A method for covert processing of spaceborne signals based on Tent mapping
By combining the chaotic sequence generated by Tent mapping with Box-Muller transform and segmented reconstruction mechanism, the problems of hardware resource overhead and insufficient signal recovery accuracy in covert transmission of spaceborne signals are solved, achieving low power consumption and high efficiency in signal recovery.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NORTHWESTERN POLYTECHNICAL UNIV
- Filing Date
- 2026-05-25
- Publication Date
- 2026-07-31
AI Technical Summary
While existing covert satellite signal transmission technologies reduce hardware resource consumption, they struggle to improve the statistical matching and cancellation accuracy of interference signals, resulting in insufficient signal recovery accuracy.
Chaotic sequences are generated using Tent mapping and Gaussianized by fixed-point quantization and Box-Muller transform. A segmented reconstruction and verification mechanism is implemented, and positive and negative fractional time delays and frequency offset step sizes are introduced to cancel interference subspace projection, thereby achieving fine signal compensation.
It reduces hardware resource consumption, improves anti-interception capability and signal recovery accuracy, and has good robustness and anti-interference capability.
Smart Images
Figure CN122339658B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of signal processing, and specifically to a method for covert processing of spaceborne signals based on Tent mapping. Background Technology
[0002] In spaceborne signal transmission systems, a common method to achieve covert signal transmission is to superimpose spurious noise or interference signals at the transmitting end and recover the target signal at the receiving end through reconstruction and cancellation. Existing technologies following this approach mainly focus on three areas: chaotic sequence construction, noise statistical characteristic matching, and time-frequency synchronization and interference cancellation.
[0003] In the construction of chaotic sequences, existing research has formed a relatively complete technical chain. For example, there are methods such as constructing chaotic interference piecemeal and reconstructing and canceling it at the receiver, or methods for cloaking signals based on the fractional Fourier transform domain, as well as application scenarios expanded from low-interception communication systems and chaotic modulation and demodulation. At the encryption implementation level, existing work has employed improved Logistic and Chebyshev mappings to construct composite chaotic sequences, or encryption systems based on chaotic sequence mappings, or methods for data encryption and decryption using chaotic system parameters. However, these methods for generating chaotic sequences generally require multiplication operations, resulting in significant hardware resource overhead and limitations in low-power spaceborne scenarios.
[0004] Existing research has also made valuable explorations in matching the statistical characteristics of interference signals. For example, hardware Gaussian noise generators based on the Box-Muller method and their error analysis provide a basis for constructing the statistical characteristics of interference. Some works have verified the feasibility of chaotic spread spectrum, but they mostly focus on covert transmission processes or modulation and demodulation mechanisms, lacking a mechanism for consistent matching between the Gaussianized chaotic sequence and the actual channel noise statistical characteristics. This results in insufficient fusion of the interference signal and the channel background noise, making it easy for third parties to detect through high-order statistical analysis.
[0005] In terms of time-frequency synchronization and interference cancellation, the proposed joint estimation method of time delay and frequency offset has improved the parameter acquisition capability, and related research has been extended to satellite communication and MIMO-OFDM scenarios. However, existing research mainly focuses on the acquisition of synchronization parameters or the reconstruction cancellation process, and the joint suppression of fractional-order time delay and fractional-order frequency offset residuals is still insufficient, which can easily form residual interference basis and affect the recovery accuracy of weak target signals.
[0006] Therefore, how to improve the statistical matching capability and cancellation accuracy of interference signals while reducing the resource overhead of spaceborne implementation is a key problem that urgently needs to be solved in the current technology of covert transmission of spaceborne signals. Summary of the Invention
[0007] To address the shortcomings of existing technologies, this invention provides a method for covert processing of spaceborne signals based on Tent mapping. It achieves multiplier-free iteration through fixed-point quantization using Tent mapping, reducing hardware overhead; it Gaussiansizes chaotic sequences using Box-Muller transform, enabling interference signals to match channel noise; it employs a segmented independent reconstruction and verification mechanism, with each segment achieving local reconstruction through the transmission of its initial state value; and it introduces positive and negative fractional time delays and frequency offset step sizes, using interference subspace projection to cancel and finely compensate residuals, thereby improving signal recovery accuracy.
[0008] To achieve the above objectives, the present invention adopts the following technical solution:
[0009] This invention proposes a method for covert processing of spaceborne signals based on Tent mapping, including transmitting-end processing and receiving-end processing;
[0010] The transmitting end processing includes the following steps:
[0011] S1. Set the initial theoretical value for the Tent mapping, perform fixed-point quantization on the initial theoretical value to obtain the initial quantized value, normalize the initial quantized value to obtain the initial normalized value, and use the initial normalized value as the initial value for the iterative Tent mapping to generate a length of... The Tent chaotic sequence; The length is the same as the target signal and is even.
