ZHANG Hailong ,ZHANG Gong ,XUE Biao ,and YUAN Jiawen

1.Key Laboratory of Radar Imaging and Microwave Photonics,Ministry of Education,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China;2.Nanjing Marine Radar Institute,Nanjing 211153,China

Abstract:This study deals with the problem of mainlobe jamming suppression for rotated array radar.The interference becomes spatially nonstationary while the radar array rotates,which causes the mismatch between the weight and the snapshots and thus the loss of target signal to noise ratio (SNR) of pulse compression.In this paper,we explore the spatial divergence of interference sources and consider the rotated array radar anti-mainlobe jamming problem as a generalized rotated array mixed signal (RAMS) model firstly.Then the corresponding algorithm improved blind source separation (BSS) using the frequency domain of robust principal component analysis (FDRPCA-BSS) is proposed based on the established rotating model.It can eliminate the influence of the rotating parts and address the problem of loss of SNR .Finally,the measured peakto-average power ratio (PAPR) of each separated channel is performed to identify the target echo channel among the separated channels.Simulation results show that the proposed method is practically feasible and can suppress the mainlobe jamming with lower loss of SNR.

Keywords:mainlobe jamming,blind signal separation (BSS),robust principal component analysis (RPCA),peak to average power ratio (PAPR).

1.Introduction

Anti-mainlobe jamming is a major research issue in antijamming signal processing [1].With the rapid development of modern electronic countermeasure (ECM) techniques,mainlobe jamming is becoming more and more significant in the modern battlefield.The mainlobe jamming can be generally categorized into two main types.The first type is called self-defensive interference where the jammer is installed on the target.The second type is called escort-support interference where the jammer is located near the target [2].

The side-lobe jamming could be effectively suppressed in traditional radar systems employing spatial signal processing such as side-lobe blanking (SLB),sidelobe canceling (SLC),and space-time adaptive processing (STAP) [3].

However,spatial signal processing is no longer sufficient when the radar system is in the face of mainlobe jamming.Reference [4] proposed a new target detection method based on distributed monopulse arrays in solving mainlobe jamming.This method is able to cancel mainlobe jamming and maintain the target echo by exploiting the different correlation characteristics between the target echo and the mainlobe jamming on distributed antennas.An algorithm of radar deception jamming suppression using joint approximate diagonalization of eigen matrices (JADE) method was proposed in [5].It uses the techaracrs of signal phase quantization and blind source separation (BSS) for sorting and identifying the target and deception jamming.Recently,BSS is becoming more and more efficient in the presence of mainlobe jamming.In [6,7],the BSS algorithm was effective in suppressing the mainlobe jamming being investigated.They both exploit the time domain characteristics of the signal and the jamming.New methods have been proposed based on the BSS method.To deal with the mainlobe interrupted sampling repeater jamming in distributed radar,[8] proposed a method which is based on minimum variance distortionless response.It estimates a covariance matrix by obtaining small-sample pure jamming signals through jamming recognition.All the methods mentioned above commonly work under the condition that the radar array stays static.However,when the radar array rotates,the received covariance matrix of complex signals is different compared with the matrix of complex signals received from the static radar array,so the sparse signal recovery method with subarray configuration cannot work properly.The calculated fourth-order cumulant is incorrect,thus the traditional BSS method cannot fit correctly.The received statistical model changes,therefore the above method based on minimum variance distortion less response could not be used smoothly.Obviously,it is difficult to deal with the mainlobe jamming especially with rotating radar arrays .

Generally,the first step in using the traditional BSS method is a whitening process [9].It supposes that the whitening process obeys a linear static model in which the jammer or the radar array stays static.Then the covariance matrix of the received signal vector can be established and the unitary matrix can also be calculated.However,the actual situation is that the jammer becomes divergent and spatial nonstationary interference can lead to the mismatch between the weight and the snapshots.The traditional BSS mathematical model becomes not suitable for this rotated array situation.The whitening process could not be commonly regarded as a linear static model easily.So far no specific methods have been proposed for solving the mainlobe jamming effectively.Therefore,a new mathematical model must be established to deal with the mainlobe jamming with lower loss of target signal to noise ratio (SNR) after pulse compression.When the radar array rotates,the fast Fourier transform (FFT) matrix of received signals commonly includes two parts including rotating parts and traditional static parts.In addition,the two parts can be divided into a low-rank matrix and a sparse counterpart.The above situation well fits the robust principal component analysis (RPCA) condition,then the RPCA method is introduced in the first step which replacs the traditional whitening process.This paper mainly works on suppressing the mainlobe jamming using RPCA-based BSS algorithm in frequency domain (FD-RPCA-BSS) with lower loss of SNR according to the established rotated array mixed signal (RAMS) model.

