A short wave spectrum efficient sampling method and system based on compressed sensing

Abstract

This invention relates to the field of wireless communication and signal processing technology, specifically to a shortwave spectrum high-efficiency sampling method and system based on compressed sensing. The method includes: acquiring power spectral density data across the entire frequency band using a low-speed scanning receiver; determining a set of strong interference frequency points; generating a binary null observation sequence; loading the binary null observation sequence onto an analog front-end mixer circuit to perform analog domain orthogonal mixing and integration processing on the input RF signal, outputting voltage sample values; calculating signal sparsity coefficients using a compressed sensing reconstruction algorithm; calculating the reconstruction residual based on the voltage sample values ​​and the signal sparsity coefficients; triggering a re-acquisition process of power spectral density data in response to the reconstruction residual exceeding a preset error threshold; and outputting the signal sparsity coefficients in response to the reconstruction residual being less than or equal to the preset error threshold. This invention solves the problems of limited dynamic range and weak signal overload, significantly improving the receiving sensitivity of weak signals under strong interference environments.

Description

Technical Field

[0001] This invention relates to the field of wireless communication and signal processing technology, specifically to a method and system for efficient shortwave spectrum sampling based on compressed sensing. Background Technology

[0002] In the current electromagnetic environment of shortwave communication and spectrum monitoring, although the spectrum resources faced by broadband receivers are generally sparse, there are often individual high-power strong interference signals, and these interference signals coexist with the weak effective signals to be received.

[0003] To obtain full-band spectrum information, existing solutions generally adopt a full-band direct sampling architecture, which directly uses a high-speed analog-to-digital converter (ADC) to digitize analog RF signals containing strong interference. Although this solution can theoretically cover a wide spectrum, the physical performance of the ADC is limited by its finite dynamic range. When there is significant strong interference in the input signal, the system must reduce the front-end gain to prevent device saturation distortion, causing the amplitude of weak signals in the same frequency band to drop below the quantization noise floor and be submerged. In addition, the high-speed data stream generated by full-band Nyquist sampling also puts enormous hardware pressure on back-end storage and signal processing. Therefore, how to actively suppress strong interference energy at the physical level in the analog domain to remove the dynamic range limitation of the ADC and achieve high-precision reconstruction of weak signals at low sampling rates has become an urgent technical problem to be solved. Summary of the Invention

[0004] The purpose of this invention is to provide a high-efficiency shortwave spectrum sampling method and system based on compressed sensing. This method can actively suppress strong interference at the physical level in the analog domain, solving the problem of weak signal overwhelmance caused by the limited dynamic range of the analog-to-digital converter. It also significantly reduces the sampling rate requirement and data processing pressure, achieving high-precision reconstruction of weak signals under low-speed sampling. Specifically, the technical solution of this invention is as follows:

[0005] A shortwave spectrum efficient sampling method based on compressed sensing includes:

[0006] Power spectral density data across the entire frequency band were acquired using a low-speed scanning receiver;

[0007] Step 1: Based on power spectral density data, determine the set of strong interference frequency points through statistical characteristic analysis and constant false alarm rate detection processing;

[0008] Step 2: Using the set of strong interference frequency points as constraints, a binary null observation sequence is generated through spectral energy minimization modeling and iterative binarization correction.

[0009] Step 3: Load the binary null observation sequence into the analog front-end mixer circuit, perform analog domain quadrature mixing and integration on the input RF signal, and output the voltage sample value;

[0010] Step 4: Based on the voltage sample values ​​and the preset sparse basis matrix, the signal sparsity coefficients are calculated using the compressed sensing reconstruction algorithm.

[0011] Step 5: Calculate the reconstruction residual based on the voltage sample value and the signal sparsity coefficient;

[0012] Step 6: In response to the reconstruction residual being greater than the preset error threshold, a process for reacquiring the power spectral density data is triggered.

[0013] Step 7: In response to the reconstruction residual being less than or equal to a preset error threshold, output the sparse coefficients of the signal.

[0014] Optionally, determine the set of strong interference frequency points, including:

[0015] Sort the amplitude values ​​of all frequency points in the power spectral density data in ascending order;

[0016] Extract frequency data that falls within a preset low-energy ratio range after sorting;

[0017] Calculate the average energy value of the frequency point data as an estimate of the Gaussian white noise variance;

[0018] Based on the Gaussian white noise variance estimate and the preset false alarm probability constraint, the dynamic decision threshold is calculated.

[0019] Frequency points with amplitudes greater than the dynamic decision threshold in the power spectral density data are classified into the set of strong interference frequency points;

[0020] Frequency points with amplitudes less than or equal to the dynamic decision threshold in the power spectral density data are excluded from the set of strong interference frequency points.

