Broadband spectrum detection method and device driven by three paths of coprime spectrums

Abstract

The invention discloses a three-path coprime spectrum driven broadband spectrum detection method and device, and belongs to the technical field of broadband electromagnetic spectrum sensing. The method comprises the following steps: carrying out undersampling on a real signal by adopting a three-path coprime sampling rate, and obtaining three paths of branch spectrums with different resolutions through multi-phase filtering, IDFT (Inverse Discrete Fourier Transform) and cross-correlation operation; and after the resolution is unified through up-sampling, adaptive merging judgment is carried out by using saliency measurement based on spectrum similarity, and a real spectrum peak and an aliasing false peak are effectively distinguished. The device core comprises a radio frequency front end, a three-channel low-speed ADC and a digital signal processing platform. According to the method, pseudo-peak-free panoramic spectrum sensing in the frequency band of 300MHz-10GHz under the under-sampling condition is realized, and the method has the advantages of low hardware complexity, high engineering feasibility, high robustness to dense signals and the like, and is particularly suitable for non-cooperative electronic reconnaissance scenes.

Description

Technical Field

[0001] This invention belongs to the field of broadband electromagnetic spectrum sensing technology, specifically involving a broadband spectrum analysis method under an undersampling architecture. It is particularly suitable for fully digital blind detection of high-frequency (300 MHz-10 GHz), large-bandwidth, low probability of intercept (LPI / LPD) signals in non-cooperative electronic reconnaissance scenarios. The method solves the spectral aliasing problem caused by undersampling of real signals through a three-path coprime spectrum collaborative mechanism. Background Technology

[0002] Electronic signals radiated by electronic information equipment exhibit significant characteristics such as high frequency, wide bandwidth, low probability of intercept (LPI / LPD), short bursts, and power management. This trend poses an unprecedented and severe challenge to the field of electronic reconnaissance, especially in non-cooperative signal reception scenarios. In such scenarios, receivers typically lack prior information about the target signal (i.e., "blind detection"), yet need to perform real-time, large-scale scanning and monitoring of a broad radio spectrum to quickly intercept, identify, and locate potential threat signals. In this context, the primary step in analyzing intercepted signals is to obtain their carrier frequency location, requiring the system to quickly generate a global spectrum map and identify frequencies of interest.

[0003] Current mainstream electronic receivers are still based on superheterodyne architecture, which requires analog circuit components such as mixers, intermediate frequency filters, and local oscillators. The use of these analog components not only results in large and bulky equipment, but also means that superheterodyne receivers typically only employ linear scanning (i.e., scanning segment by segment from low to high frequency with a fixed step size). This inherently leads to slow scanning speeds and a tendency to lose transient targets. For example:

[0004] Reference 1: A Ali, W Hamouda. Advances on spectrum sensing forcognitive radio networks: theory and applications[J]. IEEE CommunicationsSurveys & Tutorials, 2017, 19(2): 1277-1304. doi: 10.1109 / COMST.2016.2631080.;

[0005] Reference 2: ZHANG Ling, WEI Zhiqing, WANG Lin, et al. Spectrum sharing in the sky and space: a survey[J]. Sensors. 2023; 23(1):342. doi: 10.3390 / s23010342.

[0006] Donoho D L. Compressed sensing[J]. IEEE Transactions on informationtheory, 2006, 52(4): 1289-1306. Therefore, the adoption of fully digital spectrum sensing technology has become an inevitable development trend in this field.

[0007] However, according to Shannon's sampling theorem, distortion-free spectrum analysis of a signal requires a sampling rate that is at least twice the highest frequency of the signal. As the signal spectrum continues to expand to higher frequency bands and the bandwidth continues to increase, the sampling devices and analog-to-digital converters (ADCs) in practical applications can hardly meet the extremely high sampling rate requirements of Nyquist sampling. At the same time, performing Nyquist sampling on high-frequency broadband signals will generate massive amounts of data, which brings huge computational load and cost pressure to the subsequent real-time signal processing stage. Therefore, how to achieve efficient and reliable spectrum sensing under the condition that the sampling rate is much lower than the highest frequency of the signal (i.e., undersampling) has become a key technical bottleneck that needs to be overcome in the field of signal processing. The existing undersampling spectrum sensing methods mainly include compressed sensing [4] and coprime spectrum analysis algorithm [5].

[0008] While compressed sensing methods (such as modulated wideband converter (MWC) and multiple co-collection sampling) reduce the sampling rate requirements and data volume of ADCs to some extent, they face significant challenges in engineering implementation. The MWC method requires a high-speed pulse generation circuit and relies on multiple parallel analog filter banks to complete the undersampling operation, leading to increased system hardware complexity and significantly higher costs. The multiple co-collection sampling method requires the driving clocks of each branch ADC to maintain an extremely high precision time delay relationship at the sub-nanosecond level. This stringent synchronization requirement greatly increases the difficulty of engineering implementation and the risk of system stability. Currently, this method mainly remains in the simulation research stage, and there are few reports of actual engineering application cases. In addition, the spectrum sensing method based on compressed sensing also has inherent defects such as low carrier frequency estimation accuracy and high constraint on the sparsity of the source frequency band distribution. The specific reasons are as follows: (1) The compressed sensing spectrum reconstruction algorithm can only locate the carrier frequency within a limited spectral support area. The Nyquist sequence generation process is only a simple spectrum slice merging operation, and its frequency estimation accuracy is limited by the accuracy of the spectral support area; (2) The compressed sensing reconstruction condition has strict requirements on the sparse distribution characteristics of the source. When multiple sources are densely distributed (for example, when the source spans multiple spectral support areas), the method will lose its effectiveness.

