阅读说明：本技术 一种适用于lte外辐射源雷达的时域杂波抑制方法 (Time domain clutter suppression method suitable for LTE external radiation source radar ) 是由 饶云华 王雅莉 王胜涛 胡海霞 周健康 潘登 聂文洋 于 2019-09-03 设计创作，主要内容包括：本发明公开了一种适用于LTE外辐射源雷达的时域杂波抑制方法,将原始的监测信号进行sinc函数内插得到由有限个整数延迟的参考信号线性组合的监测信号；内插后的监测信号和参考信号分别进行分段；将分段后的监测信号、参考信号和滤波器权系数进行快速傅里叶变换,从而使信号从时域变换到频域；在频域根据最小均方算法进行杂波抑制,并进行自适应的变步长权值更新；最后,将每段的输出结果组合。与现有技术相比,本发明不用准确的估计出分数延迟时间,对内插后的监测信号以及参考信号进行批处理最小均方自适应的滤波,当估计值接近于真实值时,其输出结果就是所需要的目标回波信号,提升了监测通道杂波抑制性能,有利于雷达系统的目标探测。(The invention discloses a time domain clutter suppression method suitable for an LTE external radiation source radar, which comprises the steps of carrying out sinc function interpolation on an original monitoring signal to obtain a monitoring signal linearly combined by a finite number of integer-delayed reference signals; the interpolated monitoring signal and the interpolated reference signal are segmented respectively; performing fast Fourier transform on the segmented monitoring signal, the reference signal and the filter weight coefficient so as to transform the signal from a time domain to a frequency domain; performing clutter suppression in a frequency domain according to a least mean square algorithm, and updating a self-adaptive variable step weight; finally, the output results of each segment are combined. Compared with the prior art, the method does not need to accurately estimate the fractional delay time, carries out batch processing least mean square adaptive filtering on the interpolated monitoring signal and the reference signal, and outputs a required target echo signal when the estimated value is close to a real value, thereby improving the clutter suppression performance of the monitoring channel and being beneficial to target detection of a radar system.)

1. A time domain clutter suppression method suitable for an LTE external radiation source radar is characterized by comprising the following steps:

step 1, establishing an LTE external radiation source radar detection signal model, and performing fractional multiple interpolation, wherein the method comprises the following substeps;

step 1a, establishing models of a target echo signal and a reference signal, wherein the target echo signal is a monitoring signal, and the reference signal is a direct wave signal;

step 1b, carrying out sinc function interpolation on the original monitoring signal to obtain a monitoring signal linearly combined by a finite number of integer delayed reference signals, thereby obtaining an expression of fractional time delay of the monitoring signal;

step 2, designing an FIR filter aiming at the data subjected to fractional time interpolation so as to filter out fractional time delayed clutter in an FDBLMS algorithm;

step 3, performing fractional delay-based variable-step frequency domain batch least mean square algorithm FDBLMS, wherein the specific operation process of the whole FDBLMS algorithm is as follows,

step 3a, partitioning the reference signal, the monitoring signal and the weight coefficient vector, wherein each block is used as input data of one batch processing;

step 3b, FFT is carried out on the weight coefficient vector so as to implement a clutter suppression algorithm in a frequency domain;

step 3c, FFT is carried out on the input k-1 th and k-th data block vectors;

step 3d, calculating an estimated value of the kth data block according to the kth data block X (k) and the weight coefficient W (k);

step 3e, calculating an output error estimation value of the kth data block;

step 3f, performing FFT on the output error estimated value of the kth data block, and converting time domain data into frequency domain data;

step 3g, updating the step size factor and the weight coefficient vector;

and 4, combining the output results of each block to obtain the monitoring signal subjected to clutter suppression.

2. The method for time-domain clutter suppression for LTE external radiation source radar according to claim 1, wherein: in step 1a, the reference signal received by the LTE external radiation source radar is represented as,

s_ref(t)＝d(t)+v_ref(t)

wherein d (t) is direct wave, v_ref(t) noise of the reference channel;

the received original monitoring signal is represented as,

the first term in the above equation is the received direct wave, the second term is the multipath clutter, the third term is the target echo, the fourth term is the noise, wherein c₀、Δτ₀Complex envelope amplitude and fractional delay relative to a reference signal for direct wave interference; t is_sIs a sampling period of a radar receiving end, c_l、Δτ_l(l＝1,2,...,N_c) The complex envelope amplitude of the ith multipath clutter and the sampling period T relative to the reference signal_sFractional delay of; n is a radical of_cIs the total number of multipath; m (t) is a target echo signal; v. of_survAnd (t) monitoring channel noise.

3. The method for suppressing time domain clutter applicable to the LTE external radiation source radar according to claim 2, wherein: the specific implementation of step 1b is as follows,

a band-limited signal f (T) is set, the signal after fractional time delay delta tau is f (T-delta tau), and the sampling period is T_sThe sinc interpolation formula is expressed as:

discretization, i.e. t ═ nT_s+ Δ τ, yielding:

now, let k be n-i, and i, n, k are integers, and we get:

according to the graphical characteristics of the sinc function, the maximum value is taken at the origin, and the function value of the point farther from the origin decays faster, so that a smaller interval of k between (- ∞, infinity) can obtain a higher interpolation accuracy, and assuming that this interval is (-p, p), a corrected interpolation function is obtained:

if the reference signal is denoted as s_ref(t)＝d(t)+v_ref(T) when the sampling interval T_sAt ≦ Δ τ |, the monitor signal is expressed as:

in the formula,. DELTA.tau_l＝Δτ-lT_s，l∈Z，Δτ_l＜T_s(ii) a With a sampling period T_sDiscretizing and interpolating to obtain:

in the formula, c₀、Δτ₀Complex envelope amplitude and fractional delay relative to a reference signal for direct wave interference; c. C_l、Δτ_l(l＝1,2,...,N_c) The complex envelope amplitude of the ith multipath spur and the fractional delay relative to the reference signal; n is a radical of_cIs the total number of multipath; m (n) is a target echo signal; v. of_surv(n) monitoring channel noise; v. of_ref(n) is reference channel noise; h is_l,k＝c_lsinc(k-Δτ_l)。