[0021] Optionally, generate a binary null-trapped observation sequence, including:

[0022] Row vectors corresponding to the set of strong interference frequency points are extracted from the standard discrete Fourier transform matrix to construct the interference frequency point submatrix;

[0023] Establish a sequence optimization model;

[0024] The sequence optimization model takes minimizing the total energy of the sequence under the projection of the interference frequency submatrix as the objective function and assumes that the sequence has a constant total power as a constraint.

[0025] Solving the sequence optimization model yields a continuous-valued null trap sequence;

[0026] Using the alternating projection algorithm, continuous null sequences are mapped to binary null observation sequences that satisfy hardware switching constraints.

[0027] Optionally, an alternating projection algorithm may be used, including:

[0028] Construct the interference null space projection operator;

[0029] Among them, the interference null space projection operator is used to ensure that the energy response of the projected vector is zero at the set of strong interference frequency points;

[0030] The current iteration sequence is projected using the interference null space projection operator to obtain an intermediate transition sequence;

[0031] The intermediate transition sequence is symbolized by mapping each element of the intermediate transition sequence to a binary level to obtain the next round of iteration sequence;

[0032] Repeat the projection and symbolization process until the sequence converges, and output the binary null observation sequence.

[0033] Optional, output voltage sample values, including:

[0034] Set the time constant and integration period of the analog integrator;

[0035] The binary zero-trap observation sequence is used as a control signal to control the switching on and off of the analog front-end mixer circuit;

[0036] During the integration period, the product of the input radio frequency signal and the binary null observation sequence is continuously integrated over time.

[0037] The integral result is normalized to output discrete voltage sample values;

[0038] The integration process involves orthogonally eliminating signal components corresponding to the set of strong interference frequency points at the physical level.

[0039] Optionally, the signal sparsity coefficients are calculated, including:

[0040] Construct the observation matrix;

[0041] Each row of the observation matrix corresponds to the discrete form of the binary null observation sequence;

[0042] Establish a reconstruction optimization model;

[0043] Among them, the reconstruction optimization model aims to minimize the L1 norm of the signal sparse coefficients, and is constrained by approximating the voltage sampling value by the product of the observation matrix, the preset sparse basis matrix, and the signal sparse coefficients.

[0044] The reconstructed optimization model is solved using a convex optimization algorithm, and the output signal sparsity coefficients are obtained.

[0045] Optionally, triggering a process to reacquire the power spectral density data includes:

[0046] Determine if there are new interference sources in the current environment that are not covered by the set of strong interference frequencies;

[0047] Control the low-speed scanning receiver to initiate full-band scanning;

[0048] Based on the new power spectral density data obtained from the scan, the noise floor estimation and constant false alarm rate detection are re-executed to generate an updated set of strong interference frequency points.

[0049] Based on the updated set of strong interference frequency points, a new binary null observation sequence is generated.

[0050] A high-efficiency shortwave spectrum sampling system based on compressed sensing, comprising:

[0051] The spectrum sensing module is used to acquire power spectral density data across the entire frequency band using a low-speed scanning receiver and to determine the set of strong interference frequency points.

[0052] The sequence generation module is used to generate binary null observation sequences with a set of strong interference frequency points as constraints.

[0053] The analog sampling module is used to load the binary null observation sequence into the analog front-end mixer circuit, process the input RF signal and output the voltage sample value;

[0054] The signal reconstruction module is used to calculate the signal sparsity coefficients based on the voltage sample values ​​using a compressed sensing reconstruction algorithm.

[0055] The feedback control module is used to calculate the reconstruction residual; in response to the reconstruction residual being greater than the preset error threshold, it triggers the spectrum sensing module to update the set of strong interference frequency points; in response to the reconstruction residual being less than or equal to the preset error threshold, it outputs the signal sparsity coefficients.

[0056] Compared with the prior art, the present invention has the following beneficial effects:

[0057] 1. This invention solves the problems of limited dynamic range and weak signal overwhelmance; by generating a binary null observation sequence for a set of strong interference frequency points, the radio frequency signal is directly orthogonally eliminated at the physical level in the analog front-end mixer circuit; this active suppression mechanism in the analog domain effectively prevents strong interference energy from entering the back-end quantization stage, solves the problem of forced gain reduction due to the limited dynamic range of the analog-to-digital converter, prevents weak effective signals from being overwhelmed by quantization noise, and significantly improves the receiving sensitivity of weak signals in strong interference environments;

[0058] 2. This invention reduces sampling rate requirements and data processing pressure; combining compressed sensing theory, it uses an integrator to perform analog compressed sampling of broadband signals; since significant interference components have been eliminated in the analog domain, the sparsity of the signal is enhanced, and the system only needs to use low-speed voltage sampling values ​​in conjunction with a sparse reconstruction algorithm to accurately recover the original signal; this breaks the limitation of the Nyquist sampling theorem, significantly reduces the sampling rate specifications of the analog-to-digital converter, and at the same time reduces the storage and transmission pressure of massive amounts of data at the back end;

