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Direction-of-arrival (DOA) estimation in multipath environment is an important issue for passive bistatic radar (PBR) using frequency agile phased array VHF radar as illuminator of opportunity. Under such scenario, the main focus of this paper is to cope with the closely spaced uncorrelated and coherent signals in low signal-to-noise ratio and limited snapshots. Making full use of the characteristics of moduli of eigenvalues, the DOAs of the uncorrelated signals are firstly estimated. Afterwards, their contributions are eliminated by means of spatial difference technique. Finally, in order to improve resolution and accuracy DOA estimation of remaining coherent signals while avoiding the cross-terms effect, a new beamforming solution based iterative adaptive approach (IAA) is proposed to deal with a reconstructed covariance matrix. The proposed method combines the advantages of both spatial difference method and the IAA algorithm while avoiding their shortcomings. Simulation results validate its effectiveness; meanwhile, the good performances of the proposed method in terms of resolution probability, detection probability, and estimation accuracy are demonstrated by comparison with the existing methods.

Passive bistatic radar (PBR) exploiting illuminators of opportunity as uncooperative transmitters has become an emerging technology because it allows target detection and localization with advantages such as low cost, covert detection, and low vulnerability to electronic jamming [

At present, many high resolution algorithms have been developed to cope with the scenario when uncorrelated and coherent signals coexist. The most popular solutions are the forward/backward spatial smoothing techniques [

Motivated by previous work, we propose a new DOA estimation method in multipath environment for PBR. By making full use of the property of moduli of eigenvalues, the DOAs of the uncorrelated signals are estimated. Then the contribution of the uncorrelated signals is eliminated by using spatial difference technique; that is, only coherent signals remain in the spatial difference matrix. To eliminate the cross-terms effect while improving the resolution and accuracy of DOA estimation of the remaining coherent signals, a new IAA-based beamforming solution is conducted on a reconstructed covariance matrix. Simulation results validate the better performance of the proposed method by comparison with the existing algorithms.

The basic operating scenario of PBR system is illustrated in Figure

Basic operating scenario of PBR system.

However, the types of illuminator are enriched, while the difficulties for PBR signal processing also come along. In case of PBR exploiting uncooperative illuminator of opportunity as the transmitter, there is a problem that the instantaneous parameters of transmitting signal are unknown at the receiver; thus, a dedicated reference antenna needs to steer toward the uncooperative illuminator to receive the transmitting signal. Meanwhile, the frequency agility technology destroys the coherency between pulses and the ability of rapidly changing beam scanning makes it impossible for PBR to predict the next beam position. Therefore, these problems make the SNR become low and the number of snapshots is finite.

Furthermore, among the characteristics of the environment, the multipath propagation in VHF band is serious. As shown in the solid line box, the received signal is a mixture of transmitting signal of the exploited illuminator, the direct signal of target, and its multipath signal. The direct signal and multipath signal are coherent and closely spaced in the mainlobe. Meanwhile, the transmitting signal is received simultaneously and may come from the same direction as the direct signal.

Therefore, under such scenarios, the problems of DOA estimation in multipath environment for PBR system are summarized as how to deal with the closely spaced uncorrelated and coherent signals with high resolution and accuracy in the low SNR with limited snapshots.

Without loss of generality, in PBR scenario, a uniform linear array (ULA) with

Assume that

After that, the array covariance matrix can be obtained

For the DOA estimation of the uncorrelated signals, the eigenvalue decomposition (EVD) of the covariance matrix

Moreover, the

The DOAs of the remaining signals are then estimated by using a novel IAA-based beamforming solution. Herein, the equation in (

To solve the aforementioned problems, we propose a new IAA-based beamforming solution with respect to an improved covariance matrix. Then, we rewrite (

Afterwards, according the IAA algorithm [

In this subsection, the proposed method is summarized and discussed as follows:

(i) Since the pervious analysis of practical PBR application scenario, the covariance matrix of the received signal is unavailable: thus it is replaced by the sample-average estimated array autocovariance matrix.

(ii) Then, by performing the EVD of the matrix

(iii) Based on the property of moduli of eigenvalues, the uncorrelated signals are resolved from coherent signals while the DOAs of the uncorrelated signals are estimated

(iv) To eliminate the contribution of uncorrelated signals and improve the resolution and accuracy DOA estimation of coherent signals, the spatial difference matrix

(v) Finally, the DOAs of remaining coherent signals are estimated by performing IAA algorithm on the reconstructed covariance matrix

It is noteworthy that our proposed method combines the advantages of both spatial difference method and the IAA algorithm while avoiding their disadvantages. When the uncorrelated and coherent signals coexist in multipath environment, especially the uncorrelated signal coming from the same direction as the coherent signals do, the method can still resolve them, whereas the IAA algorithm fails to work. The performance of the spatial difference method degrades significantly in the low SNR with limited snapshots, but our proposed method can still work well. Besides, by exploiting our method, the DOAs of uncorrelated and coherent signals are estimated separately, which can be parallelized easily to speed up the processing in practical application.

In this section, the performance of the proposed method is investigated by simulation experiments. For PBR system, a ULA of

In the first simulation, we consider five uncorrelated signals from

Spatial spectrums of the uncorrelated and coherent signals.

The second simulation studies the superresolution performance of two closely spaced signals with the proposed method. In the simulation, we define the probability of resolution as

The angular gap between two closely spaced coherent signals is defined as

The resolution probability versus the angular gap.

In the third simulation, we investigate the high accuracy performance of DOA estimation with our proposed method. The detection probability in the simulation is defined as

The DOAs detection result is considered successful when the difference between the estimated DOA and the true DOA is less than

The detection probability versus the SNR with

The detection probability versus the number of snapshots with

In the last simulation, we further examine the performance of the proposed method by comparison. We select the method in [

The RMSE of DOA estimation versus SNR.

The RMSE of DOA estimation versus the number of snapshots.

It can be seen from the RMSE curves of DOA estimation with different methods that the DOA estimation performance of our method is better than the method in [

In this paper, we propose a novel DOA estimation method in the multipath environment for PBR using frequency agile phased array VHF radar as illuminator of opportunity. The proposed method combines the advantages of spatial difference method and the IAA algorithm while avoiding their shortcomings and then performs a new IAA-based beamforming solution on an improved covariance matrix to deal with closely spaced uncorrelated and coherent signals. The simulation results show that it has satisfactory DOA estimation performance in the scenario of low SNR and small number of snapshots. Furthermore, in the proposed method, the DOAs of uncorrelated and coherent signals are estimated separately, which can be parallelized easily to speed up processing, and can be a viable solution for PBR applications. Since the presented PBR system operates in the VHF band, multipath propagation in complex terrain is serious and unavoidable. In order to further improve the performance of target detection and localization, the dynamic characteristics of electromagnetic and geographical environment and antimultipath technology should be taken into consideration in future works.

The IAA algorithm is a data-dependent, nonparametric method which is based on a weighted least squares (WLS) approach. Firstly, we define the covariance matrix of noise based on the above sparse signal model

After that, using the matrix inversion lemma to yield

No data were used to support this study.

The authors declare that they have no conflicts of interest.

This work was partly supported by the National Natural Science Foundation of China under Grant 61401489.