector, including: Based on the processed received signal { Prior information of the transmitted signal updated at the nonlinear end Through memory matched filter The orthogonalization module is used to estimate the transmitted time-domain signal. Iterative index from Start, Initialization Estimated signal satisfy: ; in, Represents the normalization coefficient. Denotes the orthogonalization coefficients. Indicates the first Estimate the combination of signals in the next iteration. Prior information of the transmitted signal updated at the nonlinear end And obtained through damping operation: ; in, This represents the damping vector, which is a linearly weighted superposition of all estimated signals. Obtain the noise vector covariance matrix : ; in, , Indicates the noise variance. express and There is a sampling offset The filter autocorrelation function at time; ; For noise vector covariance matrix Cholesky decomposition is used, i.e. ,in The noise whitening module was obtained. The output is represented as: ; in, , , Represents the time-domain channel matrix; ; Through memory matched filter ,get: ; in, ; ; ; express The maximum and minimum eigenvalues; The inverse random transformation module performs a cross-domain operation from the time domain to the symbol domain, resulting in the nonlinear estimation module to be input into the symbol domain. signal and variance The specific implementation includes: ; ; in, This represents the output variance of the time-domain linear estimation module; Through the symbol-domain nonlinear estimation module Input to the symbolic domain nonlinear estimation module signal and variance After processing, the symbolic domain nonlinear estimation module is obtained. output signal and output variance : ; ; in, , This represents the constellation point constraint set of the transmitted symbol. Represents the normalization parameter. Indicates the orthogonalization parameters; The random transformation module performs cross-domain operations from the symbol domain to the time domain to obtain the result to be input into the time-domain linearity detection module. signal and variance The specific implementation includes: ; .

[0049] It should be noted that the orthogonalization operation in linear detection (time-domain linear estimation) and nonlinear detection (symbolic-domain nonlinear estimation) ensures that the output estimation error is orthogonal to the input estimation error, thereby eliminating the correlation between update messages. This also guarantees that the input error of nonlinear detection is independent and identically distributed Gaussian, and is consistent with the true signal. Irrelevant.

[0050] In one possible embodiment, such as Figure 4 As shown, Figure 4 This is a schematic diagram of an enhanced OS-CD-MAMP detector for a MIMO-RM system provided in an embodiment of this application. The enhanced OS-CD-MAMP detector is specifically designed for low-resolution ADCs. Taking a MIMO-RM system as an example, embodiments of this application investigate low-resolution... Enhanced OS-CD-MAMP detector under quantization to effectively address nonlinear quantization This presents challenges for signal recovery.

[0051] In one possible embodiment, if the oversampling cross-domain message passing detector uses a low-resolution analog-to-digital converter, and after processing the received time-domain signal at the receiving end to obtain the processed received signal, the method provided in this application embodiment further includes: remember The signal from each receiving antenna is oversampled. The received signal is times that of the previous generation. , Receive signal Quantization via low-resolution analog-to-digital converter get ; ; Quantizer in low-resolution analog-to-digital converters In the middle, the first A multi-level quantizer is represented as , Used for quantization processing of received signals The first in Received signal value at each sampling point Prequantized signal for: ; in, , Indicates phase shift; After quantizing the received signal, the quantized signal... It is expressed as follows: ; in, Indicates the output level. and They represent the real part and the imaginary part, respectively. Quantizer of a low-resolution analog-to-digital converter in matrix form. The input-output relationship is expressed by the following formula: ; in, ; ; and Quantizer The phase shift matrix in the input-output relationship.

