Xianyu Dong,Wu Ren,Zhenghui Xue,Xuetian Wang,Weiming Li

Abstract:In this paper,a time-frequency associated multiple signal classification (MUSIC) algorithm which is suitable for through-wall detection is proposed.The technology of detecting human targets by through-wall radar can be used to monitor the status and the location information of human targets behind the wall.However,the detection is out of order when classical MUSIC algorithm is applied to estimate the direction of arrival.In order to solve the problem,a time-frequency associated MUSIC algorithm suitable for through-wall detection and based on S-band stepped frequency continuous wave (SFCW) radar is researched.By associating inverse fast Fourier transform (IFFT) algorithm with MUSIC algorithm,the power enhancement of the target signal is completed according to the distance calculation results in the time domain.Then convert the signal to the frequency domain for direction of arrival (DOA) estimation.The simulations of twodimensional human target detection in free space and the processing of measured data are completed.By comparing the processing results of the two algorithms on the measured data,accuracy of DOA estimation of proposed algorithm is more than 75%,which is 50% higher than classical MUSIC algorithm.It is verified that the distance and angle of human target can be effectively detected via proposed algorithm.

Keywords:through-wall radar;multiple signal classification (MUSIC) algorithm;inverse fast Fourier transform (IFFT) algorithm;target detection

1 Introduction

In recent years,the multiple signal classification(MUSIC) algorithm is widely used in the field of direction of arrival (DOA) estimation on account of its high resolution,estimation accuracy and stability for direction finding.Using this algorithm,the direction estimation of multiple human targets can be realized at the same time.The MUSIC algorithm was first proposed by Schmidt,and then many scholars studied and improved MUSIC algorithm [1?3].The algorithm is mainly used in sound source location of microphone array.Combining the algorithm with linear antenna array in free space,it can also obtain high resolution [4].The application of it can improve efficiency in rescue and anti-terrorism activities,as well as monitoring the elderly living alone in real time.In the rapidly developing application field of human body communication in the future,each application point should be interconnected [5].In order to realize the communication between human bodies,the position of signal nodes must be determined,which requires position discrimination.Especially when the signal node is behind the obstacle,the algorithm can play an important role combined with through-wall radar.Therefore,the improvement of this algorithm has important practical significance.However,when the algorithm is applied to the through-wall detection,the algorithm will be restricted because of the refraction and attenuation of the wall. In order to make MUSIC algorithm serve the detection of human targets by through-wall radar effectively,some changes on the basis of classical MUSIC algorithm are needed.

Based on S-band stepped frequency continuous wave (SFCW) radar,a time-frequency domain associated MUSIC algorithm which can be applied to through-wall detection is proposed in this paper.The algorithm associates the IFFT algorithm for range detection with the MUSIC algorithm for angle detection.The core of this algorithm is,as follows,the correct pulse detected in the range dimension that is enhanced and transmitted to the frequency domain,and then estimating the angle spectrum.The algorithm is applied to the detection of human body by through-wall radar,which can effectively reduce the distance and angle deviation caused by the existence of wall.Finally,the human body behind the wall was detected with S-band,one transmitter and two receivers through-wall radar.Compared with classical signal processing algorithm,the proposed algorithm has higher accuracy,correct angle recognition and smaller error.It is verified that this algorithm can effectively detect human targets.

2 Application Scenarios and Models

The proposed algorithm can be used for two-dimensional detection of human targets in the space behind obstacles.In order to complete target positioning,it is necessary to obtain the range and azimuth of the target with the help of antenna array.If N human targets need to be detected,at least (N+1) receiving antennas are needed to work at the same time.The radar antenna adopts a linear uniform array,and receiving antenna is evenly arranged on one side of transmitting antenna [6],as shown in Fig.1.

Fig.1 Target detection scene

SFCW radar contains multiple frequency components [7],and the frequency band width of it is easy to control [8].The SFCW has strong penetration in the wall with uneven medium,and can improve the efficiency of energy emission.The formula of SFCW [9] is as follows

where X(t) is the step frequency signal generated by radar,n means that the frequency is divided into n parts within bandwidth,t is time,f0is the starting frequency,T is the pulse emission period,Tpis the width of the transmitted pulse,and Δf is frequency step.

where τ is the duration of transmitted pulse.When Tp=T,the waveform is shown in Fig.2.

