International Journal of Antennas and Propagation

Volume 2018, Article ID 1569590, 13 pages

https://doi.org/10.1155/2018/1569590

## A Novel Waveform Design Method for Shift-Frequency Jamming Confirmation

^{1}The Graduate Management Group, Air Force Early Warning Academy, Huangpu Avenue, Wuhan, China^{2}The First Department, Air Force Early Warning Academy, Huangpu Avenue, Wuhan, China

Correspondence should be addressed to Chang Zhou; moc.uhos@radar_cz

Received 31 January 2018; Accepted 19 April 2018; Published 2 July 2018

Academic Editor: Pierfrancesco Lombardo

Copyright © 2018 Chang Zhou 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

Shift-frequency jamming is generally used to form range false targets for ground-based early-warning radar systems; the frequency shift value of such interference is larger than the Doppler shift value of the moving target, and the key element to suppress the shift-frequency jamming is the frequency shift value estimation. However, in the low- or medium-pulse repetition frequency (PRF) mode, it is challenging to estimate the accurate frequency shift due to the velocity ambiguity. To solve this problem, a novel sparse Doppler-sensitive waveform is designed based on the ambiguity function theory, where the basic idea is to design a waveform sensitive to a specific Doppler but insensitive to other Dopplers; therefore, this waveform can recognize the specific Doppler of the target unambiguously. To apply the designed waveform in practice, the detection and estimation processing flow is provided based on the waveform diversity technique and the family of the sparse Doppler-sensitive waveforms. Simulation experiments are presented to validate the efficiency of the proposed method, and we conclude that the advantage of this method is that it can be used to confirm the specific Doppler of the target unambiguously with few pulses even under the condition of a low PRF.

#### 1. Introduction

Linear frequency-modulated (LFM) signals are widely used in radar systems due to their large time-bandwidth product and large Doppler tolerance [1]. Taking advantage of the range-Doppler coupling characters of LFM signals, shift-frequency jamming [2, 3] has been extensively studied, as this approach can form false targets ahead of true targets by adjusting the parameters of the frequency shift even if the radar adopts the working mode of the frequency agility or pulse repetition frequency (PRF) agility. Since the frequency shift modulation of the jammer is similar to the Doppler modulation of the moving target, it is even more challenging to recognize shift-frequency jamming. However, the frequency shift amount of the jamming is much larger than the Doppler of the moving target in ground-based early-warning radar. For example, when the L-band radar operating wavelength cm, the speed of a conventional aircraft is less than Mach (Ma) 3; thus, the Doppler frequency is less than 5.4 kHz, while the L-band signal bandwidth is several MHz. To form a false target with at least one range cell offset, the minimum frequency shift should be many tens of kHz, which can be considered much larger than the Doppler of moving targets. Therefore, accurate estimation of the frequency shift amount or Doppler frequency can enable shift-frequency interference recognition and suppression in ground-based early-warning radar. However, for low- and medium-PRF radars, it is challenging to obtain the actual Doppler because of the velocity ambiguity. To address this challenge, the PRF agility technology is typically used for velocity ambiguity resolution [1] in practice, while the existing ambiguity resolution algorithm has the following shortcomings [4, 5]: (1) the algorithm requires a relatively high Doppler resolution in each PRF even in the presence of noise pollution and quantization errors, (2) the maximum unambiguous Doppler improvement is limited, and (3) the computation complexity is expensive, particularly in the case of multiple moving targets. Therefore, this study attempts to achieve the frequency shift estimation from the perspective of waveform design.

Many waveform design studies have focused on the low autocorrelation sidelobe [6–10], which can improve the detection performance for weak targets. The research hotspots have developed from the design of binary-phase sequences to polyphase sequences and from fixed-length sequences to arbitrary-length sequences. In recent years, related algorithms can produce unimodular sequences of the length or even longer, with favourable autocorrelation properties [8]. In addition, several new applications, such as the sparse frequency waveform [11, 12], weighted sidelobe waveform [8], and orthogonal signal [6], have been developed. The autocorrelation of the waveform is equivalent to the zero-Doppler cut of the ambiguity function [13]; despite the fact that a satisfactory autocorrelation sidelobe waveform cannot guarantee the detection performance of moving targets, the design methods can be easily generalized for a proper ambiguity function cut design.

To detect a moving target, other possible Doppler cuts of the ambiguity function must be considered. In other words, we must consider the ambiguity function for a nonzero Doppler. The studies of [14–16] focused on synthesizing an arbitrary desired ambiguity function. Although extensive work has been performed, there is no universal method to solve this problem because it is challenging to determine whether the desired ambiguity function can be synthesized; in addition, the process is time-consuming.

Therefore, to reduce complexity, some scholars have relied on satisfying the partial constraints, such as ensuring a clear area near the origin [6] and minimizing the integral sidelobe level (ISL) in a certain area [17]. More specifically, the output response in certain range-Doppler areas, which cover the interferences, should be as small as possible, whereas the output response in certain range-Doppler areas with targets must ensure a level that is as high as possible [18]. In [19–21], the authors addressed the waveform design in the presence of coloured Gaussian disturbance noise and solved the problem through semidefinite relaxation to achieve the optimal detection performance. For the unknown Doppler, an algorithm to guarantee that the minimum Doppler matches the output maximum has been proposed [22, 23], but the signal bandwidth and ISL were not considered. The unimodular quadratic programme (UQP) and computational approaches to tackle the UQP were summarized in [24]. In [25], the clutter model was established, and a slow-time ambiguity function design was performed, which is a more intuitive way to implement the moving target detection (MTD) response. This problem has also been solved based on the maximum-block-improvement (MBI) method [26], and the majorization-minimization (MM) method was used in [18] to solve this problem and obtain improved performance. However, the ambiguity design method still addresses the velocity ambiguity problem, and few references consider the bandwidth of the coding signal, which further limits the application in radar.

In the present study, a sparse Doppler-sensitive waveform is designed that can be used to confirm the specific Doppler of the target unambiguously. By designing a different waveform with a different specific Doppler to confirm the different target Doppler, the large shift-frequency interference can be identified and suppressed.

The remainder of this paper is organized as follows. Section 2 presents the problem statement. Section 3 examines the signal spectrum based on the optimal detection criterion for a specific Doppler, and the waveform design algorithm is discussed. Subsequently, the method of Doppler confirmation processing is proposed based on the designed waveform in Section 4. The simulation experiments are presented in Section 5. Finally, Section 6 presents the conclusions.

#### 2. Problem Statement

The ambiguity function is the most intuitive description of the signal output performance for different Dopplers. To facilitate the design of the coding signal, the discrete ambiguity function is expressed as [1] where denotes the discrete delay series, is the discrete Doppler frequency, is the discrete coded signal, and represents the discrete Fourier transform (DFT) of .

With regard to the zero-Doppler cut of arbitrary complex coded signals, the maximum value is and maximum position is . For the other Doppler cuts, however, the shape is unknown. Assuming that the specific Doppler is , to design a waveform that is sensitive to a specific Doppler but insensitive to the others, the ambiguity figure must satisfy three shape constraints, as shown in Figure 1. (1)The specific Doppler cut (when ) should exist as a clear peak value as the mainlobe, where represents the position of the mainlobe (peak value) in this cut, and this cut can be set according to the actual requirements.(2)The sidelobe of the specific Doppler cut (when and ) should be as small as possible.(3)Other Doppler cuts (when and ) should not have significant peak values.