[0052] Based on the Bussgang decomposition algorithm, the quantized signal is... After linear processing, we get: ; in, , represents the linearized coefficient matrix; , representing quantization noise; ; In low resolution Under quantization, it is assumed that all sampling branches have the same power. ,but: ; ; in, It is a dimension of The identity matrix; Furthermore, the received signal after linear processing for: ; in, Represents equivalent noise, and Its covariance matrix Represented as: ; Represents the oversampled temporal noise vector The covariance matrix, ; Indicates the relationship with the first The equivalent noise power corresponding to the Bussgang decomposition of each sampling branch; In one possible embodiment, the time-domain linear estimation module is: And the time-domain linear estimation module Includes: Noise whitening module Memory Matched Filter Noise covariance estimation module based on interference cancellation Symbolic domain nonlinear estimation module Includes: demodulator and orthogonalization modules; The oversampled cross-domain message passing detector is used to recover the processed received signal, resulting in a recovered symbol vector, including: Based on prior information Equivalent noise is obtained Estimated parameters : ; Noise covariance estimation based on interference cancellation Equivalent noise is obtained covariance matrix : ; when Update the noise covariance matrix at that time. ; Indicates a preset threshold; Using noise The received signal is whitened to eliminate noise correlation caused by oversampling; The inverse random transformation module performs a cross-domain operation from the time domain to the symbol domain, resulting in the nonlinear estimation module to be input into the symbol domain. signal and variance The specific implementation includes: ; ; in, This represents the output variance of the time-domain linear estimation module; Through the symbol-domain nonlinear estimation module Input to the symbolic domain nonlinear estimation module signal and variance After processing, the symbolic domain nonlinear estimation module is obtained. output signal and output variance : ; ; in, , This represents the constellation point constraint set of the transmitted symbol. Represents the normalization parameter. Indicates the orthogonalization parameters; The random transformation module performs cross-domain operations from the symbol domain to the time domain to obtain the result to be input into the time-domain linearity detection module. signal and variance The specific implementation includes: ; .

[0053] Understandably, the enhanced OS-CD-MAMP detector optimizes the estimated noise covariance during the iteration process, achieving more accurate noise whitening and data recovery, thereby significantly improving detection performance under low-resolution ΣΔ quantization.

[0054] It is understandable that, such as Figure 5 As shown, Figure 5 This application provides a schematic diagram illustrating the bit error rate of an RM detector under OS-CD-MAMP in a SISO system, OTFS and AFDM under OS-CD-OAMP, and OTFS detector under noise-whitened MRC. Compared to existing technologies, in the SISO scenario, for the RM system, based on oversampling... The OS-CD-MAMP scheme is superior to Nyquist sampling. A gain of 3dB was achieved. The RM receiver using a low-complexity OS-CD-MAMP detector is approximately 3.5dB and 3.7dB higher than the AFDM and OTFS receivers using OS-CD-OAMP detectors, respectively, and 4dB higher than the OTFS receiver using a noise-whitened maximum ratio combining (MRC) receiver. Figure 6 As shown, Figure 6 This application provides a schematic diagram illustrating the bit error rate of the RM detector under OS-CD-MAMP, OTFS and AFDM under OS-CD-OAMP, and OTFS detector under noise-whitening MRC in a MIMO system. In a MIMO scenario ( Under low-complexity quantization conditions, the RM using the low-complexity OS-CD-MAMP detector achieves a performance gain of approximately 9.7 dB compared to AFDM and OTFS using the OS-CD-OAMP detector. Furthermore, the RM using the enhanced OS-CD-MAMP detector shows a significant performance improvement under low-resolution quantization conditions, and solves the high-error leveling problem encountered in OTFS using GER-SC. The performance of this scheme is consistent with the state evolution prediction results, confirming that it achieves Bayesian optimal performance under low complexity.

[0055] It is also understandable that, compared to existing technologies, OS-CD-MAMP achieves near-linear computational complexity. Its complexity is comparable to that of a maximum ratio combining receiver and significantly lower than that of a TurboMessage Passing (TMP) receiver and a state-of-the-art OS-CD-OAMP detector. Furthermore, the enhanced OS-CD-OAMP detector based on a linearized model outperforms OTFS using GER-SC in terms of computational complexity.

[0056] like Figure 7 As shown, Figure 7 An antenna correlation coefficient under low-resolution quantization provided in the embodiments of this application and RM employing an enhanced OS-CD-MAMP detector and OTFS employing a GEC-RC detector, and low resolution RM using an enhanced OS-CD-MAMP detector under quantization, and in Benchmark performance of OS-CD-MAMP under certain conditions; for the enhanced OS-CD-MAMP detector applied to the RM system, the antenna correlation coefficient... (Unrelated) and Under moderate correlation, the bit error rate is consistently low, and the iterative interference cancellation mechanism (such as the estimation of the noise covariance matrix) effectively models quantization noise, avoiding error planes. However, for the OTFS system using the GEC-SR detector, high error planes appear at medium-to-high SNR because the linearization model does not accurately model quantization noise. (The last sentence appears to be incomplete and possibly refers to a different system or model.) Under these conditions, the bit error rate curve of OS-CD-MAMP serves as an ideal reference, showing that the enhanced detector is close to the baseline, thus verifying the effectiveness of the iterative estimation.

