# An Efficient Algorithm for De-Interleaving Staggered PRI Signals
## 1 Introduction  
Radar signal de-interleaving is one of the most critical problems of radar countermeasures systems. Its performance directly affects the effectiveness of the electronic support measures (ESM) system [1]. According to different signal parameters, the signal de-interleaving algorithm can be divided into pre-de-interleaving and main de-interleaving. The pre-de-interleaving algorithm preliminarily classifies the signal by carrier frequency (CF), pulse width (PW), pulse amplitude (PA), and angle of arrival (TOA). The main de-interleaving algorithm further processes the classification results. This paper focuses on the PRI-based main de-interleaving algorithm, which uses TOA parameters to accomplish pulse signal de-interleaving. The pulse repetition interval (RPI) is the core parameter of pulse radar signals and the crucial characteristic used to distinguish different radar radiation sources during signal de-interleaving. With the development of radar technology, various PRI modulation approaches have been developed for different radar applications. One of the essential PRI modulation types, the staggered PRI, can both provide high azimuth resolution and a broad SAR swath [2; 3; 4] while removing the blind speed of the moving target indicator (MTI) radar system [5; 6; 7]. Several pulse sequences with the same PRI value and variousbeginning phases make up the staggered PRI signal. The phase intervals are referred to as sub-PRIs, and the frame period is the same PRI value as the PRI. It is challenging to estimate the frame period of the staggered PRI signal due to its sub-PRIs interference. In addition, extracting the staggered PRI signal from mixed signals is also tricky. Moreover, the complex electromagnetic environment results in dense pulse signals, a wide PRI range, PRI jitter, and pulse missing [8]. The real-time performance of the ESM system is affected by the dense pulse signals and the wide PRI range. With the development of modern radar electronic technology, radar signal de-interleaving technology has also been improved. Typical signal de-interleaving algorithms include histogram-based de-interleaving algorithms, PRI transform-based de-interleaving algorithms, and period estimation-based de-interleaving algorithms. The histogram-based de-interleaving algorithm is advantageous because it is fast and straightforward [9; 10; 11]. In 2019, [PERSON] et al. [10] proposed a pulse correlation algorithm that can de-interleave staggered PRI signals. However, it is sensitive to pulse missing. In 2021, [PERSON] et al. [11] proposed a histogram algorithm based on the association of pulse interval and single pulse. This algorithm utilizes the association of the pulse pair interval and the single pulse to obtain the pulse interval distribution matrix (PIDM). A histogram is obtained by accumulating the row of the matrix. It can de-interleave staggered PRI signals well. However, computation efficiency and sensitivity to PRI jitter are not considered. [PERSON] et al. proposed the PRI transform algorithm in 1993 [12]. [PERSON] et al. proposed a correction for the traditional PRI transform algorithm [13]. The improved algorithm handles PRI jitter and pulse loss well; however, it is computationally wasteful and unable to de-interleave staggered PRI signals. Numerous enhanced algorithms based on PRI transform have been presented due to the robustness of the improved PRI transform method [14; 15; 16]. However, they are not appropriate for de-interleaving staggered PRI signals. In 1999, [PERSON] et al. compared the signal's projection energy on several period subspaces to determine the signal period [17]. In 2016, an orthogonal Ramanujan period subspace was established [18]. In 2020, a correlation-matching method (CMM) was proposed based on orthogonal Ramanujan period subspace [19], which adapted to staggered PRI well but was sensitive to PRI jitter. In addition, the algorithm requires prior PRI information and is computationally inefficient. In 2021, an improved algorithm based on [19] was proposed [20].