Multi-target direction of arrival estimation method for single Rydberg atom receiver

Abstract

The invention discloses a single Rydberg atom receiver multi-target direction of arrival estimation method based on spatial resolution fluorescence spectrum analysis. According to the method, a modulation pattern formed by interference of a plurality of radio frequency signals and a local oscillation field in the steam chamber is obtained through spatial resolution fluorescence imaging, traditional lumped power measurement is replaced, and therefore multi-target spatial information is completely reserved. On the basis, complex spatial modulation caused by a plurality of signals is linearized into superposition of sine waves with different spatial frequencies by utilizing a strong local oscillation condition, so that a multi-target direction-of-arrival estimation problem is converted into a classical frequency spectrum estimation problem. And finally, through spectrum analysis, extracting each spatial frequency and calculating a corresponding direction of arrival. According to the method, through the core steps of spatial resolution imaging, linear modeling and spectral analysis, the limitation that a single Rydberg atom receiver can only estimate a single target is fundamentally broken through, and simultaneous estimation of the directions of arrival of a plurality of signal sources by using a single receiver is realized.

Description

Technical Field

[0001] This application relates to the fields of quantum sensing, precision measurement and wireless communication technology, specifically to a method and system for estimating the direction of arrival of radio waves by utilizing the high sensitivity response characteristics of Rydberg atoms to radio frequency fields, and in particular, a method and system for simultaneously estimating the direction of arrival of multiple signal sources using only a single Rydberg atom receiver. Background Technology

[0002] Direction of Arrival (DoA) estimation is a key technology in radar, wireless positioning, communications, and spectrum monitoring. Traditional methods rely on arrays of physically separated antenna elements to invert the DoA by measuring the phase difference of signals at various points in space. However, this phased array system based on conductor antennas has inherent drawbacks such as sensitivity limited by thermal noise, bandwidth limitation, system complexity, and high cost.

[0003] In recent years, quantum sensors based on Rydberg atoms have provided a revolutionary new approach for radio frequency (RF) field detection. Rydberg atoms are atoms excited to high principal quantum number levels, possessing extremely large electric dipole moments and being highly sensitive to external RF electric fields. By detecting the Stark shift of atomic energy levels under the influence of an RF field using optical methods (such as electromagnetically inductive transparency, EIT), the amplitude, phase, and frequency of the RF field can be measured with high precision. Compared to antennas, their core advantages include near-quantum-limit sensitivity, inherent immunity to thermal noise, and the ability to tune across an ultra-wide frequency band from MHz to THz without altering the hardware structure.

[0004] Research on DoA estimation based on Rydberg atoms subsequently unfolded. Early methods followed the traditional array approach, using multiple spatially separated atomic gas cells as sensor units to form an array. However, this also led to high system complexity and the need for precise calibration. Later, a DoA estimation method based on single-atom gas cells emerged: utilizing the standing wave pattern formed by the interference of the signal field and the local oscillator field within the gas cell, the overall transmission power of the probe laser was modulated, and the DoA of a single signal was inverted through an optimized algorithm. However, this method has two fundamental limitations: first, its model and algorithm are difficult to extend to multi-signal scenarios, essentially only capable of handling single targets; second, its accuracy is heavily dependent on the physical length L of the gas cell, making it incompatible with broadband operation (different frequencies require gas cells of different lengths). The root cause is that this method only measures the total power after spatial integration, losing spatial resolution information.

[0005] Therefore, in response to the demands of 6G and future integrated communication and sensing, there is an urgent need to develop a new technology that can overcome the above-mentioned shortcomings and achieve multi-target, broadband, and high-precision DoA estimation using a single Rydberg atom receiver. Summary of the Invention

[0006] The purpose of this application is to provide a method and system for estimating the direction of arrival (DOA) of multiple targets using a single Rydberg atom receiver based on spatially resolved fluorescence spectral analysis, in order to solve the problems of existing single-receiver methods being unable to handle multiple targets and being limited by specific wavelength-cell length constraints. To achieve the above objective, this application adopts the following technical solution.

[0007] In a first aspect, embodiments of this application provide a method for estimating the direction of arrival (DOA) of multiple targets using a single Rydberg atom receiver, including:

[0008] Based on a single vapor chamber containing atomic vapor, electromagnetic induction transparency conditions are constructed using probe lasers and coupling lasers. By superimposing the local oscillator radio frequency field with the incident radio frequency signal field to be measured, a fluorescence spatial distribution associated with the spatial distribution of the total radio frequency field intensity is formed in the vapor chamber.

[0009] A lateral fluorescence image of the steam chamber is acquired, and based on the fluorescence image, a calibrated signal measurement sequence reflecting the spatial variation of the local atomic absorption coefficient within the steam chamber is calculated.

[0010] The calibrated signal measurement sequence is modeled as a signal model consisting of the linear superposition of multiple spatial frequency components.

[0011] A spectrum estimation algorithm based on a linear prediction model is used to estimate each spatial frequency component from the signal model;

[0012] Based on the mapping relationship between the spatial frequency components and the direction of arrival, the direction of arrival of each of the multiple incident radio frequency signals is calculated.

[0013] Furthermore, the field strength of the local oscillator radio frequency field is configured to be greater than a preset multiple of the sum of the field strengths of all incident radio frequency signals to be measured, so that the nonlinear relationship between the local atomic absorption coefficient and the total radio frequency field strength can be linearized, and thus the calibrated signal measurement sequence can be expressed as a linear combination of multiple spatial frequency cosine terms.

[0014] Further, the calibrated signal measurement sequence is obtained through the following steps:

[0015] With only the local oscillator radio frequency field turned on, the first fluorescence spatial distribution is obtained and the first atomic absorption coefficient spatial distribution is calculated. Based on a preset family of virtual spatial window functions, the first set of measurement values ​​is obtained.

[0016] Simultaneously turn on the local oscillator radio frequency field and all incident radio frequency signals to be measured, obtain the second fluorescence spatial distribution and calculate the second atomic absorption coefficient spatial distribution, and obtain the second set of measurement values ​​based on the same virtual space window function family;

[0017] The difference between the second set of measurements and the first set of measurements is used to eliminate the DC offset, thus obtaining the calibrated signal measurement sequence.

