Perception interleaving frequency division multiplexing waveform system oriented to communication perception integration

Abstract

The invention relates to the technical field of wireless communication, in particular to a perception interleaving frequency division multiplexing waveform system oriented to communication perception integration, and the system comprises a transmitter which is used for modulating a symbol sequence into a time domain signal through a modulation matrix of a perception interleaving frequency division multiplexing waveform, and transmitting the time domain signal to a channel; the communication receiver is used for receiving the received signal transmitted by the channel and carrying out iterative processing on the received signal by utilizing a low-complexity detector so as to realize optimal recovery of the symbol sequence; the sensing receiver is used for realizing target identification through matched filtering and analyzing the sensing performance of the sensing interleaving frequency division multiplexing waveform through a fuzzy function; according to the scheme, optimal communication signal transmission, signal recovery and excellent sensing performance can be realized in a scene of integrating various communication sensing while the advantage of waveform randomness is reserved.

Description

Sensing Interleaved Frequency Division Multiplexing Waveform System for Integrated Communication and Sensing Technical Field

[0001] The embodiments of this application relate to the field of wireless communication technology, and in particular to a sensing interleaved frequency division multiplexing waveform system for integrated communication and sensing. Background Technology

[0002] With the rapid development of 6G wireless networks, Integrated Sensing and Communications (ISAC) technology has become a key research direction. It aims to simultaneously achieve information transmission and environmental perception functions through a unified waveform, hardware platform, and signal processing chain to support emerging applications such as Vehicle-to-Everything (V2X), Unmanned Aerial Vehicles (UAVs), and satellite networks. To this end, communication-centric ISAC solutions are constantly evolving, offering advantages such as high spectral efficiency, excellent communication performance, compatibility with existing standards, and flexible waveform design.

[0003] However, in communication-centric ISAC research, although the ambiguity functions of waveforms such as Orthogonal Frequency Division Multiplexing (OFDM), Orthogonal Time Frequency Space (OTFS), and Affine Frequency Division Multiplexing (AFDM) have been extensively studied in various scenarios, the design of efficient signal detection algorithms remains an unresolved challenge, which significantly hinders the realization of reliable communication in practical ISAC applications. On the other hand, although Interleaved Frequency Division Multiplexing (IFDM), Interleaved Block-Sparse Transform (IBST), and Random Multiplexing (RM) can achieve Bayesian optimal performance through low-complexity detection algorithms, their ambiguity functions have not been explored, and their applicability in sensing tasks remains an unsolved problem. Summary of the Invention

[0004] In view of this, embodiments of this application propose a sensing interleaved frequency division multiplexing waveform system for integrated communication and sensing, which aims to retain the advantages of waveform randomness while achieving optimal communication signal transmission, signal recovery, and excellent sensing performance in various integrated communication and sensing scenarios, thereby achieving synergistic improvement of communication and sensing performance.

[0005] To achieve the above objectives, embodiments of this application propose a sensing interleaved frequency division multiplexing waveform system for integrated communication and sensing. The system includes: a transmitter for modulating a symbol sequence into a time-domain signal using a modulation matrix of the sensing interleaved frequency division multiplexing waveform, and transmitting the time-domain signal to a channel; wherein the modulation matrix of the sensing interleaved frequency division multiplexing waveform consists of a sensing matrix and a random unitary matrix, and the modulation matrix is ​​a unitary matrix to preserve the randomness of the equivalent channel; the time-domain signal is represented based on the sensing interleaved frequency division multiplexing waveform; a communication receiver for receiving the received signal after transmission through the channel, and iteratively processing the received signal using a low-complexity detector to achieve optimal recovery of the symbol sequence; wherein the low-complexity detector also predicts its asymptotic performance using a state evolution method; and a sensing receiver for achieving target recognition through matched filtering and analyzing the sensing performance of the sensing interleaved frequency division multiplexing waveform using a fuzzy function; wherein the fuzzy function employs a discrete signal interpolation reconstruction method and normalization processing.

[0006] This application proposes a sensing-interleaved frequency division multiplexing waveform system for integrated communication and sensing, comprising: a transmitter modulating a symbol sequence into a time-domain signal using the modulation matrix of the sensing-interleaved frequency division multiplexing waveform, and transmitting the time-domain signal to the channel; a communication receiver receiving the received signal after transmission through the channel, and using a low-complexity detector to iteratively process the received signal to achieve optimal recovery of the symbol sequence; a sensing receiver achieving target recognition through matched filtering, and analyzing the sensing performance of the sensing-interleaved frequency division multiplexing waveform through fuzzy function analysis; since the modulation matrix of the sensing-interleaved frequency division multiplexing waveform consists of a sensing matrix and a random unitary matrix, and the modulation matrix is ​​a unitary matrix, the randomness of the equivalent channel is preserved; the time-domain signal is represented based on the sensing-interleaved frequency division multiplexing waveform, thus preserving the advantage of waveform randomness; since the low-complexity detector also predicts the asymptotic performance of the low-complexity detector through a state evolution method, optimal communication signal transmission and signal recovery can be achieved in various integrated communication and sensing scenarios; Furthermore, by employing discrete signal interpolation reconstruction and normalization processing through fuzzy functions, superior sensing performance can be achieved in various integrated communication and sensing scenarios. Based on this, this scheme can achieve optimal communication signal transmission, signal recovery, and superior sensing performance in various integrated communication and sensing scenarios while retaining the advantage of waveform randomness, thereby achieving a synergistic improvement in communication and sensing performance.

[0007] To achieve the above objectives, embodiments of this application also propose a signal processing method for sensing interleaved frequency division multiplexing waveforms for integrated communication and sensing. The method includes: acquiring a symbol sequence using a transmitter; modulating the symbol sequence into a time-domain signal using the modulation matrix of the sensing interleaved frequency division multiplexing waveform; and transmitting the time-domain signal to the channel. The modulation matrix of the sensing interleaved frequency division multiplexing waveform consists of a sensing matrix and a random unitary matrix, with the modulation matrix being a unitary matrix to preserve the randomness of the equivalent channel. The time-domain signal is represented based on the sensing interleaved frequency division multiplexing waveform. A communication receiver receives the received signal after transmission through the channel, and a low-complexity detector iteratively processes the received signal to achieve optimal recovery of the symbol sequence. The low-complexity detector also predicts its asymptotic performance using a state evolution method. A sensing receiver performs target recognition through matched filtering and analyzes the sensing performance of the sensing interleaved frequency division multiplexing waveform using a fuzzy function. The fuzzy function employs a discrete signal interpolation reconstruction method and normalization processing.

[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 a signal processing method for sensing interleaved frequency division multiplexing waveforms oriented towards communication and sensing integration 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 a signal processing method for sensing interleaved frequency division multiplexing waveforms oriented towards integrated communication and sensing as described above.

[0010] Optionally, the modulation of the interleaved frequency division multiplexing waveform into a time-domain signal using the modulation matrix of the sensing interleaved frequency division multiplexing waveform, and the transmission of the time-domain signal to the channel, specifically includes: transmitting the time-domain signal. It can be expressed by the following formula: ;in, Represents a sequence of symbols; The modulation matrix representing the sensing interleaved frequency division multiplexing waveform; the modulation matrix representing the sensing interleaved frequency division multiplexing waveform. Represented as: ;in, and To perceive unitary matrices, And satisfy ; The unitary matrix represents a random matrix, which is obtained based on the interleaving matrix and the transformation matrix; the modulation matrix... It is a unitary matrix, that is, it satisfies ; Indicates the length of the symbol vector; in the case of time-domain signals After introducing the cyclic prefix, a time-domain signal carrying the cyclic prefix is ​​sent to the channel. The cyclic prefix is ​​used to mitigate multipath interference delay, and its length is not less than the maximum channel delay. The specific implementation of receiving the received signal after channel transmission includes: receiving the received signal after channel transmission. It can be expressed by the following formula: ;in, , Indicates a time-varying multipath channel. This represents Gaussian white noise.