[0012] S2. For the Tent chaotic sequence, starting from the first data, perform Box-Muller transform on two adjacent data to obtain Gaussian sample pairs; merge all the obtained Gaussian sample pairs to obtain the first interference signal.
[0013] S3. Divide the Tent chaotic sequence into equal parts. A segment of chaotic subsequence, ≥2, divide the first interference signal into equal parts The first interference subsequence of the segment;
[0014] The quantized value corresponding to the first data in each chaotic subsequence is converted into a binary number, and the converted binary number is used as the segment head state field to construct the corresponding identification signal; the identification signal includes a synchronization flag field, a segment head state field, and a verification field;
[0015] S4. Divide the target signal into equal parts. For each segment of the target subsequence, an amplitude adjustment coefficient is determined for each segment of the first interference subsequence, ensuring that the power spectral density of the adjusted first interference subsequence is not lower than the power spectral density of the corresponding segment of the target subsequence. Each segment of the target subsequence is superimposed with the corresponding segment of the adjusted first interference subsequence to obtain a mixed subsequence. A corresponding identification signal is added before each segment of the mixed subsequence to obtain a segment of the marked mixed subsequence. All the marked mixed subsequences are sequentially concatenated to form a forwarding signal, which is then sent to the receiving end.
[0016] The receiving end processing includes the following steps:
[0017] Step 1: Match the synchronization flag field of the marked mixed subsequence in the received signal using a sliding window to locate the identification signal of each marked mixed subsequence. Verify the verification field in each identification signal. If the verification passes, parse the quantization value from the corresponding segment head state field. Normalize the parsed quantization value and use it as the initial value for iteration. Reconstruct the second interference subsequence of the corresponding segment locally using the Tent mapping iteration and Box-Muller transform. At the same time, remove the identification signal from the located marked mixed subsequence to obtain the received mixed subsequence of each segment.
[0018] Step 2: Perform a two-dimensional mutual ambiguity function operation of time delay and frequency offset on each received mixed subsequence and the corresponding second interference subsequence to obtain the corresponding coarse time delay estimate and coarse frequency offset estimate;
[0019] Step 3: Apply time delay and frequency offset to each second interference subsequence based on the corresponding coarse time delay and coarse frequency offset estimates to obtain the corresponding candidate vectors. Concatenate all candidate vectors column by column to obtain the corresponding time delay-frequency offset estimation matrix.
[0020] Step 4: Project each received mixed subsequence to the interference subspace formed by the corresponding time delay-frequency offset estimation matrix, solve for the corresponding least squares weights, and obtain the corresponding estimated interference subsequence based on the least squares weights; cancel the corresponding estimated interference subsequence from each received mixed subsequence to obtain the corresponding received target subsequence; concatenate all the received target subsequences in sequence to obtain the received target signal.
[0021] Furthermore, in S1, the iterative formula for the Tent mapping is:
[0022]
[0023] In the formula, The first chaotic sequence signal in the Tent One data point, For control parameters, , The first chaotic sequence signal in the Tent The theoretical value corresponding to each data point;
[0024] right By sequentially performing fixed-point quantization and normalization, the first element in the Tent chaotic sequence is obtained. Data .
[0025] Furthermore, in S1, the bit width of the fixed-point quantization is 16 bits or 32 bits.
[0026] Furthermore, in S2, the formula for the Box-Muller transform is:
[0027]
[0028]
[0029] In the formula, and For the first Gaussian sample pairs, and The first chaotic sequence in Tent For adjacent data;
[0030] The first interference signal is a Gaussian distribution sequence with a mean of 0 and a variance of 1.
[0031] Furthermore, in S3, the synchronization flag field is a preset fixed codeword with a length greater than or equal to 6 bits, and the verification field is a cyclic redundancy check code or a hash check value.
[0032] Furthermore, in step 2, the formula for the time delay-frequency offset two-dimensional mutual ambiguity function operation is as follows:
[0033]
[0034] In the formula, For the first The segment receives the mixed subsequence and the first The mutual ambiguity function value of the second interference subsequence. For discrete sampling point numbers, For the first The first segment receives the mixed subsequence One data point, For the first The second interference subsequence of segment 1 One data point, For integer sample point level delay search values, This indicates the conjugate operation. The imaginary unit, This is the normalized frequency offset search value; To receive the length of the mixed subsequence, When the value is at its maximum, the corresponding and The first Coarse estimation of time delay and coarse estimation of frequency offset corresponding to the second interference subsequence of segment.
