## 1 Introduction  
With the rapid development of information technology, the generation of microwave signals with low phase noise and a widely tunable frequency range plays a crucial role in wireless communication, radar and optical communication [1; 2; 3; 4; 5]. The microwave signals generated by traditional electrical methods traditionally demonstrate poor phase noise. This fails to satisfy the requirements of modern communication and radar systems, especially in high-frequency regimes. Recently, OEOs have been proposed as effective solutions to replace traditional electrical methods, allowing for a higher central frequency and lower phase noise [6; 7; 8; 9]. OEOs can generate microwave signals (based on the microwave photonic technique) to overcome the limitations of microwave signal sources realized by traditional electrical methods in terms of tunable frequency range and phase noise performance. In addition, the phase noise of the microwave signals generated by OEOs is usually independent from oscillation frequency. Therefore, OEOs have broad prospects in microwave systems with high frequency and large bandwidth. Amongst the proposed OEO techniques, electrical band-pass filters (EBPFs) have usually been the ones adopted. The resultant microwave signals thus show poor tunability, as limited by the EBPFs [10]. To improve the frequency tunability of the obtained microwave signal, EBPFswere replaced by using microwave photonic filters (MPFs). In Ref. [11], an MPF-based widely tunable OEO was proposed. The MPF was used based on a polarization beam splitter (PBS), a chirped fiber Bragg grating (CFBG) and a polarization modulator present in the structure. By changing the polarization state via a polarization controller (PC) in the link, the signal's frequency was varied from 5.8 to 11.8 GHz. In Ref. [12], a MPF was realized via cascading of the phase modulator (PM) and the optical band-pass filter (OBPF) to complete the conversion from phase modulation to intensity modulation. This could be used in the OEO structure to generate tunable microwave signals from 4.74 to 38.38 GHz. Unfortunately, the MPF usually has a relatively large 3-dB bandwidth. Thus, it is difficult to suppress the side modes of the microwave signals when the OEO has a long cavity that will reduce the spectral purity of the generated signals. It is also difficult to suppress other spurious signals by utilizing the common MPF in the OEO loop. Furthermore, the structures of the MPFs are usually complex. This will deteriorate the phase noise of the oscillation signals. Therefore, a multiple-loop OEO has been considered as an effective way to solve these problems. In Ref. [13], a dual-loop OEO relying on a polarization-multiplexed structure was advanced by utilizing the phase-shifted fiber Bragg grating (PS-FBG), PBS and polarization beam combiner (PBC) in the structure. This allowed for the generation of microwave signals ranging from 1 to 4 GHz. Additionally, the SMSR of the generated signal could be improved by this scheme. In this configuration, the PS-FBG could be utilized as an OBPF to choose the oscillation frequency. The PBS and PBC could be used to obtain the proposed dual-loop OEO. Then, the side modes could be effectively suppressed due to the Vernier effect. It should be noted that the PS-FBG is very sensitive to environmental fluctuations. Thus, the generated microwave signal's frequency of the PS-FBG-based OEO will drift. This decreases the frequency stability of the microwave signals. In Ref. [14], a dual-loop OEO was proposed on the basis of OISL to construct an MPF in the system, with a tunable frequency range from 9.63 to 19.11 GHz. In this method, the obtained 13.74 GHz microwave signal's phase noise was \(-\)103.2 dBc/Hz at 10 kHz frequency offset. To simplify the structure of the OEO loop, a directly modulated semiconductor laser was utilized to replace the PM in [15].