Mathematical Problems in Engineering

Volume 2017 (2017), Article ID 1424835, 9 pages

https://doi.org/10.1155/2017/1424835

## A Novel Interference Detection Method of STAP Based on Simplified TT Transform

Air and Missile Defense College, Air Force Engineering University, Xi’an, Shaanxi 710051, China

Correspondence should be addressed to Qiang Wang; moc.qq@3811169101

Received 20 June 2017; Accepted 26 October 2017; Published 21 November 2017

Academic Editor: Fazal M. Mahomed

Copyright © 2017 Qiang Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Training samples contaminated by target-like signals is one of the major reasons for inhomogeneous clutter environment. In such environment, clutter covariance matrix in STAP (space-time adaptive processing) is estimated inaccurately, which finally leads to detection performance reduction. In terms of this problem, a STAP interference detection method based on simplified TT (time-time) transform is proposed in this letter. Considering the sparse physical property of clutter in the space-time plane, data on each range cell is first converted into a discrete slow time series. Then, the expression of simplified TT transform about sample data is derived step by step. Thirdly, the energy of each training sample is focalized and extracted by simplified TT transform from energy-variant difference between the unpolluted and polluted stage, and the physical significance of discarding the contaminated samples is analyzed. Lastly, the contaminated samples are picked out in light of the simplified TT transform-spectrum difference. The result on Monte Carlo simulation indicates that when training samples are contaminated by large power target-like signals, the proposed method is more effective in getting rid of the contaminated samples, reduces the computational complexity significantly, and promotes the target detection performance compared with the method of GIP (generalized inner product).

#### 1. Introduction

The homogeneous clutter environment is the prerequisite of STAP to suppress ground/sea clutter and detect targets effectively [1–3]. In terms of the classical STAP [4, 5], obtaining the CCM (clutter covariance matrix) is important. CCM is estimated by the training samples that have the IID (independent and identically distributed) feature with the CUT (cell under test). In general, the number of IID training samples needs to be twice the DOF (degrees of freedom) of the system in order to get the approximate optimal performance [6]. This can be ensured in the homogeneous clutter environment. However, in the actual condition, the heterogeneity of clutter affects the IID relationship between the training samples and the CUT. Furthermore, the great reduction in the number of satisfactory samples leads to inaccurate CCM estimation. Finally, the target detection performance of STAP is obviously deteriorated [7–11].

Training samples containing target-like signals, namely, the samples contaminated by the target-like signals, is one of the major factors that cause clutter heterogeneity [12, 13]. Before calculating the CCM, the interference detection of each sample is required, because the existing contaminated samples have a bad influence on the estimated accuracy of CCM [14]. Hence, it is important to find a more effective method to solve the interference detection problem. At present, GIP (generalized inner product) is a common method which builds the test statistics by calculating the inversion of CCM to pick out the contaminated samples [15]. GIP is available when fewer target-like signals are contained or the jamming intensity of the contained ones is smaller. Nevertheless, in the condition of target-like signals with big jamming intensity, for example, when JNR (jamming noise ratio) is 20 dB greater than SNR (signal-to-noise ratio), there is no possibility of picking out the contaminated samples due to the obvious inaccuracy in CCM estimation and the dramatic fluctuation in test statistics. Meanwhile, the CCM estimation and its inversion are required in the processing of GIP, which lead to the heavy computational complexity of STAP and go against efficient target detection. In addition, SR (sparse recovery) is another solution. Recently, considering the sparse physical property of clutter in space-time plane, SR is applied in STAP [6, 16]. As for SR-STAP, the space-time spectrum of CUT is directly estimated to calculate the CCM, which avoids the contamination problem of training samples. However, high computational complexity has arisen from sparse grid partition, and clutter suppression performance deterioration caused by big CCM estimation error has appeared when the isolated interference signals exist in the CUT.

Based on the above analysis, TT (time-time) transform is considered to solve the interference detection problem of the training samples in this paper [17–19]. TT transform was proposed by Pinnegar and Mansinha [20, 21] as a new transform in 2003, which came from the inverse Fourier form of the time-frequency analysis S transform [22–25]. One-dimensional time series is expressed as a two-dimensional time-time series by TT transform, which is good for observing the local features of the signal [26]. An important feature of TT transform is that the main energy of the signal can be focalized in the main diagonal position [27]. In this letter, the signal energy in the main diagonal position is only extracted to realize the rejection of the contaminated samples and the reduction of the computational cost. The method is called simplified TT transform. When the training samples are contaminated by some target-like signals with bigger jamming intensity, the energy of these samples varies greatly between the unpolluted stage and the polluted stage. Therefore, a kind of interference detection method based on simplified TT transform is put forward from the viewpoint of time-domain energy in this letter. Firstly, the data on each training sample is converted into one-dimensional discrete slow time series, respectively. Then, the transform-spectrum energy of each series is extracted to separate the contaminated samples and the clean samples in the simplified TT transform domain. Lastly, the polluted training samples are rejected. Through the above treatment, the target detection performance on STAP is improved and the total computational cost is reduced in the heterogeneous clutter environment.

#### 2. Signal Model of STAP

Assuming the side-looking antenna array is in the airborne radar, this array is shown as the uniform linear arrays via the column equivalent synthesis. pulses are contained in a CPI (coherent processing interval) and the number of the observed range cells is . The data sampling process about STAP can be described by the element-pulse-range domain, and then data collection is composed of sampling points. Each range cell is a matrix of . If the matrix is converted into a vector of which corresponds with the slow time (pulse domain), a slow time sequence of each range cell is obtained. Its specific form is denoted in Figure 1.