Non-orthogonal elliptic spherical wave signal detection method based on cross terms among signals

Abstract

The invention provides a non-orthogonal elliptic spherical wave signal detection method based on cross terms among signals, and belongs to the technical field of information transmission. According to the method, signal detection is expanded to a time-frequency two-dimensional energy domain from a single energy domain of a time domain / frequency domain, and signal detection is carried out by using local area energy of the time-frequency domain, so that interference between non-orthogonal signals is effectively reduced, and the non-orthogonal PSWFs signal detection performance is improved. Compared with coherent detection, the method provided by the invention has better performance on non-orthogonal PSWFs signal detection.

Description

Technical Field

[0001] The invention relates to a non-orthogonal ellipsoidal wave signal detection method based on cross terms between signals, belonging to the technical field of information transmission. Background Art

[0002] As society develops towards digitalization, the rate of information transmission is growing exponentially. According to Edholm's law, the amount of information transmission will reach TB level by 2030. How to achieve high spectrum efficiency information transmission has become a hot topic in B5G / 6G communication research. In order to cope with the increasing demand for information transmission, experts and scientists in related fields have introduced the idea of ​​"non-orthogonality" into the design of communication signal waveforms from the perspective of increasing the signal dimension used for information transmission. Non-orthogonal modulation and access technologies such as Multi-carrier Faster-than-Nyquist (MFTN), Nonorthogonal Shape Modulation with Prolate Spheroidal Wave Functions (NSM-PSWFs) based on elliptical spheroidal wave signals, and Non-Orthogonal Multiple Access (NOMA) have been proposed one after another, which effectively improves the system spectrum efficiency and has great application value and promotion prospects. In particular, NSM-PSWFs, which uses the PSWFs signal with the best time-frequency energy concentration as the basic waveform, not only has the advantages of high spectral efficiency, but also has the advantages of high time-frequency energy concentration. It is in line with the B5G / 6G communication signal waveform design requirements and can be used as a potential waveform solution for B5G / 6G.

[0003] However, since the PSWFs signals used for information transmission by NSM-PSWFs are no longer strictly orthogonal, different branches interfere with each other during signal detection, resulting in the problem of low signal detection performance, which is also a common problem faced by non-orthogonal modulation and access technologies. Regarding how to reduce the interference between non-orthogonal PSWFs signals, whitening transformation, serial interference elimination, power domain multiplexing and other processing have been introduced successively, reducing the impact of interference between PSWFs signals on the system error performance. However, because the detection statistics based on the above processing are still obtained through coherent detection, the energy of non-orthogonal PSWFs signals in the entire time interval and frequency domain interval will interfere with the signal, and the interference between signals is reduced on the basis of inheriting the "global" interference in the energy domain. Therefore, if the "local" characteristics of the energy domain can be used as the detection statistic, that is, the interference between signals is first reduced at the detection statistic level, and then combined with the above-mentioned whitening transformation and other processing technologies, it is expected to reduce the interference between non-orthogonal PSWFs signals to a greater extent. Previous studies have found that different-order PSWFs signals have different energy distribution characteristics in the time-frequency domain, especially different energy concentration, which provides the possibility for exploring the detection of non-orthogonal PSWFs signals based on "local" characteristics ([1] Research on time-frequency distribution characteristics of cross terms between ellipsoidal spherical wave signals [J]. Journal of Electronics & Information Technology, 2017, 39(6): 1319-1325.). Summary of the invention

[0004] The purpose of the present invention is to propose a new non-orthogonal ellipsoidal wave signal detection method based on cross terms between signals, give full play to and utilize the time-frequency distribution characteristics of PSWFs signals in the two-dimensional energy domain of time and frequency, expand signal detection from a single energy domain in the time domain / frequency domain to the two-dimensional energy domain of time and frequency, and use the local area energy in the time and frequency domain for signal detection, so as to reduce the interference between non-orthogonal signals and improve the detection performance of non-orthogonal PSWFs signals. Compared with the coherent detection method used in the existing non-orthogonal PSWFs signal detection method ([1] Non-orthogonal pulse waveform modulation method based on PSWF framework [J]. Journal of Electronics, 2016, 44(3): 620-626. [2] Elliptical spherical wave function non-orthogonal modulation method based on power multiplexing [J]. Acta Aeronautica Sinica, 2019, 40(9): 323102-323102. [3] Non-sinusoidal system demodulation method based on serial interference elimination [J]. Journal of Radio Science, 2013, 28(5): 112-124.), the signal detection method provided by the present invention has better system error performance.