One of the main questions in the BSS method lies in how to estimate the number of sources of mainlobe jamming before separating target echo signals from the mixed source signals.In [10-15],several direction-ofarrival (DOA) estimation methods have been introduced to estimate the number of sources of mainlobe jamming.However,multipath propagation degrades the quality of the estimating results [16-18].In this paper,synthesized vector maximum likelihood (SVML) is introduced to tackle the problem of multipath propagation [19].

This paper is organized as follows: The number of sources of the mainlobe jamming is confirmed,and the SVML algorithm is illuminated in Section 2.The proposed RAMS model and FD-RPCA-BSS method are established in Section 3.Simulation results and analysis are given in Section 4.Conclusions are summarized in Section 5.

2.Estimating the number of sources of the mainlobe jamming based on DOA estimation

The BSS algorithm must have to satisfy that the number of source signals does not exceed the number of observed signals.Therefore,it is necessary to pre-estimate the number of source signals.Many super-solution estimation algorithms have been proposed for solving this issue such as the algorithm multiple signal classification (MUSIC)[19-21],the algorithm estimation of signal parameters via rotational invariance techniques (ESPRIT) [22-25],and the maximum likelihood (ML) algorithm [26] .However,in practice,these algorithms are not suitable for the low-elevation targets DOA estimation,especially in the multipath signal environment.

The radar in this paper is defined as a long-range surface surveillance radar.The main task is to detect the low elevation targets as early as possible even under the mainlobe jamming.To determine the number of the sources,the SVML method is proposed which utilizes the symmetry of the direct signal and the multipath signal.

The received synthesized steering vector of radar signals can be represented as follows：

whereA(θd) andA(θs) are the direct and indirect array steering vectors.θis the independent variable,θdrepresents the incident angle of the direct wave,θsrepresents the incident angle of the multipath reflected waves.ΔRis the minus of the lengths of direct path and indirect path.λrepresents the wavelength of the radar signal and ρ represents the reflection coefficient.The projection matrix of the steering vector which can be used in solving the multipath signal environment problem can be represented as

Through the synthetic steering vector ML estimation,the angle of arrival can be obtained as

whereRXXis the covariance matrix of the received signals.

Based on the eigenvalues,Akaike information criterion (AIC) is considered as a common method used in estimating the number of signal sources.It is evident that the power of sources is one of the main characteristics of the signal sources,then signal eigenvalues can be replaced by the power of the sources.The criterion based on the power of the sources can be described [27] as follows:

The SVML method utilizes the symmetry of the direct signal and the multipath signal and adopts a multipath model to solve this problem.Fortunately,when the radar rotates with some angular velocity,the decrease of the performance of the SVML method is unconscious.It can work properly even under the situation of multipath reflection.

Through establishing the multipath model and using the received synthesized vector of radar signals,the SVML method can effectively improve DOA estimation performance,especially for weak signal sources.

3.mainlobe jamming canceling based on FDRPCA-BSS method

In this section,considering the influence of the rotation of the radar array,a generalized RAMS model for improved BSS method applied in the anti-mainlobe jamming is provided.Then a novel FFT pre-process based on RPCA method is designed to eliminate the rotating parts of the low-rank matrix.Finally,pulse compression is performed for distinguishing the target channel from the separated channels according to the measured peak-to-average power ratio (PAPR).Detailed steps are introduced as follows.

3.1 RAMS model

The uniform linear array (ULA) ofMomnidirectional sensors withdinterelement spacing is utilized for the rotated phased array radar.

In the surveillance area,it is assumed that all far-field targets are located atPorientations.We also assume that there areNttargets andNjjamming in all thePorientations.The detailed description is shown in Fig.1.