[0035] Further, in step 3, the formula for calculating the candidate vector is:
[0036]
[0037] In the formula, For discrete sampling point numbers, For the first The second interference subsequence corresponding to the first The th candidate vector One element, This is the inverse Fourier transform operation. For Fourier transform operations, This is a fractional delay offset index. For fractional frequency offset index, For the first The second interference subsequence of segment 1 One data point, The imaginary unit, For frequency index, For the first A rough estimate of the time delay corresponding to the second interference subsequence of the segment. For the first Coarse estimation of frequency offset corresponding to the second interference subsequence of segment . The fractional-order time delay search step size, This is the fractional frequency offset search step size.
[0038] Further, in step 4, the interference subsequence is estimated from the received mixed subsequence by canceling out the corresponding segments using the following formula:
[0039]
[0040]
[0041] when When the condition is pathological or irreversible:
[0042]
[0043] In the formula, For the first The segment receives the target subsequence. For the first The segment receives the mixed subsequence. for The corresponding time delay-frequency offset estimation matrix, for The corresponding least squares weights, for The conjugate transpose of the matrix. The inverse of the matrix. for The corresponding Moore-Penrose pseudoinverse.
[0044] Compared with the prior art, the beneficial effects of the present invention are as follows:
[0045] (1) This invention uses Tent mapping to generate chaotic sequences. In fixed-point quantization, when the control parameter takes a specific value, the iterative process can be simplified to a simple transformation operation. In the fixed-point number domain, numerical transformation can be achieved through shift and two's complement operations, avoiding multipliers. Compared with traditional chaotic sequence generation algorithms such as Logistic mapping that require multiplication operations, this invention only requires one comparator, one adder, and one shifter, significantly reducing the amount of logic resources required and improving the iteration speed, which can effectively meet the low power consumption and real-time processing requirements of spaceborne payloads.
[0046] (2) This invention transforms the uniformly distributed chaotic sequence generated by the Tent mapping into a standard Gaussian distribution through the Box-Muller transform, making the probability density function of the interference signal highly coincide with the theoretical Gaussian distribution of the satellite channel background noise. Compared with the prior art that directly uses the uniformly chaotic sequence as interference or uses Box-Muller to generate Gaussian noise alone, this invention combines the Box-Muller transform with the segmented sequence of the Tent mapping, making the transformed Gaussian interference signal difficult to distinguish from the channel noise in terms of statistical characteristics. Third parties cannot identify the presence of useful signals through conventional detection methods such as power spectrum analysis and higher-order cumulants, thereby greatly improving the anti-interception capability of the system. On this basis, this invention determines the amplitude adjustment coefficient for each segment of the first interference subsequence, so that the power spectral density of the adjusted interference subsequence in the frequency band occupied by the target signal is not lower than the power spectral density of the corresponding segment of the target subsequence. Unlike existing technologies that use a globally fixed amplitude, this invention employs segmented adaptive amplitude modulation. The adjustment coefficient for each segment can be calculated independently based on the power level of the target signal in that segment. While ensuring the concealment of each segment, it avoids using uniform high-power interference across the entire segment, significantly reducing the total transmission power overhead and achieving flexible control of the interference signal power.
[0047] (3) This invention divides the chaotic sequence into multiple segments, extracts the quantized value of the first data in each segment, constructs an identification signal including a synchronization flag field, a segment head state field, and a check field, and adds it before the corresponding segment's mixed subsequence. The receiving end locates the segment boundary by matching the synchronization flag through a sliding window, and can independently reconstruct the interference signal of that segment after parsing the segment head quantized value, without relying on global initial value synchronization. At the same time, the check field can detect whether the identification signal has bit errors during transmission. Segments that fail the check are marked as invalid segments, which does not affect the reconstruction and cancellation processing of other segments. This segmented independent reconstruction mechanism gives the system good robustness. Even if the identification signal of a certain segment is damaged, the other segments can still recover the target signal normally.