[0057] Step 104: Predict the asymptotic performance of the oversampled cross-domain message passing detector through state evolution analysis to ensure the Bayesian optimality of signal recovery.

[0058] It is understood that the embodiments of this application establish the asymptotically independent and identically distributed (IID) Gaussianity of OS-CD-MAMP, enabling accurate asymptotic performance prediction through error analysis.

[0059] In one possible embodiment, step 104 includes: When the errors generated by the time-domain linear estimation module and the symbol-domain nonlinear estimation module are orthogonal to the input signal, the estimation errors include: ; ; in, , = , , ; This represents the estimation error in the time domain. This represents the estimation error in the symbolic domain. Represents the estimated value in the time domain. Represents the estimated value in the symbolic field; Error analysis describes performance evolution through recursive equations: Using the mean square error function and Predicting the asymptotic performance of the oversampled cross-domain message passing detector: Time-domain linear estimation: ; in, ; This represents the covariance matrix of the estimation error during the linear estimation process in the time domain; Mean square error refers to the error in the linear estimation process in the time domain; mean square error function. Used to suppress errors in encapsulated linear estimates (such as noise whitening).

[0060] Symbol-domain nonlinear estimation: ; in, , This represents the covariance matrix of the estimation error during the linear estimation process in the time domain. This represents the covariance matrix of the estimation error during nonlinear estimation in the symbolic domain. An example is the mean squared error function. It is used to reflect the error correction of MMSE demodulation.

[0061] By iteratively calculating the above equations, the SE predictive detector eventually converges to a unique fixed point, corresponding to the optimal Bayesian performance.

[0062] Since the random multiplexing modulation matrix is ​​a random unitary matrix (satisfy The transformation between the time domain and symbol domain is energy-preserving. Therefore, random transformations and inverse random transformations do not change the variance property of the signal, i.e.: ; ; By ensuring variance invariance, it can be ensured that state evolution analysis can seamlessly transfer error information between the time domain and the symbolic domain.

[0063] It should be noted that in the oversampling reception and quantization joint signal recovery method for random multiplexing systems proposed in the embodiments of this application, the oversampling RM system can provide an efficient and low-complexity signal recovery scheme for various complex communication scenarios. Complex communication scenarios can be multi-user communication systems, distributed scenarios, multi-relay scenarios, smart metasurface and fluid antenna scenarios, etc.

[0064] For example, in multi-user communication systems (such as multi-user MIMO or uplink multiple access), oversampling RM systems can effectively handle inter-user interference and channel correlation to reduce the correlation between user signals.

[0065] For example, in distributed antenna systems or cooperative multi-point reception scenarios, multiple distributed nodes cooperate to receive signals, but oversampling can lead to strong correlations between the channel responses and noise samples between nodes. The oversampling RM system in this application can eliminate these strong correlations.

[0066] For example, by extending the oversampled RM system to multi-relay scenarios, stochastic unitary matrix modulation can be used to ensure the equivalent channel randomness of each relay link.

[0067] For example, by extending the oversampling RM system to scenarios such as smart metasurfaces and fluid antennas, random unitary matrix modulation can be used to ensure that the correlation between transmitted and received signals is eliminated by adjusting the phase of the smart metasurface or the angle of the fluid antenna, thereby achieving the maximum transmission rate or the minimum bit error rate.

