## 1 Introduction  
Passive bistatic radar (PBR) is a radar system that operates in a receive-only mode. It detects and tracks targets by utilizing signals emitted from illuminators of opportunity (IOs) [1, 2]. In the conventional PBR system using correlation detection, signal processing operations are performed, including reference signal purification [3], clutter cancellation [4, 5], and cross ambiguity function (CAF) computation [6]. The peak of CAF reflects the bistatic time delay and Doppler frequency, corresponding to the target's position and velocity information [7]. As PBR receives signals from IOs and has a separated transmitter-receiver structure, it possesses advantages such as interference resistance, anti-stealth capabilities, resistance to low-altitude penetration, cost-effectiveness and efficient spectrum utilization. Common IOS include frequency modulation (FM) [8], digital audio broadcasting (DAB) [9], digital video broadcasting terrestrial (DVB-T) [10], digital terrestrial multimedia broadcasting (DTMB) [11], digital video broadcasting satellite (DVB-S) [12], global system for mobile communications (GSM) [13], bediou navigation satellite system (BDS) [14], global positioning system (GPS) [15], and so on. However, as these signals are not specifically designed for PBR, their ambiguity functions do not exhibit a spike-like nature. As shown in Figure 1, taking DVB-T, DTMB, and 5 th generation mobile communication technology (5G) downlink signals as examples, their ambiguity functions show mainlobe and sidelobe widening. Additionally, due to the special frame structures of these signals, there are side peaks in the ambiguity functions [16; 17; 18]. These non-ideal factors pose challenges in the weak targets detection. Sparse representation and recovery techniques have been widely applied in various fields such as communication [19; 20; 21], image [22; 23; 24], and radar [25; 26; 27]. In the field of PBR, the two technologies are utilized for weak target detection. Among them, the authors of [28; 29] applied sparse representation and recovery techniques to PBR target detection. However, their models relied on the orthogonality between subcarriers of orthogonal frequency-division multiplexing (OFDM) and the cyclic prefix of OFDM symbols. As a result, the applicable types of signals were limited. References [30; 31; 32; 33; 34; 35] utilised the sparsity of surveillance signals in the delay-Doppler domain for the sparse recovery of CAF. These approaches based on this idea have the characteristic of wide applicability and have been widely adopted. Based on the source of the measurement matrix, the research results based on this idea can be classified into the following categories: (1) The measurement matrix is constructed by adding different delays and Doppler frequencies to the reference signal [30; 31; 32; 33]. (2) Based on the computation of CAF, the Doppler-shifted Fourier transform matrix is derived as the measurement matrix [34]. (3) The measurement matrix consists of CAFs with different delays and Doppler frequencies [35]. Among these, Method (1) has a simple construction of the measurement matrix and a lower computational complexity. However, it demands a higher signal-to-noise ratio (SNR) for the surveillance signal, resulting in a poor detection performance for weak targets. Method (2) exhibits a better detection performance for weak targets than Method (1) because of coherent accumulation. In this method, it divides the signal into multiple batches and randomly utilizes some of them. In this way, memory resources and computational complexity are saved. However, utilization of the Doppler dimension is reduced, lowering the detection performance for weak targets. Although Method (3) achieves the best detection performance for weak targets among the three methods, its measurement matrix has a large scale. So, the requirements of memory resources is hard to guarantee.