[0011] Optionally, the low-complexity detector is a cross-domain memory approximate message-passing detector, comprising: a time-domain linear estimation module, a cross-domain transformation module, and a symbol-domain nonlinear estimation module; the time-domain linear estimation module generates a time-domain estimated signal based on a memory matched filter and orthogonalization operation; the cross-domain transformation module converts the time-domain estimated signal to the symbol domain through the inverse of the modulation matrix; the symbol-domain nonlinear estimation module performs symbol estimation based on a minimum mean square error demodulator; wherein, the low-complexity detector ensures that the estimation error follows an asymptotically independent and identically distributed Gaussian distribution through iterative updates and damping operations, achieving Bayesian optimal performance.

[0012] Optionally, a low-complexity detector is used to iteratively process the received signal to achieve optimal recovery of the symbol sequence, including: a time-domain linear estimation module. The symbolic domain nonlinear estimation module is Time-domain linear estimation module Including memory matched filters Modules, orthogonalization module and damping operation module, symbolic domain nonlinear estimation module Including symbol-by-symbol minimum mean square error demodulator Orthogonalization module; utilizing memory matched filter The module, orthogonalization module, and damping operation module are based on the received signal. and the prior information of the transmitted signal updated by the symbol domain nonlinear estimation module Iterative index from Start, Initialization To enable memory matched filters output signal satisfy: ;in, Represents the normalization coefficient. Represents the orthogonalization coefficients; Indicates preceding The combination of signals estimated in each iteration; Indicates based on input Low-complexity memory matched filter Specifically, it is expressed by the following formula: ; ;in, ; ; This represents the scaling factor. , express The largest eigenvalue, express The smallest eigenvalue, Represents weighting coefficients; memory matched filter The output depends on the time-varying multipath channel. and ;in, Through the and prior information The damping operation yields the following formula: ;in, Denotes the damping vector, and Then the memory matched filter Output time-domain estimation error Specifically, it is expressed by the following formula: ;in, The length of the transmitted signal; the cross-domain transformation module, based on the inverse matrix of the modulation matrix of the sensing interleaved frequency division multiplexing waveform. A cross-domain operation from the time domain to the symbol domain is performed to obtain the nonlinear estimation module to be input into the symbol domain. input signal Input variance The specific implementation includes: ; ;in, The output variance of the time-domain linear estimation module; 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 error The specific implementation includes: ; ;in, Represents the normalization coefficient. Indicates the orthogonalization parameters; , Indicates signal The set of discrete constellation points that obeys Constraints; Cross-domain transform module, based on the modulation matrix of the perceptual interleaved frequency division multiplexing waveform. A cross-domain operation is performed from the symbol domain to the time domain to obtain the result to be input into the time-domain linear estimation module. input signal Input variance The specific implementation includes: ; .

[0013] Optionally, the state evolution method represents the prediction of the asymptotic performance of a low-complexity detector using the covariance matrix; specifically, the prediction of the asymptotic performance of the low-complexity detector using the state evolution method includes: obtaining the temporal estimation error covariance matrix. And the symbolic domain estimation error covariance matrix ; through the mean square error function and The target estimation error covariance matrix is ​​iteratively updated to predict the asymptotic performance of the low-complexity detector; where the mean square error function in the time domain... Mean square error function in the sign domain This can be expressed by the following formula: ; ;in, , The covariance matrix representing the time-domain estimation error; , and The covariance matrix represents the estimation error in the symbolic domain.

[0014] Optionally, target recognition is achieved through matched filtering, and the sensing performance of the interleaved frequency division multiplexing waveform is analyzed using a fuzzy function, including: discrete signals based on the interleaved frequency division multiplexing waveform. By defining discrete fuzzy functions To analyze the waveform's time delay and Doppler sensing performance; among them, the discrete fuzzy function Represented as: ;in, Indicates integer delay. Indicates an integer Doppler index; Represents a time-domain signal sequence. Indicates signal length; by introducing an oversampling factor in the time delay dimension. Oversampling factor and Doppler dimension For discrete signals Interpolation reconstruction is performed to obtain a high-precision interpolated discrete sequence. This leads to the high-precision discrete fuzzy function. : ; ;in, ; ; Represents the smoothing window function; This indicates half the length of the windowed sinc function; and This represents the oversampled index; further, it utilizes the time delay normalization parameter. and Doppler normalization parameters High-precision discrete fuzzy function Mapping to a normalized coordinate system yields the normalized fuzzy function. And expressed by the following formula: ;in, Indicates the time delay range. This represents the Nyquist-limited Doppler interval; metrics based on the normalized ambiguity function are used to evaluate the sensing performance of the sensing interleaved frequency division multiplexing waveform; these metrics include 3dB bandwidth, peak sidelobe ratio, and combined sidelobe ratio.

[0015] Optionally, after evaluating the sensing performance of the sensing interleaved frequency division multiplexing waveform based on the index of the normalized ambiguity function, the transmitter is also used to: obtain the 3dB bandwidth, peak sidelobe ratio, and combined sidelobe ratio from the sensing receiver; and construct an optimization function for the sensing matrix based on the 3dB bandwidth, peak sidelobe ratio, and combined sidelobe ratio. ;in, , and Indicates the preset weighting coefficients; Indicates 3dB bandwidth; Indicates the peak-to-sidelobe ratio; Represents the overall sidelobe ratio; the optimization function of the sensing matrix is ​​solved using an engineering optimization algorithm to achieve... and Optimal.

[0016] Optionally, target recognition is achieved through matched filtering, and the sensing performance of the interleaved frequency division multiplexing waveform is analyzed using a fuzzy function. This includes: analyzing the sensing performance of the interleaved frequency division multiplexing waveform in single-station or multi-station sensing scenarios using a fuzzy function; wherein: when the system is applied to a single-station sensing scenario, the sensing performance of the interleaved frequency division multiplexing waveform is analyzed using a fuzzy function with random data signals or constant modulus signals; wherein, the random data signal is a randomly generated symbol sequence mapped to a time-domain signal by the interleaved frequency division multiplexing modulation matrix; the constant modulus signal is an all-1 sequence or a unit modulus signal; when the system is applied to a multi-station sensing scenario, the sensing performance of the interleaved frequency division multiplexing waveform is analyzed using a fuzzy function with pilot signals; wherein, the pilot signal is the data signal agreed upon by the transmitter and the sensing receiver. Attached Figure Description

[0017] 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.

[0018] Figure 1 is an architecture diagram of a sensing interleaved frequency division multiplexing waveform system for integrated communication and sensing according to an embodiment of this application; Figure 2 is a schematic diagram of a cross-domain memory approximate message passing detector for a sensing interleaved frequency division multiplexing waveform system according to an embodiment of this application; Figure 3 is a schematic diagram of the bit error rate of different waveforms using the same detector in a single-input single-output system according to an embodiment of this application; Figure 4 is a schematic diagram of zero-delay truncation of different waveform ambiguity functions under a given random signal in a single-station ISAC scenario according to an embodiment of this application; Figure 5 is a schematic diagram of zero-delay truncation of different waveform ambiguity functions under a given random signal in a single-station ISAC scenario according to an embodiment of this application. Figure 6 is a schematic diagram of zero-delay truncation of different waveform ambiguity functions under a given all-1 signal in a multi-station ISAC scenario provided in one embodiment of this application; Figure 7 is a schematic diagram of zero Doppler truncation of different waveform ambiguity functions under a given all-1 signal in a multi-station ISAC scenario provided in one embodiment of this application; Figure 8 is a schematic diagram of signal transmission and recovery in a sensing interleaved frequency division multiplexing waveform system provided in one embodiment of this application; Figure 9 is a flowchart of a signal processing method for sensing interleaved frequency division multiplexing waveforms oriented towards communication and sensing integration provided in another embodiment of this application; Figure 10 is a structural schematic diagram of an electronic device provided in another embodiment of this application. Detailed Implementation

[0019] 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.