[0059] 3. This invention ensures the hardware feasibility of the sequence; by employing an alternating projection algorithm, the theoretically optimal continuous null sequence is mapped to a binary sequence that satisfies hardware switching constraints; this method ensures that while maintaining deep suppression of strong interference at specific frequencies, the elements of the observed sequence only take binary levels, which can directly drive the switching mixer of the analog front end; this effectively solves the problem that complex beamforming algorithms are difficult to deploy directly on low-cost analog switching hardware, ensuring the engineering feasibility of the solution;

[0060] 4. This invention achieves adaptive adjustment to the dynamic electromagnetic environment; it constructs a closed-loop feedback control mechanism based on reconstruction residuals; the system can calculate and monitor reconstruction errors in real time, and once an uncovered new interference source appears in the environment, causing the residual to exceed the preset threshold, the system will automatically trigger a full-band scanning and interference set update process; this adaptive adjustment strategy enables the system to sensitively detect the dynamic changes in the electromagnetic environment and promptly correct the interference suppression strategy, ensuring long-term stable operation in non-stationary environments. Attached Figure Description

[0061] The present invention will be further explained below with reference to the accompanying drawings and embodiments:

[0062] Figure 1 This is a flowchart of the method of the present invention;

[0063] Figure 2 This is a structural diagram of the system of the present invention. Detailed Implementation

[0064] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0065] Example 1:

[0066] Please see Figure 1 A shortwave spectrum efficient sampling method based on compressed sensing, comprising:

[0067] Power spectral density data across the entire frequency band were acquired using a low-speed scanning receiver;

[0068] Step 1: Based on power spectral density data, determine the set of strong interference frequency points through statistical characteristic analysis and constant false alarm rate detection processing;

[0069] Step 2: Using the set of strong interference frequency points as constraints, a binary null observation sequence is generated through spectral energy minimization modeling and iterative binarization correction.

[0070] Step 3: Load the binary null observation sequence into the analog front-end mixer circuit, perform analog domain quadrature mixing and integration on the input RF signal, and output the voltage sample value;

[0071] Step 4: Based on the voltage sample values ​​and the preset sparse basis matrix, the signal sparsity coefficients are calculated using the compressed sensing reconstruction algorithm.

[0072] Step 5: Calculate the reconstruction residual based on the voltage sample value and the signal sparsity coefficient;

[0073] Step 6: In response to the reconstruction residual being greater than the preset error threshold, a process for reacquiring the power spectral density data is triggered.

[0074] Step 7: In response to the reconstruction residual being less than or equal to a preset error threshold, output the sparse coefficients of the signal.

[0075] This embodiment provides a high-efficiency shortwave spectrum sampling method based on compressed sensing. The method aims to solve the problem of weak signal submersion caused by the limited dynamic range of analog-to-digital converters in broadband receivers under strong interference environments. This technical solution senses the energy distribution of the entire frequency band, actively suppresses strong interference at the physical level in the analog domain, and performs low-speed sampling and reconstruction.

[0076] The system uses a low-speed scanning receiver to collect power spectral density data across the entire frequency band. Here, the low-speed scanning receiver refers to a frequency-scanning receiving device with high sensitivity and narrowband characteristics. Its function is to obtain the fine spectral distribution of the current electromagnetic environment and provide prior environmental knowledge for subsequent processing.

[0077] In step 1, the system determines the set of strong interference frequency points based on the collected power spectral density data through statistical characteristic analysis and constant false alarm rate detection. Since the spectrum of the shortwave band is sparse and most of the frequency band is at the noise floor level, by distinguishing the noise floor from significant signals, the system can screen out frequency points that significantly exceed the background noise, thus forming the set of strong interference frequency points.

[0078] Step 2 is executed based on the assumption that the shortwave channel exhibits quasi-static characteristics within a millisecond-level time window, or by quickly verifying the existence of current strong interference frequencies before generating the sequence. The system uses the determined set of strong interference frequencies as constraints, and generates a binary null observation sequence through spectral energy minimization modeling and iterative binarization correction. This sequence must exhibit an extremely low response at the strong interference frequencies in the frequency domain, and must satisfy the binary constraint of the hardware switch in the time domain, i.e., take a value of positive 1 or negative 1.

[0079] After generating the control sequence, step 3 is executed, loading the binary null observation sequence into the analog front-end mixer circuit. During this process, the analog front-end mixer circuit performs analog domain quadrature mixing and integration on the input RF signal and outputs the voltage sample value. The binary null observation sequence is used as the local oscillator signal and is directly multiplied with the RF signal in the analog domain. Since the sequence has null characteristics at the interference frequency, strong interference signals are physically suppressed during the mixing process, and the integrator only accumulates the remaining effective weak signal energy.

[0080] In step 4, the system calculates the signal sparsity coefficients based on the output voltage sample value and the preset sparse basis matrix using the compressed sensing reconstruction algorithm. Since strong interference has been eliminated in step 3, the sparsity of the signal to be reconstructed is significantly reduced, thus ensuring that the algorithm can accurately recover the original signal from a small number of observations.

