Model and data driven disturbance rejection method

Abstract

The model and data double-driven interference suppression method disclosed by the application comprises: generating two non-stationary frequency modulation interferences; generating a signal of missing samples received by a receiver under a single interference and two interference conditions respectively; calculating a ambiguity function, smoothing the ambiguity function through an adaptive optimal kernel, and converting the smoothed ambiguity function into an autocorrelation function processed by the adaptive optimal kernel; sparsely reconstructing the interference by using an orthogonal matching pursuit algorithm to obtain an instantaneous frequency of the interference; correcting the instantaneous frequency of the interference by using a support vector regression; restoring the interference waveform by using the obtained instantaneous frequency, and removing the interference by using a subspace orthogonal projection method. The inaccurate non-stationary interference time-frequency characteristics obtained by sparse reconstruction are corrected by using the support vector regression, the imperfect instantaneous frequency is eliminated, the data information is fully utilized, the model driving and the data driving are combined, and the non-stationary interference suppression and elimination are realized.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of communication anti-interference, and particularly relates to a model and data double-driven interference suppression method. BACKGROUND

[0002] In a wideband wireless communication and navigation system, desired signals are often interfered by intentional and unintentional interference signals, which can be single-tone interference, multi-tone interference, narrowband interference, wideband interference, etc. Among these interference forms, it is challenging and particularly important for a receiver to eliminate the influence of non-stationary interference because non-stationary interference adopts frequency modulation or polynomial phase signal waveform and covers the entire working frequency band. A compression sensing method can be used to eliminate non-stationary interference.

[0003] Traditional anti-interference methods such as frequency domain filtering, time domain filtering, adaptive filtering, etc. cannot effectively process non-stationary interference. When there is no difference in propagation direction between the interference source and the transmitter, spatial domain filtering cannot eliminate non-stationary interference. Based on the relationship between ambiguity function (AF) and instantaneous autocorrelation function (IAF), a compression sensing (CS) method can be used to reconstruct non-stationary interference, and then a subspace projection-based interference suppression technology can be used to suppress non-stationary interference to recover the desired signal. Antenna array technology can improve the accuracy of interference signal reconstruction. However, the above methods only use model-based signal processing theory to reduce interference, without using information hidden in data, and the time-frequency characteristics of the interference obtained by sparse reconstruction are not accurate enough, and the interference suppression effect is not good enough. SUMMARY

[0004] The application aims to provide a model and data double-driven interference suppression method, which solves the problem of not fully utilizing information hidden in data in the existing anti-interference method, and the time-frequency characteristics of the interference obtained by sparse reconstruction are not accurate enough.

[0005] The technical scheme adopted by the application is as follows: a model and data double-driven interference suppression method, comprising the following steps:

[0006] Step 1: generating two non-stationary frequency modulation interferences; Step 2: generating a signal of missing samples received by a receiver under single interference and two interference conditions respectively; Step 3: calculating an ambiguity function, smoothing the ambiguity function through an adaptive optimal kernel, and converting the smoothed ambiguity function into an autocorrelation function processed by the adaptive optimal kernel; Step 4: using an orthogonal matching pursuit algorithm to sparsely reconstruct the interference to obtain an instantaneous frequency of the interference; Step 5: using a support vector regression to correct the instantaneous frequency of the interference; Step 6: using the obtained instantaneous frequency to recover the interference waveform, and using a subspace orthogonal projection method to remove the interference.

[0007] The application has the following characteristics:

[0008] The instantaneous frequency of the frequency-modulated jamming obtained in step 1 is represented as:

[0009]

[0010] In formula (1), T is the jamming time length, t is time, t = 1, 2,..., T.

[0011] Step 3 specifically comprises the following steps:

[0012] Step 3 specifically comprises the following steps:

[0013] Step 3.1, the instantaneous autocorrelation functions of the received signals are calculated in the two cases in step 2 respectively according to the following formula, and the ambiguity function and the WVD distribution are calculated based on the instantaneous autocorrelation functions:

[0014] The instantaneous autocorrelation function is:

[0015]

[0016] The ambiguity function is:

[0017]

[0018] The WVD distribution is:

[0019]

[0020] Step 3.2, the smoothing of the ambiguity function is realized using the adaptive optimal kernel, that is, the cross terms and noise artifacts are filtered out:

[0021] A s (θ,τ)=A xx (θ,τ)Φ(θ,τ) (5)

[0022] The adaptive optimal kernel time-frequency kernel is obtained by solving the following optimization problem:

[0023]

[0024] In formula (6), α is the kernel capacity;

[0025] Step 3.3, the ambiguity function A s (θ,τ) after smoothing is converted into the autocorrelation function C s (t,τ) after adaptive optimal kernel processing:

[0026]

[0027] In formula (7), A s (θ,τ) is a fuzzy function conversion, C s (t,τ) is an autocorrelation function.