Fig.1 Detection scenario of the radar

The baseband-transmitted signal is a narrowband linear frequency modulation (LFM) monopulse signal:

whereTpis the pulse width,Kis the chirp rate,B=KTpis the signal bandwidth,and rect(t/Tp) denotes a rectangular pulse of the duration ofTp,defined as

The received zero intermediate frequency signal can be described as

whereng,N(t) represents the additive white Gaussian noise.Xg,T(t) representsNttargets fromPorientations.It can be described as

where λ is the wavelength of the radar signal,αT,p,nis the amplitude of each target,τT,p,nis the time delay of each target.θT,prepresents the angle of the target fromPorientations.

Consider the interference is the noise frequency modulation jamming (NFMJ).Xg,J(t) representsNjinterference fromPorientations which can be described as

where θJ,pis the jamming’s angle from thepth orientation.βT,p,iis the amplitude parameter of theith jamming signal from thepth orientation.fT,J,p,iis the random frequency of theith jamming from thepth orientation.

With the radar array rotating with angular velocityωg,(8) should be revised as follows:

whereAT,ωrepresents the rotating component modulated by the radar array’s rotation.θT,ω=ωgTg,andTgrepresents the pulse repetition interval.n′g,N(t) represents the new additive white Gaussian noise which is also influenced by the radar array’s rotation.

3.2 Analysis of the FD-RPCA-BSS method

As described above,in BSS,echo signal and jamming signal are collected called mixed signals and they must have different statistical characteristics and be independent of each other.However this assumption no longer holds when the radar is rotating to cover 360°.The first step of the traditional BSS method which is commonly called the whitening process is not suitable for this new challenge.Moreover,the rotating components do not meet the required linear process.The conflict between conditions and requirements cannot be solved using the traditional BSS method.

Furthermore,if the rotating parts can be removed,the received signal model (11) satisfies the BSS signal model[5].Hence,the BSS technique can be applied to the separation of theNttarget echoes andNjjamming signals.In general,it must be satisfied thatNt+Nj≤Mto ensure the success process of the BSS method.

Hence,a new method should be provided according to the rotating state of the radar array.In terms of the received echo,the FFT matrix of the received signals could be divided into two parts including rotating parts and traditional static parts.The mathematical model well fits the requirements of the RPCA method.Then RPCA method is considered as replacing the traditional whitening process eliminating the rotating parts.

Firstly,the received signals should be pre-treated other than whitening.It could be expressed as

The matrixYg(t) can be decomposed into two independent components by the Go Decomposition algorithm,which is an optimization problem [29-32] as follws:

where ‖·‖F(xiàn)denotes the Frobenius norm,rank(·) denotes the rank operator and card(·) denotes the cardinality of the sparse matrix.rand ε represent the rank ofL(t) and sparse degree ofS(t),respectively.According to (13),the received complex signals can be decomposed into two independent components.In addition,the sparse matrixS(t)which includes the target and jamming signal can be processed in the next step.However,the low-rank matrixL(t)which includes the rotating component is eliminated.

Secondly,the pre-treated process should be processed in a method called joint diagonalization.Furthermore,the covariance matricesRg(τ) of the sparse signal(t) can be expressed as

According to the results given above,ifmsource signals are estimated in the received signal matrix,then we will getmseparatedKs(t) signals (suppose there are more than one type of jamming signal then there will be more separated jamming signal channels).As a consequence,the problems which are caused by the radar array’s rotation can be solved.

3.3 Distinguishing the target echo channel from the separated channels

According to literature searches,BSS technique has still not been widely used in radar anti-jamming till now.One main question lies in the order of the separated channels after BSS is uncertain.Although we can put jamming signal into one separated channel and put target signal into another separated channel,we still can not distinguish which separated channel is the right target channel between themseparated signal channels.In addition,it will result in the uncertainty of permutation results by this means.The proposed method utilizes PARA to distinguish themseparated signals.Firstly,the principle of the matched filter (MF) can be utilized with the separated signals.Suppose the pulse compression results ofKs(t)signals can be described asMs(t),then normalization[30] could be processed as follows:

whereNsrepresents the sampling points.We also define PAPR of the time domain as

PAPR measures the envelope fluctuation of the pulse compression waveform.Theoretically,the value of the PARA is mainly up to the main-to-side lobe after pulse compression which is only related to the type of window when the pulse width and bandwidth of the transmit signal are determined.

When the source signal is polluted by mainlobe jamming such as noise frequency modulation,the PARA of the source signals will be much lower than the source signals which are not polluted by mainlobe jamming.