[0068] This application proposes a joint signal recovery method for oversampling reception and quantization in a stochastic multiplexing system. The transmitting end uses a stochastic unitary matrix to perform stochastic multiplexing modulation on the symbol vector to obtain a time-domain signal, which is then transmitted to the receiving end. The receiving end processes the received time-domain signal to obtain a processed received signal. An oversampling cross-domain message passing detector is used to recover the processed received signal, yielding the recovered symbol vector. State evolution analysis is used to predict the asymptotic performance of the oversampling cross-domain message passing detector, ensuring Bayesian optimality of the signal recovery. Because the stochastic unitary matrix is ​​used for stochastic multiplexing modulation of the symbol vector, the randomness of the equivalent channel matrix after sampling is ensured, thereby reducing channel correlation caused by oversampling. The oversampling cross-domain message passing detector utilizes the randomness of the stochastic unitary matrix to iteratively perform time-domain linear estimation and symbol-domain nonlinear estimation, and exchanges information through cross-domain operations to optimize... By optimizing noise covariance and signal estimation, the oversampled cross-domain message passing detector can fully utilize the sparsity of the time-domain channel and the randomness of the equivalent channel to achieve efficient signal detection. Furthermore, by predicting the asymptotic performance of the oversampled cross-domain message passing detector through state evolution analysis, its asymptotic optimality can be theoretically proven, and its final performance under different signal-to-noise ratio conditions can be accurately predicted without time-consuming Monte Carlo simulations. Based on this, this scheme can utilize the randomness of the RM modulation matrix to solve the channel correlation problem caused by oversampling, and leverage the sparsity of the time-domain channel and the randomness of the equivalent channel matrix to achieve Bayesian optimal detection performance with low complexity. Simultaneously, combined with an iterative interference cancellation mechanism, it significantly improves detection performance under low-resolution analog-to-digital converter conditions, thereby solving the technical problems of channel correlation caused by oversampling, nonlinear distortion introduced by low-resolution quantization, and the resulting limitations in detection performance.

[0069] In summary, the embodiments of this application can achieve the following technical effects: 1. An oversampling RM system is proposed, and the RM modulation matrix is ​​utilized. The randomness of the oversampled channel is ensured, thus fundamentally solving the problem of oversampled channel correlation.

[0070] 2. For oversampled RM systems, a low-complexity, Bayesian-optimal OS-CD-MAMP detector is proposed, along with accurate SE analysis. This detector fully utilizes the sparsity of the time-domain channel and the randomness of the equivalent channel to achieve efficient signal detection. Furthermore, the detector design principle is applicable not only to MAMP but also to, but not limited to, other message passing algorithms, such as Orthogonal Approximate Message Passing (OAMP), Unitary Approximate Message Passing (UAMP), Vector Approximate Message Passing (VAMP), and Oversampling Cross-Domain Orthogonal Approximate Message Passing (OS-CD-MAMP), etc.

[0071] 3. For devices with low resolution A low-complexity enhanced OS-CD-MAMP detector is proposed for quantized oversampling RM systems based on a linearization model. By iteratively optimizing the noise covariance matrix, this enhanced detector successfully reduces the performance loss caused by quantization and achieves a significant performance improvement. Furthermore, the quantization techniques involved are applicable not only to... Quantization is also applicable to other types of multi-resolution quantization, such as common uniform and non-uniform quantization.

[0072] The steps described above are for clarity only. In implementation, they can be combined into one step, or some steps can be broken down into multiple steps, as long as they involve the same logical relationship, they are all within the scope of protection of this application. Adding insignificant modifications or introducing insignificant designs to the algorithm or process, without changing the core design of the algorithm and process, are also within the scope of protection of this application.

[0073] Another embodiment of this application proposes a joint signal recovery device for oversampling reception and quantization in a random multiplexing system. The details of this device are described below for ease of understanding and are not essential for implementing this example. Figure 8 This is a schematic diagram of a joint signal recovery device for oversampling reception and quantization in a random multiplexing system proposed in this embodiment, including: The signal modulation module 810 is used at the transmitting end to perform random multiplexing modulation on the symbol vector using a random unitary matrix to obtain a time-domain signal, and then transmits the time-domain signal to the receiving end; wherein, the random unitary matrix is ​​used to realize the randomness of the equivalent channel matrix to reduce the channel correlation caused by oversampling; The signal processing module 820 is used by the receiving end to perform signal processing on the received time-domain signal to obtain the processed received signal; wherein, the signal processing includes oversampling processing and quantization processing; The signal recovery module 830 is used to recover the processed received signal using an oversampled cross-domain message passing detector to obtain the recovered symbol vector. The oversampled cross-domain message passing detector is used to iteratively perform time-domain linear estimation and symbol-domain nonlinear estimation by utilizing the randomness of the random unitary matrix, and to exchange information through cross-domain operations to optimize noise covariance and signal estimation. The analysis and prediction module 840 is used to predict the asymptotic performance of the oversampled cross-domain message passing detector through state evolution analysis, ensuring the Bayesian optimality of signal recovery.