[0028] Step 4 is specifically: a one-dimensional vector of autocorrelation functions of all delays τ at a specific time t after adaptive optimal kernel is recorded as:

[0029] c s (t)=[C s (t,τ1),......,C s (t,τ T )] T (8)

[0030] The one-dimensional Fourier transform relationship of the autocorrelation function and the TF domain is specifically represented as follows:

[0031]

[0032] In formula (9), G f is a discrete inverse Fourier transform matrix relative to f, d x (t)=[D xx (t,f1),......,D xx (t,f T )] T , d x (t) is a one-dimensional WVD vector to be estimated at a specific time t, d x1 (t) and d x2 (t) are obtained by using the orthogonal matching pursuit algorithm for sparse reconstruction, d x1 (t) and d x2 (t) are obtained by sparse reconstruction, and the instantaneous frequency f p (t) of the interference is obtained.

[0033] Step 5 is specifically: the sparse reconstructed instantaneous frequency of the interference obtained in step 4 is used to find a first instantaneous frequency regression curve by support vector regression, n points farthest from the original instantaneous frequency f p (t) on the first instantaneous frequency regression curve are discarded, support vector regression is performed on the remaining points again, a second modified instantaneous frequency regression curve is obtained, n points farthest from the original instantaneous frequency f p (t) on the second modified instantaneous frequency regression curve are discarded, the discarded points cannot be the same as the previously discarded points, and the iteration is repeated L times to obtain the modified instantaneous frequency of the interference

[0034] Step 6 specifically includes the following steps:

[0035] Step 6.1, the instantaneous frequency of the interference is:

[0036]

[0037] In formula (12), Q is an interference number;

[0038] The instantaneous phase is:

[0039]

[0040] Therefore, the interference signal is represented as d j (t):

[0041]

[0042] The time characteristic of the jth interference is represented as:

[0043]

[0044] The subspace orthogonal projection method is used to project the interference signal in the received signal into the waveform orthogonal space thereof, so that the interference suppression is realized; specifically, the received signal X is projected into the projection matrix P generated by the interference subspace V:

[0045]

[0046] P=I-V(V H V) -1 V H (16)

[0047] In formula (16),

[0048] The interference in the received signal is suppressed, and the subspace projected signal Y is obtained:

[0049] Y=PX (17)。

[0050] The model and data dual-driven interference suppression method has the advantages that: the model and data dual-driven algorithm is used, the non-stationary interference is reconstructed based on the compression sensing (CS) and support vector regression (SVR) technology, so that the non-stationary interference is reduced. The inaccurate non-stationary interference time-frequency characteristics obtained by sparse reconstruction are corrected by using the support vector regression (SVR), and the imperfect instantaneous frequency is removed by using the iterative method, so that the information hidden in the data is fully utilized, the model driving and data driving are combined, the purpose of non-stationary interference suppression and elimination is achieved. In the case of missing observation data, the non-stationary interference can be accurately reconstructed, and the non-stationary interference can be effectively suppressed and eliminated, so that the method has certain practical significance and good application prospect. BRIEF DESCRIPTION OF DRAWINGS

[0051] Figure 1 ​is a flowchart of the model and data dual-driven interference suppression method of the present application;

[0052] Figure 2 is a schematic diagram of the WVD distribution of a single interference plus signal in the model and data dual-driven interference suppression method of the present application;

[0053] Figure 3 is a schematic diagram of the AOK time-frequency kernel processing of a single interference plus signal in the model and data dual-driven interference suppression method of the present application;

[0054] Figure 4 is a schematic diagram of the WVD distribution of a single interference using the interference waveform recovered by the present application in the model and data dual-driven interference suppression method of the present application;

[0055] Figure 5 is a schematic diagram of the WVD distribution of a single interference after interference suppression by the method of the present application in the model and data dual-driven interference suppression method of the present application;