[0009] In summary, given the stringent requirements of non-cooperative, real-time, large-scale spectrum monitoring in the field of electronic reconnaissance, there is an urgent need to develop a novel broadband spectrum sensing technology that can operate efficiently under under-sampling conditions, possesses low hardware complexity and high engineering feasibility, and effectively overcomes the inherent shortcomings of existing methods (such as the high cost of MWC and the stringent synchronization requirements of multi-coset sampling). This invention aims to implement under-sampling broadband spectrum analysis functionality on a general-purpose digital signal processing platform, using coprime spectrum under-sampling analysis as a breakthrough.

[0010] Traditional coprime spectrum analysis algorithms complete broadband spectrum analysis tasks by performing low-speed parallel digital signal processing on two coprime sampling channels. The key operations on any channel only include three basic digital signal processing operations: polyphase filtering, IDFT, and cross-correlation [8]. It has the characteristics of having a small number of sampling channels and low design complexity, and can complete global spectrum sensing in a short time. However, in actual electronic signal reconnaissance tasks, the signals sensed are all real signals. The undersampling operation of real signals combined with the remainder algorithm requirements contained in the coprime spectrum algorithm will produce a remainder pair selection ambiguity problem in the signal reconstruction process, which will inevitably lead to spectrum aliasing. Specifically, the spectrum band of the original real signal (symmetrically distributed at half sampling rate) presents a disordered distribution state on the entire frequency axis. Therefore, it is necessary to organically combine the undersampling mode with the spectrum reconstruction method to eliminate such aliasing problems.

[0011] Based on this, this invention proposes a broadband spectrum detection method driven by three coprime spectra on the basis of traditional coprime spectrum analysis. Its main innovations are reflected in the following three aspects: (1) Real-time scanning and monitoring of broadband spectrum signals are realized based on the coprime spectrum undersampling analysis algorithm, and global spectrum drawing is completed; (2) The fully digital broadband spectrum analysis method based on direct undersampling at the radio frequency end is adopted to replace the traditional superheterodyne broadband spectrum analysis system based on analog front-end circuit; (3) The spectrum aliasing problem caused by the conjugate symmetry of the real signal spectrum is effectively eliminated. Summary of the Invention

[0012] The purpose of this invention is to propose a broadband spectrum detection method and device driven by three coprime spectra. By introducing the third coprime spectrum analysis and combining it with the Chinese remainder theorem, the uniqueness of frequency point mapping is ensured, thereby eliminating spurious peaks. The three coprime spectrum cooperative mechanism is used to eliminate the spectrum aliasing problem caused by undersampling of real signal coprime.

[0013] To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0014] In a first aspect, the present invention proposes a broadband spectrum detection method driven by three coprime spectra, comprising the following steps:

[0015] (a) For the input real signal By sampling rate , , Three-way undersampling is performed to obtain three digital signals. , , Where M, N, and S are pairwise coprime positive integers. This represents the upper limit of the signal frequency coverage range.

[0016] (b) Perform multiphase decimation and filtering on each sampled signal to obtain six sets of sub-signals;

[0017] (c) Perform inverse discrete Fourier transform on the six groups of sub-signals respectively to obtain six groups of transformed signals;

[0018] (d) Perform cross-correlation operations on each pair of the six transformed signals to obtain the three-branch spectrum. , , ;

[0019] (e) Perform upsampling interpolation on the three branch spectra respectively, so that the number of frequency points is uniformly MNS and the resolution is uniformly MNS. ;

[0020] (f) Based on significance measure The branch spectra after sampling from the three paths are merged and decided to output a global spectrum without aliasing. ,in:

[0021] ;

[0022] when When the arithmetic mean of the three spectra is taken, The minimum value of the three spectra is taken at time, and A is a preset threshold.

[0023] In some implementations, the polyphase filtering in step (b) uses three sets of cutoff frequencies respectively. , and The low-pass filter bank.

[0024] In some implementations, the cross-correlation operation in step (d) includes the cross-correlation of the following three pairs of signal combinations:

[0025] Depend on and The derived upper and lower channel signals;

[0026] Depend on and The derived upper and lower channel signals;

[0027] Depend on and The derived upper and lower channel signals.

[0028] In some implementations, the significance threshold A is in the range of 0.8 ≤ A ≤ 0.9, preferably 0.85.

[0029] In some implementations, the ranges of the three coprime parameters M, N, and S satisfy the following:

[0030] M, N, S ≥10, and are pairwise coprime;

[0031] Each channel has a sampling rate of less than 500 MS / s, making it suitable for direct RF sampling in the 300 MHz to 10 GHz frequency band.