[0020] With the rapid development of 6G wireless networks, Integrated Sensing and Communications (ISAC) technology has become a key research direction. It aims to simultaneously achieve information transmission and environmental perception functions through a unified waveform, hardware platform, and signal processing chain to support emerging applications such as Vehicle-to-Everything (V2X), Unmanned Aerial Vehicles (UAVs), and satellite networks. To this end, communication-centric ISAC solutions are constantly evolving, offering advantages such as high spectral efficiency, excellent communication performance, compatibility with existing standards, and flexible waveform design.

[0021] Currently, two ISAC technology solutions have been proposed: (1) Waveform evolution for communication: The core waveform of the existing 5G communication system is Orthogonal Frequency Division Multiplexing (OFDM), which is designed to suppress inter-symbol interference in quasi-static multipath channels. However, in high-speed time-varying multipath channels, Doppler frequency shift can easily destroy subcarrier orthogonality and introduce severe inter-carrier interference, resulting in a significant performance degradation and limiting OFDM's ability to support high-mobility applications. To address this challenge, a variety of new modulation waveforms have emerged in recent years. For example, the paper "Orthogonal time frequency space modulation" proposes an Orthogonal Time Frequency Space (OTFS) waveform, which maps the data signal to a two-dimensional time delay-Doppler domain and passes it through the Inverse Symplectic Finite Fourier Transform (ISFFT) and Heisenberg Transform. Furthermore, the paper "Affinefrequency division multiplexing for next generation wireless communications" proposes an Affine Frequency Division Multiplexing (AFDM) waveform that maps the data signal to the time domain using a one-dimensional chirp-based affine Fourier transform, effectively decoupling time delay and Doppler effects. Although OTFS and AFDM waveforms can achieve near-full diversity or full diversity gain under computationally complex maximum likelihood detection, the lack of low-complexity and highly reliable detectors severely limits their signal recovery performance in practical systems. Recently, the paper "Interleave frequency division multiplexing" proposed an Interleave Frequency Division Multiplexing (IFDM) waveform based on a densely randomized equivalent channel. By employing a randomly interleaved Inverse Fast Fourier Transform (IFFT) matrix as the modulation matrix, it ensures that the equivalent channel matrix satisfies a right-unitary invariant distribution and is statistically stationary.Based on IFDM waveforms, a low-complexity cross-domain memory approximate messagepassing (CD-MAMP) detector is proposed, achieving Bayesian optimal performance. To further reduce the implementation complexity of large-scale IFDM systems, the paper "Interleaved block-sparse transform" proposes an interleaved block-sparse transform (IBST) modulation matrix, composed of multiple small-scale IFFT matrices on block diagonals and a global interleaver, achieving near-IFDM performance while reducing complexity. Furthermore, the paper "Randommodulation: Achieving asymptotic replica optimality over arbitrary norm-bounded and spectrally convergent channel matrices" generalizes IFDM to random multiplexing (RM) based on random matrices, providing a complete theoretical foundation.

[0022] (2) Communication-centric waveform sensing technology: In communication-centric ISAC waveform design, the ambiguity function (AF) is widely analyzed and optimized to characterize the inherent sensing capability of communication waveforms, without relying on the propagation channel or specific system configuration. Specifically, the main lobe width of AF in the time delay and Doppler dimensions determines the range resolution and velocity resolution, respectively, while the sidelobe level quantifies the interference from adjacent targets. For example, the paper "CP-OFDM achieves the lowest averageranging sidelobe under QAM / PSK constellations" shows that for random communication signals using Quadrature Amplitude Modulation (QAM) and Phase-Shift Keying (PSK) constellations, OFDM is the globally optimal modulation scheme for Cyclic Prefix (CP) signals under Nyquist sampling, achieving the lowest average ranging sidelobe level. Furthermore, the paper "From OTFS to DD-ISAC: Integrating sensing and communications in the delay doppler domain" focuses on OTFS, demonstrating that a rapidly decaying ambiguity function with sidelobes can be generated using only a single pilot subcarrier. The paper "Ambiguity function analyses of AFDM under random ISAC signaling" studies the ambiguity function (AF) of AFDM waveforms where all communication data is defined as 1. The paper "Ambiguity function analysis of AFDM signals for integrated sensing and communications" analyzes the AF of continuous-time AFDM signals, revealing the spike-like local behavior and quasi-periodic global structure of AFDM pilot subcarriers, as well as the thumb-like characteristics of AFDM symbols. To facilitate comparison of the sensing performance of these waveforms, the paper "Normalized ambiguity function characteristics of OFDM, OTFS, AFDM, and CP-AFDM for ISAC" proposes a unified evaluation framework based on discrete-time AF, employing normalized time delay and Doppler coordinates, allowing it to be directly mapped to any practical system configuration based on physical bandwidth, sampling frequency, or symbol duration.

[0023] However, in communication-centric ISAC research, although the ambiguity functions of waveforms such as OFDM, OTFS, and AFDM have been extensively studied in various scenarios, the design of efficient signal detection algorithms remains an unresolved challenge, which significantly hinders the realization of reliable communication in practical ISAC applications. On the other hand, although IFDM, IBST, and RM can achieve Bayesian optimal performance through low-complexity detection algorithms, their ambiguity functions have not yet been explored, and their applicability in perception tasks remains an unsolved problem.

[0024] Specifically, under quasi-static or dual-selection channel conditions, ISAC schemes centered on communication waveforms, such as orthogonal frequency division multiplexing (OFDM), orthogonal time-frequency-space multiplexing (TFO), and pseudo-RF division multiplexing (RFD), have been widely studied in various sensing scenarios. However, the equivalent communication channels corresponding to these waveforms are usually sparse, susceptible to deep fading, and lack efficient signal detection algorithms, making it difficult to guarantee reliable signal transmission in communication scenarios. This significantly limits their application in practical ISAC scenarios. Therefore, existing technologies have not solved the problem of coordinated optimization between communication and sensing.

[0025] In view of this, embodiments of this application propose a Sensing Interleave Frequency Division Multiplexing (sIFDM) waveform system for integrated communication and sensing. It aims to retain the advantages of waveform randomness while achieving optimal communication signal transmission, signal recovery, and excellent sensing performance in various integrated communication and sensing scenarios, thereby achieving a synergistic improvement in communication and sensing performance.

[0026] First, an exemplary description is given of a sensing interleaved frequency division multiplexing waveform system for communication and sensing integration proposed in one embodiment of this application.

[0027] For example, the sensing interleaved frequency division multiplexing waveform system proposed in the embodiments of this application can be used to simultaneously achieve optimal recovery of communication signals and sensing performance under quasi-static channel or dual-selection channel conditions, and is suitable for integrated communication and sensing applications in vehicle networking, drones or satellite networks.

[0028] As shown in Figure 1, Figure 1 is an architecture diagram of a sensing interleaved frequency division multiplexing waveform system for integrated communication and sensing proposed in an embodiment of this application. The system includes: a transmitter 110, a communication receiver 120, and a sensing receiver 130.