[0074] It is not difficult to see that this embodiment is a system embodiment corresponding to the above method embodiments, and this embodiment can be implemented in conjunction with the above method embodiments. The relevant technical details and technical effects mentioned in the above method embodiments are still valid in this embodiment, and will not be repeated here to reduce repetition. Accordingly, the relevant technical details mentioned in this embodiment can also be applied to the above method embodiments.

[0075] It is worth mentioning that all modules and units involved in this embodiment are logical modules. In practical applications, a logical unit can be a physical unit, a part of a physical unit, or a combination of multiple physical units. Furthermore, to highlight the innovative aspects of this application, this embodiment does not introduce units that are not closely related to solving the technical problems proposed in this application; however, this does not mean that other units do not exist in this embodiment.

[0076] Another embodiment of this application provides an electronic device, such as Figure 9As shown, it includes a processor 91 and a memory 92. The memory 92 stores instructions that the processor 91 can execute. When the processor 91 is configured to execute the instructions, the electronic device can implement a method for oversampling reception and quantization joint signal recovery for a random multiplexing system as described in the above method embodiment.

[0077] The memory and processor are connected via a bus, which includes any number of interconnecting buses and bridges, connecting various circuits of one or more processors and the memory. The bus can also connect various other circuits such as peripheral devices, voltage regulators, and power management circuits, which are well known in the art and will not be described further herein. The bus interface provides an interface between the bus and the transceiver. The transceiver can be a single component or multiple components, such as multiple receivers and transmitters, providing a unit for communicating with various other devices over a transmission medium. Data processed by the processor is transmitted over the wireless medium via an antenna, which further receives data and transmits it to the processor.

[0078] The processor manages the bus and general processing, and also provides various functions, including timing, peripheral interfaces, voltage regulation, power management, and other control functions. Memory is used to store data used by the processor during operation.

[0079] Another embodiment of this application proposes a computer-readable storage medium storing a computer program that, when executed by a processor, can implement a method for oversampling reception and quantization joint signal recovery for a random multiplexing system as described in the above method embodiments.

[0080] That is, those skilled in the art will understand that all or part of the steps in the above method embodiments can be implemented by a program instructing related hardware. The program is stored in a storage medium and includes several instructions to cause a device (such as a microcontroller, chip, etc.) or processor to execute all or part of the steps of the method described in the method embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory, random access memory, magnetic disks, or optical disks.

[0081] Those skilled in the art will understand that the above embodiments are specific implementations of this application, and in practical applications, various changes can be made in form and detail without departing from the spirit and scope of this application. For those skilled in the art, several improvements and modifications can be made without departing from the principles of this application, and these improvements and modifications are also considered to be within the scope of protection of this application.

Claims

1. A method for joint signal recovery of oversampling reception and quantization in a random multiplexing system, characterized in that, The method includes: The transmitter uses a random unitary matrix to perform random multiplexing modulation on the symbol vector to obtain a time-domain signal, and then sends the time-domain signal to the receiver. The random unitary matrix is ​​used to achieve randomness in the equivalent channel matrix to reduce channel correlation caused by oversampling. The receiving end performs signal processing on the received time-domain signal to obtain the processed received signal; the signal processing includes oversampling and quantization. The oversampled cross-domain message passing detector is used to recover the processed received signal and obtain the recovered symbol vector. The oversampled cross-domain message passing detector is used to perform iterative time-domain linear estimation and symbol-domain nonlinear estimation by taking advantage of the randomness of the random unitary matrix, and to exchange information through cross-domain operations to optimize noise covariance and signal estimation. By using state evolution analysis to predict the asymptotic performance of the oversampled cross-domain message passing detector, the Bayesian optimality of signal recovery is ensured.