4. The method for suppressing time domain clutter applicable to the LTE external radiation source radar according to claim 3, wherein: the specific implementation of step 2 is as follows,

in order to suppress clutter in the monitoring signal, the monitoring signal is segmented for subsequent processing, if the monitoring signal is divided into data segments with the length of N, fractional multiple interpolation can be carried out when a receiving end receives N data, and the length of the data segment after interpolation is changed from N to N + p; then, improving the FIR filter to change the FIR filter from N order to N + p order;

and (3) carrying out variable replacement on the monitoring signal expression, namely l '-l-k and k' -k + p:

wherein

Z-transforming the reference signal and the monitor signal to obtain:

the following steps are provided:

M(z)＝S_surv(z)-H(z)S_ref(z)

the transfer function of the filter is then expressed as:

wherein H_l'(z) is h'_l’Z-transform of (c);

in order to suppress clutter with fractional delay, the filter is increased by p orders, the total order of the reconstructed filter is M ═ p + N, and the reference signal and the filter weight coefficient vector input at the time N are x (N) ═ x (N + p), x (N +1),.. once, x (N-N +1) respectively]^TAnd w (n) ═ w_-p(n),w_-1(n),...,w_N-1(n)]^TAnd if the input monitoring signal is d (n), the output signal estimation value obtained after filtering is as follows:

y(n)＝w^T(n)x(n)

the output error signal generated is: e (n) ═ d (n) — y (n) ═ d (n) — w^TAnd (n) x (n), and the optimal inhibition effect is achieved by utilizing a mean square error function (MSE) minimization criterion, namely continuously adjusting the weight coefficient until the MSE of the output estimation value and the monitoring signal is minimum.

5. The method for time-domain clutter suppression for LTE external radiation source radar according to claim 4, wherein: the specific implementation of the blocking of the reference signal, the monitor signal and the weight coefficient vector in step 3a is as follows,

blocking the monitoring signal after interpolation in step 1, where the blocking length is L ═ M ═ p + N, N is the data blocking length before interpolation, p is the number of interpolation points, and the vector of the monitoring signal of the kth block is obtained as:

x(k)＝s_surv(k)＝[s_surv(kL-p),...,s_surv(kL-1),s_surv(kL)...,s_surv(kL+N-1)]^T

similarly, the reference signal and the weight coefficient vector are partitioned, and the kth data block and the weight coefficient vector are respectively obtained as follows:

d(k)＝s_ref(k)＝[s_ref(kL-p),...,s_ref(kL-1),s_ref(kL)...,s_ref(kL+N-1)]^T

w(k)＝[w_-p(k),...,w_-1(k),w₀(k)...,w_N-1(k)]^T

for k equal to 0,1,2, let the initial value W (0) equal to 0.

6. The method for suppressing time domain clutter applicable to the LTE external radiation source radar according to claim 5, wherein: the specific implementation of steps 3 b-3 d is as follows,

step 3b, firstly, continuously adding M zeros behind the filter weight coefficient with the order of M, and then expressing the frequency domain weight coefficient vector after performing 2M point FFT as:

W(k)＝FA^Tw(k)

in this case, w (k) is a 2M × 1 dimensional matrix, and w (k) is an M × 1 dimensional matrix, F is a 2M × 2M dimensional FFT matrix, and a ═ I_M0_M]Is an M x 2M dimensional matrix, I_MIs an M × M dimensional identity matrix, 0_MIs an M x M dimensional zero matrix;

step 3c, FFT is carried out on the input (k-1) th and k-th monitoring data block vectors,

X(k)＝diag{F[x(kM-M),...,x(kM-1),x(kM),...,x(kM+M-1)]}

wherein x (kM-M),.. times, x (kM-1) is data of the (k-1) th block, x (kM),. times, x (kM + M-1) is data of the kth block, and x (k) is an N × N dimensional vector;

step 3d, solving the linear convolution of the post-FFT data in step 3c by using 1/2 overlap-save method to obtain:

y^T(k)＝[y(kM),y(kM+1),...,y(kM+M-1)]

＝KF^-1X(k)W(k)

wherein, K is [0 ═ C_MI_M]Is an M × 2M dimensional matrix.

7. The method for suppressing time domain clutter applicable to the LTE external radiation source radar according to claim 6, wherein: the specific implementation of calculating the output error estimate for the kth data block in step 3e is as follows,

for the kth block, let the expected response vector in dimension M × 1 be:

d(k)＝[d(kM),d(kM+1),...,d(kM+M-1)]^T

then the error signal vector is obtained as

e(k)＝[e(kM),e(kM+1),...,e(kM+M-1)]^T＝d(k)-y^T(k)。

8. The method for time-domain clutter suppression for LTE external radiation source radar according to claim 7, wherein: the specific implementation of updating the step-size factor and the weight coefficient vector in step 3g is as follows,

defining a step factor matrix as

U(k)＝diag{μ_-M(k),...,μ_-1(k),μ₀(k),μ₁(k),...,μ_M-1(k)}

The step size factor of the M (M ═ M., -1,0, 1., M-1) frequency point in the k data block is:

since the input signal x (n) and the estimated value e (n) of the output error signal are known, the power spectral density and the cross spectral density are estimated by recursively smoothing the discrete fourier transform DFT coefficients:

S_x,m(k)＝λS_x,m(k-1)+(1-λ)|X_m(k)|²

S_e,m(k)＝λS_e,m(k-1)+(1-λ)|E_m(k)|²

wherein S is_x,m(k) Is X_m(k) Power spectral density of (1), S_e,m(k) Is E_m(k) Power spectral density of (1), S_xe,m(k) Is E_m(k) And X_m(k) 0 < lambda < 1, X_m(k) Is an element of the m-th frequency point of X (k), E_m(k) Is the m-th frequency bin element of E (k),

