Mathematical Problems in Engineering

Volume 2019, Article ID 8515606, 8 pages

https://doi.org/10.1155/2019/8515606

## An Improved Spatial Difference Smoothing Method Based on Multistage Wiener Filtering

^{1}School of Communication and Information Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan, China^{2}Air and Missile Defense College, Air Force Engineering University, Xi’an, Shaanxi, China^{3}Tong Fang Electronic Science and Technology Co. Ltd., Jiujiang, Jiangxi 332007, China

Correspondence should be addressed to Yiduo Guo; moc.621@111oudiyoug

Received 27 April 2019; Revised 15 July 2019; Accepted 9 October 2019; Published 7 November 2019

Academic Editor: Filippo Cacace

Copyright © 2019 Jian Gong 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

In order to solve the angle estimation problem of coherent sources in the colored background noise, an improved forward and backward spatial difference smoothing algorithm is proposed by combining the improved spatial smoothing algorithm with the spatial difference algorithm. By the algorithm we can not only decoherent the coherent source but also suppress the influence of the color noise. In order to further reduce the computational complexity of the IFBSDS algorithm, an improved forward and backward spatial difference smoothing algorithm based on Wiener filtering is also proposed. Thus, the eigenvalue decomposition operation of subspace class algorithm can be avoided, and at the same time, the same performance with the IFBSDS algorithm can be obtained, which is more consistent with the real demand of MIMO radar signal real-time processing.

#### 1. Introduction

At present, the study of MIMO radar target angle estimation generally assumes that the environmental noise is white noise obeying Gauss distribution [1–3]. However, in practical applications, there are many factors such as the electronic interference caused by the enemy, the random scattering caused by distributed source, and the mutual coupling characteristics between the receiving channels and so on, and ambient noise often appears as a nonideal colored noise with unknown statistical characteristics. Besides, electronic jamming and low-altitude multipath effect make MIMO radar need angle estimation for coherent sources [4–6]. Under the condition of colored noise background and coherent source, the performance of the classical subspace algorithm such as multiple signal classification (MUSIC) algorithm and estimating signal parameter via rotational invariance techniques (ESPRITs) algorithm will become very poor [7–9]. The four-order cumulant matrix of echo data is constructed in [10, 11], and the angle of the target can be estimated effectively, under the background of colored noise and white noise, but the influence of coherent sources is not eliminated. In [12], an extended rotation invariance factor is obtained for the implementation of the four-order cumulative data, which has high aperture utilization and no phase ambiguity, but the computational complexity is high. In [13, 14], the covariance matrix is reconstructed through the Toeplitz submatrix of a set of received data, but the Gauss color noise cannot be suppressed. In [15], an improved spatial differencing method (ISD) is proposed by constructing a spatial differencing matrix with neighboring subarrays, and the proposed method performs better under the coexistence of both uncorrelated and coherent signals. In [16], by extracting all the data information of each subarray, both the forward only ISD (FO-ISD) and forward backward ISD (FB-ISD) methods are proposed using the reconstructed submatrices.

In this paper, an improved spatial difference smoothing algorithm based on multistage Wiener filtering is proposed. The remainder of this paper is organized as follows. In Section 2, the echo model is established and its characteristics under color noise are analyzed. Then, an improved spatial difference smoothing (ISDS) algorithm based on multistage Wiener filtering is proposed in Section 3, followed by performance analysis of ISDS algorithm based on multistage Wiener filtering (MWF-ISDS) in Section 4. Some simulations are conducted to verify the performance of the proposed method in Section 5. Finally, we conclude the paper in Section 6.

Notation: denotes the conjugate operator; (.)^{H} denotes the matrix conjugate-transpose operator; (.)^{T} denotes the matrix transpose operator; denotes the Kronecker product operator; denotes the sum operator; denotes the multiplication operator.

#### 2. Echo Model and Its Characteristics under Color Noise

Considering the single base MIMO radar as shown in Figure 1, the transmitting and receiving antenna adopt *M* and *N* elements, respectively. The spacing of array elements is , and is the carrier wavelength. Assuming that the direction of arrival (DOA) and the direction of departure (DOD) both are , the echo signal is processed by matching filtering as below:where , the transmit steering vector of the *pth* target is , the receive steering vector is , , is the reflection coefficient of the *pth* target, is the normalized Doppler frequency of the *pth* target, and representation of noisy column vectors.