[0048] (4) Due to the sampling rate limitation of satellite signals, traditional time delay estimation can only be accurate to an integer number of sampling periods. Fractional time delay residuals and fractional frequency offset residuals cannot be effectively estimated and canceled, forming an interference basis and affecting the recovery accuracy of weak target signals. This invention obtains a coarse estimate after two-dimensional correlation between time delay and frequency offset. Positive and negative fractional time delay steps and positive and negative fractional frequency offset steps are applied near the coarse estimate to generate multiple candidate vectors and construct a time delay-frequency offset estimation matrix. The received mixed subsequence is projected onto the interference subspace spanned by the column vectors of this matrix. The optimal weights of each candidate vector are solved by least squares to achieve accurate reconstruction and cancellation of the actual interference components. This mechanism effectively compensates for sub-sampling level time delay deviations and subcarrier level frequency offset residuals, significantly reduces the residual interference basis, and improves the recovery accuracy of weak target signals. Attached Figure Description
[0049] Figure 1 The flowchart shows the spaceborne signal covert processing method based on Tent mapping according to the present invention.
[0050] Figure 2 The following are time-domain waveform comparison diagrams of the Tent chaotic sequence and the first interference signal; where (a) is the waveform diagram of the Tent chaotic sequence and (b) is the waveform diagram of the first interference signal obtained after Box-Muller transformation.
[0051] Figure 3 The diagram shows a comparison of the probability density of the Tent chaotic sequence and the first interference signal; where (a) is the probability density distribution of the Tent chaotic sequence and (b) is the probability density distribution of the first interference signal.
[0052] Figure 4 The spectrum comparison diagrams are of the target signal, the first interference signal, and the forwarding signal; where (a) is the spectrum diagram of the target signal, (b) is the spectrum diagram of the first interference signal, and (c) is the spectrum diagram of the forwarding signal.
[0053] Figure 5 This is the spectrum diagram of the second interference signal of the present invention;
[0054] Figure 6 This is a two-dimensional correlation result diagram of a received mixed subsequence and the corresponding second interference subsequence in an embodiment of the present invention;
[0055] Figure 7 This is a spectrum diagram of the target signal received by the present invention. Detailed Implementation
[0056] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0057] Example
[0058] refer to Figure 1 This embodiment provides a method for covert processing of spaceborne signals based on Tent mapping, including transmitting-end processing and receiving-end processing.
[0059] Transmitter processing includes the following steps:
[0060] S1. Set initial theoretical values , For the initial theoretical value Perform fixed-point quantization to obtain the initial quantized value. The initial quantized values are normalized to obtain the initial normalized values. , initial normalized value As the initial value for the Tent mapping iteration; generating a length of The Tent chaotic sequence; The length is the same as the target signal and is even. The first data in the Tent chaotic sequence is the initial normalized value. .
[0061] The iterative formula for the Tent mapping is:
[0062]
[0063] In the formula, The first in the Tent chaotic sequence One data point, , The first chaotic sequence signal in the Tent Data The corresponding theoretical value; For control parameters, .
[0064] right Perform fixed-point quantization to obtain Corresponding quantization value ,right Normalization yields... .
[0065] The bit width of fixed-point quantization is , Choose 16 or 32.
[0066] In this embodiment, =0.31415926, the length of the target signal is 32768. ,but ,in This is the rounding function; .
[0067] In practice, The values should be avoided as much as possible, such as 0, 0.5, and 1, to prevent the Tent chaotic sequence from degenerating.
[0068] In this embodiment, ,when At this point, the Tent mapping is in a fully mapped chaotic state. The Tent chaotic sequence generated in this step is uniformly distributed on [0,1). The iterative formula can be implemented by left shift and inversion plus one operation, without the need for a multiplier. For Its corresponding quantization value is , which can be determined by Left shift by one bit to get; for Its corresponding quantization value is You can start with Take the two's complement to get The algorithm then shifts the bit to the left. This implementation avoids multiplication and requires only one comparator, one adder, and one shifter. Compared to chaotic sequence generation algorithms such as Logistic mapping that require multipliers, this invention offers faster iterative computation and reduces logic resource consumption, effectively meeting the low-power real-time processing requirements of spaceborne payloads.
[0069] S2. For the Tent chaotic sequence, starting from the first data, take two adjacent data as a pair of inputs and perform Box-Muller transformation to obtain Gaussian sample pairs; merge all the obtained Gaussian sample pairs to obtain the first interference signal.
[0070] The formula for the Box-Muller transform is:
[0071]
[0072]
[0073] In the formula, and For the first Gaussian sample pairs, and The first chaotic sequence in Tent For adjacent data, .
[0074] when (Right now When ), use the preset minimum positive number. Replace this input, make The definition ensures that the Box-Muller output corresponds one-to-one with the input in length and position, and the segment boundary relationship is not broken.
[0075] Will and according to The order of the numbers is alternating, resulting in a length of... First interference signal .
[0076] In this embodiment, the first interference signal is a Gaussian distribution sequence with a mean of 0 and a variance of 1.