[0032] Secondly, the present invention proposes a broadband spectrum detection device driven by three coprime spectra, comprising:

[0033] The radio frequency front-end module is used to receive and preprocess electromagnetic signals in the 300MHz to 10GHz frequency band.

[0034] A sample-and-hold module, connected to the RF front end, is used for signal sampling and holding;

[0035] A three-channel analog-to-digital converter, with sampling rates of... , , Undersample the signal;

[0036] A digital signal processing module, including an FPGA and / or a processor, for performing the method as described in any one of claims 1 to 5;

[0037] The digital signal processing module further includes:

[0038] A multiphase filtering unit is used to implement multiphase decimation and filtering;

[0039] The IDFT unit is used to perform the inverse discrete Fourier transform;

[0040] Cross-correlation calculation unit, used to calculate branch spectrum;

[0041] Upsampling and merging decision unit, used for spectral interpolation and spurious peak suppression.

[0042] In some implementations, the ADC is a low-speed ADC with a sampling rate of less than 500 MS / s, preferably the ADIAD9434 model.

[0043] In some implementations, the digital signal processing module is based on a Xilinx Zynq UltraScale+MPSoC, where the FPGA is used for pipelined processing and the ARM core is used for adaptive decision algorithm execution.

[0044] In some implementations, the sample-and-hold module uses an HMC661 chip that supports full-power bandwidth up to 18 GHz.

[0045] In some implementations, the device is suitable for non-cooperative electronic reconnaissance scenarios, enabling blind detection and panoramic spectrum mapping of signals with low probability of intercept.

[0046] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0047] 1) Based on the theory of coprime spectrum undersampling, this invention proposes a three-way coprime spectrum collaborative driving architecture. By adding a third sampling channel, a unique solution space of the remainder is constructed, eliminating the aliasing defect when reconstructing the spectrum after undersampling of the real signal. Combining RF direct sampling and all-digital processing, it achieves pseudo-peak-free global spectrum perception in the 300MHz-10GHz frequency band, overcoming the bottleneck of high-precision real-time detection of undersampled broadband signals in non-cooperative reconnaissance.

[0048] 2) By creatively introducing a third coprime constraint, the problem of spectral aliasing caused by undersampling of real signals is eliminated from a mathematical perspective, overcoming the inherent defects of traditional dual-path coprime spectra and the requirements of compressed sensing methods on signal sparsity and high hardware complexity. Attached Figure Description

[0049] Figure 1 This is a flowchart of the broadband spectrum detection method driven by three coprime spectra of the present invention.

[0050] Figure 2 This is a roadmap of the broadband spectrum detection technology driven by the three coprime spectra of the present invention.

[0051] Figure 3 This is a DFT filter bank.

[0052] Figure 4 This is a flowchart of traditional coprime spectrum analysis.

[0053] Figure 5 This refers to the spectral aliasing effect of undersampled real signals.

[0054] Figure 6 This is a schematic diagram of upsampling the three-channel global spectrum.

[0055] Figure 7 The results are from the three-way cross-correlation spectrum analysis.

[0056] Figure 8 This is a schematic diagram of the broadband spectrum detection device driven by three coprime spectra of the present invention. Detailed Implementation

[0057] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0058] This disclosure first presents the overall architecture and computational process of the invention, then elaborates on its technical principles and implementation process, and finally verifies the process and performance through specific experiments.

[0059] Example 1, such as Figure 1 The diagram shows the flow chart of the broadband spectrum detection method driven by three coprime spectra of the present invention, which specifically includes the following steps:

[0060] (a) For the input real signal By sampling rate , , Three-way undersampling is performed to obtain three digital signals. , , Where M, N, and S are pairwise coprime positive integers. This represents the upper limit of the signal frequency coverage range.

[0061] (b) Perform multiphase decimation and filtering on each sampled signal to obtain six sets of sub-signals;

[0062] (c) Perform inverse discrete Fourier transform on the six groups of sub-signals respectively to obtain six groups of transformed signals;

[0063] (d) Perform cross-correlation operations on each pair of the six transformed signals to obtain the three-branch spectrum. , , ;

[0064] (e) Perform upsampling interpolation on the three branch spectra respectively, so that the number of frequency points is uniformly MNS and the resolution is uniformly MNS. ;

[0065] (f) Based on significance measure The branch spectra after sampling from the three paths are merged and decided to output a global spectrum without aliasing. ,in:

[0066] ;

[0067] when When the arithmetic mean of the three spectra is taken, The minimum value of the three spectra is taken at time, and A is a preset threshold.

[0068] The three-channel coprime spectrum driving system proposed in this invention eliminates spectral aliasing of real signals through a three-channel cross-sampling and joint decision mechanism, comprising six core steps: sampling, polyphase decimation and filtering, IDFT, cross-correlation, upsampling, and combined decision. Among these, the polyphase decimation and filtering operations require three cutoff frequencies. , and The filters correspond to M-channel, N-channel, and S-channel polyphase filtering processes, respectively, where M, N, and S are pairwise coprime. The specific technical approach is as follows: Figure 2 As shown:

[0069] Input: Analog signal The coverage range value of the frequency axis (The upper limit of the corresponding real signal frequency detection is) ), significance threshold A, and three integer values ​​that satisfy pairwise coprime relationships. .