[0029] For example, the communication receiver 120 and the sensing receiver 130 can be two devices integrated in the same device, or they can be two independent devices, depending on the specific application scenario.

[0030] For example, if the application scenario is a single-station sensing scenario, the communication receiver 120 and the sensing receiver 130 can be the same device. In this case, the transmitter 110 can also be integrated with the communication receiver 120 and the sensing receiver 130 into the same device.

[0031] For example, if the application scenario is a multi-station sensing scenario, the communication receiver 120 and the sensing receiver 130 can be the same device or two independent devices, depending on the actual situation.

[0032] Next, the transmitter 110, the communication receiver 120, and the sensing receiver 130 will be described in detail.

[0033] Transmitter 110 is used to modulate a symbol sequence into a time-domain signal by sensing the modulation matrix of the interleaved frequency division multiplexing waveform and to transmit the time-domain signal to the channel.

[0034] The modulation matrix of the sensing interleaved frequency division multiplexing waveform (i.e., sIFDM waveform) consists of a sensing matrix and a random unitary matrix, and the modulation matrix is ​​a unitary matrix to preserve the randomness of the equivalent channel; the time-domain signal is represented based on the sensing interleaved frequency division multiplexing waveform.

[0035] For example, the sensing matrix can be located at both ends of the modulation matrix.

[0036] In one possible embodiment, the modulation matrix of the sensed interleaved frequency division multiplexing waveform is modulated into a time-domain signal, and the time-domain signal is transmitted to the channel. Specifically, this includes transmitting the time-domain signal. It can be expressed by the following formula: ;in, Represents a sequence of symbols; The modulation matrix representing the sensing interleaved frequency division multiplexing waveform; the modulation matrix representing the sensing interleaved frequency division multiplexing waveform. Represented as: ;in, and To perceive unitary matrices, And satisfy ; The unitary matrix represents a random matrix, which is obtained based on the interleaving matrix and the transformation matrix; the modulation matrix... It is a unitary matrix, that is, it satisfies ; Indicates the length of the symbol vector.

[0037] For example, a random unitary matrix is ​​obtained based on an interleaving matrix and a transformation matrix, specifically by multiplying the random unitary matrix by the interleaving matrix and the transformation matrix.

[0038] Random unitary matrices can be orthogonalized using Singular Value Decomposition (SVD) or Haar matrices, thereby maintaining the randomness of the equivalent signal.

[0039] For example, the interleaving matrix is ​​a random permutation matrix, which may include a completely random permutation matrix or a pseudo-random permutation matrix; the transformation matrix is ​​any one of the inverse fast Fourier transform matrix, Hadamard matrix, or discrete cosine transform matrix.

[0040] This is a random permutation matrix used to randomly permutate symbol sequences. The location.

[0041] For example, if the interleaving matrix is ​​a completely random permutation matrix and the transformation matrix is ​​an inverse fast Fourier transform matrix, then the modulation matrix of the sensing interleaved frequency division multiplexing waveform... Represented as: ;in, and To perceive unitary matrices, And satisfy ; Let represent a completely random permutation matrix, and ; Let represent the inverse fast Fourier transform matrix, and ; Describe a unitary matrix, that is, one that satisfies ; It is a normalized inverse fast Fourier transform matrix, whose The element at is .

[0042] For example, if the interleaving matrix is ​​a pseudo-random permutation matrix and the transformation matrix is ​​a discrete cosine transform matrix, then the modulation matrix of the sensing interleaved frequency division multiplexing waveform... Represented as: ;in, Let represent a pseudo-random permutation matrix, and , Represents the discrete cosine transform matrix; Discrete cosine transform matrix exist The element at that location is: ; where the normalization coefficient satisfy: Specifically, the perception matrix This represents two sensing matrices, which are unitary matrices by mathematical definition. They do not affect detection performance. In terms of sensing, careful design can enable sensing interleaved frequency division multiplexed waveforms to have excellent sensing performance.

[0043] It is understandable that sIFDM is a principle framework, although its modulation matrix is ​​constructed by introducing auxiliary sensing matrices at both ends of a random unitary matrix, such as introducing auxiliary sensing matrices at both ends of an inverse fast Fourier transform matrix cascaded with a random interleaver (i.e., the IFDM modulation matrix). However, the embodiments of this application are not limited to such a structure, and auxiliary sensing matrices can also be introduced at both ends of IBST, RM, etc., where a random unitary matrix is ​​used as the modulation matrix.

[0044] For example, for IBST, the replaced modulation matrix for: ;in, Let represent the stochastic unitary matrix corresponding to IBST; for example, for RM, the replaced modulation matrix for: ;in, This represents the random unitary matrix corresponding to RM; optionally, the type of sensing matrix is ​​not limited to a unitary matrix, such as commonly used radar sensing matrices, precoding matrices, or beamforming matrices similar to those of mobile antennas or fluid antennas.

[0045] In the time domain signal After introducing the cyclic prefix, a time-domain signal carrying the cyclic prefix is ​​sent to the channel. The cyclic prefix is ​​used to mitigate multipath interference delay, and its length is not less than the channel's maximum delay. It should be noted that after the communication receiver 120 receives the received signal, it needs to remove the cyclic prefix before further processing.

[0046] In the following embodiments, the communication and sensing performance based on sIFDM is discussed from two aspects: communication signal recovery and fuzzy function analysis, using a communication receiver 120 and a sensing receiver 130.

[0047] The communication receiver 120 is used to receive the received signal after it has been transmitted through the channel, and to perform iterative processing on the received signal using a low-complexity detector in order to achieve optimal recovery of the symbol sequence.

[0048] Among them, the low-complexity detector also predicts the asymptotic performance of the low-complexity detector through the state evolution method.

[0049] For example, a low-complexity detector could be a low-complexity cross-domain memory approximate message passing (CD-MAMP) detector.

[0050] Optionally, in addition to the CD-MAMP detector, embodiments of this application may also employ detectors based on expectation propagation-based detection algorithms; detectors based on approximate message passing (AMP)-based detection algorithms; detectors based on generalized approximate message passing (GAMP) algorithms; detectors based on iterative detection algorithms or linear detection algorithms such as variational message passing algorithms; and embodiments of this application do not impose specific limitations on these.

[0051] In one possible embodiment, receiving the received signal after transmission through the channel is specifically implemented by: receiving the received signal after transmission through the channel. It can be expressed by the following formula: ;in, , Indicates a time-varying multipath channel. This represents Gaussian white noise.

[0052] In one possible embodiment, the low-complexity detector is a cross-domain memory approximation message-passing detector, comprising: a time-domain linear estimation module, a cross-domain transformation module, and a symbol-domain nonlinear estimation module; the time-domain linear estimation module generates a time-domain estimated signal based on a memory matched filter and orthogonalization operation; the cross-domain transformation module converts the time-domain estimated signal to the symbol domain through the inverse of the modulation matrix; the symbol-domain nonlinear estimation module performs symbol estimation based on a minimum mean square error demodulator; wherein, the low-complexity detector ensures that the estimation error follows an asymptotically independent and identically distributed Gaussian distribution through iterative updates and damping operations, achieving Bayesian optimal performance.

[0053] As exemplarily shown in FIG2, FIG2 is a schematic diagram of a CD-MAMP detector for an sIFDM system provided in an embodiment of the present application.