[0005] The present invention discloses a non-orthogonal ellipsoidal wave signal detection method based on cross terms between signals. The signal detection is extended from a single energy domain in the time domain / frequency domain to a two-dimensional energy domain in the time-frequency domain. The local features of the cross terms between signals are used as detection statistics in the time-frequency domain to detect the non-orthogonal ellipsoidal wave function signal. The method is special in that it includes the following steps:

[0006] Step 1) using a signal receiving device to receive the ellipsoidal spherical wave modulated signal after signal transmission;

[0007] Step 2) constructing a set of ellipsoidal wave signals with the same duration and bandwidth parameters as the received ellipsoidal wave modulation signal as local template signals;

[0008] Step 3) calculating a cross term between the modulated signal received by the receiving device and the local template signal;

[0009] Step 4) Calculate the energy density value of the cross term at the center frequency in the frequency domain, and use it as the time-frequency domain feature detection quantity for decision detection, and demodulate the information loaded by the ellipsoidal wave signals of different branches.

[0010] Preferably, the ellipsoidal wave modulation signal is: a modulation signal generated by multiplying different branch ellipsoidal wave signals and modulation symbols in the time domain and linearly superposing them;

[0011] Preferably, at the frequency corresponding to the peak point of the energy density of the cross-terms between the different branch ellipsoidal wave signals themselves, the cross-terms between the modulated signal received by the receiving device and the local template signal are integrated in the time domain as a time-frequency domain feature detection quantity; the cross-terms between the different branch ellipsoidal wave signals themselves and the cross-terms between the modulated signal received by the receiving device and the local template signal are discretized to obtain a matrix A corresponding to the cross-terms between the different branch ellipsoidal wave signals themselves and a matrix B corresponding to the cross-terms between the modulated signal received by the receiving device and the local template signal, calculate the vector C corresponding to the energy density peak value of the cross-terms between the different branch ellipsoidal wave signals themselves at different times, divide the matrix B by the vector C to obtain the vector D, and use the numerical value corresponding to the frequency corresponding to the peak point of the energy density of the cross-terms between the different branch ellipsoidal wave signals themselves in the vector D as the time-frequency domain feature detection quantity.

[0012] Preferably, the specific steps of step 1) are: discretizing the cross terms between the different branch ellipsoidal wave signals themselves and the cross terms between the modulated signal received by the receiving device and the local template signal, and obtaining the matrix A corresponding to the cross terms between the different branch ellipsoidal wave signals themselves, that is:

[0013]

[0014] The cross term between the modulated signal received by the receiving device and the local template signal corresponds to the matrix B, that is:

[0015]

[0016] In the formula, is the PSWFs signal of the i-th branch, a i,j is the energy density value of the cross term at the jth moment and the ith frequency in the time-frequency domain, m is the number of discretization points of the cross term in the frequency domain, and n is the number of discretization points of the cross term in the time domain.

[0017] Preferably, the specific steps of step 2) are: calculating the energy density peak value corresponding vector C of the cross terms between the ellipsoidal wave signals of different branches at different times, that is, when is a 0-order PSWFs signal, then That is, after the cross terms are discretized, the frequency of their energy density peak points is in the pth row, and the corresponding cross terms have energy peaks in the pth row and different columns.