[0070] Step 1: For By sampling rate , , Undersampling was performed to obtain three digital signals. , , .

[0071] Step 2: Perform multiphase decimation and filtering on each sampled signal, outputting a total of six sets of signals. Specifically, the signal obtained in Step 1 after M-fold downsampling... Multiphase decimation and filtering are performed on N-channel and S-channel signals respectively, resulting in N-channel output signals. and S-channel signal The signal obtained by downsampling N times in Step 1 Multiphase decimation and filtering are performed on M-channel and S-channel signals respectively, resulting in the output of M-channel signals. and S-channel signal The signal obtained by downsampling by S times in Step 1 Multiphase decimation and filtering are performed on M and N channels respectively, and M channels of signals are output respectively. and N-channel signals .

[0072] Step 3: Perform IDFT operations on the six sets of signals output from Step 2 respectively, outputting six sets of signals in the following order: , , , , , .

[0073] Step 4: Divide the six groups of signals output from Step 3 into pairs, resulting in three pairs of signals, and then perform cross-correlation operations on each pair. Among these, and For a pair of signals, and For a pair of signals, and This is a pair of signals. After cross-correlation, the output consists of the following three branch spectra.

[0074] ;

[0075] ;

[0076] ;

[0077] Step 5: Analyze the spectrum of each branch. , , Performing nearest-neighbor repetition interpolation operations of S times, N times, and M times respectively, the spectrum of each branch is uniformly extended to MNS frequency points (with a unified resolution). ), its interpolated branch spectrum (“ " indicates rounding down) is represented as

[0078] ;

[0079] Step 6: Perform the following merging and decision-making process on each branch spectrum: Take the ratio of the arithmetic mean to the geometric mean of the three branch spectra at each frequency point as the significance measure, i.e.:

[0080] ;

[0081] Then, based on the significance value, the following threshold processing is performed to obtain the final output global spectrum. As shown in the following formula:

[0082] ;

[0083] The specific technical principles behind the above steps are detailed below.

[0084] 2.1 Traditional Coprime Spectrum Analysis Algorithm

[0085] Traditional coprime spectrum analysis technology originates from the spectral decomposition principle of multi-channel filter banks. It achieves efficient sensing of broadband signals through dual-path coprime downsampling and remainder mapping mechanism. Its core architecture is built on two theoretical foundations: the filter bank spectrum segmentation principle and the frequency point mapping mechanism of the Chinese remainder theorem.

[0086] (1) Principle of filter bank spectrum segmentation

[0087] Design a prototype low-pass filter with complementary cutoff frequencies. and Its frequency response satisfies:

[0088] ;

[0089] Where M and N are coprime positive integers, and the global spectral resolution is... .

[0090] Introducing a rotation factor , From the properties of the Fourier transform, we know that... Downsampling by N times to obtain This is equivalent to modifying the prototype low-pass filter. The transmission curve shrinks by N times, while at the same time The inner period is extended to produce (N-1) intervals with a width of The mirror curve. Multiply get This is equivalent to performing a frequency domain analysis on these N transmission curves. The entire translation. Similarly, the overall translation. Multiply This is equivalent to performing the following on these M transmission curves in the frequency domain: The overall translation. For example... Figure 3 As shown (taking M=4, N=3 as an example), the frequency domain response characteristics of the above filter bank are shown. After downsampling and frequency shifting, the two filters form a gridded passband array covering the entire frequency band.

[0091] (2) Frequency mapping mechanism of Chinese remainder theorem

[0092] For input signal Parallel execution of dual-path coprime sampling: the sampling rate of the upper branch is... The output sequence is denoted as The adoption rate of the lower branch is The output sequence is denoted as .

[0093] According to the Chinese Remainder Theorem (CRT), since M and N are coprime, the product response of the two filter banks formed after downsampling and frequency shifting is... There exists only one overlapping passband in the range [0, 2π), with a center frequency of . The center frequency point and the remainder pair The following relationship must be satisfied:

[0094] ;

[0095] That is, each sub-band consists of a unique pair of remainders. Index identifier.

[0096] (3) Traditional coprime spectrum analysis process

[0097] Based on the two theoretical foundations mentioned above, and combined with multiphase decomposition, the traditional coprime spectrum analysis process can be realized. The prototype filter is decomposed into parallel sub-filter banks through multiphase decomposition, and its expression is:

[0098] ;

[0099] Further expressed as:

[0100] ;

[0101] like Figure 4 The diagram shown is a flowchart of traditional coprime spectrum analysis; the downsampling is moved to the sub-filter. , On the left, the efficient implementation of generating coprime filter banks based on polyphase filter structures is the traditional coprime spectrum analysis process.