2. The method according to claim 1, characterized in that, The transmitting end uses a random unitary matrix to randomly multiplex and modulate the symbol vector to obtain a time-domain signal. Specific implementation methods include: Transmitted time-domain signal Represented as: ； in, , represents the random unitary matrix corresponding to random multiplexing modulation, and ; Represents the identity matrix; , Represents a random matrix. Represents the fast transformation matrix; , representing a symbol vector, where each element is independently derived from the constellation set. Extract from, Indicates the length of the symbol vector; The receiving end performs signal processing on the received time-domain signal to obtain the processed received signal. This can be expressed by the following formula: ； The length of the data segment transmitted by each antenna is 1. And in the SISO scenario, ,but ; ,express The Segment data, , indicating the first Road sampling branch road The received signal vector of each receiving antenna; , indicating the first Road sampling branch road Noise vector of each receiving antenna; , indicating the first Road sampling branch road The first transmitting antenna and the first The time-domain channel matrix between the receiving antennas , , Indicates the length of each data segment; Indicates the number of receiving antennas; This represents the oversampling factor, reflecting the sampling rate as a multiple of the Nyquist rate.

3. The method according to claim 2, characterized in that, The oversampling cross-domain message passing detector includes: a time-domain linear estimation module, an inverse random transformation module, a symbol-domain nonlinear estimation module, and a random transformation module; The time-domain linear estimation module estimates the time-domain signal based on the processed received signal and prior information through noise whitening, memory matched filtering and orthogonalization operations. The time-domain signal is converted to the symbol-domain signal using the inverse random transformation module; The symbol estimation is updated based on the symbol domain signal by using a nonlinear estimation module in the symbol domain, through minimum mean square error demodulation and posterior probability decoding. The symbol domain signal is converted back to the time domain signal through a random transformation module, and the signal recovery is iteratively optimized.

4. The method according to claim 3, characterized in that, If the oversampling cross-domain message passing detector uses a full-precision analog-to-digital converter, the processed received signal is This can be expressed by the following formula: ； Let the time-domain linear estimation module be... And the time-domain linear estimation module Includes: Noise whitening module A memory matched filter Orthogonalization module and damping operation module; let the symbolic domain nonlinear estimation module be denoted as . And the symbolic domain nonlinear estimation module Includes: demodulator and orthogonalization modules; The oversampled cross-domain message passing detector is used to recover the processed received signal, resulting in a recovered symbol vector, including: Based on the processed received signal { Prior information of the transmitted signal updated at the nonlinear end Through memory matched filter The orthogonalization module is used to estimate the transmitted time-domain signal. Iterative index from Start, Initialization Estimated signal satisfy: ； in, Represents the normalization coefficient. Denotes the orthogonalization coefficients. Indicates the first In each iteration, the combination of signals is estimated, and the prior information of the transmitted signal is updated at the nonlinear end. And obtained through damping operation: ； in, This represents the damping vector, which is a linearly weighted superposition of all estimated signals. Obtain the noise vector covariance matrix : ； in, , Indicates the noise variance. express and There is a sampling offset The filter autocorrelation function at time; ; For noise vector covariance matrix Cholesky decomposition is used, i.e. ,in The noise whitening module was obtained. The output is represented as: ； in, , , Represents the time-domain channel matrix; ; Through memory matched filter ,get: ； in, ; ; ; express The maximum and minimum eigenvalues; The inverse random transformation module performs a cross-domain operation from the time domain to the symbol domain, resulting in the nonlinear estimation module to be input into the symbol domain. signal and variance The specific implementation includes: ； ； in, This represents the output variance of the time-domain linear estimation module; ； ； in, , This represents the constellation point constraint set of the transmitted symbol. Represents the normalization parameter. Indicates the orthogonalization parameters; The random transformation module performs cross-domain operations from the symbol domain to the time domain to obtain the result to be input into the time-domain linearity detection module. signal and variance The specific implementation includes: ； 。 5. The method according to claim 3, characterized in that, If the oversampling cross-domain message passing detector uses a low-resolution analog-to-digital converter, after processing the received time-domain signal at the receiving end to obtain the processed received signal, it also includes: remember The signal from each receiving antenna was oversampled. The received signal is times that of the previous generation. , Receive signal Quantization via low-resolution analog-to-digital converter get ; ; Quantizer in low-resolution analog-to-digital converters In the middle, the first A level quantizer is represented as , Used for quantization processing of received signals The first in Received signal value at each sampling point Prequantized signal for: ； in, , Indicates phase shift; After quantizing the received signal, the quantized signal... It is expressed as follows: ； in, Indicates the output level. and They represent the real part and the imaginary part, respectively. Quantizer of a low-resolution analog-to-digital converter in matrix form. The input-output relationship is expressed by the following formula: ； in, ; ; and Quantizer The phase shift matrix in the input-output relationship; Based on the Bussgang decomposition algorithm, the quantized signal is... After linear processing, we get: ； in, , represents the linearized coefficient matrix; , representing quantization noise; ； In low resolution Under quantization, it is assumed that all sampling branches have the same power. ,but: ； ； in, It is a dimension of The identity matrix. Furthermore, the received signal after linear processing for: ； in, Represents equivalent noise, and Its covariance matrix Represented as: ; Represents the oversampled temporal noise vector The covariance matrix, ; Indicates the relationship with the first The equivalent noise power corresponding to the Bussgang decomposition of each sampling branch.