E(k)＝FK^Te(k)＝FK^T(d(k)-y^T(k))

＝FK^T(d(k)-KF^-1X(k)W(k))

＝FK^Td(k)-FK^TKF^-1X(k)W(k)

＝FK^Td(k)-FQF^-1X(k)W(k)

in the above formula, Q ═ K^TK is a 2 mx 2M dimensional matrix, the weight coefficient vector update formula becomes:

W(k+1)＝W(k)+2FGF^-1U(k)X^H(k)W(k)

wherein G ═ I_2MQ is a 2M x 2M dimensional matrix and I is an identity matrix with elements on the diagonal from the top left to the bottom right being 1 and all except 0.

Technical Field

The invention belongs to the technical field of passive radars and the technical field of communication, and particularly relates to a monitoring signal processing and variable step length self-adaptive minimum mean square clutter suppression method based on fractional interpolation when direct waves and fractional delayed multipath clutter exist in a received signal of an LTE external radiation source radar.

Background

Compared with an active radar system of a traditional system, a receiving system of the external radiation source radar is completely passive, does not radiate any electromagnetic wave, and extracts parameters such as time delay information, Doppler frequency and incoming wave direction of a target by receiving and processing radio waves transmitted in space by a non-cooperative radiation source reflected by the target, so that the target is detected, positioned and tracked. The third party radiation source signal used by the method belongs to a non-cooperative signal, and a wide variety of radiation sources can be utilized, such as mobile communication signals, broadcast signals, digital audio signals, GPS signals and the like. Therefore, the external radiation source radar system has good concealment, low cost, less waste of spectrum resources and wide signal space domain coverage. Based on the method, the research on the radar of the external radiation source has higher application value and significance.

In recent years, the widespread use of LTE signals, which are 4G communication signals, has attracted strong interest to the radar community. The wireless communication signal is one of wireless communication signals, supports a large bandwidth of 1.4-20 MHz, and has higher distance resolution compared with GSM and other signals; the large frequency range of 800-. In addition, LTE uses Orthogonal Frequency Division Multiple Access (OFDMA) to ensure low sidelobe of the ambiguity function, and due to its unique advantages, more and more domestic and foreign radar researchers are beginning to pay attention to the LTE signal-based radar system for external radiation sources.

In an external radiation source radar system, there is a signal processing step that is not negligible, i.e. clutter suppression. For a mobile communication system, the transmitting power of a base station is far less than the transmitting power of an active radar, and is generally only 20-40 w. Echo signals reflected by a target usually contain a large amount of multipath clutter and direct wave interference, the target echo power is generally about 40dB lower than the direct wave interference power and sometimes is 100dB lower than the direct wave interference power, if proper measures are not taken to suppress the clutter, the target gain obtained by only pointing to the target through an antenna beam main lobe and prolonging coherent accumulation time cannot meet the index requirement of the target to be detected, the required target echo signals are difficult to extract from the received signals, the matching filtering of the next step and purified reference signals is influenced, and accurate position information of the detected target cannot be obtained. Therefore, monitoring channel clutter suppression is a key step of signal processing in the LTE external radiation source radar system, and reliable support is provided for radar subsequent signal processing.

For an LTE external radiation source radar system, a necessary means for realizing target tracking monitoring is to perform coherent processing on a reference signal and a monitoring signal. The success of time domain clutter cancellation depends on the correlation between the reference channel and the monitoring channel, and the phase error may result in the system's weak ability to suppress clutter in the monitoring channel. And a small difference exists in time delay between the clutter in the monitoring channel and the direct wave signal in the reference channel. The delay signal typically has only a few parts located at integer multiples of the sampling interval, most located between two adjacent sampling points, and thus the fractional delay problem is dominant. As shown in fig. 1, a simple model of a bistatic radar system is now analyzed for fractional delay problems.

Suppose that the distance from the monitoring channel to the reference channel in the receiving system is R and the distance to the stationary is R₃₂(ii) a The distance from the LTE base station to the reference channel is R₁Distance to monitoring channel is R₂Distance to the rest is R₃₁(ii) a Reference signal propagation delay of tau₁When processed by the reference channelIs extended to tau'₁Then the total time delay of the reference signal is τ_r＝τ₁+τ'₁(ii) a The interference transmission time delay of direct wave is tau₂And the time delay processed by the monitoring channel is tau'₂The total time delay of the direct wave interference is tau_d＝τ₂+τ'₂(ii) a Similarly, the total time delay of multipath is τ_c＝τ₃+τ'₂＝τ₃₁+τ₃₂+τ'₂。

According to the actual radar working condition, R is generally known₁≠R₂≠(R₃₁+R₃₂) And τ'₁≠τ'₂Then τ is₁≠τ₂≠(τ₃₁+τ₃₂) Further, it is known that_c≠τ_d≠τ_rTherefore, there is a slight difference in time delay between the clutter in the monitoring channel and the direct wave signal in the reference channel. The delay signal typically has only a few parts located at integer multiples of the sampling interval, most located between two adjacent sampling points, and thus the fractional delay problem is dominant. If the actual spur signal is still represented by an integer delay, the correlation between the two channels must be reduced.

Assuming that only direct wave interference is considered and the effective bandwidth of the signal is B, the relationship between the correlation coefficient ρ and the delay difference τ between the direct wave signals of the two channels satisfies:

ρ＝sinc(τ×B)

the destructive gain of the system is defined as the multiple by which the ratio of signal energy to clutter energy increases for the effect of the correlation coefficient on the destructive gain of the two channels. The higher the cancellation gain, the better the result of clutter suppression will be. The optimal cancellation gain can be expressed as:

from the above equation, only when | ρ | → 1, the gain (CG) is cancelled₀The larger. For example, assuming correlation coefficients of 0.999, 0.99, 0.9, the calculated corresponding cancellation gains are 27dB, 17dB, 7dB, respectively. Can see, phaseA small change in the correlation coefficient has a large effect on the destructive gain.