[0018] Furthermore, the spectrum estimation algorithm based on the linear prediction model is the Prony method, specifically including:

[0019] Construct a Hankel matrix using the calibrated signal measurement sequence;

[0020] The linear prediction coefficients are obtained by solving the linear least squares problem;

[0021] Construct a characteristic polynomial with the predicted coefficients as parameters, and solve for the roots of the polynomial;

[0022] Roots with amplitudes close to unit 1 are selected from the roots, and their arguments correspond to the estimated values ​​of the spatial frequency components.

[0023] Furthermore, the length of the vapor chamber is independent of the wavelength of the incident radio frequency signal to be measured. A longer vapor chamber length directly corresponds to a larger effective sensing aperture, higher spectral resolution, and higher direction-of-arrival accuracy.

[0024] Furthermore, the process of resolving the calibrated signal measurement sequence includes logarithmic processing of the fluorescence image to directly recover the spatial distribution of the local atomic absorption coefficients, specifically: ;in, Indicates the spatial distribution of fluorescence intensity; This represents the spatial distribution of local atomic absorption coefficients.

[0025] Furthermore, it also includes:

[0026] Based on the estimated direction of arrival and combined with the amplitude information of the spatial frequency components of the signal, the relative intensity or power of multiple incident radio frequency signals is estimated.

[0027] Secondly, embodiments of this application provide a multi-target direction-of-arrival estimation system for a single Rydberg atom receiver, comprising:

[0028] The atomic sensing unit includes a vapor chamber filled with alkali metal atomic vapor, which is used to generate spatially correlated fluorescence under the combined action of laser and radio frequency field;

[0029] The optical excitation and imaging unit includes a laser system for generating probe lasers and coupling lasers, and an imaging device for acquiring the spatial distribution of fluorescence in the vapor chamber from the side.

[0030] The radio frequency field application unit includes a local oscillator source and a transmitting antenna for generating a strong local oscillator radio frequency field, and a coupling device for guiding the incident radio frequency signal to be measured into the steam chamber.

[0031] The signal processing and control unit is configured as follows:

[0032] The optical excitation and imaging unit and the radio frequency field application unit are controlled to perform calibration measurements and actual measurements;

[0033] The system receives image data from the imaging device and executes the processing flow of the direction of arrival estimation method described in any of the preceding claims, outputting direction of arrival estimation values ​​for multiple incident radio frequency signals.

[0034] Thirdly, embodiments of this application provide an electronic device, including: one or more processors;

[0035] A memory for storing one or more programs; when the one or more programs are executed by the one or more processors, the one or more processors are able to implement the steps in the direction-of-arrival estimation method described in any of the preceding claims.

[0036] Fourthly, embodiments of this application provide a computer-readable medium storing a computer program, which, when executed by a processor, can implement the steps in the direction-of-arrival estimation method described in any of the preceding claims.

[0037] This application discloses a method for estimating the direction of arrival (DOA) of multiple targets using a single Rydberg atom receiver based on spatially resolved fluorescence spectral analysis. This method addresses the problem of existing single-atom receivers losing spatial information and failing to distinguish multiple targets due to lumped power measurement. First, it acquires the spatially resolved fluorescence distribution modulated by a radio frequency field within a steam chamber through imaging, replacing the traditional single power value measurement, thus completely capturing the spatial interference pattern containing information about multiple targets. Next, the acquired one-dimensional spatial fluorescence signal sequence is linearized and modeled, transforming it into a linear superposition of multiple sinusoidal components with different spatial frequencies. This transforms the multi-target ODA problem into a classic problem of estimating multiple sinusoidal wave frequencies. Finally, spectral analysis is used to simultaneously extract each spatial frequency component and map it to its corresponding ODA. Through the core steps of "spatially resolved imaging - linearization modeling - spectral analysis," this method fundamentally overcomes the limitation of a single Rydberg atom receiver being able to estimate only a single target, achieving simultaneous estimation of the ODA of multiple signal sources using a single receiver. Attached Figure Description

[0038] Figure 1 A core flowchart of a multi-target direction-of-arrival estimation method for a single Rydberg atom receiver provided in this application embodiment;

[0039] Figure 2 A set of diagrams for verifying the linearization hypothesis provided in the embodiments of this application;

[0040] Figure 3 A comparison of estimation accuracy under strong and weak local oscillators provided for embodiments of this application, and a series of graphs showing the relationship between estimation accuracy and local oscillator strength;

[0041] Figure 4 A schematic diagram of the module structure of a multi-target direction-of-arrival estimation system with a single Rydberg atom receiver provided in an embodiment of this application;

[0042] Figure 5 This is a structural block diagram of an electronic device provided in an embodiment of this application. Detailed Implementation

[0043] To enable those skilled in the art to better understand the technical solutions of this application, exemplary embodiments of this application are described below with reference to the accompanying drawings, including various details of the embodiments of this application to aid understanding. These should be considered merely exemplary. Therefore, those skilled in the art should recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of this application. Similarly, for clarity and conciseness, descriptions of well-known functions and structures are omitted in the following description. Unless otherwise specified, the various embodiments of this application and the features within those embodiments can be combined with each other.

[0044] As used herein, the term "and / or" includes any and all combinations of one or more of the associated enumerated entries. The terminology used herein is for describing particular embodiments only and is not intended to limit the application. As used herein, the singular forms "a" and "the" are also intended to include the plural forms, unless the context clearly indicates otherwise. It should also be understood that when the terms "comprising" and / or "made of" are used herein, the presence of the stated feature, integral, step, operation, element, and / or component is specified, but the presence or addition of one or more other features, integrals, steps, operations, elements, components, and / or groups thereof is not excluded. Terms such as "connected" or "linked" are not limited to physical or mechanical connections but can include electrical connections, whether direct or indirect.

[0045] Unless otherwise specified, all terms used in this application (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art. It should also be understood that terms such as those defined in commonly used dictionaries should be interpreted as having a meaning consistent with their meaning in the context of the relevant art and this application, and will not be interpreted as having an idealized or overly formal meaning, unless expressly so defined in this application.

[0046] Brief Analysis of Technical Terms:

[0047] (1) RF field: It is an abbreviation for radio frequency field, which refers to the electromagnetic field formed when electromagnetic waves with a frequency range of 3 kHz to 300 GHz propagate in space. This electromagnetic field is generated when alternating current passes through a conductor (such as an antenna), and contains mutually perpendicular oscillating electric and magnetic field components. It can propagate in space or vacuum in the form of waves without a medium.

