Elsevier

Digital Signal Processing

Volume 104, September 2020, 102803
Digital Signal Processing

Cyclic training sample selection and cancellation technique for airborne STAP radar under nonhomogeneous environment

https://doi.org/10.1016/j.dsp.2020.102803Get rights and content

Highlights

  • A STAP algorithm in nonhomogeneous environment.

  • A STAP algorithm in the presence of interference target signals.

  • A cyclic training sample selection method based on SMI statistic.

  • An interference target signal cancellation method.

Abstract

When training samples contain interference target signals (i.e., outliers), the performance of space–time adaptive processing (STAP) will be degraded. To solve this problem, a cyclic training sample selection and cancellation (CTSSC) algorithm based on sample matrix inversion (SMI) statistic is proposed. This algorithm consists of three steps. Firstly, a cyclic process is carried out to detect outliers. In each detection cycle, the sample matrix is estimated by all the training samples contained in the training sample set, and the outliers with relatively high jamming-to-noise ratio (JNR) will be detected. Then the corresponding training samples are removed from the training sample set and the sample matrix is updated. This cycle continues until the SMI statistics of all the remaining training samples do not exceed the detection threshold. Secondly, for each outlier detected by the first step, it will be reconstructed by the estimated complex amplitude and steering vector. Then the outlier will be cancelled by the corresponding reconstructed outlier. Finally, conventional STAP will be carried out to suppress clutter. Simulation results validate the effectiveness of the CTSSC algorithm with measured data.

Introduction

The ground clutter of airborne radar is usually strong and spread in Doppler frequency due to the platform motion, and the moving targets of interest are usually covered by clutter. Space–time adaptive processing (STAP) is an effective technique for airborne radar to suppress strong clutter [1], [2], [3]. Sufficient independent and identically distributed (IID) training samples are the precondition to ensure the ideal performance of STAP. But in nonhomogeneous environment, training samples are always contaminated by interference target signals (i.e., outliers), which will cause target self-nulling phenomenon and seriously degrade the clutter suppression performance of STAP [4], [5], [6]. A large number of algorithms about this problem have been proposed, and the most common idea is to design an effective non-homogeneity detector (NHD) and eliminate the training samples containing outliers. Many factors can cause the statistical characteristics of training samples to be inconsistent, and an ideal NHD can eliminate the training samples with different statistical characteristics from the range gate under test. It should be stated that this paper mainly studies the factor of outliers.

NHD adopts a specific statistic as the index to determine whether a given training sample contains outliers. Different NHDs can be classified according to their statistics. At present, the generalized inner product (GIP) statistic [5], [6], [7], [8], [9], [10], [11] and the sample matrix inversion (SMI) statistic [12], [13], [14], [15], [16] are the most mainstream statistics. The outlier detection performance of the SMI–NHD is significantly better than that of the GIP–NHD. This is because the GIP statistic not only accumulates outliers but also accumulates noise and residual clutter, while SMI statistic mainly accumulates outliers at the Doppler channel under test. But compared with the GIP–NHD, the SMI–NHD needs to be carried out at all Doppler channels, which means more computation.

Both of the above statistics need a sample matrix, and only when the sample matrix does not contain outlier components, the NHDs based on them perform well. But the sample matrix is usually estimated by training samples, and outliers are inevitable in practice. If the training samples used to estimate the sample matrix contain outliers, the phenomenon of target self-nulling [4], [5], [6], [7] will occur, which will make it difficult to detect the outlier contained in the training sample under test. To solve this problem, lots of algorithms have been proposed.

One of the main methods is to reconstruct the sample matrix without outlier components. The algorithm in [8] reconstructs the sample matrix according to the geometric relationship between radar platform and clutter scatterers by using the prolate spheroidal wave function. But the parameter errors often degrade its performance. The algorithm in [9] estimates the needed parameters with clutter spectrum analysis, but the cost is more computational burden. The algorithm in [10] reconstructs the sample matrix based on the Capon spectrum over a region separated from the location of the outliers. This algorithm presumes that the region-of-interest in which the outliers locate is distinguishable from where clutter locates, but the above assumptions are usually not tenable in practice. The algorithm in [11] aims to remove the components of the sample matrix corresponding to outliers by resetting the corresponding eigenvalues to noise level. The cross–spectrum (CS) is adopted by this algorithm as the index to distinguish the eigenvalues corresponding to the outliers, so this algorithm will be referred to as cross–spectrum reconstruction (CSR) algorithm. The CSR algorithm always removes some clutter components while removing the outlier components, which degrades the clutter suppression ability of sample matrix.

Another effective method is the reiterative censoring (RC) method [13], [14], [15], [16] which is simple in structure. The conventional RC algorithm [13] detects outliers with GIP statistic by a cyclic process, and in each detection cycle, only the snapshot with the largest GIP statistic will be detected. This algorithm is simple in structure but the computational cost is expensive. The FRACTA algorithm proposed in [14], [15] optimizes the RC method by adopting the adaptive power residue (APR) statistic and concurrent block processing (CBP). The FRACTA.E algorithm proposed in [16] reduces the computational burden further by calculating the inverse of the sample matrix recursively. However, the present RC algorithms detect only one outlier in each detection cycle, which can be improved further. What should be stated is that in this paper, it is considered that the APR statistic and the SMI statistic are essentially the same, and they will be referred to as SMI statistic in the following.

