A parameter estimation algorithm for LFM/BPSK hybrid modulated signal intercepted by Nyquist folding receiver

Qiu et al. EURASIP Journal on Advances in Signal Processing (2016) 2016:90 DOI 10.1186/s13634-016-0387-2 RESEARCH EURASIP Journal on Advances in Signal Processing Open Access A parameter estimation algorithm for LFM/ BPSK hybrid modulated signal intercepted by Nyquist folding receiver Zhaoyang Qiu*, Pei Wang, Jun Zhu and Bin Tang Abstract Nyquist folding receiver (NYFR) is a novel ultra-wideband receiver architecture which can realize wideband receiving with a small amount of equipment. Linear frequency modulated/binary phase shift keying (LFM/BPSK) hybrid modulated signal is a novel kind of low probability interception signal with wide bandwidth. The NYFR is an effective architecture to intercept the LFM/BPSK signal and the LFM/BPSK signal intercepted by the NYFR will add the local oscillator modulation. A parameter estimation algorithm for the NYFR output signal is proposed. According to the NYFR prior information, the chirp singular value ratio spectrum is proposed to estimate the chirp rate. Then, based on the output self-characteristic, matching component function is designed to estimate Nyquist zone (NZ) index. Finally, matching code and subspace method are employed to estimate the phase change points and code length. Compared with the existing methods, the proposed algorithm has a better performance. It also has no need to construct a multi-channel structure, which means the computational complexity for the NZ index estimation is small. The simulation results demonstrate the efficacy of the proposed algorithm. Keywords: Nyquist folding receiver, LFM/BPSK hybrid modulated signal, Parameter estimation, Signal characteristics Abbreviations: ADC, Analog to digital converter; BPSK, Binary phase shift keying; CSVR, Chirp singular value decomposition ratio; FA, Frequency agile; LFM, Linear frequency modulation; LOS, Local oscillator; LPI, Low probability interception; MCRLB, Modified Cramer Rao lower bound; NRMSE, Normalized root mean square error; NYFR, Nyquist folding receiver; NZ, Nyquist zone; RF, Radio frequency; SFM, Sinusoidal frequency modulation; SNYFR, Synchronous NYFR; SVD, Singular value decomposition; ZAM, Zhao, Atlas, and Marks; ZCR, Zero crossing rising 1 Introduction Currently, the electromagnetic environment is becoming increasingly complex and many modern radar signals have very high carrier frequencies or wide operating bandwidths [1, 2]. In order to intercept the modern radar signals, some receiver architectures have been proposed in the past few decades [3, 4]. The wideband non-cooperative receivers should have the capability of wideband receiving. A typical wideband receiver is the channelization structure, which adopts a set of analog band-pass filters to reduce the bandwidth of each channel and samples each channel with a low-speed analog to digital converter (ADC) using filter bank [4]. * Correspondence: School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu, China However, this kind of structure needs a huge amount of equipment. For the purpose of realizing wideband monitoring with a small amount of equipment, the Nyquist folding receiver (NYFR) architecture is proposed and it can realize wideband monitoring using one ADC [5, 6]. The NYFR modulates the received analog signal in the front-end of the receiver, maps the Nyquist zone (NZ) information to the modulation bandwidth of the signal, and then samples the modulated signal. Based on the NYFR structure, the output signal processing using wavelet transform has been studied [7]. Then, some new NYFR architectures using different local oscillator (LOS) modulation types have been proposed. Synchronous NYFR (SNYFR) structure using simplified LOS has been proposed and its output can be processed more easily because of the synchronous LOS © 2016 The Author(s). Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Qiu et al. EURASIP Journal on Advances in Signal Processing (2016) 2016:90 [8]. Other LOS modulation types such as binary phase shift keying (BPSK) LOS and noise sequences are proposed [9, 10], which can improve the performance of NYFR because the bandwidths of these LOS modulations remain unchanged. The NYFR can realize wideband receiving with a small amount of equipment, but the information of LOS modulation will be added on its output [8], and its output will be more complex compared with the conventional receiver. Some conventional radar signals such as linear frequency modulation (LFM) signal and frequency agile (FA) signal intercepted by the NYFR have been investigated, and the parameter estimation methods using multi-channel structure have been proposed [8, 11]. Meanwhile, many low probability interception (LPI) radar waveforms have been designed. Linear frequency modulated/binary phase shift keying (LFM/BPSK) hybrid modulated signal is a novel kind of LPI radar signal. It has a double spread spectrum and has been applied in some radar and fuse systems [2]. For the parameter estimation of LFM/BPSK signal intercepted by the conventional receiver, an algorithm based on Zhao, Atlas, and Marks (ZAM) transformation has been studied [12]. However, for the parameter estimation of LFM/BPSK signal intercepted by the NYFR, there has been no public report. Therefore, considering the increasing complexity of radar waveform and the growing demand of wideband receiving, it is necessary to study the parameter estimation of LFM/BPSK signal intercepted by the NYFR. The LFM/BPSK signal intercepted by the NYFR is a typical non-stationary signal. For a non-stationary signal, a common processing idea is the time-frequency analysis. However, many time-frequency methods can achieve optimal results only for the particular modulation types [13]. Because the LFM/BPSK signal intercepted by the NYFR contains the LOS modulation, it may be difficult to find a time-frequency kernel which is optimal for the NYFR output directly. In this paper, we will study this problem in another way and make full use of the NYFR prior information which is neglected in [8] and [11]. We will model the LFM/BPSK signal intercepted by the NYFR based on the signal self-characteristic and the Fig. 1 NYFR architecture Page 2 of 15 NYFR prior information, and propose a parameter estimation algorithm which has different estimation steps compared with the existing NYFR output parameter estimation algorithm [8, 11]. This paper is organized as follows: Section 2 investigates the NYFR architecture and the LFM/BPSK hybrid modulated signal intercepted by the NYFR. Section 3 gives the parameter estimation methods for each modulations of the N (...truncated)