[0048] (2) Direction of Arrival (DoA): This is a core parameter used in array signal processing to determine the direction of arrival of spatial electromagnetic waves or sound waves. Its theoretical framework is based on spatial spectrum estimation technology and encompasses core methods such as the MUSIC algorithm, ESPRIT algorithm, and propagation operator algorithm, enabling high-precision multi-source positioning of coherent and broadband signals. The hardware implementation employs a DSP+FPGA hybrid architecture and uniform array design to meet the real-time processing requirements of scenarios such as radar reconnaissance and mobile communication. This technology has strategic value in the field of electronic warfare, suppressing interference through spatial filtering, and also demonstrates application potential in civilian fields such as 5G network optimization and sonar detection.

[0049] (3) Rydberg atom: Atoms whose valence electrons are excited to high excited state energy levels, and whose structure is described by the Rydberg energy level formula. They are also called highly excited atoms, or giant atoms or fat atoms. Rydberg atoms have many unique properties, such as large radius, small binding energy and long lifetime. Therefore, they have been used as probes for basic research and various applications, and have gradually developed into an independent discipline.

[0050] (4) Rydberg atom receiver: This is a new type of sensor that uses the quantum properties of Rydberg atoms to detect and receive electromagnetic wave signals. It represents a major shift in electromagnetic sensing technology from traditional electronics to quantum technology. The core principle of this receiver is based on the "energy level transition" phenomenon of Rydberg atoms.

[0051] (5) Local Oscillator Field: This is short for "local oscillator field," referring to the stable high-frequency electromagnetic field (or signal) generated by the local oscillator (LO) inside the equipment in radio, communication, or measurement systems, used for mixing or interfering with external signals. Its core function is to serve as a local reference frequency, mixing with the signal to be processed (such as a received radio frequency signal or a terahertz wave to be measured) to achieve frequency conversion or phase comparison. This process is a key component in superheterodyne receivers, spectrum analyzers, radar systems, and high-precision physical measurement devices (such as atomic spectrum analysis).

[0052] (6) Local atomic absorption coefficient: refers to the absorption coefficient of a specific element at a specific wavelength (usually its resonance line) in atomic absorption spectroscopy.

[0053] (7) Prony method: This is a signal analysis method that fits equally spaced sampled data by linear combination of exponential terms. This method uses a complex exponential function to construct a mathematical model and extract parameters such as amplitude, phase, damping factor and frequency from the signal.

[0054] (8) Hankel matrix: A special matrix in which all elements on each subdiagonal are equal. It was proposed and named by the German mathematician H. Hankel. This matrix has important application value in the field of control science and engineering. It describes the dynamic characteristics of linear systems in the form of a block matrix and together with the reachability matrix and the observability matrix, it constitutes the necessary and sufficient conditions for the realization of the system.

[0055] Direction of arrival (DoA) estimation is a core function of radar, navigation, and modern wireless communication systems. Traditionally, DoA estimation relies on a phased array of spatially separated antennas to measure the relative phase of the incident wavefront. However, conventional conductor antennas have inherent limitations in terms of sensitivity, thermal noise immunity, and broadband tuning capability.

[0056] In recent years, Rydberg atom receivers have emerged as a revolutionary wireless communication and sensing technology, breaking through the sensitivity limits of traditional electromagnetic sensors. This sensor utilizes the properties of Rydberg atoms, such as alkali metal rubidium (Rb) atoms excited to high principal quantum numbers, exhibiting large dipole moments and strong responses to incident radio frequency (RF) fields. This quantum-based approach can measure the amplitude, phase, frequency, and polarization of RF fields by optically probing energy level shifts within atomic vapor. Key advantages compared to traditional conductor antennas include immunity to thermal noise and the ability to achieve ultra-wideband tuning from MHz to THz without structural modifications.

[0057] In the field of DoA estimation based on Rydberg atoms, existing methods can be mainly divided into two categories: array-based methods and single-receiver-based methods.

[0058] Following the traditional phased array paradigm, early research on Rydberg DoA estimation primarily relied on arrays consisting of two or more atom receivers. For example, Robinson et al. proposed using Rydberg atom sensor arrays to determine the angle of arrival of a radio frequency source; Mao et al. studied digital beamforming and receiver arrays based on Rydberg field probes. However, array methods require multiple independent atom receiver units, resulting in high system complexity, high cost, and the need for precise array calibration.

[0059] Recently, a novel method for DoA estimation using a single Rydberg atom receiver has been proposed. This technique cleverly utilizes the interference pattern formed between the incident RF signal and the local oscillator (LO) field within a vapor chamber. By measuring the total transmitted power of the probe laser (modulated by the spatially varying field intensity along the vapor chamber), the DoA of a single incident signal can be recovered using a particle swarm optimization (PSO) algorithm.

[0060] However, the single-receiver method based on integrated power measurement faces the following challenges in broader practical applications:

[0061] (1) This method is mainly designed for estimating the DoA of a single signal, because the complexity of the optimization problem increases significantly in multi-signal scenarios.

[0062] (2) The accuracy of this method is sensitive to a specific steam chamber length, which in turn depends on the wavelength of the signal. This requirement limits the broadband operation capability of the Rydberg sensor, as the physical hardware needs to be replaced for different frequencies. Specifically, to ensure a monotonic response, the steam chamber length must meet certain requirements. The constraints are contradictory across different operating frequencies.

[0063] The core model of existing technology is based on the following principle: for a single incident plane wave signal With the local vibration field The superposition of the two forces results in a total RF field intensity of: ;in, It is the spatial frequency of the interference pattern. It's the phase difference. Existing integrated power methods measure a single value. Estimating DoA is essentially an integration of spatial information, but it loses spatial resolution information, making it difficult to distinguish multiple targets.

[0064] In the context of 6G and future wireless communications, the demand for high-precision, multi-target, and wideband DoA estimation is increasing. Rydberg atom receivers, with their unique quantum properties—immunity to thermal noise and ultra-wideband tunability—have the potential to become a key technology for next-generation wireless sensing systems.

