# Target Detection of Passive Bistatic Radar under the Condition of Impure Reference Signal
## 1 Introduction
A reference signal extraction method based on the multiprocessing method in a dual-polarization antenna PBR was proposed [19], and the authors exploited sub-carrier processing, blind adaptive oblique projection, and an extensive cancelation algorithm to reconstruct the direct-path signal. The work of [20] investigated the reference signal reconstruction method for PBR exploiting DVB-T signals, in which the authors reconstructed the pure reference signal by filtering the detected quadrature amplitude modulation symbols prior to the remodulation step. In addition, a joint low-rank and sparse method is presented to purify the reference signal in DTMB-based PBR [21]. In addition, the core ideas of other methods for reconstructing reference signals are basically based on the principle of first demodulating impure reference signals and then modulating them [22; 23]. While the aforementioned methods demonstrate effective measures for mitigating the performance degradation of target detection caused by the impure reference signal, current research primarily revolves around suppressing multipath clutter within the reference signal or reconstructing the direct path signal. Indeed, the performance of conventional target detection is susceptible to decline when the reference signal is perturbed by echo signals. However, this particular aspect has received limited research attention thus far. Among the sparse literature, a direction of arrival estimation algorithm for PBR when the reference channel contains the target echo was proposed [24]. In this study, the authors assumed the target echo in the reference channel and surveillance array is partially correlated, leading to a direction of arrival (DOA) estimation bias, and then established the array signal model to fix the bias. The emphasis of [24] is mainly on the impact of impure reference signals on DOA estimation, rather than on target detection. To address this research gap, this article investigates the impact of impure reference signals resulting from target echoes on target detection in the PBR. Notably, a novel signal model based on impure reference signals is established, enabling a comprehensive analysis of its effects on clutter suppression and Range-Doppler cross-correlation (RDCC). Moreover, a method is proposed to refine the reference signal utilizing conventional target detection feedback information. In comparison to existing works, the key innovations of this article are as follows:1. To the best of our knowledge, this paper represents the first endeavor to analyze the influence of the residual target echo present in the reference signal on the target detection performance of the PBR. The theoretical analysis presented herein offers novel insights and ideas for advancing the field of target detection research in the PBR. 2. We introduce a novel received signal model, different from the existing model [25; 26], which allows for the straightforward derivation and analysis of its impact on the fundamental modules of target detection. When compared to the conventional receiving model, the proposed model introduces a single mathematical item, yet it offers crucial attributes for addressing the target detection problem in the presence of impure reference signals. 3. Drawing upon the insights garnered from the influence of the residual target echo on target detection within the reference signal, a novel method for purifying the reference signal is presented. Leveraging detection feedback information, the proposed approach capitalizes on the inherent regularities in the influence of the impure reference signal. Unlike existing target detection methods unsuitable for this specific scenario, the proposed method involves the localization of the target echo in the impure reference signal utilizing traditional target detection results. Subsequently, a subspace projection method is employed to reconstruct the echo, followed by the elimination of the undesired target echo through subtraction from the original impure reference signal.