[0018] Preferably, the specific steps of step 3) are: dividing the matrix B by the vector C to obtain the vector D, that is, when For the 0th order PSWFs signal:

[0019]

[0020] Preferably, the specific steps of step 4) are: taking the value corresponding to the frequency of the peak point of the cross-term energy density between the different branch ellipsoidal wave signals in the vector D as the time-frequency domain feature detection quantity, when is a 0-order PSWFs signal. Since its energy density peak frequency is in the pth row, its time-frequency domain feature detection quantity is b p ,To facilitate subsequent distinction, when this detection statistic is used, it is called a non-orthogonal PSWFs signal detection method (with filtering processing) based on cross terms between signals.

[0021] Compared with the prior art, the non-orthogonal ellipsoidal wave signal detection method based on the cross terms between signals of the present invention has the following advantages:

[0022] Beneficial effects:

[0023] Compared with the traditional coherent detection that performs signal detection in a single energy domain of time domain / frequency domain, the present invention performs signal detection only in the two-dimensional energy domain of time and frequency, and expands the signal detection based on one-dimensional characteristics to the use of two-dimensional characteristics, which increases the characteristic dimension used for signal detection, provides a new idea for exploring and studying communication signal detection including PSWFs signals, and also provides a reference basis for exploring and studying new mechanisms of two-dimensional domain signal detection;

[0024] Compared with the traditional coherent detection which uses the "global" energy in the time domain / frequency domain for signal detection, the present invention only uses the "local" energy in the time and frequency domain for signal detection, which can reduce the noise energy that interferes with signal detection;

[0025] Compared with traditional coherent detection, when the PSWFs signals are non-orthogonal, the present invention effectively reduces the interference between the non-orthogonal PSWFs signals and has better system error performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 It is a principle block diagram of the non-orthogonal PSWFs signal detection method based on the cross terms between signals;

[0027] Figure 2 It is the system error performance curve. DETAILED DESCRIPTION

[0028] In the following description, many different aspects of the present invention will be described, however, for those of ordinary skill in the art, the present invention may be implemented using only a portion or all of the structures or processes of the present invention. For clarity of explanation, specific numbers, configurations, and sequences are described, but it is clear that the present invention can be implemented without these specific details. Since the specific technologies used in the present invention are basic technologies well known to those of ordinary skill in the art, many well-known features will not be described in detail in order not to confuse the present invention.

[0029] Example 1

[0030] A non-orthogonal PSWFs signal detection method based on cross terms between signals in this embodiment expands signal detection from a single energy domain in the time domain / frequency domain to a two-dimensional energy domain in the time-frequency domain, and uses the local features of the cross terms between signals in the time-frequency domain as detection statistics to detect non-orthogonal ellipsoidal wave function signals, including the following steps:

[0031] Step 1) using a signal receiving device to receive the ellipsoidal spherical wave modulated signal after signal transmission;

[0032] Step 2) constructing a set of ellipsoidal wave signals with the same duration and bandwidth parameters as the received ellipsoidal wave modulation signal as local template signals;

[0033] Step 3) calculating a cross term between the modulated signal received by the receiving device and the local template signal;

[0034] Step 4) Calculate the energy density value of the cross term at the center frequency in the frequency domain, and use it as the time-frequency domain feature detection quantity for decision detection, and demodulate the information loaded by the ellipsoidal wave signals of different branches.

[0035] The ellipsoidal wave modulation signal is a modulation signal generated by multiplying the ellipsoidal wave signals of different branches and the modulation symbol in the time domain and linearly superposing them;

[0036] At the frequency corresponding to the peak point of the energy density of the cross-terms between the different branch ellipsoidal wave signals themselves, the cross-terms between the modulated signal received by the receiving device and the local template signal are integrated in the time domain as the time-frequency domain feature detection quantity; the cross-terms between the different branch ellipsoidal wave signals themselves and the cross-terms between the modulated signal received by the receiving device and the local template signal are discretized to obtain the corresponding matrix A of the cross-terms between the different branch ellipsoidal wave signals themselves and the corresponding matrix B of the cross-terms between the modulated signal received by the receiving device and the local template signal, calculate the corresponding vector C of the energy density peak value of the cross-terms between the different branch ellipsoidal wave signals themselves at different times, divide the matrix B by the vector C to obtain the vector D, and use the corresponding value of the frequency corresponding to the peak point of the energy density of the cross-terms between the different branch ellipsoidal wave signals themselves in the vector D as the time-frequency domain feature detection quantity.