[0065] However, existing Rydberg-based DoA estimation methods either require complex receiver arrays or are limited by single-target and narrowband constraints. In particular, single-receiver methods based on integrated power measurements fail to fully utilize spatially resolved information, making multi-target detection impossible, and are subject to strict wavelength dependence on the length of the steam chamber, thus limiting their broadband application potential.

[0066] Therefore, there is an urgent need to develop a new method that can achieve multi-objective DoA estimation using a single Rydberg atom receiver, while simultaneously removing the vapor chamber length limitation to restore full-bandwidth operation capability.

[0067] refer to Figure 1 One embodiment of this application proposes a method for estimating the direction of arrival (DOA) of multiple targets using a single Rydberg atom receiver. This method mainly includes the following five core steps.

[0068] S1. Based on a single vapor chamber containing atomic vapor, electromagnetic induction transparency conditions are constructed using probe lasers and coupling lasers. Then, through the superposition of the local oscillator radio frequency field and the incident radio frequency signal field to be measured, a fluorescence spatial distribution correlated with the spatial distribution of the total radio frequency field intensity is formed within the vapor chamber. This step aims to build the core physical system and generate fluorescence carrying multi-target spatial information, as detailed below.

[0069] 1.1 Construction of Atom Sensing Unit:

[0070] A cylindrical glass vapor chamber containing a rarefied rubidium-87 atomic gas is used as the core sensor. The length L of the vapor chamber is a key but flexible design parameter, chosen based on the required angular resolution and physical size constraints, without being tied to the radio frequency wavelength λ as in existing technologies. RF Binding. Atomic density controlled at... To achieve good optical thickness and fluorescence signal intensity.

[0071] 1.2 Implementation of the four-level optical excitation scheme:

[0072] Configured with two laser beams:

[0073] Probe laser: wavelength 780 nm, frequency locked in the ground state of rubidium atoms. F=2> (denoted as |1>) to intermediate state The transition of F=3> (denoted as |2>).

[0074] Coupled laser: wavelength 480 nm, propagating in the opposite direction to the probe laser, frequency locked at |2〉 to the highest excited Rydberg state. (For example, n=60, denoted as |3〉) on the transition, the coupling Rabi frequency MHz; Coupling detuning kHz.

[0075] These two laser beams establish electromagnetic induction transparency (EIT) conditions in the steam chamber, making the steam transparent to the probe light.

[0076] 1.3 Implementation of the RF field application and local oscillator-dominant mechanism:

[0077] Local oscillation field (LO): Generated by a frequency synthesizer with a frequency of f. LO Radio frequency signals, such as f LO =2.03 GHz, this frequency corresponds to the high-excitation Rydberg state |3〉 to the adjacent Rydberg state (denoted as |4〉) transition resonance. Via a horn antenna at a fixed, known angle θ LO Irradiate the steam chamber at a 90° angle.

[0078] Signal field: M far-field plane wave radio frequency signals to be measured, at an unknown angle {θ} m (m=1,2,...,M) incident.

[0079] Key configuration: The electric field amplitude A of the local oscillator must be ensured. LO Significantly greater than the sum of the amplitudes of all incident signals, i.e., strictly satisfies A. LO >>ΣA m In practice, A is usually required to... LO It is more than 10 times the expected total signal amplitude. This is the "local oscillator-dominated mechanism," which is a prerequisite for subsequent linearization processing.

[0080] 1.4 Physical process of fluorescence generation:

[0081] The incident radio frequency field perturbs the energy level of the highly excited Rydberg state |3〉 through the alternating Stark effect, thereby altering the EIT condition. This modulates the repolarization χ of the atomic vapor at the probe laser frequency, which in turn modulates the local atomic absorption coefficient α(x). The absorbed probe laser energy is re-emitted as 780 nm fluorescence through the spontaneous emission of atoms from the |2〉 state. Therefore, the distribution of fluorescence intensity at various points in space is spatially modulated by the total local radio frequency field intensity.

[0082] S2. Acquire a lateral fluorescence image of the steam chamber, and based on this fluorescence image, calculate a calibrated signal measurement sequence reflecting the spatial variation of the local atomic absorption coefficient within the steam chamber. This step transforms the spatial fluorescence distribution into a discrete signal sequence that can be used for analysis through imaging and signal processing, as detailed below.

[0083] 2.1 Spatial-Resolved Fluorescence Imaging:

[0084] On the side of the vapor chamber, an sCMOS scientific camera, equipped with a narrowband interference filter with a center wavelength of 780 nm, was used to acquire spontaneous emission fluorescence images. The filter was used to suppress background noise such as scattered light from the 480 nm coupled laser.

[0085] 2.2 Conversion from image to absorption coefficient sequence:

[0086] The acquired two-dimensional fluorescence images are processed as follows:

[0087] By integrating or averaging the image pixels along the length of the steam chamber (x-axis) vertically (y-axis direction), a one-dimensional fluorescence intensity distribution can be obtained. .

[0088] According to physical relationships ,right Numerical logarithmic operations and differentiation (such as using the central difference method) yield a discrete sequence α[n] reflecting the local atomic absorption coefficient variation, where n corresponds to the spatial position x. n .

[0089] 2.3 Virtual Channel Construction and Sampling Constraints:

[0090] To avoid aliasing and ensure resolution, the continuous signal α[n] needs to be converted into discrete measurement values ​​y[n] that conform to the sampling theorem.

[0091] Design a virtual space window: Select the rectangular window function w n (x), with a width of W and a center position of x. n =n*Δx, where Δx is the spatial sampling interval.

[0092] Applying the sampling constraint theorem: To ensure unambiguous estimation of spatial frequency k (corresponding to DoA), the following must be satisfied:

[0093] Δx≤λ RF / (2*|sinθ max -sinθ LO |) (Prevents frequency aliasing)

[0094] W≥2λ RF / |sinθ min -sinθ LO (Ensure frequency resolution)

[0095] Among them, [θ min , θ max [ ] represents the expected range of DoA estimates.

[0096] Calculate the channel measurement value: The measurement value of the nth virtual channel is calculated as y[n] = Σα[j] * w n (x j That is, a weighted average of α[j] falling within the window.