[0056] Figure 6 is a schematic diagram of the WVD distribution of two interference plus signals in the model and data dual-driven interference suppression method of the present application;

[0057] Figure 7 is a schematic diagram of the AOK time-frequency kernel processing of two interference plus signals in the model and data dual-driven interference suppression method of the present application;

[0058] Figure 8 is a schematic diagram of the WVD distribution of two interference using the interference waveform recovered by the present application in the model and data dual-driven interference suppression method of the present application;

[0059] Figure 9 is a schematic diagram of the WVD distribution of two interference after interference suppression by the method of the present application in the model and data dual-driven interference suppression method of the present application;

[0060] Figure 10 is a schematic diagram of the root mean square error (RMSE) of the instantaneous frequency (IF) estimated by three different algorithms under different jam-to-signal ratios (JSRs) without missing samples in the model and data dual-driven interference suppression method of the present application;

[0061] Figure 11 is a schematic diagram of the relationship between the root mean square error (RMSE) and the jam-to-signal ratio (JSR) when different proportions of missing samples exist in the received signal in the model and data dual-driven interference suppression method of the present application;

[0062] Figure 12 is a schematic diagram of the interference suppression effect of the signal-to-jam noise ratio (SJNR) of three methods in the model and data dual-driven interference suppression method of the present application;

[0063] Figure 13 Figure 1 is a schematic diagram of the influence of missing samples with different proportions on interference suppression in the model and data dual-driven interference suppression method of the present application. DETAILED DESCRIPTION

[0064] The present application will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0065] Example 1

[0066] The present application provides a model and data dual-driven interference suppression method, as shown in Figure 1

[0067] Step 1, generate two non-stationary frequency modulation (FM) jammers.

[0068] The instantaneous frequency of the frequency modulation jammer is represented as:

[0069]

[0070] In formula (1), T is the interference time length, t is the time, t = 1, 2,... T.

[0071] Step 2, generate the missing sample signal received by the receiver under the conditions of single interference and two interferences, respectively.

[0072] Single FM interference f1(t) hits the receiver together with the communication signal. The jam-to-signal ratio (JSR) is 20 dB and 50% data is lost. The missing signal x1(t) received by the receiver is obtained.

[0073] Two FM interferences f1(t), f2(t) hit the receiver together with the communication signal. The jam-to-signal ratio (JSR) is 20 dB and 50% data is lost. The missing signal x2(t) received by the receiver is obtained.

[0074] Step 3, calculate the instantaneous autocorrelation function, ambiguity function and WVD distribution of the received signal under the two conditions, respectively, according to the following formula.

[0075] Instantaneous autocorrelation function:

[0076]

[0077] Ambiguity function:

[0078]

[0079] WVD distribution:

[0080]

[0081] ​Step 4, AF smoothing is achieved using an adaptive optimal kernel (AOK). The artifacts due to missing samples are removed while suppressing the undesired cross-terms in the TF domain, resulting in A s1 (θ,τ), A s2 (θ,τ).

[0082] A s (θ,τ) = A xx (θ,τ)Φ(θ,τ) (5)

[0083] The AOK TF kernel can be obtained by the following optimization problem.

[0084]

[0085] where α is the kernel capacity.

[0086] Step 5, the smoothed ambiguity function A s (θ,τ) is converted to the autocorrelation function C s (t,τ). The C s1 (t,τ), C s2 (t,τ) are obtained.

[0087]

[0088] Step 6, the interference is sparsely reconstructed using the orthogonal matching pursuit algorithm (OMP).

[0089] The autocorrelation function after the AOK kernel is denoted as c s1 (t) = [C s1 (t,τ1),..., C s1 (t,τ T )] T , c s2 (t) = [C s2 (t,τ1),..., C s2 (t,τ T )] T The relationship between the autocorrelation function and the one-dimensional Fourier transform of the TF domain is specifically expressed as follows:

[0090]

[0091]

[0092] where G f is the inverse discrete Fourier transform (IDFT) transformation matrix relative to f, d x (t) = [D xx (t,f1),..., D xx (t,f T )]T , d x (t) is the one-dimensional WVD vector to be estimated at specific time t. Since the frequency modulation (FM) interference is sparse in time-frequency domain, the orthogonal matching pursuit algorithm (OMP) is used to sparsely reconstruct d x1 (t), d x2 (t).