[0077] Figure 2 In the diagram, (a) is the waveform of the Tent chaotic sequence obtained by S1, which is uniformly distributed; (b) is the time-domain waveform of the first interference signal, which is Gaussian distributed.
[0078] Figure 3 In the diagram, (a) shows the probability density distribution of the Tent chaotic sequence, which is uniformly distributed; (b) shows the probability density distribution of the first interference signal. Figure 3 As can be seen, the probability density distribution of the first interference signal highly coincides with the theoretical Gaussian distribution, indicating that the first interference signal achieves a deep fit with the real channel noise in terms of statistical characteristics.
[0079] S3. Divide the Tent chaotic sequence into equal parts. A segment of chaotic subsequence, ≥2, divide the first interference signal into equal parts The first interference subsequence; the length of the chaotic subsequence and the first interference subsequence. The number is even. In this embodiment, =32, then =1024.
[0080] The quantized value corresponding to the first data in each chaotic subsequence is converted into a binary number, and the converted binary number is used as the segment head state field to construct the corresponding identification signal; the identification signal includes a synchronization flag field, a segment head state field, and a verification field;
[0081] The synchronization flag field is a preset fixed codeword with a length of 6 bits or more, used for segment boundary positioning; the segment head status field carries the binary representation of the quantized value corresponding to the first data in the chaotic subsequence of the segment; the check field is a cyclic redundancy check code or hash check value calculated based on the segment head status field, used to detect and identify signal transmission errors.
[0082] In this embodiment, the synchronization flag field uses a fixed codeword 111100 with a length of 6 bits; the bit length of the segment header status field is equal to the quantization bit width of 16 bits, and the check field uses 8-bit cyclic redundancy check. The total bit length of the identification signal is 6 + 16 + 8 = 30 bits.
[0083] Taking the first chaotic subsequence as an example, its corresponding identification signal is:
[0084] The synchronization flag field is 111100;
[0085] The segment start status field is =20588 corresponds to the 16-bit binary number (i.e., 0101000011001100).
[0086] The check field is an 8-bit cyclic redundancy check value calculated based on the segment header status field.
[0087] It should be noted that, for ease of subsequent direct splicing, a preset modulation method, such as BPSK (Binary Phase Shift Keying) or QPSK (Quadrature Phase Shift Keying), is required to map the identification signal into a baseband sample sequence. The baseband sample sequence and the hybrid subsequence have the same sample format and sampling rate. For ease of description, the baseband sample sequence obtained after modulation and mapping will still be referred to as the identification signal below.
[0088] S4. Divide the target signal into equal parts. For each segment of the target subsequence, an amplitude adjustment coefficient is determined for the first interference subsequence, ensuring that the power spectral density of the adjusted first interference subsequence is not lower than the power spectral density of the corresponding target subsequence.
[0089]
[0090] in, For frequency variables, For the first The power spectral density of the first interference subsequence after segment adjustment. for The corresponding number The power spectral density of the target subsequence. The frequency band occupied by the target signal.
[0091] The first The amplitude adjustment coefficient of the first interference subsequence is denoted as , The power spectrum of the target signal can be determined offline in advance, or it can be adjusted in real time through a feedback loop. In this embodiment, The calculation method is as follows:
[0092]
[0093] in, To reserve a margin factor to cope with channel fluctuations or power estimation errors, ensuring that the interference signal can completely cover the target signal under any circumstances, in this embodiment, . For the first The power spectral density of the first interference subsequence of the segment.
[0094] Compared to global single amplitude modulation, segmented amplitude modulation can match the power level of the target signal in each segment separately, reducing the total transmit power overhead of the entire segment while ensuring the stealth of each segment.
[0095] Each target subsequence is superimposed with the corresponding adjusted first interference subsequence to obtain a mixed subsequence;
[0096] In this embodiment, after each mixed subsequence is band-limited filtered, a corresponding identification signal is added before each mixed subsequence to obtain a labeled mixed subsequence. Taking the first mixed subsequence as an example, after the first mixed subsequence is band-limited filtered, the identification signal corresponding to the first chaotic subsequence is added before the first mixed subsequence to obtain the first labeled mixed subsequence.
[0097] All the labeled mixed subsequences are sequentially concatenated to form a forwarding signal, which is then sent to the receiving end.
[0098] Figure 4 In the diagram, (a) is the spectrum of the target signal, (b) is the spectrum of the first interference signal, exhibiting dense random fluctuation characteristics; and (c) is the spectrum of the relay signal. Figure 4 As can be seen, the adjusted first interference signal completely covers the spectral characteristics of the target signal.