[0081] Steps 5 and 6 constitute a closed-loop feedback mechanism; the system calculates the reconstruction residual based on the voltage sampling value and the signal sparsity coefficient, and determines whether the reconstruction residual is greater than the preset error threshold; if the reconstruction residual is greater than the preset error threshold, it indicates that the current observation sequence has failed to effectively suppress the interference in the environment, such as the appearance of new interference sources that have not been covered. At this time, the system triggers the process of re-acquiring the power spectral density data, that is, returning to the initial step to re-perceive the environment.

[0082] In step 7, if the reconstruction residual is less than or equal to the preset error threshold, it indicates that the reconstruction is successful and the environment is stable. The system outputs the sparse coefficient of the signal and completes the current sampling task. Through the above steps, this embodiment realizes the physical elimination of strong interference in the analog domain, which greatly reduces the sampling rate requirement and dynamic range pressure of the back-end analog-to-digital converter.

[0083] Example 2:

[0084] The set of strong interference frequencies was determined, including:

[0085] Sort the amplitude values ​​of all frequency points in the power spectral density data in ascending order;

[0086] Extract frequency data that falls within a preset low-energy ratio range after sorting;

[0087] Calculate the average energy value of the frequency point data as an estimate of the Gaussian white noise variance;

[0088] Based on the Gaussian white noise variance estimate and the preset false alarm probability constraint, the dynamic decision threshold is calculated.

[0089] Frequency points with amplitudes greater than the dynamic decision threshold in the power spectral density data are classified into the set of strong interference frequency points;

[0090] Frequency points with amplitudes less than or equal to the dynamic decision threshold in the power spectral density data are excluded from the set of strong interference frequency points.

[0091] This embodiment provides a detailed explanation of the process for determining the set of strong interference frequency points; in order to accurately distinguish between valid signals and strong interference, the system needs to establish a reliable environmental noise benchmark;

[0092] The system sorts the amplitudes of all frequency points in the power spectral density data in ascending order. Since most frequency points in the broadband spectrum are idle and their energy is mainly composed of environmental noise, the set of frequency points with lower energy can more realistically reflect the noise floor level.

[0093] The system extracts frequency data that falls within a preset low-energy ratio range after sorting; in this embodiment, the preset low-energy ratio range is selected as the first 20% of the sorted data; let the set of spectral amplitudes obtained from full-band scanning be... The set of low-energy frequency points after truncation is denoted as ;

[0094] The average power value of the extracted low-energy frequency data is calculated and used as an estimate of the Gaussian white noise variance under the current environment. The calculation formula is as follows:

[0095]

[0096] in, This indicates the output of the low-speed scan receiver. The spectral voltage amplitude at each frequency point has the physical dimension of volts; assuming the low-speed scanning receiver acquires a total of frequency points across the entire frequency band. ; Represents a set The number of frequency points is calculated using the following formula: ,in To pre-determine a low energy ratio, this embodiment uses 20%. Indicates the floor function; This characterizes the signal power at that frequency point; This is the calculated noise power estimate, in units of... By calculating the average power at the frequency points with the lowest energy, the influence of strong interference signals can be effectively eliminated, thereby obtaining an accurate baseline for the noise floor level.

[0097] Based on this, the system calculates a dynamic decision threshold using the Gaussian white noise variance estimate and a preset false alarm probability constraint; this embodiment uses the Neyman-Pearson criterion to set the preset false alarm probability. For example, the value is Threshold coefficient for dynamic decision threshold Calculated as ;

[0098] The system performs a decision operation: selects data from the power spectral density data whose amplitude squared is greater than a certain value. The frequency points are classified into the set of strong interference frequencies. Frequency points with amplitude squared values ​​less than or equal to the threshold are excluded. Through this adaptive threshold setting based on statistical characteristics, the system can accurately identify strong interference frequencies that are significantly higher than the noise floor while ensuring a constant false alarm rate.

[0099] Example 3:

[0100] Generate a binary null observation sequence, including:

[0101] Row vectors corresponding to the set of strong interference frequency points are extracted from the standard discrete Fourier transform matrix to construct the interference frequency point submatrix;

[0102] Establish a sequence optimization model;

[0103] The sequence optimization model takes minimizing the total energy of the sequence under the projection of the interference frequency submatrix as the objective function and assumes that the sequence has a constant total power as a constraint.

[0104] Solving the sequence optimization model yields a continuous-valued null trap sequence;

[0105] Using the alternating projection algorithm, continuous null sequences are mapped to binary null observation sequences that satisfy hardware switching constraints.