[0102] Specifically, after downsampling the prototype filter, a sub-filter bank is used. and To each and Perform polyphase filtering decomposition. This operation yields a lower data flow in the upper half of the channel. A lower data flow is obtained in the lower half of the channel. Based on this, an M-point IDFT is performed on the upper channel data sequence to obtain... Similarly, performing an N-point IDFT on the data sequence of the lower half channel yields... Subsequently, cross-correlation calculations are performed on the output points of each branch of the upper and lower channels in sequence, and the estimated power spectrum values ​​are output. ,Right now:

[0103] ;

[0104] In the formula, c represents the coefficients associated with M, N, and the filter.

[0105] The theoretical advantage of the coprime spectrum method lies in the fact that, through the formula... The established remainder pair With frequency The unique mapping relationship ensures the power of each sub-band. It is accurately estimated without aliasing (as shown in Figure 2, where the passband is non-overlapping), and thus in A global spectrum output is generated within the range.

[0106] 2.2. Aliasing defects caused by the conjugate symmetry of real signals

[0107] In non-cooperative electronic reconnaissance scenarios, while the dual-path coprime downsampling architecture of traditional coprime spectrum analysis can overcome the Nyquist limitation and achieve rapid global spectrum construction, its core reliance on the Chinese remainder theorem frequency mapping mechanism fundamentally conflicts with the physical layer characteristics of real signals. This deficiency can be attributed to a triple coupling effect:

[0108] (1) The unavoidable nature of spectral conjugate symmetry

[0109] The Fourier transform of a real signal x(t)∈R satisfies X(ω)=X∗(−ω), resulting in its spectrum exhibiting strict conjugate symmetry along the positive and negative frequency axes. This characteristic leads to image frequencies in undersampling scenarios. Forced activation ( (This refers to the actual carrier frequency).

[0110] (2) Undersampled folded aliasing amplification

[0111] downsampling operation and The spectrum is folded periodically, causing the image components to further alias into the baseband, forming multipath interference.

[0112] (3) The violation of the uniqueness of the remainder mapping

[0113] The Chinese Remainder Theorem requires global frequency points. Remainder pair with two paths Satisfying a strict double mapping relationship, taking M=4 and N=3 as an example (Table 1), the position of each frequency point... Each corresponds to a unique pair of upper and lower branch remainders. However, the mirror component of the real signal Remainder pair Mapping, creating real frequency points With mirror frequency In cross-correlation calculation The equivalent power response is generated. Table 1 shows the correspondence between the remainder pairs and the frequency points.

[0114] Table 1

[0115]

[0116] like Figure 5 As shown, taking the global spectrum of a real signal after coprime spectrum analysis as an example, let M=4, N=3, and the sampling rate be... Given a real signal at 2.5 GHz, its image frequency is located according to the conjugate symmetry of the real signal spectrum. Due to the combination of remainders and The cross-modulation of the signal causes cross-correlation calculations to fail to distinguish between the true spectrum and the aliased spectrum. Therefore, after coprime spectrum analysis, the output signal exhibits two spurious peaks (5.5 GHz and 6.5 GHz) in addition to the true and mirror frequencies. This phenomenon completely overturns the premise of the unique invertible mapping in the Chinese Remainder Theorem, leading to a surge in false alarm rates in dense signal scenarios. Therefore, traditional methods cannot meet the precise detection requirements of electronic reconnaissance, necessitating the reconstruction of the mapping's uniqueness through third-dimensional constraints.

[0117] 2.3 Mechanism for Eliminating Spectral Aliasing

[0118] In coprime spectral analysis, the spectral conjugate symmetry of real signals can lead to spurious peaks in the global spectrum, but not all frequencies will produce spurious peaks. Let the resolution of the global spectrum be... Experiments show that only when the signal frequency is False peaks only occur when certain conditions are met, and their characteristics are explained as follows.

[0119] As shown in the coprime spectrum analysis procedure, the global spectrum is divided into MN uniform spectral segments, each segment being of size [missing information]. This is the resolution. The interval of the spectrum segmentation unit is defined as follows: , are integers and satisfy The process can be understood as follows: the upper branch and the lower branch each contain MN corresponding spectral units, and the final global spectrum result is obtained by cross-correlation calculation between the spectral lines of different spectral units in the upper and lower branches.

[0120] Due to the conjugate symmetry of the spectrum of a real signal, in There are two spectral peaks within the frequency range, one corresponding to the actual signal frequency and the other to its mirror frequency. For ease of description, the positions of the two spectral lines input from the upper branch are denoted as... (True spectral lines) and (Mirror spectral lines), the positions of the two spectral lines in the lower branch are denoted as (True spectral lines) and (Mirror spectral lines). The global spectral output obtained by cross-correlating the upper and lower branch spectral lines in their corresponding spectral segmentation intervals contains four spectral peaks, corresponding to four combinations: , , , .in The correct spectral lines corresponding to the actual signal frequencies. The spectral lines are mirror images of the correct spectral lines, while and The two combinations result in erroneous false peak spectral lines and their mirror images.