Therefore, the invention starts from the problem of Fractional Delay, analyzes the influence of the correlation between the reference channel and the monitoring channel on the time domain clutter suppression effect, and provides a Fractional Delay-based variable-step Frequency Domain Batch Least Mean Square (FDBLMS) adaptive clutter suppression algorithm suitable for the LTE external radiation source radar. The method interpolates the monitoring signals, and then utilizes an FDBLMS algorithm to cancel the clutter so as to solve the problem of correlation variation between two channels.

Disclosure of Invention

The invention provides a clutter suppression method for an LTE external radiation source radar, aiming at the problems caused by clutter fractional delay of the external radiation source radar.

The technical scheme adopted by the invention is as follows: a clutter suppression method suitable for an LTE external radiation source radar is characterized by considering the problem of fractional delay and comprises the following steps:

step 1, establishing an LTE external radiation source radar detection signal model, and performing fractional multiple interpolation, wherein the method comprises the following substeps;

step 1a, establishing models of a target echo signal and a reference signal, wherein the target echo signal is a monitoring signal, and the reference signal is a direct wave signal;

step 1b, carrying out sinc function interpolation on the original monitoring signal to obtain a monitoring signal linearly combined by a finite number of integer delayed reference signals, thereby obtaining an expression of fractional time delay of the monitoring signal;

step 2, designing an FIR filter aiming at the data subjected to fractional time interpolation so as to filter out fractional time delayed clutter in an FDBLMS algorithm;

step 3, performing fractional delay-based variable-step frequency domain batch least mean square algorithm FDBLMS, wherein the specific operation process of the whole FDBLMS algorithm is as follows,

step 3a, partitioning the reference signal, the monitoring signal and the weight coefficient vector, wherein each block is used as input data of one batch processing;

step 3b, FFT is carried out on the weight coefficient vector so as to implement a clutter suppression algorithm in a frequency domain;

step 3c, FFT is carried out on the input k-1 th and k-th data block vectors;

step 3d, calculating an estimated value of the kth data block according to the kth data block X (k) and the weight coefficient W (k);

step 3e, calculating an output error estimation value of the kth data block;

step 3f, performing FFT on the output error estimated value of the kth data block, and converting time domain data into frequency domain data;

step 3g, updating the step size factor and the weight coefficient vector;

and 4, combining the output results of each block to obtain the monitoring signal subjected to clutter suppression.

Further, in step 1a, the reference signal received by the LTE external radiation source radar is represented as,

s_ref(t)＝d(t)+v_ref(t)

wherein d (t) is direct wave, v_ref(t) noise of the reference channel;

the received original monitoring signal is represented as,

the first term in the above equation is the received direct wave, the second term is the multipath clutter, the third term is the target echo, the fourth term is the noise, wherein c₀、Δτ₀Complex envelope amplitude and fractional delay relative to a reference signal for direct wave interference; t is_sIs a sampling period of a radar receiving end, c_l、Δτ_l(l＝1,2,...,N_c) The complex envelope amplitude of the ith multipath clutter and the sampling period T relative to the reference signal_sFractional delay of; n is a radical of_cIs the total number of multipath; m (t) is a target echo signal; v. of_survAnd (t) monitoring channel noise.

Further, the specific implementation manner of step 1b is as follows,

a band-limited signal f (T) is set, the signal after fractional time delay delta tau is f (T-delta tau), and the sampling period is T_sThe sinc interpolation formula is expressed as:

discretization, i.e. t ═ nT_s+ Δ τ, yielding:

now, let k be n-i, and i, n, k are integers, and we get:

according to the graphical characteristics of the sinc function, the maximum value is taken at the origin, and the function value of the point farther from the origin decays faster, so that a smaller interval of k between (- ∞, infinity) can obtain a higher interpolation accuracy, and assuming that this interval is (-p, p), a corrected interpolation function is obtained:

if the reference signal is denoted as s_ref(t)＝d(t)+v_ref(T) when the sampling interval T_sAt ≦ Δ τ |, the monitor signal is expressed as:

in the formula,. DELTA.tau_l＝Δτ-lT_s，l∈Z，Δτ_l＜T_s(ii) a With a sampling period T_sDiscretizing and interpolating to obtain:

in the formula, c₀、Δτ₀Complex envelope amplitude and fractional delay relative to a reference signal for direct wave interference; c. C_l、Δτ_l(l＝1,2,...,N_c) The complex envelope amplitude of the ith multipath spur and the fractional delay relative to the reference signal; n is a radical of_cIs the total number of multipath; m (n) is a target echo signal; v. of_surv(n) monitoring channel noise; v. of_ref(n) is reference channel noise; h is_l,k＝c_lsinc(k-Δτ_l)。

Further, the specific implementation manner of step 2 is as follows,

in order to suppress clutter in the monitoring signal, the monitoring signal is segmented for subsequent processing, if the monitoring signal is divided into data segments with the length of N, fractional multiple interpolation can be carried out when a receiving end receives N data, and the length of the data segment after interpolation is changed from N to N + p; then, improving the FIR filter to change the FIR filter from N order to N + p order;

and (3) carrying out variable replacement on the monitoring signal expression, namely l '-l-k and k' -k + p:

wherein

Z-transforming the reference signal and the monitor signal to obtain:

the following steps are provided:

M(z)＝S_surv(z)-H(z)S_ref(z)

the transfer function of the filter is then expressed as:

wherein H_l'(z) is h'_l'Z-transform of (c);

in order to suppress clutter with fractional delay, the filter is increased by p orders, the total order of the reconstructed filter is M ═ p + N, and the reference signal and the filter weight coefficient vector input at the time N are x (N) ═ x (N + p), x (N +1),.. once, x (N-N +1) respectively]^TAnd w (n) ═ w_-p(n),w_-1(n),...,w_N-1(n)]^TAnd if the input monitoring signal is d (n), the output signal estimation value obtained after filtering is as follows:

y(n)＝w^T(n)x(n)

the output error signal generated is: e (n) ═ d (n) — y (n) ═ d (n) — w^TAnd (n) x (n), and the optimal inhibition effect is achieved by utilizing a mean square error function (MSE) minimization criterion, namely continuously adjusting the weight coefficient until the MSE of the output estimation value and the monitoring signal is minimum.