[0106] This embodiment details a method for generating a binary null observation sequence; the process aims to generate a control sequence that can both suppress specific frequency interference and conform to hardware switching characteristics;

[0107] The system extracts row vectors corresponding to the set of strong interference frequency points from the standard discrete Fourier transform matrix to construct an interference frequency point submatrix; let... The length of the observation sequence corresponds to the number of sampling points in the system design; the standard discrete Fourier transform matrix is... The system is based on the set of strong interference frequencies. Frequency index in the matrix, extract the matrix The corresponding rows in the matrix constitute the interference frequency point submatrix. Its dimensions are ;

[0108] The system establishes a sequence optimization model; this model takes minimizing the total energy of the sequence under the projection of the interference frequency submatrix as the objective function, and assumes that the sequence has a constant total power as a constraint. The specific optimization model is expressed as follows:

[0109]

[0110] in, Let represent the vector of continuous values ​​to be calculated, which is the optimization variable; This refers to the aforementioned constructed interference frequency point sub-matrix; The sequence length is used as an energy constraint constant to prevent the solution from collapsing into an all-zero vector. This model is based on the linear constraint minimum variance beamforming concept, and the solution... exist The frequency points within the set have extremely low energy responses, thus forming a spectrum dead zone;

[0111] Solving the above sequence optimization model yields the continuous-value null sequence. Since continuous value sequences are difficult to drive switching mixers directly, the system uses an alternating projection algorithm to transform the continuous value null sequences. The mapping is performed as a binary null-trapped observation sequence that satisfies hardware switching constraints; this step ensures the final output sequence. Each element is taken only or Therefore, it can be executed by physical circuits.

[0112] Example 4:

[0113] Using the alternating projection algorithm, including:

[0114] Construct the interference null space projection operator;

[0115] Among them, the interference null space projection operator is used to ensure that the energy response of the projected vector is zero at the set of strong interference frequency points;

[0116] The current iteration sequence is projected using the interference null space projection operator to obtain an intermediate transition sequence;

[0117] The intermediate transition sequence is symbolized by mapping each element of the intermediate transition sequence to a binary level to obtain the next round of iteration sequence;

[0118] Repeat the projection and symbolization process until the sequence converges, and output the binary null observation sequence.

[0119] The system repeats the above projection and symbolization processes to calculate the Euclidean distance between the two iteration sequences. ;like Less than the preset convergence threshold ,For example Or the number of iterations reaches the preset maximum number of iterations. For example, if the iteration reaches 1000 times, then stop iterating and output the final binary null observation sequence. The maximum number of iterations is introduced to prevent infinite loops during the projection of non-convex sets.

[0120] This embodiment details the specific process of converting a continuous value sequence into a binary sequence using the alternating projection algorithm; the algorithm seeks the optimal solution that satisfies the dual constraints by repeatedly projecting between the disturbance null space and the binary constraint space;

[0121] Constructing the interference null spatial projection operator This operator is used to ensure that the energy response of the projected vector is zero at the set of strong interference frequencies, and its mathematical definition is as follows:

[0122]

[0123] in, For small regularization parameters, such as Used to prevent due to Numerical computation instability or failure to invert due to proximity to singular matrices; for An identity matrix of dimension 1; For the interference frequency sub-matrix; superscript Indicates conjugate transpose, superscript This represents finding the inverse of a matrix.

[0124] Initialize the iteration variables: Generate a random binary sequence that follows a Bernoulli distribution as the initial sequence. Alternatively, the sequence of all 1s can be used as the initial sequence; the iterative process begins; the system uses the interference null space projection operator to project the current iterative sequence to obtain the intermediate transition sequence. The calculation formula is: ,in For the first The sequence of the next iteration; the purpose of this step is to force the sequence to be projected into the null space of the interference, thereby eliminating the response of the interference frequency point;

[0125] The intermediate transition sequence is symbolized by mapping each element to a binary level to obtain the next iteration sequence. The specific mapping rules are as follows: ,in This is a sign function that outputs when the input is greater than or equal to 0. Otherwise output This step pulls the sequence back into the binary constrained space.

[0126] The system repeats the above projection and symbolization processes until the sequence converges or the preset maximum number of iterations is reached, and finally outputs the binary null observation sequence. This sequence possesses both deep null characteristics at strong interference frequencies and binary switching characteristics in the time domain.

[0127] Example 5:

[0128] Output voltage sample values, including:

[0129] Set the time constant and integration period of the analog integrator;

[0130] The binary zero-trap observation sequence is used as a control signal to control the switching on and off of the analog front-end mixer circuit;

[0131] During the integration period, the product of the input radio frequency signal and the binary null observation sequence is continuously integrated over time.

[0132] The integral result is normalized to output discrete voltage sample values;

[0133] The integration process involves orthogonally eliminating signal components corresponding to the set of strong interference frequency points at the physical level.

[0134] This embodiment provides a detailed explanation of the process of analog domain quadrature mixing and integration; this is a key step in achieving physical layer anti-interference.