Fig.2 Time domain waveform of step frequency wave

As shown in Fig.2,the center frequencies of the output waveform are

where f represents the center frequencies of the output waveform. The signal frequencies demodulated by the zero intermediate frequency(IF) receiver are near zero frequency,so the bandwidth is small,which can be directly used for subsequent signal processing.

3 Algorithm Principle and Simulation

3.1 Algorithm Principle

If the distance between the target and transmitting antenna is L,receiving antennas and transmitting antennas are placed together.According to the working principle of SFCW radar,the base-band signal received by the receiver can be represented as

where Y(t) is the base-band signal received by the receiver,c is the speed of light.Compared with the moving speed of the human body,the frequency scanning speed of the radar signal is very fast.Therefore,in any frequency scanning period,the human body target can be regarded as a stationary state.The signal in (4) can be directly sampled,and the obtained formula after inverse discrete sequence fast Fourier transform(IFFT) is as follows

where L is the number of sampling points after sampling Y(t) in frequency domain,Hlis the spatial spectrum of the l-th sampling point,as well as the distance spectrum.The modulus value of(5) is

According to (6),the peak value of the final amplitude is obtained at l,while l equals 2 cnΔfL.It can be obtained that the distance between the human target and the antenna is L,and L is[9].

Assuming the echo signal is written as

where X(t) is the received data vector,A(θ) is the direction matrix of the array,A(θ)=[a(θ1),a(θ2),…,a(θk)],α(θ) is the column vector of the guidance vector of the echo signal,θ represents the angle of the echo signal,S(t) is the received signal vector,N(t) is the white noise vector.Assuming that the noise and signal are independent of each other,MUSIC algorithm decomposes the covariance matrix of the array output data to further estimate the incident direction of the signal [1].The process of MUSIC algorithm [4] consists of three steps:

Step 1Calculate the covariance of the echo signal data.The calculation formula is as follows

Step 2Calculate the eigenvalue decomposition of covariance.The number of eigenvalues is consistent with the number of scattering targets,using the method of eigenvalue separation that can separate signal subspace Usfrom noise subspace Un.The signal subspace Uscomposed of large eigenvalues and the noise subspace Uncomposed of small eigenvalues,which are orthogonal to each other [10].

Step 3If the α(θ) is the column vector of the guidance vector of the echo signal,obtain the spectrum estimation formula,which is as follows

The incident direction of the echo signal can be obtained by searching the spectral peak,which represents the direction of human body target.

3.2 Algorithm Simulation

The IFFT algorithm is used to get the distance of targets,and classical MUSIC algorithm is used to get target’s direction of arrival.In order to verify the effectiveness of algorithms,the algorithm simulation is finished with the help of MATLAB.Set frequency range of SFCW as 3.1–3.42 GHz,and Δf as 1 MHz,and other simulation parameters are shown in Tab.1.IFFT simulation results are shown in Fig.3(a) and Fig.3(b).According to the results,while target at 5 m the simulate distance is 4.98 m,and while target at 10 m the simulate distance is 9.961 m.The errors are within 0.3 m.It is verified that the algorithm is effective.

Fig.3 IFFT algorithm simulation results:(a) while target at 5 m;(b) while target at 10 m

Tab.1 Simulation setup

Set the simulation parameters and conditions the same as those of IFFT simulation.The antenna array is uniformly arranged.In order to prevent the occurrence of mirror angle spectrum,the array spacing shall be met d<.So set the receiving antenna spacing d as 0.04 m,and the distance from the transmitting antenna to the first receiving antenna dR_Tas 0.12 m.The array arrangement is shown in Fig.4.

Fig.4 Antenna array model

When there is a single target at 20°,the simulation results are shown in Fig.5 (a),which is 20°. When there are targets at 10° and 20°respectively,the simulation results are shown in Fig.5 (b),which are 19.5° and 9.5°.According to the simulation results,the angle deviation is within 1°.It is verified that the algorithm is effective.

Fig.5 MUSIC algorithm simulation results:(a) while target at 20°;(b) while targets at 10° and 20°

Even though both algorithms are effective,the theory and simulation results above are obtained in free space [11].When the wall exists,the influence of the wall can not be ignored.Both range and angle estimation algorithms should be improved from two aspects:eliminating strong clutter and correcting offset.

4 Field Test and Algorithm Correction

4.1 Processing of Measured Data with Classical Algorithms

Parameters and conditions are the same as mentioned above during the simulation except the spacing of the receiving antenna. Due to the large area of the antenna used,what is different from the simulation conditions is the spacing of the receiving antenna d that is changed to 0.09 m.The experimental setup is shown in Tab.2,and experimental scene and equipment are shown in Fig.6.