[0099] The receiving end processing includes the following steps:
[0100] Step 1: The receiving end performs a sliding window matching search on the received signal according to the preset format of the identification signal (synchronization flag field + segment start status field + check field) to locate the identification signal in each segment of the marked mixed subsequence in the received signal; using the preset synchronization flag field 111100 as the matching template, the starting position of each segment of the identification signal is located.
[0101] After locating the synchronization flag field, read the immediately following W bits as the segment header status field, and then read the immediately following 8 bits as the check field. Verify the segment header status field based on the check field.
[0102] If the verification passes, the corresponding quantization value is parsed from the segment head status field. The parsed quantization value is normalized to obtain a normalized value. This normalized value is used as the initial value of the Tent mapping iterative equation. According to the Tent mapping iterative equation and Box-Muller transform of the transmitter, the corresponding segment's second interference subsequence is reconstructed locally. All the second interference subsequences are spliced together in order to obtain the second interference signal.
[0103] If the verification fails, the segment will be marked as invalid and will not participate in the subsequent steps 2 to 4.
[0104] Simultaneously, the identification signal is stripped from the located marker mixed sub-sequence to obtain each segment of the received mixed sub-sequence.
[0105] In this step, each second interference subsequence can be reconstructed independently without relying on global initial value synchronization; when a segment of the identification signal fails to be verified, the receiver continues to reconstruct from the next segment of the identification signal.
[0106] Figure 5 The spectrum diagram of the second interference signal is shown below. Figure 4 The spectrum of the first interference signal shown in (b) is statistically consistent, which proves the accuracy of the receiver's reconstruction of the interference signal.
[0107] Step 2: Due to propagation delay and Doppler frequency offset in signal transmission between the satellite and the ground, the interference component in the received mixed subsequence has an unknown integer sampling point-level delay and normalized frequency offset relative to the second interference subsequence reconstructed locally at the receiver. Therefore, a two-dimensional mutual ambiguity function operation of delay-frequency offset is performed on each segment of the received mixed subsequence and the corresponding segment of the second interference subsequence to obtain the corresponding coarse estimate of delay and coarse estimate of frequency offset.
[0108] The formula for the time delay-frequency offset two-dimensional mutual ambiguity function operation is as follows:
[0109]
[0110] In the formula, For the first The segment receives the mixed subsequence and the first The mutual ambiguity function value of the second interference subsequence. For discrete sampling point numbers, To receive the length of the mixed subsequence, , For the first The first segment receives the mixed subsequence One data point, For the first The second interference subsequence of segment 1 One data point, For integer sample point level delay search values, This indicates the conjugate operation. The imaginary unit, The normalized frequency offset search value is compared with the actual frequency offset. The relationship is , Sampling rate; The value corresponding to the maximum and The first Coarse estimation of time delay and coarse estimation of frequency offset corresponding to the second interference subsequence of segment.
[0111] In actual satellite-to-ground links, if the time delay and Doppler frequency offset are... If the time interval of each sample is approximately constant, then the coarse estimates of time delay and frequency offset for each segment are approximately consistent. In this case, the two-dimensional correlation result of any segment of the second interference subsequence can be used as the input for the subsequent step 3. If the channel changes rapidly, coarse estimates can also be obtained for each segment separately and used independently in step 3.
[0112] Figure 6 This is a two-dimensional correlation result diagram of a segment of the received mixed subsequence and the corresponding segment of the second interference subsequence in this embodiment. There is a sharp and unique correlation peak in the diagram, which is the coarse estimate of the time delay and the coarse estimate of the frequency offset corresponding to the segment of the second interference subsequence.
[0113] Step 3: Due to the limited sampling rate of the satellite signal, the coarse time delay estimation can only be accurate to integer sampling points, and the coarse frequency offset estimation can only achieve a resolution comparable to that of the correlation search grid. If the residual subsampling-level time delay deviation and subcarrier-level frequency offset deviation are not compensated, they will form a significant residual interference floor, affecting the accuracy of target signal recovery.
[0114] For each second interference subsequence, positive and negative fractional time delay steps and positive and negative fractional frequency offset steps are applied near the corresponding coarse time delay and coarse frequency offset estimates to obtain multiple candidate vectors. All candidate vectors are concatenated column-wise to obtain the corresponding time delay-frequency offset estimation matrix.