[0135] Set the time constant of the analog integrator With integration period Time constant Determined by the resistor and capacitor parameters of the hardware integrating circuit, for example Used to balance physical dimensions; integration period The compression sampling rate of the corresponding system is usually set to be much larger than the Nyquist sampling interval in order to achieve low-speed sampling;

[0136] The binary zero-trap observation sequence is used as a control signal to control the switching on and off of the analog front-end mixer circuit; the sequence contains... and The mixer is controlled to perform positive-phase or negative-phase gating of the input signal respectively;

[0137] During the integration period, the product of the input RF signal and the binary null observation sequence is integrated over continuous time; the integration result is then normalized to output discrete voltage sample values. Its physical model is expressed as:

[0138]

[0139] in, For the first The voltage sample value output at each moment, in volts; The input radio frequency voltage signal received by the antenna; For the continuous-time waveform of the binary zero-trap observation sequence; specifically, From discrete sequence The zero-order preserving generation is expressed as follows: ;in, The width of the symbol. It is a unit rectangular impulse function; and the system sets the integration period. With sequence length Satisfying Relationships This ensures that one integration period covers exactly one complete observation sequence period;

[0140] To ensure that the subsequently constructed observation matrix satisfies the cyclic matrix property, in the output of the first... voltage sample value Then, the system controller will analyze the binary zero-trap observation sequence. Perform a circular right shift operation by one bit to generate a new control sequence. For the + Mixing processing for one integration cycle; must meet the following requirements. ,in This represents the total number of samples. For the coherence time of the shortwave channel, to ensure that it is completed During the sampling process, the spectral characteristics of the input signal remain quasi-static; physically, this is equivalent to the observation window performing convolution sampling on the input signal in the time domain in the form of a sliding window, thereby forming a cyclic observation matrix in mathematical structure.

[0141] In this process, the integration operation is not merely energy accumulation, but also a physical-level orthogonal elimination of signal components corresponding to sets of strong interference frequencies; because The spectral response at the strong interference frequency is zero. According to the frequency domain convolution theorem, the strong interference components cancel each other out during integration, therefore the output... It mainly contains weak signal components that are not masked by interference, thus effectively preventing the integrator from saturating.

[0142] Example 6:

[0143] The calculated signal sparsity coefficients include:

[0144] Construct the observation matrix;

[0145] Each row of the observation matrix corresponds to the discrete form of the binary null observation sequence;

[0146] Establish a reconstruction optimization model;

[0147] Among them, the reconstruction optimization model aims to minimize the L1 norm of the signal sparse coefficients, and is constrained by approximating the voltage sampling value by the product of the observation matrix, the preset sparse basis matrix, and the signal sparse coefficients.

[0148] The reconstructed optimization model is solved using a convex optimization algorithm, and the output signal sparsity coefficients are obtained.

[0149] This embodiment details the process of calculating the signal sparsity coefficients from voltage sample values;

[0150] Constructing the observation matrix Set the number of compressed samples ,in satisfy And it meets the compressed sensing constraint isometry condition RIP; construct Dimensional observation matrix The observation matrix is ​​a cyclic matrix, where the first row corresponds to the discrete form of the binary null observation sequence, and each subsequent row is a cyclic right shift of the data from the previous row by one bit; at this point, the collected voltage sample value vector... The dimension is This structure corresponds to the physical layer where the sequence shifts cyclically at a rate higher than the integration period, ensuring that the observation matrix satisfies the constrained equidistant property, guaranteeing the mathematical solvability of accurately reconstructing the signal from a small number of sampled values, and reflecting the measurement weights of the analog integrator in different time windows.

[0151] A reconstruction optimization model is established. This model aims to minimize the L1 norm of the signal sparse coefficients and is constrained by approximating the voltage sampling value using the product of the observation matrix, the preset sparse basis matrix, and the signal sparse coefficients. The specific mathematical model is as follows:

[0152]

[0153] in, The sparse coefficients of the signal to be determined; The L1 norm of the sparse coefficients is used to induce sparsity in the solution; This is a vector of the collected voltage sample values; The observation matrix; for The sparse basis matrix of the dimension is preferably a Discrete Fourier Transform (DFT) basis, because shortwave signals, as narrowband radio frequency signals, have the best energy concentration and sparse representation capability in the Fourier frequency domain; a Discrete Cosine Transform (DFT) basis or a wavelet basis can also be selected according to the signal modulation characteristics. The system noise margin originates from inherent parameters such as circuit thermal noise.

[0154] The system solves the above reconstruction optimization model using convex optimization algorithms, such as basis pursuit denoising algorithm or orthogonal matching pursuit algorithm, and outputs the sparse coefficients of the signal. Since the front-end analog sampling has eliminated strong interference, the sparsity of the input signal is significantly better than that of the original signal, making it possible to achieve high-precision reconstruction at a low sampling rate.

[0155] Example 7:

[0156] Triggering the process of reacquiring power spectral density data includes:

[0157] Determine if there are new interference sources in the current environment that are not covered by the set of strong interference frequencies;

[0158] Control the low-speed scanning receiver to initiate full-band scanning;

[0159] Based on the new power spectral density data obtained from the scan, the noise floor estimation and constant false alarm rate detection are re-executed to generate an updated set of strong interference frequency points.

