# Target Detection of Passive Bistatic Radar under the Condition of Impure Reference Signal
## 1 Introduction  
Passive bistatic radar (PBR) employs existing non-cooperative signals, such as frequency modulation (FM) [1], digital audio broadcast (DAB) [2], digital video broadcasting--terrestrial (DVB-T) [3], digital terrestrial multimedia broadcasting (DTMB) [4], navigation signals [5, 6], and so on [7, 8], in the surrounding environment to detect and track targets within specific airspace regions of interest. Due to its distinctive attributes encompassing silent receiving, separate transmitter and receiver architecture, and the utilization of non-cooperative signals, the PBR exhibits extensive potential across various domains [9, 10, 11], including, but not limited to, anti-jamming, anti-stealth, anti-low-altitude attack, and anti-radiation missile applications, as well as spectrum sharing and utilization. Although PBR, benefiting from its inherent characteristics, has many advantages in detecting targets over traditional active radar, it also faces many challenges and difficulties. PBR works through a two-channel coherent processing scheme [12], comprising the reference channel responsible for receiving the direct path signal and the surveillance channel utilized for target detection purposes. The desired reference signal in the PBR corresponds to the original transmitter signal, commonly referred to as the direct path signal. However, no additional parameters are known for the receiving station, and only the carrier frequency, bandwidth, and location (which may be inaccurate) are known. Consequently, the acquisition of the desired reference signal, while effectively mitigating clutter and target echoes, becomes exceedingly difficult. When the received reference signal is interfered with by multipath signals or target echo signals and becomes impure, the target detection performance of the PBR will be limited. For example, real targets will be overwhelmed and cannot be detected accurately when the reference signal is heavily contaminated by an abundance of multipath clutter [13]. Indeed, several constraints, such as the site error of the transmitting station or the broad receiving beam, impose limitations on obtaining the pure reference signal. To tackle the problem of target detection in the PBR under the condition of the impure reference signal, one approach involves the utilization of a highly directive narrow beam or antenna, pointing precisely towards the transmitter station [14]. Another strategy entails the purification or precise reconstruction of the direct path signal by leveraging the known characteristics of the transmitting signal [15]. The former approach imposes stringent demands on system design and the configuration of the practical environment, making it challenging to completely mitigate the issues of impure reference signal. On the other hand, the latter approach aims to alleviate the impact of this problem on target detection through the application of advanced signal processing methods, offering a more versatile solution. To purify the reference signal contaminated by multipath clutter, according to the constant modulus feature of the transmitting signal, several equalization algorithms based on constant modulus algorithm are proposed to restrain the multipath clutter in the reference signal [16; 17; 18]. A constant modulus algorithm was proposed [16], in which the reference signal is preprocessed by channel equalization. The study of the same problem was extended to an airborne PBR scenario [17], where a modified blind equalization algorithm based on cyclostationarity is presented. Furthermore, the authors of [18] combine the time domain and space domain to suppress the multipath signal present in the reference signal, but the algorithm has requirements on the PBR hardware structure. On the other hand, in order to obtain the completely pure reference signal, some direct path signal reconstruction algorithms based on signal structure features were proposed [19; 20; 21].