[0054] The CD-MAMP detector includes: a time-domain linear estimation module. Cross-domain transformation module and symbolic domain nonlinear estimation module Among them, the time-domain linear estimation module Includes a memory matched filter module Orthogonalization module and damping operation module. Symbolic domain nonlinear estimation module. Includes a symbol-by-symbol minimum mean square error (MMSE) demodulator. The orthogonalization module and the estimated signals of the two modules are iteratively updated through cross-domain transformation. Specifically, refer to the following embodiment: In one possible embodiment, a low-complexity detector is used to iteratively process the received signal to achieve optimal recovery of the symbol sequence, including: using a memory matched filter. The module, orthogonalization module, and damping operation module are based on the received signal. and the prior information of the transmitted signal updated by the symbol domain nonlinear estimation module Iterative index from Start, Initialization To enable memory matched filters output signal satisfy: ;in, Represents the normalization coefficient. Represents the orthogonalization coefficients; Indicates preceding The combination of signals estimated in each iteration; Indicates based on input Low-complexity memory matched filter Specifically, it is expressed by the following formula: ; ;in, ; ; This represents the scaling factor. , express The largest eigenvalue, express The smallest eigenvalue, Represents weighting coefficients; memory matched filter The output depends on the time-varying multipath channel. and ;in, Through the and prior information The damping operation yields the following formula: ;in, Denotes the damping vector, and .

[0055] It should be noted that the damping vector This is achieved by linearly weighting all previous estimates, theoretically improving the convergence speed of the CD-MAMP detector. Furthermore, the parameters... , Optimization can accelerate the convergence speed of the CD-MAMP detector and ensure its Bayesian optimal performance.

[0056] Based on the above steps, the memory matched filter Output time-domain estimation error Specifically, it is expressed by the following formula: ;in, The length of the transmitted signal.

[0057] The cross-domain transform module is based on the inverse matrix of the modulation matrix of the perceptually interleaved frequency division multiplexed waveform. A cross-domain operation from the time domain to the symbol domain is performed to obtain the nonlinear estimation module to be input into the symbol domain. input signal Input variance The specific implementation includes: ; ;in, The output variance of the time-domain linear estimation module; 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 error The specific implementation includes: ; ;in, Represents the normalization coefficient. Indicates the orthogonalization parameters; , Indicates signal The set of discrete constellation points that obeys Constraints; the cross-domain transform module is also based on the modulation matrix of the sensing interleaved frequency division multiplexing waveform. A cross-domain operation is performed from the symbol domain to the time domain to obtain the result to be input into the time-domain linear estimation module. input signal Input variance The specific implementation includes: ; .

[0058] It should be noted that, due to the linear detection output The estimation error is orthogonal to the estimation error of each previous iteration. This property guarantees that the estimation error follows asymptotically independent and identically distributed (IID) Gaussian distribution, i.e.: ,in, The mean is 0 and the variance is Gaussian white noise, and with Independent; therefore, the asymptotic performance of the CD-MAMP detector can be accurately characterized by state evolution (SE), thus illustrating the Bayesian optimal performance of the CD-MAMP detector. Specifically, refer to the following embodiment: In one possible embodiment, since the output of the time-domain estimation module depends on all previous iterations, the asymptotic performance of the low-complexity detector can be predicted using the covariance matrix; the prediction of the asymptotic performance of the low-complexity detector using the state evolution method specifically includes: obtaining the time-domain estimation error covariance matrix. And the symbolic domain estimation error covariance matrix ; through the mean square error function and The target estimation error covariance matrix is ​​iteratively updated to predict the asymptotic performance of the low-complexity detector; where the mean square error function in the time domain... Mean square error function in the sign domain This can be expressed by the following formula: ; ;in, , The covariance matrix representing the time-domain estimation error; , and The covariance matrix represents the estimation error in the symbolic domain.

[0059] As can be understood, Figure 3 illustrates the bit error rates of sIFDM, OFDM, OTFS, and AFDM in a Single-Input Single-Output (SISO) system using the same CD-MAMP detector, according to an embodiment of this application. It can be seen that, with the same CD-MAMP detector, sIFDM achieves a lower bit error rate compared to OFDM, OTFS, and AFDM, especially under adverse channel conditions (such as low signal-to-noise ratio).

[0060] The sensing receiver 130 is used to achieve target recognition through matched filtering and to analyze the sensing performance of the interleaved frequency division multiplexing waveform through fuzzy function.

[0061] The ambiguity function (AF) employs discrete signal interpolation reconstruction and normalization. The ambiguity function is a key tool for analyzing the sensing performance of waveforms in radar sensing and ISAC scenarios. For transmitted continuous time-domain sIFDM waveforms... In this regard, its AF is given by the following formula: From a mathematical perspective, the ambiguity function characterizes the correlation between a waveform and its version after time delay and Doppler shift. However, since the integration of continuous signals is extremely complex, for simplicity, we can further consider the integration of discrete signals. The discrete fuzzy function can be specifically referred to in the following embodiments: In one possible embodiment, the sensing performance of the sensing interleaved frequency division multiplexing waveform is analyzed through the fuzzy function, including: based on the discrete signal of the sensing interleaved frequency division multiplexing waveform. By defining discrete fuzzy functions To analyze the waveform's time delay and Doppler sensing performance; among them, the discrete fuzzy function Represented as: ;in, Indicates integer delay. Indicates an integer Doppler index; Represents a time-domain signal sequence. Indicates the signal length.

[0062] Furthermore, to obtain higher precision discrete autofocus (AF), an oversampling factor in the time delay dimension can be introduced. Oversampling factor and Doppler dimension Furthermore, for discrete signals Perform interpolation reconstruction, and at more frequent time intervals. Desampling yields a high-precision interpolated discrete sequence. This leads to the high-precision discrete fuzzy function. Thus, the AF characteristic on fractional delay is obtained: ; ;in, ; ; Represents the smoothing window function; Indicates adding a window Half the function length; and This represents the oversampled index; furthermore, because and With symbol duration and signal length In order to eliminate the influence of these system parameters on AF, the time delay normalization parameter can be used. and Doppler normalization parameters High-precision discrete fuzzy function Mapping to a normalized coordinate system yields the normalized fuzzy function. And expressed by the following formula: ;in, Indicates the time delay range. Represents the Nyquist-constrained Doppler interval; based on the normalized fuzzy function The 3dB bandwidth, peak sidelobe ratio, and overall sidelobe ratio were obtained to evaluate the sensing performance of the sensing interleaved frequency division multiplexing waveform.

[0063] First, let's explain 3dB bandwidth, peak sidelob ratio, and overall sidelob ratio: 1. 3dB bandwidth The half-power region of the fuzzy function in the time delay or Doppler dimension is defined: assuming the peak value of the fuzzy function has been normalized. and This indicates that the modulus has decreased to its peak value. ,Right now: 3dB bandwidth Defined as: 2. Peak-to-sidelobe ratio (PSLR). The PSLR represents the relative height of the highest sidelobe peak to the central main lobe peak. Therefore, a lower (i.e., more negative) value corresponds to stronger sidelobe suppression and a lower false target probability. It is usually expressed in dB. domain( The representation of time delay or Doppler, i.e. as follows: ;in, Indicates a side lobe.

[0064] 3. Integrated sidelobe ratio (ISLR), expressed in dB, is defined as the ratio between the total energy in the sidelobes and the energy in the main lobe, given by the following formula: A smaller ISLR indicates that the energy within the main lobe is more concentrated and there is less energy leakage. Indicates the main lobe.