[0160] Based on the updated set of strong interference frequency points, a new binary null observation sequence is generated.

[0161] This embodiment describes the adaptive adjustment mechanism of the system when facing a dynamically changing environment;

[0162] System calculation reconstructed residuals And determine whether there are any new interference sources in the current environment that are not covered by the set of strong interference frequencies; if the calculated reconstruction residual Greater than the preset error threshold Before this, the system needs to perform initialization calibration: disconnect the RF antenna input and connect the matched load, run the above simulation sampling and reconstruction steps in a pure thermal noise environment, and calculate the average residual value obtained from multiple measurements, which is defined as the system noise margin. Preset error threshold The value is based on the system noise tolerance. The calculation formula is set as follows: , A safety factor greater than 1, for example, 1.2, is used to avoid false triggering caused by thermal noise fluctuations;

[0163] This indicates a significant discrepancy between the observation model and the actual collected data. The most likely reason is the emergence of new strong interference, which is outside the original null suppression range.

[0164] In response to this judgment, the system triggers a feedback mechanism, controls the low-speed scanning receiver to start full-band scanning, and suspends the current sampling task;

[0165] Based on the new power spectral density data acquired by the scan, the system re-executes the noise floor estimation and constant false alarm rate detection to generate an updated set of strong interference frequency points, ensuring that the latest interference distribution is captured.

[0166] Based on the updated set of strong interference frequencies, the system regenerates the binary null observation sequence and loads it into the hardware. Through this closed-loop control, the system can intelligently sense environmental changes and dynamically adjust the observation strategy, ensuring long-term stable operation in complex dynamic electromagnetic environments.

[0167] Example 8:

[0168] Please see Figure 2 A high-efficiency shortwave spectrum sampling system based on compressed sensing, comprising:

[0169] The spectrum sensing module is used to acquire power spectral density data across the entire frequency band using a low-speed scanning receiver and to determine the set of strong interference frequency points.

[0170] The sequence generation module is used to generate binary null observation sequences with a set of strong interference frequency points as constraints.

[0171] The analog sampling module is used to load the binary null observation sequence into the analog front-end mixer circuit, process the input RF signal and output the voltage sample value;

[0172] The signal reconstruction module is used to calculate the signal sparsity coefficients based on the voltage sample values ​​using a compressed sensing reconstruction algorithm.

[0173] The feedback control module is used to calculate the reconstruction residual; in response to the reconstruction residual being greater than the preset error threshold, it triggers the spectrum sensing module to update the set of strong interference frequency points; in response to the reconstruction residual being less than or equal to the preset error threshold, it outputs the signal sparsity coefficients.

[0174] This embodiment provides a high-efficiency shortwave spectrum sampling system based on compressed sensing, which mainly includes the following modules:

[0175] The spectrum sensing module is used to acquire power spectral density data across the entire frequency band using a low-speed scanning receiver and perform statistical analysis to determine the set of strong interference frequencies; this module is responsible for providing prior information for environmental perception.

[0176] The sequence generation module is used to calculate and generate binary null observation sequences with a set of strong interference frequency points as constraints; this module ensures that the sequences have anti-interference characteristics through mathematical optimization.

[0177] The analog sampling module is used to load the binary null observation sequence into the analog front-end mixer circuit, process the input RF signal and output voltage sample values; this module is the physical interface connecting digital control and analog signals, and performs interference cancellation in the analog domain.

[0178] The signal reconstruction module is used to calculate the signal sparsity coefficients based on the voltage sample values ​​using a compressed sensing reconstruction algorithm.

[0179] The feedback control module is used to calculate the reconstruction residual and determine the system state based on the magnitude of the residual. In response to the reconstruction residual being greater than the preset error threshold, this module triggers the spectrum sensing module to update the set of strong interference frequency points. In response to the reconstruction residual being less than or equal to the preset error threshold, the module outputs the signal sparsity coefficients. This module realizes the closed-loop adaptive control of the system.

[0180] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention.