[0121] As the frequency of a real signal increases, its true spectral line shifts to the right along the frequency axis, while its mirror spectral line shifts in the opposite direction. This is because the interval of a spectrum segmentation unit is... Only when the signal frequency is hour, and The two spectral lines corresponding to the combination can fall within the same cell interval of the upper and lower branches, thus producing a false peak after cross-correlation. However, at other frequencies, due to the reverse shift of the spectral lines, the spectral lines of these two combinations will not be in the same cell interval, thus no cross-correlation is performed and a false peak is produced. Therefore, the global spectrum only contains the correct spectral peak and its mirror spectral peak.

[0122] In summary, when the frequency of the real signal is at When determining the location, traditional dual-path coprime spectrum analysis methods cannot identify a unique frequency point. To completely eliminate aliasing, this invention proposes a three-path coprime spectrum cooperative constraint mechanism, the core mechanism of which is as follows:

[0123] (1) Three-way expansion architecture:

[0124] Introducing a third coprime parameter S, three sets of analysis channels are constructed where M, N, and S are pairwise coprime, with resolutions as follows: , , .

[0125] (2) Conditions for the existence of false peaks:

[0126] The frequencies at which spurious peaks may occur in each group must simultaneously satisfy the following:

[0127] ;

[0128] in,

[0129] ;

[0130] therefore,

[0131] ;

[0132] (3) The uniqueness of the solution is violated:

[0133] Since M, N, and S are pairwise coprime and The range of values ​​is limited ( , , ),equation Only The condition is true at the time, but the solution is outside the range of possible values.

[0134] Therefore, under the three-way joint analysis, no real signal frequency can simultaneously satisfy the three sets of spurious peak generation conditions, thus fundamentally eliminating aliasing.

[0135] 2.4 Implementation Method of Broadband Spectrum Analysis Driven by Three Coprime Spectra

[0136] First, we need to determine three pairwise coprime sampling factors M, N, and S, and denot the signals acquired by the three channels as follows: , , Set up three prototype filters. , and Its ideal cutoff frequency satisfies:

[0137] ;

[0138] It is decomposed into sub-filter banks through polyphase decomposition:

[0139] ;

[0140] For three-channel data , , Perform coprime spectrum analysis on any two data streams: and The two channels have coprime coefficients M and N. and The two channels are coprime to each other, M and S. and The two channels performed three coprime spectral analyses using N and S coprime coefficients, with each analysis process being consistent with the aforementioned dual-channel coprime spectral analysis procedure.

[0141] In these three pairs of coprime spectral analyses, k, l, and r are the remainders of the frequency index i modulo the two coprime coefficients in each combination, i.e.:

[0142] ;

[0143] Table 2 shows the remainder mapping relationship for the three-channel signals, as detailed below:

[0144] Table 2

[0145]

[0146] Note: Remainder index range , , Keep it constant.

[0147] Because of the pairwise coprime spectral analysis, the data for each channel needs to be decomposed twice, resulting in six low-speed data streams. After IDFT processing, the upper and lower channel results for the first group are as follows: and The results for the upper and lower channels of the second group are as follows: and The results for the upper and lower channels of the third group are as follows: and Subsequently, cross-correlation calculations were performed on the outputs of each branch of the upper and lower channels in each group. The power spectrum of each group's output is as follows:

[0148] ;

[0149] Although the frequency bands covered by these three coprime spectrum analyses All The global spectrum range is defined, but each has a different resolution. Within the global spectrum, there are MN, MS, and NS frequency points, which cannot be directly correlated. For example... Figure 6The diagram shows a three-way global spectrum upsampling schematic. Therefore, the three global spectrum results need to be interpolated by multiples of S, N, and M respectively. The nearest neighbor interpolation method shown in equation (1) is used to expand the three global spectrum results to MNS frequency points, unifying the resolution to [missing value]. To achieve frequency point correspondence (e.g.) Figure 5 (As shown).

[0150] After frequency point mapping is completed, the three sets of coprime spectrum analysis results are merged. Since each set of results may contain spurious peaks, and as discussed in Section 2.3, the positions of the spurious peaks do not correspond, it is necessary to determine the frequency point before merging. If the similarity of a frequency point is high across all coprime spectrum results, the power value is considered to exist; if the similarity is low, the frequency point is considered a spurious peak in a coprime spectrum result. To quantify the similarity of a frequency point across all spectrum results, a metric parameter is established. Its expression is as follows: As shown in the formula. It is obtained by dividing the geometric mean of the three coprime spectra at a certain frequency by the arithmetic mean. Since the arithmetic mean is always greater than or equal to the geometric mean, the range of values ​​for the metric parameter is [range missing]. . The larger the value, the closer the power values ​​of the three coprime spectra at that frequency are, meaning that all the results are correct and there are no false peaks. The smaller the value, the more likely it is that a component with a spurious peak exists in one of the three coprime spectrum results for that frequency point. Therefore, a threshold value is set. ,when When all three results are considered correct, their arithmetic mean is taken; when... If a branch is considered to contain a spurious peak, the minimum value among the three results is taken to avoid the influence of the spurious peak. The final global spectrum is obtained after merging. , as in the formula As shown.

