## 1 Introduction  
Full duplex (FD) relay technology enables a communication system to simultaneously transmit and receive signals on the same frequency through a relay node [1]. Inspired by this technology, simultaneous transmit and receive (STAR) technology, also referred to as in-band full-duplex (IBFD), has emerged as a novel innovation within the field. It aims to allow communication users to directly transmit and receive signals at the same carrier frequency, facilitating an even more efficient use of spectral resources. Moreover, STAR technology can be synergistically combined with other advanced technologies that enhance spectral utilization, such as reconfigurable intelligent surfaces [2], millimeter-wave technology [3], and multiple access techniques [4]. As a result, STAR technology has arisen as a promising approach to increase data throughput and solve the problem of scarce spectrum resources, which can be applied in the field of wireless communications, radar, satellites, and unmanned aerial vehicles [5; 6]. However, the self-interference (SI) signal, which is generated from the near end, can be 100-120 dB stronger than the weak received signal, thus making the receiver inoperable [7]. Therefore, self-interference cancellation (SIC) technology is key to the implementation of STAR communications. At present, the SI signal can be eliminated in several stages and various domains, as shown in Figure 1. Typically, SIC is achieved through the cascaded antenna domain [8], analog domain [9], and digital domain [10; 11; 12; 13; 14; 15]. The antenna domain SIC is passive in nature, and mainly uses antenna isolation or related beamforming algorithms to prevent RF reception path blockage. In the analog domain, directly coupled interference suppression and digital-assisted analog interference-suppression methods are commonly used at the receiver low-noise amplifier (LNA) input before the analog-to-digital conversion. The last stage is digital SIC, which aims to eliminate the remaining SI from the received signal by reconstructing the SI signal in the receiving link and reducing its power below the noise floor. These steps have been applied in some prototypes and have demonstrated the potential of STAR communications [7; 16]. The remainder of this paper focuses on digital SIC algorithm design and both the linear and nonlinear SIC algorithms are evaluated through extensive simulations, demonstrating their effectiveness in improving the performance of STAR communication systems. Digital SIC has attracted significant attention in recent years to address the SI problem in STAR communication systems. Nonetheless, the practical application of digital SIC still faces many challenges. First of all, the observed SI signal exhibits significant frequency and time selectivity due to reflections within the device and its surrounding environment, which demonstrate temporal variations. This can be regarded as a classic system identification problem, which is typically solved through adaptive finite impulse response (FIR) filters. Secondly, in practical communication environments, there are often additional sources of noise, such as electromagnetic interference, lightning noise, radar signals, and other human-made disturbances. These types of noise typically exhibit strong pulse-like characteristics within very short time durations, which can lead to performance degradation of various filtering algorithms based on the assumption of Gaussian noise. Furthermore, the significantly higher power of the SI signal compared to the desired signal at the receiver implies that even minor distortions can significantly degrade the signal of interest. These hardware impairments, such as phase noise, in-phase/quadrature (I/Q) imbalance, and power amplifier (PA) and baseband nonlinearity, among others, with PA nonlinearity are especially harmful to the digital canceler, making digital SIC insufficient. Digital cancellation algorithms accounting for impulsive noise have been proposed in earlier research [10; 17].