Further, the specific implementation manner of blocking the reference signal, the monitor signal and the weight coefficient vector in step 3a is as follows,

blocking the monitoring signal after interpolation in step 1, where the blocking length is L ═ M ═ p + N, N is the data blocking length before interpolation, p is the number of interpolation points, and the vector of the monitoring signal of the kth block is obtained as:

x(k)＝s_surv(k)＝[s_surv(kL-p),...,s_surv(kL-1),s_surv(kL)...,s_surv(kL+N-1)]^T

similarly, the reference signal and the weight coefficient vector are partitioned, and the kth data block and the weight coefficient vector are respectively obtained as follows:

d(k)＝s_ref(k)＝[s_ref(kL-p),...,s_ref(kL-1),s_ref(kL)...,s_ref(kL+N-1)]^T

w(k)＝[w_-p(k),...,w_-1(k),w₀(k)...,w_N-1(k)]^T

for k equal to 0,1,2, let the initial value W (0) equal to 0.

Further, the specific implementation manner of steps 3b to 3d is as follows,

step 3b, firstly, continuously adding M zeros behind the filter weight coefficient with the order of M, and then expressing the frequency domain weight coefficient vector after performing 2M point FFT as:

W(k)＝FA^Tw(k)

in this case, w (k) is a 2M × 1 dimensional matrix, and w (k) is an M × 1 dimensional matrix, F is a 2M × 2M dimensional FFT matrix, and a ═ I_M0_M]Is an M x 2M dimensional matrix, I_MIs an M × M dimensional identity matrix, 0_MIs an M x M dimensional zero matrix;

step 3c, FFT is carried out on the input (k-1) th and k-th monitoring data block vectors,

X(k)＝diag{F[x(kM-M),...,x(kM-1),x(kM),...,x(kM+M-1)]}

wherein x (kM-M),.. times, x (kM-1) is data of the (k-1) th block, x (kM),. times, x (kM + M-1) is data of the kth block, and x (k) is an N × N dimensional vector;

step 3d, solving the linear convolution of the post-FFT data in step 3c by using 1/2 overlap-save method to obtain:

y^T(k)＝[y(kM),y(kM+1),...,y(kM+M-1)]

＝KF^-1X(k)W(k)

wherein, K is [0 ═ C_MI_M]Is an M × 2M dimensional matrix.

Further, the specific implementation manner of calculating the output error estimation value of the kth data block in step 3e is as follows,

for the kth block, let the expected response vector in dimension M × 1 be:

d(k)＝[d(kM),d(kM+1),...,d(kM+M-1)]^T

then the error signal vector is obtained as

e(k)＝[e(kM),e(kM+1),...,e(kM+M-1)]^T＝d(k)-y^T(k)。

Further, the step-size factor and the weight coefficient vector are updated in step 3g in the following specific manner,

defining a step factor matrix as

U(k)＝diag{μ_-M(k),...,μ_-1(k),μ₀(k),μ₁(k),...,μ_M-1(k)}

The step size factor of the M (M ═ M., -1,0, 1., M-1) frequency point in the k data block is:

since the input signal x (n) and the estimated value e (n) of the output error signal are known, the power spectral density and the cross spectral density are estimated by recursively smoothing the discrete fourier transform DFT coefficients:

S_x,m(k)＝λS_x,m(k-1)+(1-λ)|X_m(k)|²

S_e,m(k)＝λS_e,m(k-1)+(1-λ)|E_m(k)|²

wherein S is_x,m(k) Is X_m(k) Power spectral density of (1), S_e,m(k) Is E_m(k) Power spectral density of (1), S_xe,m(k) Is E_m(k) And X_m(k) 0 < lambda < 1, X_m(k) Is an element of the m-th frequency point of X (k), E_m(k) Is the m-th frequency bin element of E (k),

is X_m(k) Conjugation of (1);

E(k)＝FK^Te(k)＝FK^T(d(k)-y^T(k))

＝FK^T(d(k)-KF^-1X(k)W(k))

＝FK^Td(k)-FK^TKF^-1X(k)W(k)

＝FK^Td(k)-FQF^-1X(k)W(k)

in the above formula, Q ═ K^TK is a 2 mx 2M dimensional matrix, the weight coefficient vector update formula becomes:

W(k+1)＝W(k)+2FGF^-1U(k)X^H(k)W(k)

wherein G ═ I_2MQ is a 2M x 2M dimensional matrix and I is an identity matrix with elements on the diagonal from the top left to the bottom right being 1 and all except 0.

Compared with the prior art, the method has small calculated amount, has outstanding advantages when multipath and interference are serious, improves the detection performance of a radar system, and has great significance for the practical application of the LTE external radiation source radar.

Drawings

Fig. 1 is a schematic time delay diagram of an LTE external radiation source radar system.

Fig. 2 is a reconstructed FIR adaptive filter.

Fig. 3 is a functional block diagram of an FDBLMS filter.

Fig. 4 is a block diagram of an FDBLMS algorithm implementation.

Fig. 5 is a fractional delay based variable step frequency domain least mean square FDBLMS algorithm clutter cancellation ratio.

Fig. 6 is a doppler spectrum of the target under BLMS algorithm (a) and FDBLMS algorithm (b).