[0037] The specific steps of step 1) are: discretizing the cross terms between the different branch ellipsoidal wave signals themselves and the cross terms between the modulated signal received by the receiving device and the local template signal, and obtaining the matrix A corresponding to the cross terms between the different branch ellipsoidal wave signals themselves, that is:

[0038]

[0039] The cross term between the modulated signal received by the receiving device and the local template signal corresponds to the matrix B, that is:

[0040]

[0041] In the formula, is the PSWFs signal of the i-th branch, a i,j is the energy density value of the cross term at the jth moment and the ith frequency in the time-frequency domain, m is the number of discretization points of the cross term in the frequency domain, and n is the number of discretization points of the cross term in the time domain.

[0042] The specific steps of step 2) are: calculate the energy density peak value corresponding vector C of the cross terms between the ellipsoidal wave signals of different branches at different times, that is, when is a 0-order PSWFs signal, then That is, after the cross terms are discretized, the frequency of their energy density peak points is in the pth row, and the corresponding cross terms have energy peaks in the pth row and different columns.

[0043] The specific steps of step 3) are: divide the matrix B by the vector C to obtain the vector D, that is, when For the 0th order PSWFs signal:

[0044]

[0045] The specific steps of step 4) are: taking the value corresponding to the frequency of the peak point of the cross-term energy density between the different branch ellipsoidal wave signals in the vector D as the time-frequency domain feature detection quantity, when is a 0-order PSWFs signal. Since its energy density peak frequency is in the pth row, its time-frequency domain feature detection quantity is b p ,To facilitate subsequent distinction, when this detection statistic is used, it is called a non-orthogonal PSWFs signal detection method (with filtering processing) based on cross terms between signals.

[0046] The present invention has better signal detection performance. For the convenience of theoretical analysis and without loss of generality, it is assumed that the number of non-orthogonal PSWFs signal paths is N. Under AWGN channel conditions, in the jth code element time, the signal received by the receiving end is r(t)=s(t)+n(t). The cross term between the received signal and the template signal can be expressed as

[0047]

[0048] In the formula, is the cross term between the template signals themselves, It is the cross term between the signals when the interfering PSWFs signal and the board signal have the same time domain parity; To interfere with the cross term between signals when the time domain parity of PSWFs signal and board signal is different; is the cross term between the noise template signal. From formula (1), we can see that the cross term between the received signal and the template signal is i The energy density at can be expressed as:

[0049]

[0050] At the same time, since the cross terms between PSWFs signals with different time domain parity are integrated into 0 in the time domain, equation (2) can be simplified as:

[0051]

[0052] In the formula, γ i,i for When the cross term between signals is at frequency f i The energy density value at γ j,i for and Same parity, and When the cross term between signals is at frequency f i The energy density value at ; For noise and The cross term at frequency f i The energy density value at the location is subject to the mean value E(ξ) = 0 and the variance σ 2 (ξ)=D(ξ)=N0γ i,i / 2 Gaussian distribution. At this time, the signal-to-noise ratio r between the statistical detection quantity and the noise can be expressed as:

[0053]

[0054] From the above formula, we can see that the system error performance of the PSWFs signal time-frequency detection method based on the cross terms between signals is The value of is closely related to

[0055]

[0056] Then the received signal-to-noise ratio r increases with α j changes with the transformation of d j , γ i,j , γ i,i The value of is closely related, and γ i,j , γ i,i The value of is known, only d j is a random variable. For the convenience of theoretical analysis, assume that d j The probability of taking the value ±1 is equal. At this time, α j There are 2 values ​​in total N-1 There are two situations, and they obey the equal probability distribution, that is,

[0057]

[0058] Based on the above analysis, the gap between the system error performance of the time-frequency detection method of the present invention and the coherent detection is analyzed below. When the signal-to-noise ratio SNR_dB (in dB), the noise power corresponding to the coherent detection is:

[0059]

[0060] In the formula, ε is the energy value of a single PSWFs signal in the time domain. Assume that at the center frequency, the ratio of the energy density value of the cross term between PSWFs signals to the total energy value of the cross term in the time-frequency domain is Right now:

[0061]

[0062] Substituting equation (5), equation (7) and equation (8) into equation (4), we can simplify to get

[0063]

[0064] That is the actual received signal-to-noise ratio of the time-frequency detection method of the present invention, expressed as:

[0065]

[0066] When the interference between PSWFs signals is α j When , the difference between the received signal-to-noise ratio of the coherent detection (orthogonal case) and the time-frequency detection method of the present invention is:

[0067]

[0068] Combining formula (6), it can be seen that the total difference in the received signal-to-noise ratio between the time-frequency detection method of the present invention and the coherent detection (orthogonal case) can be expressed as

[0069]

[0070] For the energy normalized PSWFs signal, that is, ε = 1, the above formula can be expressed as

[0071]

[0072] In addition, the reason why the coherent detection system of non-orthogonal PSWFs signals has low bit error performance is the interference between signals, and the time-frequency detection method of the present invention only uses the energy of the local area near the peak point of the PSWFs signal in the time-frequency domain for detection. At this time, the signal energy of other non-orthogonal PSWFs signals in this local area is small, that is, the impact on the detected signal is small. Therefore, under the AWGN channel condition, the system bit error performance of the time-frequency detection method of the present invention is better than that of coherent detection (non-orthogonal case). For example, when the template signal is a 4-6MHz 0-order PSWFs signal X31, the energy density value of the cross term between signals at some frequencies is shown in Table 1. In the table, X11 is a 1-3MHz 0th-order PSWFs signal, X12 is a 1-3MHz 1st-order PSWFs signal, X21 is a 2.5-4.5MHz 0th-order PSWFs signal, X22 is a 2.5-4.5MHz 1st-order PSWFs signal, X31 is a 4-6MHz 0th-order PSWFs signal, X32 is a 4-6MHz 1st-order PSWFs signal, X41 is a 5.5-7.5MHz 0th-order PSWFs signal, X42 is a 5.5-7.5MHz 1st-order PSWFs signal, X51 is a 7-9MHz 0th-order PSWFs signal, and X52 is a 7-9MHz 1st-order PSWFs signal. The energy difference is the difference between the absolute value of the energy density of the cross terms between X31 and X31 at the center frequency of 5 MHz and the sum of the absolute values ​​of the energy density of the cross terms between the other interference pulses and X131 at the center frequency of 5 MHz. The energy ratio is the ratio of the energy difference to the absolute value of the energy density of the cross terms between X31 and X31 at the center frequency of 5 MHz.

[0073] According to formula (12), for the X31 branch, the difference between the error performance of the time-frequency detection method of the present invention and the error performance of the coherent detection (orthogonal case) is approximately:

[0074] ΔSNR_dB=0.93dB(14)

[0075] As for the coherent detection (non-orthogonal case), the difference in bit error performance between it and the coherent detection in the orthogonal case is about 1.43 dB, that is, the method of the present invention improves the system bit error performance of the coherent detection (non-orthogonal case) by about 0.5 dB.

[0076] Example 2

[0077] Without filtering, the method of the present invention detects performance.

[0078] When the template signal is a 4-6MHz 0th order PSWFs signal X31, the energy density values ​​of the cross terms between the signals of the method of the present invention (without filtering processing) at some frequencies are as shown in Table 1. In the table, X11 is a 1-3MHz 0th order PSWFs signal, X12 is a 1-3MHz 1st order PSWFs signal, X21 is a 2.5-4.5MHz 0th order PSWFs signal, X22 is a 2.5-4.5MHz 1st order PSWFs signal, X31 is a 4-6MHz 0th order PSWFs signal, X32 is a 4-6MHz 1st order PSWFs signal, X41 is a 5.5-7.5MHz 0th order PSWFs signal, X42 is a 5.5-7.5MHz 1st order PSWFs signal, X51 is a 7-9MHz 0th order PSWFs signal, and X52 is a 7-9MHz The first-order PSWFs signal, combined with Table 1, can be seen that for the X31 branch, the error performance of the time-frequency detection method of the present invention is about ΔSNR_dB=0.93dB different from the error performance of the coherent detection (orthogonal case), while the error performance difference between the coherent detection (non-orthogonal case) and the orthogonal case is about 1.43dB, which improves the detection performance of the non-orthogonal PSWFs signal.