[0151] Example 2, as follows Figure 8 The diagram shows the architecture of the broadband spectrum detection device driven by the three coprime spectra of the present invention. After a real signal passes through this system, spurious peaks at specific frequency points will be eliminated. The device includes an RF front-end module 100, a sample-and-hold module 200, a three-channel analog-to-digital converter module 300, and a digital signal processing module 400 (e.g., an FPGA may be used).

[0152] The radio frequency front-end module 100 receives electromagnetic signals of 300 MHz–10 GHz captured by the receiving antenna and preprocesses them by a low-noise amplifier (LNA) and a band-pass filter (BPF).

[0153] The sample-and-hold module 200 is used to receive and preprocess electromagnetic signals in the 300MHz to 10GHz frequency band. Optionally, it can employ an HMC661 sample-and-hold chip design, with a maximum full-power bandwidth of up to 18GHz.

[0154] The three-channel analog-to-digital converter (ADC) 300 is connected to the RF front end and is used for signal sampling and holding. Optionally, the ADC used is the AD9434 from Analog Devices, which has a maximum sampling rate of 500 MS / s and is synchronized with the sample-and-hold circuit.

[0155] A digital signal processing module 400, including an FPGA and / or a processor, is used to execute the broadband spectrum detection method driven by the three coprime spectra of the present invention. Optionally, the core processor is: main controller: Xilinx Zynq UltraScale+MPSoCs, model XCZU15EG-2FFVB1156I; FPGA logic: implements the broadband spectrum detection method driven by the three coprime spectra of the present invention; ARM core: runs the adaptive decision algorithm (equations (11) to (12)). The algorithm is hardware-implemented by constructing a parallel processing pipeline within the FPGA, corresponding to Figure 1 The six-step operation, as shown in Table 3, represents the resources and configurations for hardware implementation.

[0156] Table 3

[0157]

[0158] 3. Verification Experiment

[0159] Assume the input real signal The signal frequency , Preset frequency axis coverage range The signal-to-noise ratio (SNR) is 0 dB. Coprime factor is used. , , If a three-channel system is constructed, the actual sampling rates of each channel are as follows:

[0160] ;

[0161] Each simulation uses 1000 snapshots. The results of three-channel coprime spectrum analysis and cross-merging are as follows: Figure 7 As shown ( ).

[0162] Three-way branch spectrum , , The frequency resolutions are as follows:

[0163] ;

[0164] As shown in Section 2.3, when the signal frequency satisfies the condition for the generation of spurious peaks (i.e., When this occurs, spurious peaks are generated due to the aliasing of real signals. The input signal... , , combined Figure 6 The following conclusions can be drawn:

[0165] 1. Scattered spurious peaks exist in each branch of the spectrum. Specifically, because... Resolution compared to the third group of spectral analyses In an integer multiple relationship, that is , The results of the coprime spectrum analysis False peaks were generated (as shown by the red arc in the third subplot); similarly, because Resolution compared to the first group of spectral analyses In an integer multiple relationship, that is , The results of the coprime spectrum analysis False peaks were also generated (as shown by the red arc in the first subplot).

[0166] 2. Final output of the global spectrum False peaks were completely eliminated. Specifically, from Figure 6 As can be seen from the fourth subgraph, after processing by the cross-merge algorithm, the pseudo-peaks of the two branch spectra above are reduced in the final output global spectrum. Both were effectively suppressed. From All identified spectral peaks were genuine spectral peaks.

[0167] 3. The final frequency estimate has super-resolution accuracy. Specifically, from The readable spectral peak frequencies were identified as 2.554 GHz and 3.934 GHz, which deviate from the input signal frequencies by 4 MHz and 8 MHz respectively. However, this error is less than the minimum frequency resolution of all undersampled channels (minimum resolution is...). Therefore, the broadband undersampling spectrum detection method proposed in this invention has the advantage of improved resolution.

[0168] The broadband spectrum detection method driven by three coprime spectra proposed in this invention can achieve the following objectives:

[0169] (1) Solve the inherent defects of superheterodyne architecture: provide a fully digital broadband spectrum sensing solution to replace the traditional superheterodyne receiver that relies on analog mixing circuits, eliminate the problems of large size of analog devices, slow linear scanning speed and loss of transient signals, and realize panoramic spectrum mapping of the 300 MHz to 10 GHz ultra-high frequency band.

[0170] (2) Overcoming the Nyquist sampling limitation: Achieving efficient spectrum sensing under under-sampling conditions (sampling rate much lower than the highest frequency of the signal), avoiding the engineering bottleneck of high-speed ADC, and significantly reducing the amount of sampled data and subsequent processing burden.

[0171] (3) Eliminate spectrum aliasing caused by undersampling of coprime real signals: By using a three-way coprime spectrum driving mechanism, the problem of remainder ambiguity and spectrum aliasing caused by the conjugate symmetry of the real signal spectrum in traditional coprime spectrum analysis is solved, ensuring accurate positioning of full-band signals without spurious peaks.