[0065] Understandably, 3dB bandwidth, peak sidelobe ratio, and combined sidelobe ratio can be used to jointly optimize the design of the sensing matrix. This enables the modulated signal to possess good sensing performance in terms of time delay and Doppler dimensions. Specifically, refer to the following embodiment: In one possible embodiment, after evaluating the sensing performance of the sensing interleaved frequency division multiplexing waveform based on the index of the normalized ambiguity function, the transmitter 110 is further configured to: obtain the 3dB bandwidth, peak sidelobe ratio, and combined sidelobe ratio from the sensing receiver 120; and construct an optimization function for the sensing matrix based on the 3dB bandwidth, peak sidelobe ratio, and combined sidelobe ratio. ;in, , and Indicates the preset weighting coefficients; Indicates 3dB bandwidth; Indicates the peak-to-sidelobe ratio; Represents the overall sidelobe ratio; the optimization function of the sensing matrix is ​​solved using an engineering optimization algorithm to achieve... and Optimal.

[0066] Optionally, embodiments of this application may also select radar signal processing using linear frequency modulated signals, second / higher frequency modulated signals, bidirectional frequency modulated signals, phase-coded chirp signals, multi-frequency / multi-carrier chirp signals, and other types of matrices with sensing and channel control characteristics.

[0067] In one possible embodiment, target recognition is achieved through matched filtering, and the sensing performance of the interleaved frequency division multiplexing waveform is analyzed using a fuzzy function. This includes: analyzing the sensing performance of the interleaved frequency division multiplexing waveform in single-station or multi-station sensing scenarios using a fuzzy function; wherein: when the system is applied to a single-station sensing scenario, random data signals or constant modulus signals are used to analyze the sensing performance of the interleaved frequency division multiplexing waveform using a fuzzy function; wherein the random data signal is a randomly generated symbol sequence mapped to a time-domain signal by the interleaved frequency division multiplexing modulation matrix; the constant modulus signal is an all-1 sequence or a unit modulus signal; when the system is applied to a multi-station sensing scenario, pilot signals are used to analyze the sensing performance of the interleaved frequency division multiplexing waveform using a fuzzy function; wherein the pilot signal is a data signal agreed upon by the transmitter and the sensing receiver.

[0068] The random data signal is a randomly generated symbol sequence, which is mapped to a time-domain signal through a sensing interleaved frequency division multiplexing modulation matrix; the constant modulus signal is an all-one sequence or a unit modulus signal. The pilot signal is the data signal agreed upon by the transmitter and the sensing receiver.

[0069] For example, the pilot signal may include a constant mode signal.

[0070] As an example, a single-site sensing scenario refers to a scenario where the transmitter, communication receiver, and sensing receiver are located in the same location, for example, integrated in the same base station or device. In this case, random data signals or constant-mode signals can be used for analysis. Random data signals refer to randomly generated symbol sequences (such as QAM or PSK constellation points), which are mapped to time-domain signals through an sIFDM modulation matrix.

[0071] As shown in Figures 4 and 5, these are schematic diagrams of a single-station ISAC scenario proposed in an embodiment of this application. Figure 4 illustrates zero-delay truncation of different waveform ambiguity functions under a given random signal, while Figure 5 illustrates zero-Doppler truncation of different waveform ambiguity functions under a given random signal. For random data signals, the sIFDM ambiguity function exhibits sensing performance comparable to existing waveforms (such as OFDM, OTFS, and AFDM). Specifically, under zero-delay truncation and zero-Doppler truncation, the main lobe width and side lobe level of the sIFDM are similar to those of the reference waveform, indicating that it can achieve reliable sensing capability under random signals.

[0072] As another example, multi-station sensing scenarios refer to scenarios where the transmitter, communication receiver, and sensing receiver are separated, such as when the satellite and ground station are separated. The system achieves sensing by analyzing the correlation between the transmitted and received signals. In this case, constant mode signals can be used for sensing analysis, thereby reducing the impact of path loss and simplifying signal processing.

[0073] As shown in Figures 6 and 7, these figures are schematic diagrams of a multi-station ISAC scenario proposed in one embodiment of this application. Figure 6 illustrates zero-delay truncation of different waveform ambiguity functions under constant-mode signals (taking an all-1 signal as an example), while Figure 7 illustrates zero-Doppler truncation of different waveform ambiguity functions under an all-1 signal. Under constant-mode signals, the sIFDM ambiguity function exhibits superior performance under both zero-delay and zero-Doppler truncation: a narrow main lobe width and low side lobe levels. Figure 6 shows that the time delay resolution of sIFDM is comparable to that of OFDM, but with lower side lobes; Figure 7 shows that its Doppler resolution is close to that of OFDM, indicating that sIFDM can achieve high-precision distance and velocity estimation in multi-station scenarios.

[0074] Figure 8 shows a schematic diagram of an sIFDM signal transmission and recovery system provided in an embodiment of this application. First, the original digital information (message bits) to be transmitted is mapped into complex digital symbols by a mapper module according to the selected modulation scheme (such as QPSK, 16QAM, etc.), forming a symbol stream. The symbol stream then passes through a serial-to-parallel (S / P) conversion module, converting the high-speed symbol sequence into a low-speed symbol sequence, which is then input to the sIFDM modulation module. Specifically, through a sensing matrix... Inverse Fast Fourier Transform Matrix random permutation matrix and perception matrix The system obtains a time-domain signal, which is then converted back to a serial time-domain waveform via parallel-to-serial conversion (P / S). After adding a cyclic prefix, the time-domain signal is transmitted to the channel. At the communication receiver, the received signal is first processed by the cyclic prefix removal module, then converted to a parallel signal via serial-to-parallel conversion (S / P). This parallel signal enters the sIFDM demodulation module, where the inverse operation corresponding to the transmitter modulation is performed. After another parallel-to-serial conversion (P / S), the demodulated signal is input to a signal detector to achieve optimal recovery of the symbol sequence.

[0075] It should be noted that the sIFDM waveforms provided in the embodiments of this application are not limited to single-input single-output scenarios, but can be directly extended to linear systems such as multiple-input multiple-output (MIMO) scenarios and multi-user communication scenarios. Furthermore, they can also be extended to generalized linear systems that consider non-ideal constraints such as analog-to-digital conversion and clipped constant amplitude.

[0076] Furthermore, the sIFDM waveform can be combined with the encoding and decoding scheme. By utilizing the information matching principle between the detector and decoder in the receiver, the optimal encoding and decoding scheme can be designed to achieve optimal channel capacity performance under any input signal.

[0077] This application proposes a sensing-interleaved frequency division multiplexing waveform system for integrated communication and sensing, comprising: a transmitter modulating a symbol sequence into a time-domain signal using the modulation matrix of the sensing-interleaved frequency division multiplexing waveform, and transmitting the time-domain signal to the channel; a communication receiver receiving the received signal after transmission through the channel, and using a low-complexity detector to iteratively process the received signal to achieve optimal recovery of the symbol sequence; a sensing receiver achieving target recognition through matched filtering, and analyzing the sensing performance of the sensing-interleaved frequency division multiplexing waveform through fuzzy function analysis; since the modulation matrix of the sensing-interleaved frequency division multiplexing waveform consists of a sensing matrix and a random unitary matrix, and the modulation matrix is ​​a unitary matrix, the randomness of the equivalent channel is preserved; the time-domain signal is represented based on the sensing-interleaved frequency division multiplexing waveform, thus preserving the advantage of waveform randomness; since the low-complexity detector also predicts the asymptotic performance of the low-complexity detector through a state evolution method, optimal communication signal transmission and signal recovery can be achieved in various integrated communication and sensing scenarios; Furthermore, by employing discrete signal interpolation reconstruction and normalization processing through fuzzy functions, superior sensing performance can be achieved in various integrated communication and sensing scenarios. Based on this, this scheme can achieve optimal communication signal transmission, signal recovery, and superior sensing performance in various integrated communication and sensing scenarios while retaining the advantage of waveform randomness, thereby achieving a synergistic improvement in communication and sensing performance.