According to (18) and the principle described above,the target signal channel and jamming signal channel could be distinguished according to the threshold which is decided by the pulse width,the bandwidth of the transmit signal and the type of the window used in the pulse compression period.If we are only interested in the target signal channel,then choose the largest value of the PARA among all the separated channels.

In contrast to the traditional BSS method,the FDPPCA-BSS method combines the characteristics of the RAMS model and components in frequency domain of RPCA algorithm,proposes a novel improved BSS method.

Particularly，the mainlobe jamming suppression procedure proposed in this paper is described in Fig.2.

Fig.2 Procedure of the mainlobe jamming suppression

4.Simulation analysis

In this section,numerical simulations are provided to evaluate the effectiveness of the proposed mainlobe jamming suppression.

In this paper,100 Monte Carlo trials are presented to assess the estimation performance.

Unless stated otherwise,it is supposed that a common scenery of a ULA of 64 sensors radar with half-wavelength spacing.The carrier frequencyf0is 2 GHz.

Assume that the radar target echo signals (T1) are LFM signals.The signal pulse width is 200 μs and the bandwidth is 2 MHz.It is assumed that the sampling rate is 2 MHz and the PRI is 2 048 μs.

The radar array has two modes which are non-rotating mode and rotating mode with the period one circle per second.The target echo signals are polluted by two mainlobe jamming.

The first mainlobe jamming (J1) is noise frequency modulation (NFM) signal whose arrival angle is 2.2°.The second mainlobe jamming (J2) is intense repeater jamming whose arrival angle is 2.8°.

Suppose the target and the two jammings are all in one radar’s mainlobe.Assume that the range bin of radar target (T1) is 1 475.

Specific parameters are listed in Table 1.

Table 1 Parameters of the target and jamming

Fig.3(a) depicts the one-dimensional range profile of the source signals after pulse compression.It can been seen that the LFM signal is wholly submerged in the noise and jamming because the energy of the jamming signal is too strong.We can hardly distinguish the target echo signal from the pulse compression signals.The algorithm proposed is used to separate the observed signals and take pulse compression on the three separated signals.Fig.3(b) shows the first separated signals after pulse compression.It can be seen that there is an obvious peak in Fig.3(b) and the target SNR after pulse compression from the rotated array declines about 4.6 dB compared with the static array.It can be inferred that when the radar array rotates with one cycle per second,the target SNR after pulse compression is lower than the static array (all using the traditional BSS method).As is shown in Fig.3,the traditional BSS method results in about 4.6 dB (normalized according to the static array) loss of SNR which can be seen from Fig.3(c),Fig.3(d),and Fig.3(e) depict the two separated jamming signal channels.The above three separated channels can be judged by their PAPR:22.7 dB,18.75 dB,and 15.67 dB.

Fig.3 Comparison between static array and rotated array with traditional BSS method

To further illustrate the effectiveness of the proposed algorithm,100 Monte Carlo trials are presented.In Fig.4,we compare the target SNR after pulse compression between static array and rotated array.While the radar stays static,it could be calculated that the mean value of target SNR after pulse compression is 23.21 dB,however,when the radar array rotates the mean value of target SNR after pulse compression becomes inclining down to 15.47 dB.Using the proposed algorithm,we can see that even the radar array rotates,the mean value of target SNR after pulse compression is 20.11 dB.

Fig.4 Comparison between static array and rotated array with traditional BSS algorithm and proposed method

5.Conclusions

BSS method can be used to suppress the mainlobe jamming in the modern radar system.Nevertheless,the mainlobe jamming will become a divergence in the spatial domain while the radar array rotates.The mathematical model of the received complex signals,the covariance matrix,and the distribution parameters used in the traditional BSS method are all ineffective.As a result,it will cause the loss of target SNR after pulse compression.

We propose a FD-RPCA-BSS method in solving mainlobe jamming especially when the radar array rotates.Firstly,the number of source signals can be ensured through SVML DOA estimation method.In addition,a generalized RAMS model is established and FFT pre-process based on RPCA algorithm is used in the separation of the received signal covariance matrix with lower target’s SNR loss compared with the traditional BSS method.Then a method that can distinguish the separated target channel and the jamming channel is verified according to their corresponding PAPR.Finally,simulation results show that the performance of the proposed method is remarkable.There are much brighter prospects for further anti-mainlobe jamming.