[0172] (4) Support non-cooperative blind detection scenarios: Under the condition of lack of prior information, realize rapid scanning of a wide range of electromagnetic spectrum and capture of transient signals, and improve the ability to intercept and locate carrier frequencies of low interception probability and short burst signals.

[0173] (5) Remove the sparsity constraint of signal distribution: break through the strong dependence of compressed sensing on the sparse distribution of information sources, ensure robust spectrum sensing in scenarios with dense distribution of multiple information sources (such as cross-spectrum support areas), and improve the accuracy of carrier frequency estimation.

[0174] (6) Provide a solid theoretical foundation and algorithm simulation for the engineering implementation of broadband spectrum sensing receivers: avoid the high cost and implementation risks of compressed sensing schemes (such as the high-speed pulse circuit / multi-path filter and sub-nanosecond synchronization requirements of multi-co-collection sampling required by MWC), design a low-complexity architecture, and improve engineering feasibility.

[0175] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0176] The above specific embodiments illustrate the principles and implementation methods of the present invention using specific examples. The descriptions of the embodiments are merely for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention. Any modifications, equivalent substitutions, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention. Additionally, any improvements and modifications made without departing from the principles of the present invention should also be considered to fall within the protection scope of the present invention.

Claims

1. A three-way co-prime spectrum-driven wideband spectrum sensing method, characterized in that, The method comprises the following steps: (a) for the input real signal are three-way undersampled at sampling rates , , respectively, to obtain three-way digital signals , , , where M, N, S are pairwise coprime positive integers, is the upper limit of the signal frequency coverage; (b) performing polyphase decimation and filtering on each of the sampling signals to obtain six groups of sub-signals; (c) performing inverse discrete Fourier transform on the six groups of sub-signals to obtain six groups of transformed signals; (d) grouping the six transformed signals two by two to perform a cross-correlation operation to obtain three branch spectra , , ; (e) up-sampling and interpolating the three branch spectrums respectively, so that the number of frequency points is unified to MNS and the resolution is unified to ; (f) based on a saliency measure Merging decision on the three up-sampled sub-band spectra, outputting the aliasing-free global spectrum wherein: ; When the arithmetic mean of the three-way spectrum is taken, when the minimum value of the three-way spectrum is taken, and A is a preset threshold value.

2. A three-way co-prime spectrum-driven wideband spectrum sensing method as claimed in claim 1, wherein, The polyphase filtering in step (b) uses a set of three low-pass filters with cut-off frequencies of , and respectively.

3. A three-way co-prime spectrum-driven wideband spectrum sensing method as claimed in claim 1, wherein, The cross-correlation operation in step (d) comprises the cross-correlation of the following three pairs of signals: derived from with up and down channel signals derived from By With derived up and down channel signals; By With derived up and down channel signals.

4. A three-way co-prime spectrum-driven wideband spectrum sensing method as claimed in claim 1, wherein, The value range of the significance threshold A is 0.8≤A≤0.9, and the preferred value is 0.

85.

5. A three-way co-prime spectrum-driven wideband spectrum sensing method as claimed in claim 1, wherein, The value range of the three-way co-prime parameters M, N, and S satisfies: M, N, S ≥ 10, and each pair of them is co-prime; Each channel has a sampling rate lower than 500 MS / s, and is suitable for radio frequency direct sampling in the frequency band of 300 MHz to 10 GHz.

6. A three-path co-prime spectrum-driven wideband spectrum sensing device, characterized in that, It comprises: a radio frequency front-end module for receiving electromagnetic signals in the frequency band of 300 MHz to 10 GHz and performing preprocessing; a sample and hold module connected to the radio frequency front-end for signal sampling and holding; A three-channel analog-to-digital conversion module, respectively, with a sampling rate 、 、 Undersampling of the signal; a digital signal processing module comprising an FPGA and / or a processor for executing the method according to any one of claims 1 to 5; The digital signal processing module further comprises: a polyphase filter unit for implementing polyphase decimation and filtering; an IDFT unit for performing inverse discrete Fourier transform; a cross-correlation calculation unit for calculating branch spectrum; an up-sampling and merging decision unit for spectrum interpolation and pseudo-peak suppression.

7. The three-way co-prime spectrum-driven wideband spectrum detection device according to claim 6, wherein The ADC is a low-speed ADC with a sampling rate lower than 500 MS / s, and the preferred model is ADI AD9434.

8. The three-way co-prime spectrum-driven wideband spectrum detection device according to claim 6, wherein The digital signal processing module is implemented based on Xilinx Zynq UltraScale+ MPSoC, wherein the FPGA is used for pipeline processing, and the ARM core is used for adaptive decision algorithm execution.

9. The three-way co-prime spectrum-driven wideband spectrum detection device according to claim 6, wherein The sample and hold module uses HMC661 chip, which supports a full power bandwidth of up to 18 GHz.

10. A three-path co-prime spectrum-driven wideband spectrum sensing device as claimed in claim 6, wherein, The device is suitable for non-cooperative electronic reconnaissance scenes and can realize blind detection and panoramic spectrum mapping of low probability of intercept signals.

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