In this paper, a cyclic training sample selection and cancellation (CTSSC) algorithm is proposed. This paper analyzes the effects of outliers on the performance of SMI–NHD in detail. And it is proved that although the existence of outliers will degrade the outlier detection performance of the SMI–NHD, only the outliers with relatively low jamming-to-noise ratio (JNR) will be difficult to be detected, while the outliers with relatively high JNR can still be detected effectively. Based on the above conclusion, some enhancements are made to the conventional RC algorithm. The CTSSC algorithm consists of three steps. Firstly, a cyclic process is carried out to detect outliers. In each detection cycle, the sample matrix is estimated by all the training samples contained in the training sample set, and the initial training sample set is consist of all the available snapshots. The outliers with relatively high JNR will be detected. Then the corresponding training samples will be removed from the training sample set and the sample matrix will be updated in the next detection cycle. This cycle continues until the SMI statistics of all the remaining training samples do not exceed the detection threshold. Secondly, for each outlier detected by the first step, it will be reconstructed by the estimated complex amplitude and steering vector. Then the reconstructed outlier will be used to cancel the corresponding outlier contained in the snapshots. After the above processing, the outliers contained in the training samples have been detected and cancelled. Therefore, the training samples can be regarded as homogeneous. So finally, conventional STAP will be carried out to suppress clutter. The proposed algorithm has low computation load and simple structure, which makes it suitable for engineering applications.

The rest of this paper is organized as follows. The conventional SMI statistic is introduced in Section 2. The effects of outliers are analyzed in Section 3. The CTSSC algorithm is developed in Section 4. Simulation results are provided in Section 5 and conclusions are given in Section 6.

Section snippets

Conventional SMI statistic

Considering an airborne radar system with N-element uniformly spaced linear array and a burst of K identical pulses is transmitted during each coherent processing interval (CPI) with a constant pulse repetition frequency (PRF) fr. Assume that there are P range gates, and the snapshot at the pth (p=1,2,,P) range gate is denoted by xp.

Take xp as the training sample under test, then the conventional SMI statistic at the mth (m=1,2,,M) Doppler channel can be expressed asηpm=|smHRp1xp|2 where sm

The effects of outliers

The sensitive coefficient is usually used to evaluate the sensitivity of a specific NHD to the outlier under test. In theory, as long as the expectation of the sensitivity coefficient is greater than 1, the outlier can be detected. The greater the sensitive coefficient is, the better the performance of the NHD. However, when Ωp contains outliers, the sensitivity coefficient will be significantly decreased, resulting in the degradation of the SMI–NHD's performance. If the sensitivity coefficient

The proposed CTSSC algorithm

In this section, the proposed CTSSC algorithm is developed. This algorithm consists of three steps. Firstly, the training samples containing outliers will be detected. Secondly, the outliers contained in the detected training samples will be cancelled. Finally, conventional STAP will be carried out to suppress the clutter.

Simulation results

In this section, simulation experiments are carried out to verify the effectiveness of the proposed algorithm based on the Mountain Top measured data. The data file t38pre01v1CPI6 is selected here. There are 403 range gates recorded by this date file, but the clutter mainly locates at the 41st∼300th range gates. So the 260 range gates are selected in the simulation experiments. To reduce the number of the required training samples, only 10 elements and 10 pulses are selected. Six outliers are

Conclusions

In this paper, effective enhancements to the RC method are developed. The proposed algorithm performs well in nonhomogeneous environment. Compared with the present relative algorithms, the proposed algorithm is more computationally efficient and more suitable for engineering application. However, the method of setting detection threshold in this algorithm is not optimal, which needs further improvement. Simulation results verify the effectiveness of the proposed algorithm with Mountain Top

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported in part by the National Defense Science and technology excellence Youth Science Foundation of China (Grant number 2019-JCJQ-ZQ-006). The authors would like to thank the anonymous reviewers and the associate editor for the insightful comments and suggestions.

Xinzhe Li was born in Shandong, China, in 1991. He received the B.S. degree and the M.S. degree from Wuhan Early Warning Academy, Wuhan, China, in 2014 and 2016, respectively. He is currently pursuing the Ph.D. degree in information and communication engineering. His research mainly concentrates in space–time adaptive processing.

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Xinzhe Li was born in Shandong, China, in 1991. He received the B.S. degree and the M.S. degree from Wuhan Early Warning Academy, Wuhan, China, in 2014 and 2016, respectively. He is currently pursuing the Ph.D. degree in information and communication engineering. His research mainly concentrates in space–time adaptive processing.

Wenchong Xie was born in Shanxi, China, in 1978. He received the Ph.D. degree in signal and information processing from National University of Defense Technology, Changsha, China, in 2006. He is currently a Professor in Wuhan Early Warning Academy. His research mainly concentrates in space–time adaptive processing, airborne radar signal processing and airborne radar target detection.

Yongliang Wang was born in Zhejiang, China, in 1965. He received the Ph.D. degree from Xidian University, Xi'an, China, in 1994. He is currently a Professor in Wuhan Early Warning Academy and he is a member of the Chinese Academy of Sciences. His research mainly concentrates in space–time adaptive processing, radar signal processing and array signal processing.

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