[0078] In summary, the embodiments of this application design an sIFDM waveform that can achieve optimal communication signal transmission and recovery, as well as excellent sensing performance, in various ISAC scenarios. Specifically: 1. An sIFDM waveform is designed by introducing auxiliary sensing unitary matrices at both ends of the IFDM modulation matrix, preserving the inherent randomness of the IFDM modulation matrix, and ensuring that the equivalent channel remains right-unitary. Simultaneously, a low-complexity CD-MAMP detection method is proposed to achieve optimal signal recovery performance, and the asymptotic performance of the sIFDM system can be accurately predicted using a state evolution method. This solves the problem of poor signal recovery performance caused by the lack of efficient signal detection in existing OFDM, OTFS, AFDM, and other waveforms.

[0079] 2. For single-station and multi-station sensing scenarios, fuzzy function analysis of sIFDM is presented under sensing conditions using random data signals and constant-mode signals, respectively. sIFDM achieves sensing performance comparable to existing waveforms under random signal conditions, while under constant-mode signals, by appropriately designing the sensing matrix, it can simultaneously achieve Doppler resolution similar to AFDM and time delay resolution similar to OFDM. This analysis can be directly extended to IBST, RM, and other modulations, filling the gap in fuzzy function analysis for IFDM, IBST, and RM, and providing the first-ever analysis of the sensing performance of these waveforms.

[0080] Therefore, compared with the prior art, the sensing interleaved frequency division multiplexing (sIFDM) model for integrated communication and sensing provided by the embodiments of this application has the following advantages: 1. The sIFDM waveform proposed in the embodiments of this application is the first waveform that can simultaneously achieve optimal recovery of communication signals and superior sensing performance. In terms of communication performance, it achieves significant performance gains compared to OFDM, OTFS, and AFDM. In terms of sensing performance, sIFDM achieves sensing performance comparable to existing waveforms under random signals, while under unit-mode signals, by reasonably designing the sensing matrix, it can simultaneously achieve Doppler resolution similar to AFDM and time delay resolution similar to OFDM.

[0081] 2. The sIFDM waveform proposed in the embodiments of this application allows for the design of an optimal sensing matrix using tools such as fuzzy functions, while ensuring data service communication performance. In contrast, the existing OFDM, OTFS, and AFDM waveform parameters are applicable to communication scenarios rather than being specifically designed for sensing scenarios, thus presenting a trade-off between communication and sensing performance.

[0082] Another embodiment of this application proposes a signal processing method for sensing interleaved frequency division multiplexing waveforms for integrated communication and sensing, 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 description. The implementation details of the signal processing method for sensing interleaved frequency division multiplexing waveforms for integrated communication and sensing proposed in this embodiment will be described in detail below. The following implementation details are provided for ease of understanding and are not necessary for implementing this solution.

[0083] The specific flow of the signal processing method for sensing interleaved frequency division multiplexing waveforms proposed in this embodiment can be shown in Figure 9, including steps 210 to 230.

[0084] For example, the signal processing method for sensing interleaved frequency division multiplexing waveforms for integrated communication and sensing proposed in this embodiment can be applied to the sensing interleaved frequency division multiplexing waveform system for integrated communication and sensing described in the above embodiment and the related descriptions in Figures 1 to 8.

[0085] Step 210: Using a transmitter, acquire the symbol sequence, and modulate the symbol sequence into a time-domain signal by sensing the modulation matrix of the interleaved frequency division multiplexing waveform, and send the time-domain signal to the channel.

[0086] The modulation matrix of the sensing interleaved frequency division multiplexing waveform consists of a sensing matrix and a random unitary matrix, and the modulation matrix is ​​a unitary matrix to preserve the randomness of the equivalent channel; the time-domain signal is represented based on the sensing interleaved frequency division multiplexing waveform.

[0087] Step 220: Use a communication receiver to receive the received signal after it has been transmitted through the channel, and use a low-complexity detector to iteratively process the received signal in order to achieve optimal recovery of the symbol sequence.

[0088] Among them, the low-complexity detector also predicts the asymptotic performance of the low-complexity detector through the state evolution method.

[0089] Step 230: Using a sensing receiver, target recognition is achieved through matched filtering, and the sensing performance of the sensing interleaved frequency division multiplexing waveform is analyzed through fuzzy function.

[0090] The fuzzy function employs discrete signal interpolation reconstruction and normalization.

[0091] For a detailed description of steps 210 to 230, please refer to the above embodiment of a sensing interleaved frequency division multiplexing waveform system for integrated communication and sensing, which will not be repeated here.

[0092] 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.

[0093] Another embodiment of this application proposes an electronic device, as shown in FIG10, including: a processor 31 and a memory 32, wherein the memory 32 stores instructions that the processor 31 can execute, and the processor 31 is configured to execute the instructions so that the electronic device can implement a signal processing method for sensing interleaved frequency division multiplexing waveforms oriented towards communication and sensing integration as described in the above method embodiment.

[0094] 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.

[0095] 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.

[0096] Another embodiment of this application proposes a computer-readable storage medium storing a computer program that, when executed by a processor, can implement a signal processing method for sensing interleaved frequency division multiplexing waveforms oriented towards integrated communication and sensing, as described in the above method embodiments.

[0097] 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.

[0098] 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 sensing interleaved frequency division multiplexing waveform system for integrated communication and sensing, characterized in that, include: The transmitter modulates the symbol sequence into a time-domain signal using the modulation matrix of the sensing interleaved frequency division multiplexing waveform and transmits the time-domain signal to the channel. The modulation matrix of the sensing interleaved frequency division multiplexing waveform consists of a sensing matrix and a random unitary matrix, with the modulation matrix being a unitary matrix to preserve the randomness of the equivalent channel. The time-domain signal is represented based on the sensing interleaved frequency division multiplexing waveform. The communication receiver receives the received signal after transmission through the channel and iteratively processes the received signal using a low-complexity detector to achieve optimal recovery of the symbol sequence. The low-complexity detector also predicts its asymptotic performance using a state evolution method. The sensing receiver performs target recognition through matched filtering and analyzes the sensing performance of the sensing interleaved frequency division multiplexing waveform using a fuzzy function. The fuzzy function employs a discrete signal interpolation reconstruction method and normalization processing.

2. The system according to claim 1, characterized in that, The specific implementation of modulating the interleaved frequency division multiplexing waveform into a time-domain signal using a modulation matrix and transmitting the time-domain signal to the channel includes: transmitting the time-domain signal. It can be expressed by the following formula: ;in, Represents a sequence of symbols; The modulation matrix representing the sensing interleaved frequency division multiplexing waveform; the modulation matrix representing the sensing interleaved frequency division multiplexing waveform. Represented as: ;in, and To perceive unitary matrices, And satisfy ； The unitary matrix represents a random matrix, which is obtained based on the interleaving matrix and the transformation matrix; the modulation matrix... It is a unitary matrix, that is, it satisfies ； Indicates the length of the symbol vector; in the case of time-domain signals After introducing the cyclic prefix, a time-domain signal carrying the cyclic prefix is ​​sent to the channel. The cyclic prefix is ​​used to mitigate multipath interference delay, and its length is not less than the maximum channel delay. The specific implementation of receiving the received signal after channel transmission includes: receiving the received signal after channel transmission. It can be expressed by the following formula: ;in, ， Indicates a time-varying multipath channel. This represents Gaussian white noise.