[0093] Step 7, the d x1 (t), d x2 (t) obtained by sparsely reconstructing, the instantaneous frequency of the interference is obtained.

[0094] Step 8, the instantaneous frequency of the interference is corrected by using support vector regression (SVR).

[0095] The obtained instantaneous frequency has errors, the inaccurate non-stationary interference time-frequency features obtained by sparsely reconstructing are corrected by using support vector regression (SVR), and an iterative method is used to eliminate imperfect instantaneous frequencies.

[0096] The principle of support vector regression (SVR) is as follows, assuming that the given training samples are:

[0097] {(x i ,y i ), i = 1, 2,..., k}, wherein x i ∈ R N is an input value, y i ∈ R is a corresponding target value, and k is the number of training samples.

[0098] First, a nonlinear mapping is used to map the data to a high-dimensional feature space, and then linear regression is performed in the high-dimensional feature space, assuming that the regression function f(x) is:

[0099]

[0100] wherein w is the weight vector of the regression function, and b is the bias.

[0101] The optimal regression function based on the support vector machine refers to the principle of minimizing the structural risk, that is, the optimization problem of minimizing the following function:

[0102]

[0103] wherein, in the above formula, C is the penalty factor, and is the minimum VC (Vapnik Chervonenkis) dimension, the VC dimension reflects the complexity of the model, thereby improving the generalization ability. ξ, ξ * are the slack variables, which measure the error of the training samples, and therefore To minimize the error. The constant C is a penalty coefficient, compromising between the two. Epsilon is a normal number, controlling the accuracy of the regression function, the difference between f(x i ) and y i is not counted as error when it is less than epsilon, and is counted as |f(x i )-y i |-epsilon when it is greater than epsilon.

[0104] The specific steps of correcting the instantaneous frequency are as follows: the instantaneous frequency of the interference is found by using support vector regression to find the first instantaneous frequency curve, the n points farthest from the curve are discarded, and the optimal fitting curve is found by repeating the iteration multiple times.

[0105] The specific steps of using SVR to reconstruct the IF algorithm are as follows:

[0106] Input: iteration number L, discarded point number n, interference instantaneous frequency f p (t), T

[0107] Output: corrected interference instantaneous frequency

[0108] The specific steps are as follows: use SVR regression to get the first corrected instantaneous frequency regression curve, discard the n points farthest from the original instantaneous frequency f p (t) on this curve, perform SVR regression on the remaining points again to get the second corrected instantaneous frequency regression curve, discard the n points farthest from the original instantaneous frequency f p (t) on this curve, the discarded points cannot be the same as the previously discarded points, and repeat the iteration L times to get the corrected interference instantaneous frequency

[0109] Step 9: use the obtained instantaneous frequency to recover the interference waveform.

[0110] The instantaneous frequency of the interference is:

[0111]

[0112] Where Q is the number of interferences.

[0113] The instantaneous phase is:

[0114]

[0115] Therefore, the interference signal can be expressed as d j (t):

[0116]

[0117] Step 10: project to remove interference.

[0118] The time characteristics of the jth interference can be expressed as:

[0119]

[0120] The interference signal in the received signal is projected into the waveform orthogonal space of the interference signal by using the subspace orthogonal projection method, and finally interference suppression is realized.

[0121] The principle of the subspace orthogonal projection method is as follows:

[0122] In the received signal, the power of the interference is much greater than the power of the signal, so in the received signal, the interference signal occupies the dominant vector space V of the received signal space, and the signal occupies the remaining subspace Q. The subspace of the interference and the subspace of the signal can be approximately orthogonal. When the projection matrix of the received signal is obtained, the dominant interference signal in the received signal can be considered to be suppressed by projecting the received signal into the non-dominant vector subspace of the vector space.

[0123] The received signal X is projected into the V projection matrix P generated by the interference subspace:

[0124] P=I-V(V H V) -1 V H (16)

[0125] Wherein

[0126] The interference in the received signal is suppressed, and the subspace projected signal Y is obtained:

[0127] Y=PX (17)

[0128] Step 11, in the case of two interferences, the interference root mean square error (RMSE) and the signal-to-interference noise ratio (SJNR) under different jamming-to-signal ratios (JSR) are simulated using the simulation algorithm, and the performance is compared with that of only using the orthogonal matching pursuit algorithm (OMP) and the polynomial regression fitting method.