[0115] No. The second interference subsequence corresponding to the first The th candidate vector element The calculation formula is:
[0116]
[0117] In the formula, This is the inverse Fourier transform operation. For Fourier transform operations, This is a fractional delay offset index. , Let f be the fractional search order in the time delay direction. For fractional frequency offset index, , Let the fractional search order be the order in the frequency offset direction. For the first The second interference subsequence of segment 1 One data point, The imaginary unit, For frequency index, For the first A rough estimate of the time delay corresponding to the second interference subsequence of the segment. For the first Coarse estimation of frequency offset corresponding to the second interference subsequence of segment . The fractional-order time delay search step size, This is the fractional frequency offset search step size.
[0118] Each candidate vector is represented as a vector of length... Column vectors:
[0119]
[0120] Will Concatenate the candidate vectors column-wise to obtain the first candidate vector. The time delay-frequency offset estimation matrix corresponding to the second interference subsequence of segment :
[0121]
[0122] The scale is The number of rows equals The number of columns is equal to the number of candidate vectors.
[0123] In this embodiment, the following is taken , Each sampling period, cycles / sample, fractional search range is ,common There are candidate vectors; The candidate vectors are concatenated column-wise to obtain a column count of 25. In this step, fractional offsets in both positive and negative directions are introduced to unbiasedly cover the true residuals around the coarse estimate.
[0124] Step 4, place the first Segment receive mixed subsequence (considered to be of length) Projecting the column vectors of the vectors onto the vectors of ... Solve for the interference subspace spanned by the column vectors of . Least square weights of all candidate vectors :
[0125]
[0126] Based on least squares weights Obtain the corresponding segment estimated interference subsequence ;
[0127] From the Segment receive mixed subsequence The interference subsequence is estimated by subtracting the corresponding segment. , obtained the Segment Received Target Subsequence :
[0128]
[0129] when When the condition is pathological (condition number is too large) or irreversible (determinant is 0), use Corresponding Moore-Penrose pseudoinverse replace ,Right now:
[0130]
[0131] In the formula, for The conjugate transpose of the matrix. It is the inverse of the matrix.
[0132] Since the mixed subsequence at the transmitting end contains amplitude adjustment coefficients, and the receiving end automatically absorbs the amplitude adjustment coefficients during the least squares weighting process, the receiving end does not need to explicitly know the amplitude adjustment coefficients of each segment.
[0133] By sequentially concatenating all the received target sub-sequences, the complete received target signal is obtained. :
[0134]
[0135] Figure 7 The spectrum of the received target signal, and Figure 4 The spectrum of the target signal shown in (a) is consistent, and the main lobe characteristics of the target signal reappear, indicating that the method of the present invention can achieve high-gain interference stripping and covert transmission.
[0136] The specific embodiments of the present invention are provided to enable those skilled in the art to understand or implement the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention.
[0137] It should be understood that the present invention is not limited to the content already described above, and various modifications and changes can be made without departing from its scope. The scope of the present invention is limited only by the appended claims.
Claims
1. A method for covert processing of spaceborne signals based on Tent mapping, characterized in that, This includes both transmitter processing and receiver processing. The transmitting end processing includes the following steps: S1. Set the initial theoretical value for the Tent mapping, perform fixed-point quantization on the initial theoretical value to obtain the initial quantized value, normalize the initial quantized value to obtain the initial normalized value, and use the initial normalized value as the initial value for the iterative Tent mapping to generate a length of... The Tent chaotic sequence; The length is the same as the target signal and is even. S2. For the Tent chaotic sequence, starting from the first data, perform Box-Muller transform on two adjacent data to obtain Gaussian sample pairs; merge all the obtained Gaussian sample pairs to obtain the first interference signal. S3. Divide the Tent chaotic sequence into equal parts. A segment of chaotic subsequence, ≥2, divide the first interference signal into equal parts The first interference subsequence of the segment; The quantized value corresponding to the first data in each chaotic subsequence is converted into a binary number, and the converted binary number is used as the segment head state field to construct the corresponding identification signal; the identification signal includes a synchronization flag field, a segment head state field, and a verification field; S4. Divide the target signal into equal parts. For each segment of the target subsequence, an amplitude adjustment coefficient is determined for each segment of the first interference subsequence, ensuring that the power spectral density of the adjusted first interference subsequence is not lower than the power spectral density of the corresponding segment of the target subsequence. Each segment of the target subsequence is superimposed with the corresponding segment of the adjusted first interference subsequence to obtain a mixed subsequence. A corresponding identification signal is added before each segment of the mixed subsequence to obtain a segment of the marked mixed subsequence. All the marked mixed subsequences are sequentially concatenated to form a forwarding signal, which is then