Detailed Description

In order to facilitate the understanding and implementation of the present invention for those of ordinary skill in the art, the present invention is further described in detail with reference to the accompanying drawings and examples, it is to be understood that the embodiments described herein are merely illustrative and explanatory of the present invention and are not restrictive thereof.

In the embodiment of the invention, the signal is an LTE signal in an FDD mode, the bandwidth is 15MHz, and the sampling rate of a receiving end is 23.04 MHz. The invention provides a clutter suppression method suitable for an LTE external radiation source radar, and a flow chart of the method in the embodiment of the invention is shown in figure 4, and the method comprises the following steps:

step 1, establishing an LTE external radiation source radar detection signal model, and performing fractional interpolation; the method comprises the following substeps:

step 1a, establishing models of a target echo signal (namely a monitoring signal) and a reference signal (namely a direct wave signal);

wherein, the reference signal received by the LTE external radiation source radar can be expressed as,

s_ref(t)＝d(t)+v_ref(t)

wherein d (t) is direct wave, v_ref(t) is the noise of the reference channel.

The received raw monitoring signal may be expressed as,

the first term in the above equation is the received direct wave, the second term is the multipath clutter, the third term is the target echo, and the fourth term is the noise. Wherein, c₀、Δτ₀Complex envelope amplitude and fractional delay relative to a reference signal for direct wave interference; t is_sIs a sampling period of a radar receiving end, c_l、Δτ_l(l＝1,2,...,N_c) The complex envelope amplitude of the ith multipath clutter and the sampling period T relative to the reference signal_sFractional delay of; n is a radical of_cIs the total number of multipath; m (n) is a target echo signal; v. of_survAnd (n) is monitoring channel noise.

It can be seen that there is a fractional delay of the sampling period in the clutter signal, and if the data is directly sampled by an integer multiple of the sampling period T in the time domain_sThe time-domain clutter suppression is performed for a time unit, so that the correlation between the monitoring channel signal and the reference channel signal is destroyed, and the clutter suppression performance is reduced, so that the fractional time delay needs to be considered.

Step 1b, carrying out sinc function interpolation on the original monitoring signal to obtain a monitoring signal linearly combined by a finite number of integer delayed reference signals, thereby obtaining an expression of fractional time delay of the monitoring signal;

aiming at the problem of clutter signal fractional time delay, the invention interpolates the monitoring signal by adopting a sinc function interpolation mode, thereby leading the interpolated monitoring signal to approach to an actual fractional time delay signal. The principle of sinc interpolation is to convolute the sinc function with the original sampling signal and to express the signals at fractional multiple intervals by the linear sum of the signals at integral multiple intervals.

A band-limited signal f (T) is set, the signal after fractional time delay delta tau is f (T-delta tau), and the sampling period is T_sThe sinc interpolation formula is expressed as:

discretization, i.e. t ═ nT_s+ Δ τ, yielding:

now, let k be n-i, and i, n, k are integers, and we get:

according to the graphical characteristics of the sinc function, the maximum value is taken at the origin, and the function values decay more rapidly for points further away from the origin. Therefore, a small interval of k between (-infinity, ∞) can obtain a high interpolation accuracy, and assuming that the interval is (-p, p), a corrected interpolation function can be obtained:

in the present invention, if the reference signal is denoted as s_ref(t)＝d(t)+v_ref(T) when the sampling interval T_sAt ≦ Δ τ |, the monitor signal may be expressed as:

in the formula,. DELTA.tau_l＝Δτ-lT_s，l∈Z，Δτ_l＜T_s. With a sampling period T_sDiscretizing and interpolating to obtain:

in the formula, c₀、Δτ₀Complex envelope amplitude and fractional delay relative to a reference signal for direct wave interference; c. C_l、Δτ_l(l＝1,2,...,N_c) The complex envelope amplitude of the ith multipath spur and the fractional delay relative to the reference signal; n is a radical of_cIs the total number of multipath; m (n) is a target echo signal;v_surv(n) monitoring channel noise; v. of_ref(n) is reference channel noise; h is_l,k＝c_lsinc(k-Δτ_l)。

It can be seen that when fractional delays are present in the clutter signals, a linear combination of a finite number of integer delayed reference signals can be used to fit the monitor signal.

Step 2, designing an FIR filter aiming at the data subjected to fractional time interpolation so as to filter out fractional time delayed clutter in an FDBLMS algorithm;

in order to suppress clutter in the monitoring signal, the monitoring signal needs to be segmented for subsequent processing, if the monitoring signal is divided into data segments with the length of N, the receiving end receives N data and can perform fractional interpolation, and the length of the interpolated data segment is changed from N to N + p.

After the fractional delay problem is considered and interpolation is carried out on the data, the original FIR filter with the least mean square algorithm needs to be correspondingly improved, so that the N order is changed into the N + p order, and the actual requirement is met.

And (3) carrying out variable replacement on the monitoring signal expression, namely l '-l-k and k' -k + p:

whereinZ-transforming the reference and monitor signals to obtain:

the following steps are provided:

M(z)＝S_surv(z)-H(z)S_ref(z)

the transfer function of the filter can be expressed as:

wherein，H_l'(z) is h'_l'Z-transform of (c). Coefficients h 'of the FIR filter transfer function H (z) in practice'_l'Are unknown and the adaptive filtering process is the process of estimating them according to some particular criterion. h'_l'The fractional delay value is contained in the digital signal, and an accurate fractional delay estimation value does not need to be known through self-adaptive filtering.