Claims

1. A shortwave spectrum efficient sampling method based on compressed sensing, characterized in that, include: Step 0: Acquire power spectral density data across the entire frequency band using a low-speed scanning receiver; Step 1: Based on power spectral density data, determine the set of strong interference frequency points through statistical characteristic analysis and constant false alarm rate detection processing; Step 2: Using the set of strong interference frequency points as constraints, a binary null observation sequence is generated through spectral energy minimization modeling and iterative binarization correction. Step 3: Load the binary null observation sequence into the analog front-end mixer circuit, perform analog domain quadrature mixing and integration on the input RF signal, and output the voltage sample value; Step 4: Based on the voltage sample values ​​and the preset sparse basis matrix, the signal sparsity coefficients are calculated using the compressed sensing reconstruction algorithm. Step 5: Calculate the reconstruction residual based on the voltage sample value and the signal sparsity coefficient; Step 6: In response to the reconstruction residual being greater than the preset error threshold, a process for reacquiring the power spectral density data is triggered. Step 7: In response to the reconstruction residual being less than or equal to a preset error threshold, output the sparse coefficients of the signal; Generate a binary null observation sequence, including: Row vectors corresponding to the set of strong interference frequency points are extracted from the standard discrete Fourier transform matrix to construct the interference frequency point submatrix; Establish a sequence optimization model; The sequence optimization model takes minimizing the total energy of the sequence under the projection of the interference frequency submatrix as the objective function and assumes that the sequence has a constant total power as a constraint. Solving the sequence optimization model yields a continuous-valued null trap sequence; Using the alternating projection algorithm, continuous null sequences are mapped to binary null observation sequences that satisfy hardware switching constraints.

2. The shortwave spectrum high-efficiency sampling method based on compressed sensing according to claim 1, characterized in that, The set of strong interference frequencies was determined, including: Sort the amplitude values ​​of all frequency points in the power spectral density data in ascending order; Extract frequency data that falls within a preset low-energy ratio range after sorting; Calculate the average energy value of the frequency point data as an estimate of the Gaussian white noise variance; Based on the Gaussian white noise variance estimate and the preset false alarm probability constraint, the dynamic decision threshold is calculated. Frequency points with amplitudes greater than the dynamic decision threshold in the power spectral density data are classified into the set of strong interference frequency points; Frequency points with amplitudes less than or equal to the dynamic decision threshold in the power spectral density data are excluded from the set of strong interference frequency points.

3. The shortwave spectrum high-efficiency sampling method based on compressed sensing according to claim 2, characterized in that, Using the alternating projection algorithm, including: Construct the interference null space projection operator; Among them, the interference null space projection operator is used to ensure that the energy response of the projected vector is zero at the set of strong interference frequency points; The current iteration sequence is projected using the interference null space projection operator to obtain an intermediate transition sequence; The intermediate transition sequence is symbolized by mapping each element of the intermediate transition sequence to a binary level to obtain the next round of iteration sequence; Repeat the projection and symbolization process until the sequence converges, and output the binary null observation sequence.

4. The shortwave spectrum high-efficiency sampling method based on compressed sensing according to claim 1, characterized in that, Output voltage sample values, including: Set the time constant and integration period of the analog integrator; The binary zero-trap observation sequence is used as a control signal to control the switching on and off of the analog front-end mixer circuit; During the integration period, the product of the input radio frequency signal and the binary null observation sequence is continuously integrated over time. The integral result is normalized to output discrete voltage sample values; The integration process involves orthogonally eliminating signal components corresponding to the set of strong interference frequency points at the physical level.

5. The efficient shortwave spectrum sampling method based on compressed sensing according to claim 1, characterized in that, The calculated signal sparsity coefficients include: Construct the observation matrix; Each row of the observation matrix corresponds to the discrete form of the binary null observation sequence; Establish a reconstruction optimization model; Among them, the reconstruction optimization model aims to minimize the L1 norm of the signal sparse coefficients, and is constrained by approximating the voltage sampling value by the product of the observation matrix, the preset sparse basis matrix, and the signal sparse coefficients. The reconstructed optimization model is solved using a convex optimization algorithm, and the output signal sparsity coefficients are obtained.

6. The efficient shortwave spectrum sampling method based on compressed sensing according to claim 1, characterized in that, Triggering the process of reacquiring power spectral density data includes: Determine if there are new interference sources in the current environment that are not covered by the set of strong interference frequencies; Control the low-speed scanning receiver to initiate full-band scanning; Based on the new power spectral density data obtained from the scan, the noise floor estimation and constant false alarm rate detection are re-executed to generate an updated set of strong interference frequency points. Based on the updated set of strong interference frequency points, a new binary null observation sequence is generated.

7. A shortwave spectrum high-efficiency sampling system based on compressed sensing, applied to the shortwave spectrum high-efficiency sampling method based on compressed sensing according to any one of claims 1-6, characterized in that, include: The spectrum sensing module is used to acquire power spectral density data across the entire frequency band using a low-speed scanning receiver and to determine the set of strong interference frequency points. The sequence generation module is used to generate binary null observation sequences with a set of strong interference frequency points as constraints. The analog sampling module is used to load the binary null observation sequence into the analog front-end mixer circuit, process the input RF signal and output the voltage sample value; The signal reconstruction module is used to calculate the signal sparsity coefficients based on the voltage sample values ​​using a compressed sensing reconstruction algorithm. The feedback control module is used to calculate the reconstruction residual; in response to the reconstruction residual being greater than a preset error threshold, the spectrum sensing module is triggered to update the set of strong interference frequency points. In response to the reconstruction residual being less than or equal to a preset error threshold, the output signal sparsity coefficients are adjusted.

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