[0097] 2.4 Calibrate measurements to eliminate DC offset (this step is crucial for improving signal-to-noise ratio and accuracy):

[0098] Calibration Measurement: Turn off all target signal sources and only turn on the local oscillator. Acquire fluorescence images and repeat steps 2.2-2.3 for processing to obtain the background measurement sequence y. cal [n]. This sequence mainly includes the system's inherent DC response α0 and static spatial inhomogeneity.

[0099] Signal Measurement: Under the same local oscillator field conditions, all target signals are activated. Images are acquired and processed again to obtain the total measurement sequence y.sig [n].

[0100] Obtaining a clean signal: Calculate the calibrated signal sequence s[n] = y sig [n]-y cal [n]. This operation effectively eliminates the constant term α0 in the model, resulting in a sequence containing only the modulated signal caused by the target signal.

[0101] S3. Model the calibrated signal measurement sequence as a signal model composed of the linear superposition of multiple spatial frequency components. This step establishes the calibrated signal sequence s[n] as a linear superposition mathematical model, which is the basis for transforming the problem into spectrum estimation, as detailed below.

[0102] 3.1 Signal Model Derivation:

[0103] Based on the local oscillator-dominant mechanism (A) in step S1 LO >>ΣA m The total radio frequency field strength can be approximated as:

[0104]

[0105] Among them, s LO =A LO 2 k m =k RF (sinθ m -sinθ LO ) is the key spatial frequency corresponding to the m-th signal, Δφ m =φ m -φ LO .

[0106] Under these conditions, the response of the local atomic absorption coefficient α(x) to s(x) can be expanded and linearized using a first-order Taylor series, yielding:

[0107]

[0108] Among them, C m ∝2A LO A m .

[0109] 3.2 Final Measurement Model:

[0110] Combining the calibration operation in step S2 (subtracting α0), the final model of the calibrated signal sequence is obtained:

[0111]

[0112] This model shows that s[n] is M integers with different spatial frequencies {k m}, Amplitude {Cm} and initial phase {Δφ m The linear superposition of real cosine signals}. Thus, the multi-objective DoA estimation problem has been successfully transformed into a classical spectral estimation problem of estimating the parameters of multiple sinusoidal components from a one-dimensional signal sequence s[n].

[0113] S4. Using a spectrum estimation algorithm based on a linear prediction model, estimate each spatial frequency component from the signal model. This step employs the high-resolution Prony method to accurately extract each spatial frequency component {k} from s[n]. m The details are as follows.

[0114] 4.1 Constructing a linear prediction model:

[0115] Suppose that s[n] is generated by the sum of P complex exponential functions (for M real cosine signals, P = 2M). This sequence satisfies a P-order linear prediction equation:

[0116] ; where a[0]=1.

[0117] 4.2 Solving for the prediction coefficients {a[p]}:

[0118] Using N samples of s[n] (N>P), construct a (N-P)×(P+1) Hankel matrix S. Solve the least squares problem min||S*a|| 2 (where a=[a[1],...,a[P]] T ), thus obtaining the linear prediction coefficient vector a.

[0119] 4.3 Obtaining frequencies by finding roots:

[0120] Construct the characteristic polynomial from the prediction coefficients:

[0121] z P +a[1]z {P－1} +...+a[P-1]z+a[P]=0

[0122] Find the P roots {z} of this polynomial. i For an unattenuated pure sinusoidal signal, each frequency component corresponds to a pair of conjugate complex roots z with amplitudes close to 1. i and z i *

[0123] 4.4 Extracting spatial frequency {k m}:

[0124] For each satisfying ||z i Calculate the argument ω of the root of |-1|<ε (ε is a small threshold, such as 0.05). i =arg(zi The corresponding digital spatial frequency is ω. i The actual spatial frequency is:

[0125] k i =ω i / Δx.

[0126] The Prony method directly estimates signal parameters and has high frequency resolution with limited data length.

[0127] 4.5 Signal Amplitude Estimation:

[0128] The spatial frequency k is obtained using the Prony method. m and its corresponding complex amplitude A m Then, the magnitude of the complex amplitude |A m | and the amplitude B of the m-th incident signal m Proportional (in the linearized model, |A) m ∣∝2B m A LO Therefore, by comparing different |A m The magnitude of | can be used to sort and estimate the relative field strength or power of multiple target signals while estimating the direction of arrival, providing additional signal features besides directional information, thereby enhancing the system's sensing capability.

[0129] S5. Based on the mapping relationship between the spatial frequency components and the direction of arrival, the direction of arrival of each of the multiple incident radio frequency signals is calculated. This step completes the mapping from the signal processing result to the final physical quantity, as detailed below.

[0130] 5.1 Mapping from spatial frequency to direction of arrival:

[0131] According to the relation k defined in step S3 m =k RF (sinθ m -sinθ LO ), where k RF =2π / λ RF By performing the inverse operation, the estimated direction of arrival (DOA) of the m-th target can be obtained:

[0132] θ m =arcsin((k m / k RF )+sinθ LO )

[0133] 5.2 Output Results:

[0134] Finally, the system outputs M estimated directions of arrival {θ1',θ2',...,θ MThis enables simultaneous estimation of DoA for multiple targets using a single Rydberg atom receiver.

[0135] refer to Figure 4 One embodiment of this application proposes a multi-target direction-of-arrival estimation system for a single Rydberg atom receiver, which may specifically include the following four functional units.

[0136] (1) An atomic sensing unit, including a vapor chamber filled with alkali metal atomic vapor, is used to generate spatially related fluorescence under the combined action of laser and radio frequency field.

[0137] At the core of the atomic sensing unit is a cylindrical glass vapor chamber filled with a rarefied rubidium-87. Atomic vapor. Atomic density. The length of the vapor chamber along the laser propagation direction is denoted as L. This is a key design freedom; L can be selected according to the required aperture and resolution, and is not tied to the operating frequency.

[0138] (2) An optical excitation and imaging unit, including a laser system for generating probe lasers and coupling lasers, and an imaging device for acquiring the spatial distribution of fluorescence in the vapor chamber from the side.

[0139] Energy level scheme: A four-level stepped system is adopted. ① The ground state |1> of the rubidium atom is , F=2; ② Intermediate state |2〉 is , F=3; ③ Highly excited Rydberg state |3〉 is (e.g., n=60); ④ Adjacent Rydberg states |4〉 are .