sent to the receiving end. The receiving end processing includes the following steps: Step 1: Match the synchronization flag field of the marked mixed subsequence in the received signal using a sliding window to locate the identification signal of each marked mixed subsequence. Verify the verification field in each identification signal. If the verification passes, parse the quantization value from the corresponding segment head state field. Normalize the parsed quantization value and use it as the initial value for iteration. Reconstruct the second interference subsequence of the corresponding segment locally using the Tent mapping iteration and Box-Muller transform. At the same time, remove the identification signal from the located marked mixed subsequence to obtain the received mixed subsequence of each segment. Step 2: Perform a two-dimensional mutual ambiguity function operation of time delay and frequency offset on each received mixed subsequence and the corresponding second interference subsequence to obtain the corresponding coarse time delay estimate and coarse frequency offset estimate; Step 3: Apply time delay and frequency offset to each second interference subsequence based on the corresponding coarse time delay and coarse frequency offset estimates to obtain the corresponding candidate vectors. Concatenate all candidate vectors column by column to obtain the corresponding time delay-frequency offset estimation matrix. Step 4: Project each received mixed subsequence to the interference subspace formed by the corresponding time delay-frequency offset estimation matrix, solve for the corresponding least squares weights, and obtain the corresponding estimated interference subsequence based on the least squares weights; cancel the corresponding estimated interference subsequence from each received mixed subsequence to obtain the corresponding received target subsequence; concatenate all the received target subsequences in sequence to obtain the received target signal.
2. The method for covert processing of spaceborne signals based on Tent mapping according to claim 1, characterized in that, In S1, the Tent mapping iterative formula is: In the formula, The first chaotic sequence signal in the Tent One data point, For control parameters, , The first chaotic sequence signal in the Tent The theoretical value corresponding to each data point; right By sequentially performing fixed-point quantization and normalization, the first element in the Tent chaotic sequence is obtained. Data .
3. The method for covert processing of spaceborne signals based on Tent mapping according to claim 1, characterized in that, In S1, the bit width of the fixed-point quantization is 16 bits or 32 bits.
4. The method for covert processing of spaceborne signals based on Tent mapping according to claim 1, characterized in that, In S2, the formula for the Box-Muller transform is: In the formula, and For the first Gaussian sample pairs, and The first chaotic sequence in Tent For adjacent data; The first interference signal is a Gaussian distribution sequence with a mean of 0 and a variance of 1.
5. The method for covert processing of spaceborne signals based on Tent mapping according to claim 1, characterized in that, In S3, the synchronization flag field is a preset fixed codeword with a length greater than or equal to 6 bits, and the verification field is a cyclic redundancy check code or a hash check value.
6. The method for covert processing of spaceborne signals based on Tent mapping according to claim 1, characterized in that, In step 2, the formula for the time delay-frequency offset two-dimensional mutual ambiguity function operation is as follows: In the formula, For the first The segment receives the mixed subsequence and the first The mutual ambiguity function value of the second interference subsequence. For discrete sampling point numbers, For the first The first segment receives the mixed subsequence One data point, For the first The second interference subsequence of segment 1 One data point, For integer sample point level delay search values, This indicates the conjugate operation. The imaginary unit, This is the normalized frequency offset search value; To receive the length of the mixed subsequence, When the value is at its maximum, the corresponding and The first Coarse estimation of time delay and coarse estimation of frequency offset corresponding to the second interference subsequence of segment.
7. The method for covert processing of spaceborne signals based on Tent mapping according to claim 1, characterized in that, In step 3, the formula for calculating the candidate vector is: In the formula, For discrete sampling point numbers, For the first The second interference subsequence corresponding to the first The th candidate vector One element, This is the inverse Fourier transform operation. For Fourier transform operations, This is a fractional delay offset index. For fractional frequency offset index, For the first The second interference subsequence of segment 1 One data point, The imaginary unit, For frequency index, For the first A rough estimate of the time delay corresponding to the second interference subsequence of the segment. For the first Coarse estimation of frequency offset corresponding to the second interference subsequence of segment . The fractional-order time delay search step size, This is the fractional frequency offset search step size.
8. The method for covert processing of spaceborne signals based on Tent mapping according to claim 1, characterized in that, In step 4, the interference subsequence is estimated by canceling the corresponding segment from the received mixed subsequence using the following formula: when When the condition is pathological or irreversible: In the formula, For the first The segment receives the target subsequence. For the first The segment receives the mixed subsequence. for The corresponding time delay-frequency offset estimation matrix, for The corresponding least squares weights, for The conjugate transpose of the matrix. The inverse of the matrix. for The corresponding Moore-Penrose pseudoinverse.