6. The method according to claim 5, characterized in that, Let the time-domain linear estimation module be... And the time-domain linear estimation module Includes: Noise whitening module Memory Matched Filter Noise covariance estimation module based on interference cancellation Symbolic domain nonlinear estimation module Includes: demodulator and orthogonalization modules; The oversampled cross-domain message passing detector is used to recover the processed received signal, resulting in a recovered symbol vector, including: Based on prior information Equivalent noise is obtained Estimated parameters : ； Noise covariance estimation based on interference cancellation Equivalent noise is obtained covariance matrix : ； when Update the noise covariance matrix at that time. ; Indicates a preset threshold; Using noise The received signal is whitened to eliminate noise correlation caused by oversampling; The inverse random transformation module performs a cross-domain operation from the time domain to the symbol domain, resulting in the nonlinear estimation module to be input into the symbol domain. signal and variance The specific implementation includes: ； ； in, This represents the output variance of the time-domain linear estimation module; Through the symbolic domain nonlinear estimation module Input to the symbolic domain nonlinear estimation module signal and variance After processing, the symbolic domain nonlinear estimation module is obtained. output signal and output variance : ； ； in, , This represents the constellation point constraint set of the transmitted symbol. Represents the normalization parameter. Indicates the orthogonalization parameters; The random transformation module performs cross-domain operations from the symbol domain to the time domain to obtain the result to be input into the time-domain linearity detection module. signal and variance The specific implementation includes: ； 。 7. The method according to any one of claims 1 to 6, characterized in that, The method of predicting the asymptotic performance of the oversampled cross-domain message passing detector through state evolution analysis to ensure the Bayesian optimality of signal recovery includes: When the errors generated by the time-domain linear estimation module and the symbol-domain nonlinear estimation module are orthogonal to the input signal, the estimation errors include: ； ； in, , = , , ; This represents the estimation error in the time domain. This represents the estimation error in the symbolic domain. Represents the estimated value in the time domain. Represents the estimated value in the symbolic field; Using the mean square error function and Predicting the asymptotic performance of the oversampled cross-domain message passing detector: ； ； in, , ; This represents the covariance matrix of the estimation error during the linear estimation process in the time domain. and This represents the covariance matrix of the estimation error during the nonlinear estimation process in the symbolic domain.

8. A joint signal recovery device for oversampling reception and quantization in a random multiplexing system, characterized in that, The device includes: The signal modulation module is used by the transmitter to perform random multiplexing modulation on the symbol vector using a random unitary matrix to obtain a time-domain signal, and then transmit the time-domain signal to the receiver. The random unitary matrix is ​​used to achieve randomness in the equivalent channel matrix to reduce channel correlation caused by oversampling. The signal processing module is used by the receiving end to process the received time-domain signal to obtain the processed received signal; the signal processing includes oversampling and quantization. The signal recovery module is used to recover the processed received signal using an oversampled cross-domain message passing detector to obtain the recovered symbol vector. The oversampled cross-domain message passing detector is used to perform iterative time-domain linear estimation and symbol-domain nonlinear estimation by utilizing the randomness of the random unitary matrix, and to exchange information through cross-domain operations to optimize noise covariance and signal estimation. The analysis and prediction module is used to predict the asymptotic performance of the oversampled cross-domain message passing detector through state evolution analysis, ensuring the Bayesian optimality of signal recovery.

9. An electronic device, characterized in that, include: A processor and a memory, wherein the memory stores instructions executable by the processor, and the processor is configured to, when executing the instructions, enable the electronic device to implement the oversampling reception and quantization joint signal recovery method for random multiplexing systems as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it can implement the oversampling reception and quantization joint signal recovery method for random multiplexing systems as described in any one of claims 1 to 7.

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