[0079] Table 1. Detection statistics of the method of the present invention when the template signal is X31 (without filtering)

[0080]

[0081] Example 3

[0082] When there is filtering, the method of the present invention detects performance.

[0083] When the time-frequency detection method of the present invention adopts filtering processing, the detection statistic values ​​are shown in Table 2. In the table, X11 is a 1-3MHz 0-order PSWFs signal, X12 is a 1-3MHz 1-order PSWFs signal, X21 is a 2.5-4.5MHz 0-order PSWFs signal, X22 is a 2.5-4.5MHz 1-order PSWFs signal, X31 is a 4-6MHz 0-order PSWFs signal, X32 is a 4-6MHz 1-order PSWFs signal, X41 is a 5.5-7.5MHz 0-order PSWFs signal, X42 is a 5.5-7.5MHz 1-order PSWFs signal, X51 is a 7-9MHz 0-order PSWFs signal, and X52 is a 7-9MHz 1-order PSWFs signal. It can be seen from the table that, compared with the case where no filtering is used, the sampling filtering process can increase the value of the detection feature value from the original 0.897867 to 0.999995≈1. At the same time, according to formula (12), combined with Table 2, it can be seen that for the X31 branch, the error performance of the time-frequency detection method of the present invention is about ΔSNR_dB=0.02dB, that is, compared with the case where no filtering is used, the system error performance is improved by about 0.9dB by using filtering.

[0084] Table 2. Detection statistics of the method of the present invention when the template signal is X31 (with filtering processing)

[0085]

[0086] System error performance Figure 2 As shown, from the simulation results we can see:

[0087] The method of the present invention has better system error performance than coherent detection in non-orthogonal conditions. For example, when the bit error rate is 4×10 -5 When compared with coherent detection (non-orthogonal case), the system error performance of the method of the present invention (without filtering processing) is improved by about 0.5 dB, and the system error performance of the method of the present invention (with filtering processing) is improved by about 1 dB. Figure 2 shown.

[0088] The system error performance of the method of the present invention using filtering is better than that of the system without filtering. For example, when the bit error rate is 4×10 -5 When the filtering process is used, the system error performance of the system is improved by about 0.5 dB compared with that of the system without filtering process. It should be noted that since the frequency band of the 4-6MHz 0th order (numbered X31 in Table 1 and Table 2) PSWFs signal is located at the center of the frequency band used in the simulation, its time-frequency detection effect is the worst relative to other branches, so the total system error performance of the method of the present invention is better than the system error performance of the X31 single branch.

[0089] Combined with the analysis of the embodiments, it can be seen that, in general, the non-orthogonal PSWFs signal detection method based on cross terms between signals provided by the present invention has the following beneficial effects compared with the prior art:

[0090] The non-orthogonal PSWFs signal detection is transformed from traditional coherent detection based on the "global" energy in the time domain / frequency domain to "local" energy in the time and frequency domain. This effectively reduces the interference between non-orthogonal PSWFs signals and greatly improves the detection performance of non-orthogonal PSWFs signals. It not only provides new ideas for exploring and studying communication signal detection including PSWFs signals, but also provides a reference basis for exploring and studying new mechanisms for two-dimensional domain signal detection.

[0091] Finally, it should be noted that the above specific implementation methods and examples are intended to illustrate the technical solution of the present invention rather than to limit the technical method. The present invention can be extended to other modifications, changes, applications and embodiments in application, and therefore it is believed that all such modifications, changes, applications and embodiments are within the spirit and teaching scope of the present invention.