[0140] Laser configuration:

[0141] Probe laser, 780 nm distributed feedback (DFB) laser, wavelength λ p =780 nm, frequency tuned to |1〉→|2〉 transition resonance.

[0142] Coupled laser, 480 nm external cavity frequency-doubled laser, wavelength λ c =480 nm, propagating in the opposite direction to the probe laser, the frequency is tuned to the |2〉→|3〉 transition resonance, and its coupling Rabi frequency MHz.

[0143] Optical components include isolators, λ / 2 waveplates, polarizing beam splitters (PBS), beam expanders, etc., used for beam collimation, polarization control, and backpropagation beam combining.

[0144] Imaging configuration: A high-sensitivity sCMOS camera is placed on the side of the steam chamber, with a 780 nm narrow-band interference filter (center wavelength 780 nm) positioned in front to block stray light. The spatial resolution of the camera along the length of the steam chamber (defined as the x-axis) must meet subsequent requirements.

[0145] (3) Radio frequency field application unit, including a local oscillator source and a transmitting antenna for generating a strong local oscillator radio frequency field, and a coupling device for guiding the incident radio frequency signal to be tested into the steam chamber.

[0146] Local oscillation field (LO): frequency f LO Tune to the transition frequency from |3〉 to |4〉. Using a fixed known angle θ. LO (e.g., 90°) Incident angle. Its electric field amplitude A LO It must be much larger than the sum of the amplitudes of all the signals to be measured, that is, satisfy A. LO >>ΣA m The local oscillator includes a frequency synthesizer, connected to a horn antenna, and aligned with the steam chamber at an angle θ. LO fixed.

[0147] Signal field: M far-field plane wave signals to be measured, the electric field amplitude, phase, and direction of arrival of the m-th signal are A, A, and A, respectively. m φ m and θ m The signal coupling device includes a receiving antenna and an adjustable attenuator, used to guide radio frequency signals from the environment under test into the steam chamber area.

[0148] (4) The signal processing and control unit is configured to: control the optical excitation and imaging unit and the radio frequency field application unit to perform calibration measurement and actual measurement; receive image data from the imaging device and execute the aforementioned direction of arrival estimation method processing flow to output the direction of arrival estimation values ​​of multiple incident radio frequency signals.

[0149] The signal processing and control unit specifically includes an industrial control computer, equipped with an image acquisition card and a GPIB / USB control interface. Its software modules include:

[0150] Equipment control module: controls laser current, camera exposure, and RF source switching.

[0151] Image processing module: Performs logarithmic, differential, window function integral, and calibration difference operations on fluorescence images.

[0152] Spectrum estimation module: Implements the Prony algorithm.

[0153] Results display module: Outputs and displays multiple estimated DoA values.

[0154] After the system is powered on and initialized, the signal processing and control unit first controls only the local oscillator field and laser to be turned on, performs calibration measurements, and stores the data. Subsequently, when the signal to be measured is present, the control unit controls the actual measurement to be performed. The computer automatically executes all the processing steps described in the aforementioned embodiment of the direction-of-arrival estimation method, and finally displays the direction-of-arrival estimation results for multiple targets on the interface.

[0155] Figure 2 The effectiveness of the linearized model was verified. When the local oscillator intensity is much greater than the signal intensity, the actual nonlinear absorption curve closely matches the linearized model curve; conversely, the deviation is significant. This intuitively demonstrates the necessity of the "local oscillator-dominated mechanism" condition.

[0156] Figure 3 The multi-target estimation performance was demonstrated. In simulations with two target angles, the strong local oscillator condition accurately estimated both angles, while the weak local oscillator condition failed to estimate due to model instability. Furthermore, the error curves show that when the local oscillator-to-signal power ratio exceeds 10, the estimation error approaches the theoretical lower limit. This supports the practical guidelines for multi-target estimation capabilities and local oscillator strength settings.

[0157] The embodiments of the direction-of-arrival estimation method and the embodiments of the direction-of-arrival estimation system are identical or related in technical concept, and they can be referenced and learned from each other in terms of technical details and technical effectiveness, which will not be repeated here.

[0158] Overall, the advantages of this application compared to the prior art include:

[0159] 1. It breaks through the single-target limitation of single-atom receivers and achieves simultaneous direction finding of multiple targets for the first time.

[0160] Existing DoA estimation methods based on a single Rydberg atom receiver rely on optimizing and inverting a single measurement of the total fluorescence or transmitted light power within the vapor chamber. This "lumped power measurement" inherently loses spatial distribution information, and its mathematical model and algorithmic complexity are ill-suited to handling the simultaneous presence of multiple signals, thus only estimating the direction of arrival (DoA) of a single target. This application abandons the "lumped power measurement" approach and instead adopts spatially resolved fluorescence imaging to directly acquire the complete distribution of fluorescence intensity along the length of the vapor chamber. Through linearization processing dominated by the local oscillator, the complex spatial modulation generated by multiple signals is decoupled into a linear superposition of multiple sinusoidal waves with different spatial frequencies, thereby transforming multi-target DoA estimation into a classic multi-sinusoidal frequency estimation problem (e.g., using the Prony method). This allows for the simultaneous estimation of the DoA of multiple incident RF signals using only a single Rydberg atom vapor chamber, thus overcoming the fundamental limitations of existing single-receiver methods.

[0161] 2. The coupling between the operating frequency band and the physical size of the sensor has been removed, realizing true broadband operation capability.

[0162] Existing single-receiver lumped power methods rely on specific interference patterns for estimation accuracy. To obtain a monotonic response curve, the steam chamber length L must satisfy L < λ / |sinθ. s -sinθ LO The stringent conditions imposed by the Rydberg sensor mean that different lengths of physical hardware must be used for different operating frequencies (wavelength λ), severely limiting its application in broadband scenarios. This application analyzes the spatial spectrum, eliminating the need for the aforementioned monotonicity constraint. Instead, a longer vapor chamber length L directly corresponds to a larger spatial sensing aperture and more effective sampling points. In this way, a single fixed-size sensor can operate over a wide range of radio frequency frequencies without requiring hardware replacements for frequency changes. At higher frequencies (shorter wavelengths), the same physical aperture provides higher angular resolution due to the higher spatial frequency, thus restoring the inherent ultra-wideband potential of the Rydberg sensor.