3. The system according to claim 2, characterized in that, The low-complexity detector is a cross-domain memory approximation message-passing detector, comprising: a time-domain linear estimation module, a cross-domain transformation module, and a symbol-domain nonlinear estimation module; the time-domain linear estimation module generates a time-domain estimated signal based on a memory matched filter and orthogonalization operation; the cross-domain transformation module converts the time-domain estimated signal to the symbol domain through the inverse of the modulation matrix; the symbol-domain nonlinear estimation module performs symbol estimation based on a minimum mean square error demodulator; wherein, the low-complexity detector ensures that the estimation error follows an asymptotically independent and identically distributed Gaussian distribution through iterative updates and damping operations, achieving Bayesian optimal performance.

4. The system according to claim 3, characterized in that, The method of iteratively processing the received signal using a low-complexity detector to achieve optimal recovery of the symbol sequence includes: a time-domain linear estimation module. The symbolic domain nonlinear estimation module is Time-domain linear estimation module Including memory matched filters Modules, orthogonalization module and damping operation module, symbolic domain nonlinear estimation module Including symbol-by-symbol minimum mean square error demodulator Orthogonalization module; utilizing memory matched filter The module, orthogonalization module, and damping operation module are based on the received signal. and the prior information of the transmitted signal updated by the symbol domain nonlinear estimation module Iterative index from Start, Initialization To enable memory matched filters output signal satisfy: ;in, Represents the normalization coefficient. Represents the orthogonalization coefficients; Indicates preceding The combination of signals estimated in each iteration; Indicates based on input Low-complexity memory matched filter Specifically, it is expressed by the following formula: ； ;in, ； ； This represents the scaling factor. ， express The largest eigenvalue, express The smallest eigenvalue, Represents weighting coefficients; memory matched filter The output depends on the time-varying multipath channel. and ;in, Through the and prior information The damping operation yields the following formula: ;in, Denotes the damping vector, and Then the memory matched filter Output time-domain estimation error Specifically, it is expressed by the following formula: ;in, The length of the transmitted signal; the cross-domain transformation module, based on the inverse matrix of the modulation matrix of the sensing interleaved frequency division multiplexing waveform. A cross-domain operation from the time domain to the symbol domain is performed to obtain the nonlinear estimation module to be input into the symbol domain. input signal Input variance The specific implementation includes: ； ;in, The output variance of the time-domain linear estimation module; 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 error The specific implementation includes: ； ;in, Represents the normalization coefficient. Indicates the orthogonalization parameters; ， Indicates signal The set of discrete constellation points that obey Constraints; Cross-domain transform module, based on the modulation matrix of the perceptual interleaved frequency division multiplexing waveform. A cross-domain operation is performed from the symbol domain to the time domain to obtain the result to be input into the time-domain linear estimation module. input signal Input variance The specific implementation includes: ； 。 5. The system according to claim 4, characterized in that, The state evolution method represents the prediction of the asymptotic performance of a low-complexity detector using the covariance matrix; specifically, the prediction of the asymptotic performance of the low-complexity detector using the state evolution method includes: obtaining the temporal estimation error covariance matrix. And the symbolic domain estimation error covariance matrix ; through the mean square error function and The target estimation error covariance matrix is ​​iteratively updated to predict the asymptotic performance of the low-complexity detector; where the mean square error function in the time domain... Mean square error function in the sign domain This can be expressed by the following formula: ； ;in, ， The covariance matrix representing the time-domain estimation error; ， and The covariance matrix represents the estimation error in the symbolic domain.

6. The system according to claim 1, characterized in that, The method of achieving target recognition through matched filtering and analyzing the sensing performance of the interleaved frequency division multiplexing waveform using fuzzy functions includes: discrete signals based on the interleaved frequency division multiplexing waveform. By defining discrete fuzzy functions To analyze the waveform's time delay and Doppler sensing performance; among them, the discrete fuzzy function Represented as: ;in, Indicates integer delay. Indicates an integer Doppler index; Represents a time-domain signal sequence. Indicates signal length; by introducing an oversampling factor in the time delay dimension. Oversampling factor and Doppler dimension For discrete signals Interpolation reconstruction is performed to obtain a high-precision interpolated discrete sequence. This leads to the high-precision discrete fuzzy function. ： ； ;in, ； ； Represents the smoothing window function; This indicates half the length of the windowed sinc function; and This represents the oversampled index; further, it utilizes the time delay normalization parameter. and Doppler normalization parameters High-precision discrete fuzzy function Mapping to a normalized coordinate system yields the normalized fuzzy function. And expressed by the following formula: ;in, Indicates the time delay range. This represents the Nyquist-constrained Doppler interval; the sensing performance of the perceptual interleaved frequency division multiplexing waveform is evaluated based on the index of the normalized fuzzy function; the index includes 3dB bandwidth, peak sidelobe ratio and composite sidelobe ratio.

7. The system according to claim 6, characterized in that, After evaluating the sensing performance of the interleaved frequency division multiplexing waveform based on the index of the normalized ambiguity function, the transmitter is also used to: obtain the 3dB bandwidth, peak sidelobe ratio, and combined sidelobe ratio from the sensing receiver; and construct an optimization function for the sensing matrix based on the 3dB bandwidth, peak sidelobe ratio, and combined sidelobe ratio. ;in, 、 and Indicates the preset weighting coefficients; Indicates 3dB bandwidth; Indicates the peak-to-sidelobe ratio; Represents the overall sidelobe ratio; the optimization function of the sensing matrix is ​​solved using an engineering optimization algorithm to achieve... and Optimal.

8. The system according to claim 1, characterized in that, The method of achieving target recognition through matched filtering and analyzing the sensing performance of interleaved frequency division multiplexing waveforms through fuzzy functions includes: analyzing the sensing performance of interleaved frequency division multiplexing waveforms in single-station or multi-station sensing scenarios using fuzzy functions; wherein: when the system is applied to a single-station sensing scenario, random data signals or constant modulus signals are used to analyze the sensing performance of interleaved frequency division multiplexing waveforms through fuzzy functions; wherein, the random data signal is a randomly generated symbol sequence, which is mapped to a time-domain signal through the interleaved frequency division multiplexing modulation matrix; the constant modulus signal is an all-1 sequence or a unit modulus signal; when the system is applied to a multi-station sensing scenario, pilot signals are used to analyze the sensing performance of interleaved frequency division multiplexing waveforms through fuzzy functions; wherein, the pilot signal is the data signal agreed upon by the transmitter and the sensing receiver.

9. A signal processing method for sensing interleaved frequency division multiplexing waveforms for integrated communication and sensing, applied to the system as described in any one of claims 1 to 8, characterized in that, include: A transmitter acquires a symbol sequence, modulates it into a time-domain signal using the modulation matrix of the perceptual interleaved frequency division multiplexing (FDM) waveform, and transmits the time-domain signal to the channel. The modulation matrix of the perceptual interleaved FDM waveform consists of a perceptual matrix and a random unitary matrix, with the modulation matrix being a unitary matrix to preserve the randomness of the equivalent channel. The time-domain signal is represented based on the perceptual interleaved FDM waveform. A communication receiver receives the received signal after transmission through the channel, and a low-complexity detector iteratively processes the received signal to achieve optimal recovery of the symbol sequence. The low-complexity detector also uses a state evolution method to predict its asymptotic performance. Using the perceptual receiver, matched filtering is used to achieve target recognition, and the perceptual performance of the perceptual interleaved FDM waveform is analyzed using a fuzzy function. The fuzzy function employs a discrete signal interpolation reconstruction method and normalization processing.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it can realize the signal transmission method of the sensing interleaved frequency division multiplexing waveform for communication and sensing integration as described in claim 9.

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