Claims

1. A non-orthogonal ellipsoidal wave signal detection method based on cross terms between signals, characterized in that The following steps are involved: Step 1) using a signal receiving device to receive the ellipsoidal spherical wave modulated signal after signal transmission; Step 2) constructing a set of ellipsoidal wave signals with the same duration and bandwidth parameters as the received ellipsoidal wave modulation signal as local template signals; Step 3) calculating a cross term between the modulated signal received by the receiving device and the local template signal; Step 4) Calculate the energy density value of the cross term at the center frequency in the frequency domain, and use it as the time-frequency domain feature detection quantity for decision detection, and demodulate the information loaded by the ellipsoidal wave signals of different branches.

2. A non-orthogonal ellipsoidal wave signal detection method based on signal cross terms according to claim 1, characterized in that The ellipsoidal wave modulation signal is a modulation signal generated by multiplying ellipsoidal wave signals of different branches and modulation symbols in the time domain and linearly superposing them.

3. A non-orthogonal ellipsoidal wave signal detection method based on cross terms between signals according to claim 2, characterized in that At the frequency corresponding to the peak point of the energy density of the cross-terms between the different branch ellipsoidal wave signals themselves, the cross-terms between the modulated signal received by the receiving device and the local template signal are integrated in the time domain as the time-frequency domain feature detection quantity; the cross-terms between the different branch ellipsoidal wave signals themselves and the cross-terms between the modulated signal received by the receiving device and the local template signal are discretized to obtain the corresponding matrix A of the cross-terms between the different branch ellipsoidal wave signals themselves and the corresponding matrix B of the cross-terms between the modulated signal received by the receiving device and the local template signal, calculate the corresponding vector C of the energy density peak value of the cross-terms between the different branch ellipsoidal wave signals themselves at different times, divide the matrix B by the vector C to obtain the vector D, and use the numerical value corresponding to the frequency corresponding to the peak point of the energy density of the cross-terms between the different branch ellipsoidal wave signals themselves in the vector D as the time-frequency domain feature detection quantity.

4. A non-orthogonal ellipsoidal wave signal detection method based on cross terms between signals according to claim 3, characterized in that The specific steps of step 1) are: discretizing the cross terms between different branch ellipsoidal wave signals themselves and the cross terms between the modulated signal received by the receiving device and the local template signal, and obtaining the matrix A corresponding to the cross terms between different branch ellipsoidal wave signals themselves, that is: The cross term between the modulated signal received by the receiving device and the local template signal corresponds to the matrix B, that is: In the formula, is the PSWFs signal of the i-th branch, a i,j is the energy density value of the cross term at the jth moment and the ith frequency in the time-frequency domain, m is the number of discretization points of the cross term in the frequency domain, and n is the number of discretization points of the cross term in the time domain.

5. A non-orthogonal ellipsoidal wave signal detection method based on cross terms between signals according to claim 4, characterized in that The specific steps of step 2) are: calculate the energy density peak value corresponding vector C of the cross terms between different branch ellipsoidal wave signals at different times, that is, when is a 0-order PSWFs signal, then That is, after the cross terms are discretized, the frequency of their energy density peak points is in the pth row, and the corresponding cross terms have energy peaks in the pth row and different columns.

6. A non-orthogonal ellipsoidal wave signal detection method based on cross terms between signals according to claim 3, characterized in that The specific steps of step 3) are: divide the matrix B by the vector C to obtain the vector D, that is, when For the 0th order PSWFs signal:

7. A non-orthogonal ellipsoidal wave signal detection method based on cross terms between signals according to claim 6, characterized in that The specific steps of step 4) are: taking the value corresponding to the frequency of the peak point of the cross-term energy density between the different branch ellipsoidal wave signals in the vector D as the time-frequency domain feature detection quantity, when is a 0-order PSWFs signal. Since its energy density peak frequency is in the pth row, its time-frequency domain feature detection quantity is b p .

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