Tab.2 Experimental setup

Fig.6 Experimental equipment

The zero IF receiver is used in the field test,and the static background cancellation method is used for background clutter elimination. The background data is saved before collecting the target echo signal.Then the received I and Q signals are combined into complex signals to complete the distance and angle detection.The data processing flow is shown in Fig.7.

Fig.7 Flow chart of data processing

The wall used in the field test is a 37 cmthick brick wall,plus surface cement and lime,with a total thickness of about 40 cm.320 frequency points were used.When the human body target is at 3 m and 0°,the distance results after processing the measured data of the two receiving antennas are shown in Fig.8.Both of the distance results are 2.93 m.And the angle results are shown in Fig.9,which are 16°.

Fig.8 Obtained distance results

Fig.9 DOA estimation result

It can be seen from the figure that the range detection accuracy is relatively high. After a large number of experiments,the range detection error is within 0.3 m.However,the direct calculation angle deviation is large,and there is mirror angle spectrum peak interference,which leads to the failure of completing the accurate positioning of the target.Therefore,current MUSIC algorithm needs to be optimized to be suitable for through-wall radar.

4.2 Algorithm Optimization and Actual Measurement Verification

In different environment,many optimization algorithms have been proposed [12?13].After analysis and research,there are two main reasons for the large angle deviation in the environment of through-wall test.One is the refraction of electromagnetic wave by the wall which makes the angle deviation.The other one is the array spacing problem which causes the mirror angle spectrum to interfere with the identification of the correct angle. To solve this problem,we proposed a time-frequency correlation MUSIC algorithm in this paper.Compared with the classical MUSIC algorithm,three optimizations are made as follows:

a) Perform a frequency domain interpolation before processing the composite signal.The purpose is to increase the number of calculation points,making the signal smoother and reducing the interference of noise.The interpolation method is to add a point between each pair of two points,and the amplitude and phase of the point is equal to the average of its two adjacent points.

b) Instead of directly analyzing the angle spectrum with full-band signal,the method of strengthening the pulse where the target is located in the range image and returning it to the frequency domain to calculate the angle is adopted.This measure will reduce the interference of other target echoes.

c) Angle statistical results after multiple measurements are used as the final results rather than obtaining the angle of the target directly from the angle spectrum.This measure can effectively reduce the impact of accidental errors and mirror angle spectrum on the final results.

The optimized algorithm flow chart is shown in Fig.10.

Fig.10 Optimized algorithm flow chart

Data and test conditions are the same as those before optimization. The distance processing results of the two antennas after optimization are shown in Fig.11,which are 3.076 m and 3.076 m respectively.Then enhance the pulse of the target by 4 times,and return the range image to the frequency domain by fast Fourier transform (FFT) for DOA.The angle statistical results equal 0°,as shown in Fig.12.The influence of mirror angle spectrum is reduced,and the angle is also accurate.

Fig.11 Obtained distance result

Fig.12 Statistical result of target’s direction of arrival

According to the test results of experimental verification,the range-profile error is less than 0.3 m,and angle error can be well controlled within ±2.5° after optimization.It is proved that the optimized MUSIC algorithm and signal processing flow can be applied to the detection of human targets behind the wall.

Finally,the comparison of DOA estimation using two algorithms when targets are in different positions is shown in Tab.3.

According to Tab.3,with the tolerance of±2.5°,angle calculated by time-frequency associated MUSIC algorithm is more accurate and more reliable than angle calculated by classical MUSIC algorithm.

Tab.3 Direction of arrival calculated by two algorithms

5 Conclusion

Based on the classical MUSIC algorithm and Sband SFCW radar,a time-frequency associated MUSIC algorithm suitable for human target detection behind wall is proposed in this paper.Aiming at the problems in the application of classical MUSIC algorithm in through-wall detection to estimate the direction of arrival,some improvements are made.By associating IFFT algorithm with MUSIC algorithm,the power enhancement of the target signal is completed according to the distance calculation results in the time domain,and then convert the signal to the frequency domain for DOA estimation.By comparing the processing results of two algorithms,accuracy of DOA estimation of proposed algorithm is more than 75%,which is 50% higher than classical MUSIC algorithm.The proposed algorithm lays a theoretical foundation for three dimensional detection,especially suitable for the application on the detection of human targets behind obstacles,and has great significance to the early target locking of directional coupling signals in the development of human communication.