As is clear from the above equation, the spurs with fractional delay problem cannot be cancelled by the conventional adaptive filter, and the structure of the filter must be changed. In order to suppress the clutter with fractional delay, the filter may be increased by p, and the total order of the reconstructed filter is M ═ p + N, and the structure is shown in fig. 2. In fig. 2, if the order of the filter is M ═ p + N, then the reference signal and the filter weight vector input at time N are x (N) ═ x (N + p), x (N +1),.., x (N-N +1), respectively]^TAnd w (n) ═ w_-p(n),w_-1(n),...,w_N-1(n)]^TThe input monitor signal is d (n). Then the estimated value of the output signal obtained after filtering is:

y(n)＝w^T(n)x(n)

the output error signal generated is: e (n) ═ d (n) — y (n) ═ d (n) — w^TAnd (n) x (n), and the optimal inhibition effect is achieved by utilizing a mean square error function (MSE) minimization criterion, namely continuously adjusting weight coefficients until the MSE of the output estimation value and the monitoring signal is minimum.

Therefore, the reference signal is used as a reference training set, the monitoring signal is used as expected output data to estimate the error, and the estimated error value is used for adaptively adjusting the coefficient of the transfer function, so that S can be enabled to be close to the true value when the estimated value of the coefficient approaches to the true value_surv(z)-H(z)S_ref(z) is just equal to M (z), and the target echo signal without clutter is output.

And step 3, performing a variable step Frequency Domain Batch Least Mean Square (FDBLMS) algorithm based on fractional delay, and performing clutter suppression by the FDBLMS, wherein the wider bandwidth of an LTE signal is compared with signals such as DAB and GSM, so that the cancellation order is too high when the LMS algorithm is applied, and the calculation complexity is increased. This algorithm is an improved BLMS algorithm, except for the way in which the filter tap weights are updated. The FDBLMS filter is a functional block diagram as shown in fig. 3, an input signal is first divided into a plurality of data blocks with a length of L through serial/parallel conversion, and then sent to a batch FIR filter with an order of M (generally, L is M) block by block, interference cancellation is performed block by block, and each cancellation completion weight value is updated once. As shown in fig. 4, the whole FDBLMS algorithm operation process is:

step 3a, partitioning the reference signal, the monitoring signal and the weight coefficient vector, wherein each block is used as input data of one batch processing;

blocking the monitoring signal interpolated in the step 1, wherein the blocking length is L ═ M ═ p + N, and the obtained k-th block monitoring signal vector is as follows:

x(k)＝s_surv(k)＝[s_surv(kL-p),...,s_surv(kL-1),s_surv(kL)...,s_surv(kL+N-1)]^T

since the data is divided into a plurality of blocks, k is the kth block, and each block has a plurality of time values. Similarly, the reference signal and the weight coefficient vector are partitioned, and the kth data block and the weight coefficient vector are respectively obtained as follows:

d(k)＝s_ref(k)＝[s_ref(kL-p),...,s_ref(kL-1),s_ref(kL)...,s_ref(kL+N-1)]^T

w(k)＝[w_-p(k),...,w_-1(k),w₀(k)...,w_N-1(k)]^T

for k equal to 0,1,2, let the initial value W (0) equal to 0.

Step 3b, FFT is carried out on the weight coefficient vector so as to implement a clutter suppression algorithm in a frequency domain;

because the linear convolution processing in the frequency domain is to carry out periodic continuation on the sequence, and the length of x (k) and w (k) linear convolution is 2M-1, the period N is ensured to be more than or equal to 2M-1, the continuation period is taken as 2M, therefore, M zeros are continuously added behind the filter weight coefficient with the order M, and then the frequency domain weight coefficient vector after 2M-point FFT is expressed as:

W(k)＝FA^Tw(k)

in this case, w (k) is a 2M × 1 dimensional matrix, and w (k) is an M × 1 dimensional matrix, F is a 2M × 2M dimensional FFT matrix, and a ═ I_M0_M]Is an M x 2M dimensional matrix, I_MIs an M × M dimensional identity matrix, 0_MIs an M x M dimensional zero matrix.

Step 3c, FFT is carried out on the input k-1 th and k-th data block vectors;

X(k)＝diag{F[x(kM-M),...,x(kM-1),x(kM),...,x(kM+M-1)]}

where x (kM-M),.. times, x (kM-1) is data of the (k-1) th block, and x (kM),. times, x (kM + M-1) is data of the k-th block. X (k) is an NxN-dimensional vector.

Step 3d, calculating an estimated value of the kth data block according to the kth data block X (k) and the weight coefficient W (k);

solving the linear convolution by using 1/2 overlap-save method on the FFT data in the step 3c to obtain:

y^T(k)＝[y(kM),y(kM+1),...,y(kM+M-1)]

＝KF^-1X(k)W(k)

wherein, K is [0 ═ C_MI_M]Is an M × 2M dimensional matrix.

Step 3e, calculating an output error estimation value of the kth data block;

for the kth block, let the expected response vector in dimension M × 1 be:

d(k)＝[d(kM),d(kM+1),...,d(kM+M-1)]^T

the error signal vector can be obtained as

e(k)＝[e(kM),e(kM+1),...,e(kM+M-1)]^T＝d(k)-y^T(k)

Step 3f, performing FFT on the output error estimated value of the kth data block, and converting time domain data into frequency domain data;

E(k)＝FK^Te(k)＝FK^T(d(k)-y^T(k))

＝FK^T(d(k)-KF^-1X(k)W(k))

＝FK^Td(k)-FK^TKF^-1X(k)W(k)

＝FK^Td(k)-FQF^-1X(k)W(k)

in the above formula, Q ═ K^TK is a 2M × 2M dimensional matrix.