[0129] By the above mode, the model and data double-driven interference suppression method of the application uses support vector regression (SVR) to correct the inaccurate non-stationary interference time-frequency characteristics obtained by sparse reconstruction, and simultaneously uses an iterative method to eliminate imperfect instantaneous frequency, fully utilizes data information, combines model driving and data driving, and further realizes non-stationary interference suppression and elimination, and has certain applicability.

[0130] Example 2 (simulation diagram)

[0131] 1. Simulation conditions

[0132] MATLAB

[0133] 2. Simulation content

[0134] Simulation results under single interference signal:

[0135] Simulation results under two interference signals are shown in FIG. 6, Figures 2-5 Figure 2 For the WVD distribution of the interference plus signal with 50% information loss, the artifacts caused by the loss of information can be clearly seen. After the AOK time-frequency kernel processing of the received signal, the artifacts are obviously eliminated, as shown in FIG. 5. Figure 3 Since there is a Fourier transform relationship between the instantaneous autocorrelation function and the time-frequency distribution, and the interference has sparsity in the time-frequency distribution, the instantaneous frequency of the interference can be recovered by the orthogonal matching pursuit algorithm (OMP), as shown in FIG. 6. Figure 4 Finally, more accurate instantaneous frequency is obtained by using support vector machine regression, the interference waveform is recovered, and the received signal is projected into the subspace orthogonal to the interference by the projection method, to obtain the WVD distribution after interference suppression, as shown in FIG. 7. Figure 5 Compared with FIG. 6, Figure 2 the interference is obviously eliminated.

[0136] Simulation results under two interference signals:

[0137] Simulation results under two interference signals are shown in FIG. 6, Figures 6-9 Figure 6 For the WVD distribution of the interference plus signal with 50% information loss, the artifacts caused by the loss of information can be clearly seen. After the AOK time-frequency kernel processing of the received signal, the artifacts are obviously eliminated, as shown in FIG. 5. Figure 7 Since there is a Fourier transform relationship between the instantaneous autocorrelation function and the time-frequency distribution, and the interference has sparsity in the time-frequency distribution, the instantaneous frequency of the interference can be recovered by the orthogonal matching pursuit algorithm (OMP), as shown in FIG. 6. Figure 8 Finally, more accurate instantaneous frequency is obtained by using support vector machine regression, the interference waveform is recovered, and the received signal is projected into the subspace orthogonal to the interference by the projection method, to obtain the WVD distribution after interference suppression, as shown in FIG. 7. Figure 9 Compared with FIG. 6, Figure 6 the interference is obviously eliminated.

[0138] Example 3 (performance analysis diagram)

[0139] Figure 10 ​​The root mean square error (RMSE) of the instantaneous frequency (IF) estimates of the three different algorithms is shown as a function of the jam-to-signal ratio (JSR). The average root mean square error (RMSE) of all algorithms is decreasing as the jam-to-signal ratio (JSR) is increasing. This is because when the jammer is much larger than the signal, it can be easily and accurately reconstructed. The support vector regression (SVR) method proposed in the present invention outperforms the orthogonal matching pursuit algorithm (OMP) and the polynomial regression algorithm. Because the present invention uses support vector regression (SVR) to discover the underlying information hidden in the data. Through data analysis, the "bad points" are discarded and replaced with new estimates. The non-stationary frequency modulation (FM) jammer can thus be reconstructed more accurately.

[0140] Figure 11 The root mean square error (RMSE) as a function of the jam-to-signal ratio (JSR) is shown when there are missing samples in the received signal. As the proportion of missing samples increases, the root mean square error (RMSE) becomes larger and the IF estimate of the jammer becomes less and less accurate. Therefore, the loss of samples severely reduces the jammer reconstruction accuracy. It can be seen in practice that it is important to maintain the integrity of the received signal. When the proportion of missing samples is less than 10%, the root mean square error (RMSE) is about 10 -3 , similar to the case without missing data. The robustness of the method of the present invention is demonstrated, and in practice, when a small proportion of samples is lost, the method of the present invention can still accurately reconstruct the jammer.