[0163] 3. The system structure has been greatly simplified, reducing complexity and cost.

[0164] To achieve multi-target direction finding, another approach in existing technologies uses multiple Rydberg atom receiver units to form a physical array. This results in high system complexity, high cost, and requires precise amplitude and phase calibration between units, making engineering implementation difficult. This application requires only a single atomic vapor chamber, a laser system, and an imaging camera. It achieves the sampling function of the "array" by calculating a virtual spatial sampling channel, thus completely avoiding the calibration challenges associated with multiple physical units. In this way, while achieving multi-target direction finding, the system hardware is greatly simplified, the structure is more compact, the potential cost is lower, and there are no calibration errors between units.

[0165] 4. By using local oscillator-dominated linearization and high-resolution algorithms, the estimation accuracy and robustness are improved.

[0166] In existing technologies, when multiple signals coexist, the interaction terms between signals introduce nonlinear interference, complicating the model and making traditional optimization algorithms prone to getting trapped in local optima, leading to decreased accuracy. This application addresses this issue by setting a strong local oscillation field (A... LO >>ΣA m This approach, by suppressing signal-signal cross terms at the physical level, linearizes the system response and simplifies the model. Subsequently, high-resolution spectral estimation algorithms such as the Prony method are employed, enabling accurate differentiation of closely spaced spatial frequency components from finite-length data. This linearized model ensures theoretical accuracy, while algorithms like Prony provide excellent frequency resolution. The combination of these two approaches allows for high-precision and stable DoA estimation results even under multi-target, low signal-to-noise ratio conditions.

[0167] 5. It provides enabling technologies for future continuous aperture sensing and advanced wireless architectures.

[0168] In existing technologies, traditional discrete arrays are limited by the number and spacing of array elements, resulting in problems such as grating lobes. This application, by imaging and sampling continuous fluorescence distribution, essentially creates a continuous and seamless radio frequency field spatial sampler. This provides a physical basis for realizing continuous aperture sensing and can serve as a key receiving technology in future novel integrated wireless communication and sensing architectures such as holographic MIMO (Multiple-Input Multiple-Output), possessing forward-looking technological value.

[0169] Based on the same inventive concept, embodiments of this application also provide an electronic device. Figure 5 This is a structural block diagram of an electronic device provided in an embodiment of this application. Figure 5 As shown in the embodiments of this application, an electronic device includes: one or more processors 101, a memory 102, and one or more I / O interfaces 103. The memory 102 stores one or more programs, which, when executed by the one or more processors, cause the one or more processors to implement any of the direction-of-arrival estimation methods described in the above embodiments; the one or more I / O interfaces 103 are connected between the processor and the memory, configured to enable information interaction between the processor and the memory.

[0170] The processor 101 is a device with data processing capabilities, including but not limited to a central processing unit (CPU); the memory 102 is a device with data storage capabilities, including but not limited to random access memory (RAM, more specifically SDRAM, DDR, etc.), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), and flash memory (FLASH); the I / O interface (read / write interface) 103 is connected between the processor 101 and the memory 102, and can realize information interaction between the processor 101 and the memory 102, including but not limited to a data bus (Bus).

[0171] In some embodiments, the processor 101, memory 102, and I / O interface 103 are interconnected via bus 104, and thus connected to other components of the computing device.

[0172] In some embodiments, the one or more processors 101 include a field-programmable gate array.

[0173] This application also provides a computer-readable medium. The computer-readable medium stores a computer program, which, when executed by a processor, implements the steps in any of the direction-of-arrival estimation methods described above. The computer-readable storage medium can be volatile or non-volatile.

[0174] This application also provides a computer program product, including computer-readable code, or a non-volatile computer-readable storage medium carrying computer-readable code. When the computer-readable code is run in the processor of an electronic device, the processor in the electronic device executes the above-described direction-of-arrival estimation method.

[0175] Those skilled in the art will understand that all or some of the steps, systems, and apparatuses disclosed above, and their functional modules / units, can be implemented as software, firmware, hardware, or suitable combinations thereof. In hardware implementations, the division between functional modules / units mentioned above does not necessarily correspond to the division of physical components; for example, a physical component may have multiple functions, or a function or step may be performed collaboratively by several physical components. Some or all physical components may be implemented as software executed by a processor, such as a central processing unit, digital signal processor, or microprocessor, or as hardware, or as an integrated circuit, such as an application-specific integrated circuit (ASIC). Such software can be distributed on a computer-readable storage medium, which may include computer storage media (or non-transitory media) and communication media (or transient media).

[0176] As is known to those skilled in the art, the term computer storage medium includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information, such as computer-readable program instructions, data structures, program modules, or other data. Computer storage media includes, but is not limited to, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM), static random access memory (SRAM), flash memory or other memory technologies, portable compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical disc storage, magnetic cartridges, magnetic tape, disk storage or other magnetic storage devices, or any other medium that can be used to store desired information and is accessible to a computer. Furthermore, it is known to those skilled in the art that communication media typically contain computer-readable program instructions, data structures, program modules, or other data in modulated data signals such as carrier waves or other transmission mechanisms, and may include any information delivery medium.

[0177] The computer-readable program instructions described herein can be downloaded from computer-readable storage media to various computing / processing devices, or downloaded via a network, such as the Internet, local area network, wide area network, and / or wireless network, to an external computer or external storage device. The network may include copper transmission cables, fiber optic transmission, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards them to the computer-readable storage media in the respective computing / processing device.

[0178] The computer program instructions used to perform the operations of this application may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, status setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk, C++, etc., and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The computer-readable program instructions may be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or may be connected to an external computer (e.g., via the Internet using an Internet service provider). In some embodiments, electronic circuits, such as programmable logic circuits, field-programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), are personalized by utilizing the status information of the computer-readable program instructions. These electronic circuits can execute the computer-readable program instructions to implement various aspects of this application.

[0179] The computer program product described herein can be implemented specifically through hardware, software, or a combination thereof. In one alternative embodiment, the computer program product is specifically embodied in a computer storage medium; in another alternative embodiment, the computer program product is specifically embodied in a software product, such as a software development kit (SDK), etc.

[0180] Various aspects of this application are described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer-readable program instructions.