Step 3g, updating the step size factor and the weight coefficient vector;

defining a step factor matrix as

U(k)＝diag{μ_-M(k),...,μ_-1(k),μ₀(k),μ₁(k),...,μ_M-1(k)}

The step size factor of the M (M ═ M., -1,0, 1., M-1) frequency point in the k data block is then

Since the input signal x (n) and the estimated value e (n) of the output error signal are known, the power spectral density S can be estimated by recursively smoothing the discrete fourier transform DFT coefficients_x,m(k)、S_xe,m(k) And cross spectral density S_xe,m(k)：

S_x,m(k)＝λS_x,m(k-1)+(1-λ)|X_m(k)|²

S_e,m(k)＝λS_e,m(k-1)+(1-λ)|E_m(k)|²

Wherein S is_x,m(k) Is X_m(k) Power spectral density of (1), S_e,m(k) Is E_m(k) Power spectral density of (1), S_xe,m(k) Is E_m(k) And X_m(k) 0 < lambda < 1, X_m(k) Is an element of the m-th frequency point of X (k), E_m(k) Is the m-th frequency bin element of E (k),

is X_m(k) Conjugation of (1).

The weight coefficient vector update formula becomes:

W(k+1)＝W(k)+2FGF^-1U(k)X^H(k)W(k)

wherein G ═ I_2MQ is a 2 Mx 2M dimensional matrix and I is a singleThe bit matrix, the elements on the diagonal (called the main diagonal) from the top left to the bottom right of the matrix are all 1's, and all except 0's.

And 4, combining the output results of each block to obtain the monitoring signal subjected to clutter suppression.

The traditional LMS gradient vector is the estimation value of the current moment, while the estimation value of the FDBLMS gradient vector is more accurate, and is the accumulated average value of all sample point gradient vectors of a data block, so that the noise is smoothed. The accuracy will improve with increasing block length, but the convergence speed cannot be improved. Meanwhile, the block processing can reduce the occupancy rate of the memory to a great extent, and can work together with a processor supporting parallel operation to achieve a better inhibition effect.

5 Fourier transforms are performed on each block clutter suppression, requiring 5Nlog₂Multiplying for N times; calculating the output vector and the cross-correlation operation associated with the gradient vector estimate each requires 4N multiplications. Thus, a total of 5Nlog is required for FDBLMS₂N+8N＝10Mlog₂M +26M multiplications. Whereas the classical BLMS algorithm proceeds 2M in total²Multiplication by a ratio of (5 log)₂M+13)/M。

The ratio of different complexities obtained by different M values is shown in table 1, and it can be known that the larger the order of the filter is, the more obvious the advantage of FD BLMS calculated amount is.

TABLE 1 ratio of computational complexity of two algorithms under different filter order values

Simulation and clutter suppression performance analysis

In order to evaluate the performance of various algorithms, the clutter cancellation ratio, the clutter suppression effect and the calculation complexity are analyzed. The simulation still uses FDD-LTE signals with a bandwidth of 15MHz, the order of the transversal filter is set to 110, and the control parameter λ is set to 0.9. The coherent integration time was set to 0.5 s. For the fractional delay simulation, the monitoring signal is sampled by a high sampling rate (230.4MHz), then is extracted by 10 times, and finally the monitoring signal with the sampling rate of 23.04MHz is obtained. It can be seen that the fractional delay is between 4.34ns and 43.40 ns. The number of segments B is set to 20 and the cancellation distance delay unit k is set to 110. Other simulation parameters are shown in table 2.

TABLE 2LTE external radiation source radar system simulation parameters

(1) Clutter cancellation ratio: the method is used for evaluating the attenuation capability of the time domain adaptive filtering algorithm on the noise in the monitoring channel. If the clutter power of the monitoring channel before attenuation is P₁Monitoring the power of the channel clutter to be P after attenuation₂Then it is defined as:

CA(dB)＝10lg(P₁/P₂)

it can be seen that in order to obtain a better inhibition effect, the larger the CA should be, the better.

When p takes different values, the influence of fractional delay on clutter cancellation ratio is observed by using a fractional delay-based variable step-size Frequency Domain Batch Least Mean Square (FDBLMS) algorithm, and the result is shown in fig. 5.

It can be seen from fig. 5 that the clutter cancellation ratio has been increased significantly when the early stage p takes a smaller value. Although p is increased in the later stage, the clutter cancellation ratio of the algorithm is not changed and fluctuated greatly, which shows that the phase problem caused by fractional delay is compensated, and the maximum clutter suppression performance of the algorithm is realized. An excessively large p value causes an increase in the amount of calculation, and therefore, p takes 6 under this simulation condition.

On the other hand, when p is zero, the method is equivalent to a batch least mean square BLMS algorithm which does not consider fractional delay. It can be seen that not considering the fractional delay problem greatly reduces the suppression performance of the algorithm. After the fractional delay is considered, when the fractional delay interpolation p value is smaller, the inhibition performance of the fractional delay interpolation p value is increased rapidly along with the increase of the p value, and when the p value is increased to a certain degree, the variable step size frequency domain batch processing least mean square (FDBLMS) algorithm based on the fractional delay maintains a relatively constant clutter cancellation ratio, namely the clutter inhibition performance of the method tends to be stable, and the influence caused by the fractional delay problem is solved.

(2) Clutter suppression effect

When the fractional delay is 5ns and p is 6, performing mutual fuzzy function operation on the monitoring signal and the reference signal by respectively adopting a batch processing minimum mean square BLMS algorithm and a variable step size frequency domain batch processing minimum mean square FDBLMS algorithm based on the fractional delay to obtain a Doppler spectrum of a target section as shown in figure 6, and observing the clutter suppression effect.

As can be seen from fig. 6, the amplitude value of the target at the doppler frequency of 100Hz is not decreased due to the improvement of the algorithm, which shows that the fractional delay based variable step size frequency domain batch least mean square FDBLMS algorithm does not cause power loss to the target during the interference cancellation process. Comparing graphs (a) and (b), the fractional delay based variable step size frequency domain batch least mean square FDBLMS algorithm improves the target signal-to-noise ratio by about 5 dB. The above results show that the improved algorithm considers the fractional delay problem, so that the improved algorithm has a better effect on clutter suppression, mainly because the part of the direct wave signal with the phase advance is also eliminated.

It should be understood that the above description of the preferred embodiments is given for clarity and not for any purpose of limitation, and that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.