[0141] Figure 12 The jammer suppression performance of the three different methods in terms of the signal-to-jammer noise ratio (SJNR) is shown. The method of the present invention can significantly improve the jammer suppression performance compared to the simple orthogonal matching pursuit algorithm (OMP) algorithm. In addition, because the method of the present invention iterates to eliminate "bad points", the method of the present invention outperforms the polynomial regression algorithm in terms of jammer suppression.

[0142] Figure 13 The effect of missing samples on jammer suppression is shown. As the number of missing samples increases, the jammer suppression performance decreases even when the jam-to-signal ratio (JSR) is low. This shows that it is crucial to receive the entire signal intact. When the percentage of missing samples is greater than 30%, the suppression performance decreases significantly. This is because in this case, the sparsity recovery capability is limited.

Claims

1. A model and data dual-driven interference mitigation method, characterized in that, The method comprises the following steps: Step 1, generating two non-stationary frequency modulation interferences; Step 2, generating a signal of missing samples received by a receiver under single interference and two interferences respectively; Step 3, calculating a ambiguity function, smoothing the ambiguity function through an adaptive optimal kernel, and converting the smoothed ambiguity function into a self-correlation function processed by the adaptive optimal kernel; specifically comprising the following steps: Step 3.1, calculating the instantaneous self-correlation function of the received signal under the two conditions in step 2 according to the following formula, and calculating the ambiguity function and WVD distribution based on the instantaneous self-correlation function: Instantaneous self-correlation function: （2） Ambiguity function: （3） WVD distribution: （4） Step 3.2, smoothing the ambiguity function by using an adaptive optimal kernel, that is, filtering out cross terms and noise artifacts: （5） The adaptive optimal kernel time-frequency kernel is obtained by solving the following optimization problem: （6） In formula (6), is the nuclear volume; Step 3.3, blurring function after smoothing autocorrelation function after conversion to adaptive optimal kernel processing : （7） In formula (7), is a blurring function transform, is an autocorrelation function; Step 4, sparse reconstruction of the interference using the orthogonal matching pursuit algorithm to obtain the instantaneous frequency of the interference; specifically, the one-dimensional vector of the autocorrelation function of all delays after the adaptive optimal kernel is denoted as: ​ （8） The relationship between the self-correlation function and the one-dimensional Fourier transform of the TF domain is specifically expressed as follows: （9） In formula (9), is relative to inverse discrete Fourier transform transform matrix, , is a specific time one-dimensional WVD vector to be estimated, using the orthogonal matching pursuit algorithm sparse reconstruction , , and then through sparse reconstruction , get the instantaneous frequency of interference ; Step 5, correct the instantaneous frequency of the interference by using support vector regression; specifically, find the first instantaneous frequency regression curve by using support vector regression on the sparse reconstructed instantaneous frequency of the interference obtained in step 4, and find the second instantaneous frequency regression curve by using support vector regression on the remaining points after discarding the n points farthest from the original instantaneous frequency on the first instantaneous frequency regression curve ; repeat the iteration L times, and obtain the corrected instantaneous frequency of the interference ; wherein the discarded points are different from the previously discarded points ; Step 6, using the obtained instantaneous frequency to restore the interference waveform, and removing the interference by using a subspace orthogonal projection method.

2. The model and data dual-driven interference mitigation method of claim 1, wherein, The instantaneous frequency of the frequency modulation interference obtained in step 1 is represented as: （1） In formula (1), is the length of the interference time, is the time, .

3. The model and data dual-driven interference mitigation method of claim 2, wherein, The step 3 is specifically: single frequency modulation interference Impinging on the receiver with the communication signal, resulting in a lost signal received by the receiver ; two frequency modulation interferences , Impinging on the receiver with the communication signal, resulting in a lost signal received by the receiver .

4. The model and data dual-driven interference mitigation method of claim 3, wherein, Step 6 specifically comprises the following steps: Step 6.1, the instantaneous frequency of the interference is: （12） In formula (12), Q is the number of interferences; The instantaneous phase is: （13） So the interference signal is expressed as : （14） Step 6.2, the time characteristic of the interference is represented as: （15） The subspace orthogonal projection method is used to project the interference signal in the received signal into its waveform orthogonal space, so as to realize interference suppression; specifically: Projecting the received signal X onto the interference subspace generated by Projection matrix In: （16） In formula (16), ; Suppressing the interference in the received signal, a signal Y after subspace projection is obtained: （17）。

Images