[0181] These computer-readable program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus to produce a machine such that, when executed by the processor of the computer or other programmable data processing apparatus, they create means for implementing the functions / actions specified in one or more blocks of the flowchart and / or block diagram. These computer-readable program instructions can also be stored in a computer-readable storage medium that causes a computer, programmable data processing apparatus, and / or other device to operate in a particular manner; thus, the computer-readable medium storing the instructions comprises an article of manufacture that includes instructions for implementing aspects of the functions / actions specified in one or more blocks of the flowchart and / or block diagram.

[0182] Computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process, thereby causing the instructions executed on the computer, other programmable data processing apparatus, or other device to perform the functions / actions specified in one or more boxes of a flowchart and / or block diagram.

[0183] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of an instruction containing one or more executable instructions for implementing a specified logical function. In some alternative implementations, the functions marked in the blocks may occur in a different order than those marked in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

[0184] Exemplary embodiments have been disclosed in this application, and while specific terminology has been used, it is used only and should be interpreted in a general illustrative sense and is not intended to be limiting. In some embodiments, it will be apparent to those skilled in the art that features, characteristics, and / or elements described in conjunction with particular embodiments may be used alone, or in combination with features, characteristics, and / or elements described in conjunction with other embodiments, unless otherwise expressly indicated. Therefore, those skilled in the art will understand that various changes in form and detail may be made without departing from the scope of this application as set forth by the appended claims.

Claims

1. A method for estimating the direction of arrival (DOA) of multiple targets using a single Rydberg atom receiver, characterized in that, include: Based on a single vapor chamber containing atomic vapor, electromagnetic induction transparency conditions are constructed using probe lasers and coupling lasers. By superimposing the local oscillator radio frequency field with the incident radio frequency signal field to be measured, a fluorescence spatial distribution associated with the spatial distribution of the total radio frequency field intensity is formed in the vapor chamber. A lateral fluorescence image of the steam chamber is acquired, and based on the fluorescence image, a calibrated signal measurement sequence reflecting the spatial variation of the local atomic absorption coefficient within the steam chamber is calculated. The calibrated signal measurement sequence is modeled as a signal model consisting of the linear superposition of multiple spatial frequency components. A spectrum estimation algorithm based on a linear prediction model is used to estimate each spatial frequency component from the signal model; Based on the mapping relationship between the spatial frequency components and the direction of arrival, the direction of arrival of each of the multiple incident radio frequency signals is calculated.

2. The direction-of-arrival estimation method according to claim 1, characterized in that, The field strength of the local oscillator radio frequency field is configured to be greater than a preset multiple of the sum of the field strengths of all incident radio frequency signals to be measured, so that the nonlinear relationship between the local atomic absorption coefficient and the total radio frequency field strength can be linearized, and thus the calibrated signal measurement sequence can be expressed as a linear combination of multiple spatial frequency cosine terms.

3. The direction-of-arrival estimation method according to claim 2, characterized in that, The calibrated signal measurement sequence is obtained through the following steps: With only the local oscillator radio frequency field turned on, the first fluorescence spatial distribution is obtained and the first atomic absorption coefficient spatial distribution is calculated. Based on a preset family of virtual spatial window functions, the first set of measurement values ​​is obtained. Simultaneously turn on the local oscillator radio frequency field and all incident radio frequency signals to be measured, obtain the second fluorescence spatial distribution and calculate the second atomic absorption coefficient spatial distribution, and obtain the second set of measurement values ​​based on the same virtual space window function family; The difference between the second set of measurements and the first set of measurements is used to eliminate the DC offset, thus obtaining the calibrated signal measurement sequence.

4. The direction-of-arrival estimation method according to any one of claims 1-3, characterized in that, The spectrum estimation algorithm based on the linear prediction model is the Prony method, which specifically includes: Construct a Hankel matrix using the calibrated signal measurement sequence; The linear prediction coefficients are obtained by solving the linear least squares problem; Construct a characteristic polynomial with the predicted coefficients as parameters, and solve for the roots of the polynomial; Roots with amplitudes close to unit 1 are selected from the roots, and their arguments correspond to the estimated values ​​of the spatial frequency components.

5. The direction-of-arrival estimation method according to claim 1, characterized in that, The length of the vapor chamber is independent of the wavelength of the incident radio frequency signal to be measured. A longer vapor chamber length directly corresponds to a larger effective sensing aperture, higher spectral resolution, and higher direction of arrival accuracy.

6. The direction-of-arrival estimation method according to claim 1, characterized in that, The process of resolving the calibrated signal measurement sequence includes logarithmic processing of the fluorescence image to directly recover the spatial distribution of the local atomic absorption coefficients, specifically: ;in, Indicates the spatial distribution of fluorescence intensity; This represents the spatial distribution of local atomic absorption coefficients.

7. The direction-of-arrival estimation method according to claim 1, characterized in that, Also includes: Based on the estimated direction of arrival and combined with the amplitude information of the spatial frequency components of the signal, the relative intensity or power of multiple incident radio frequency signals is estimated.

8. A multi-target direction-of-arrival estimation system for a single Rydberg atom receiver, characterized in that, include: The atomic sensing unit includes a vapor chamber filled with alkali metal atomic vapor, which is used to generate spatially correlated fluorescence under the combined action of laser and radio frequency field; The optical excitation and imaging unit includes a laser system for generating probe lasers and coupling lasers, and an imaging device for acquiring the spatial distribution of fluorescence in the vapor chamber from the side. The radio frequency field application unit includes a local oscillator source and a transmitting antenna for generating a strong local oscillator radio frequency field, and a coupling device for guiding the incident radio frequency signal to be measured into the steam chamber. The signal processing and control unit is configured as follows: The optical excitation and imaging unit and the radio frequency field application unit are controlled to perform calibration measurements and actual measurements; The system receives image data from the imaging device and executes the processing flow of the direction-of-arrival estimation method according to any one of claims 1-7, outputting direction-of-arrival estimation values ​​for multiple incident radio frequency signals.

9. An electronic device, characterized in that, include: One or more processors; Memory, used to store one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors are enabled to implement the steps in the direction-of-arrival estimation method as described in any one of claims 1 to 7.

10. A computer-readable medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it can implement the steps in the direction-of-arrival estimation method as described in any one of claims 1 to 7.

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