# A Novel Cross-Correlation Algorithm Based on the Differential for Target Detection of Passive Radar
## 1 Introduction  
Passive radar is a new type of radar that uses low-power signals as signal sources, such as non-cooperative civil base station signals and satellite signals [1]. With the continuous improvement of stealth technology, the radar cross-sectional area (RCS) of aircraft, ships, and other stealth targets has been reduced by one or two orders of magnitude, and significantly decreasing the signal-to-noise ratio (SNR) of the target echo. According to the principle of radar target detection, the output SNR by the signal is proportional to the detection probability on the premise of maintaining a constant false alarm probability [2]. Therefore, increasing the output SNR is critical to improving the target detection probability. Long time accumulation of the target signal and interference and noise suppression are widely used to improve the output SNR. Many studies in the radar field focus on the suppression of the active or passive jamming. Examples of such methods are through digital beamforming (DBF) [3], interference suppression based on blind source separation [4], space time adaptive processing (STAP) [5], and time domain interference cancellation [6]. The accumulation of the target signal consists of coherent accumulation and incoherent accumulation [7]. Coherent accumulation is based on the fact that the phase relationship of the target echo is determined while the phase relationship of noise interference is uncertain. When the amplitude of the target echo is increased, its energy is increased directly. Coherent accumulation consists of moving target indication (MTI) [8] and Range-Doppler (R-D) processing [9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23]. Incoherent accumulation occurs after taking the envelope of the signal. At this time, the complex signal information is lost and only the modulus is retained. Common incoherent processing methods include the Hough transform (HT) [24], radon transform (RT) [25], and track before detect (TBD) [26]. For signals with additive noise, the gain in coherent accumulation is obtained from the addition of \(N\) signal samples in phase. The gain in signal component energy is represented by \(N^{2}\), while the gain in noise accumulation is represented by \(N\). During accumulation, phase addition is realized after compensation of the phase modulation signal, and the SNR is increased by \(N\) times. Thus, when the hardware conditions cannot be changed, the passive radar often uses the R-D two-dimensional correlation method to achieve the coherent accumulation of the target echo, for example, by using the passive radar [9; 10; 11; 12], in which the FM broadcast signal is used as the irradiation source; the passive radar [13; 14; 15; 16] using an analog/digital TV signal as the irradiation source; the passive radar [17; 18; 19] using the communication signal as the irradiation source; and the passive radar using the navigation satellite signal [20; 21; 22]. In these methods, for target detection, the signal emitted by civil or military radiation sources is taken as the reference and coherent processing with the target echo signal is carried out. The signal energy reflected by the target is detected to obtain the target parameters and realize the positioning and tracking. Among the above algorithms, increasing the accumulation time is the most effective method to improve the SNR of target signal detection [27]. However, if the accumulation time is too long, new problems will be introduced, such as Doppler spread (the target echo Doppler is no longer constant), range walk (the target echo envelope moves across units), and so on [28; 29]. In this paper, a new cross-correlation algorithm is proposed, which can break through the constraints of traditional algorithm optimization theory under certain conditions and obtain a higher output SNR with the same accumulation time. Firstly, the algorithm performs differential operations on the echo signal and the reference signal at different orders to obtain multiple echo signals and multiple reference signals.