## 1 Introduction  
The civil aviation transportation industry is experiencing rapid growth, leading to an unprecedented demand for advanced air traffic management (ATM) systems to accommodate the expanding aviation sector and its need for cutting-edge technologies [1, 2, 3]. However, the capability of existing communication links to support such ATM systems is hindered by spectrum limitations [4]. To ensure the sustainable growth and safety of aviation services, the Future Communication Infrastructure (FCI) has modernized the existing ATM system. It proposes the LDACS, which is based on Orthogonal Frequency Division Multiplexing (OFDM) technology [5, 6]. According to the International Civil Aviation Organization's plan, the LDACS system is deployed in an embedded way between the channels of L-band DME, which brings the problem of the interference of DME pulse signals to the receiver of the LDACS system [7, 8]. Extensive research has been conducted both domestically and internationally to reduce the mutual influence between LDACS and DME systems across time and frequency domains. To mitigate DME interference, researchers have proposed pulse blanking and clipping strategies. These techniques zero out or limit any received signal components exceeding a predefined threshold, based on the time-domain characteristics of DME signal waveforms [9, 10, 11, 12]. However, in practice, setting appropriate thresholds for pulse blanking and clipping is challenging, leading to potential signal loss and inter carrier interference (ICI). Thus, several studies have explored the reconstruction of DME signals, employing methods such as compressed sensing, wavelet transform, and orthogonal transform [13; 14; 15]. However, these methods are noted to have limitations, including reconstruction errors and residual interference. To address the issue of multi-user interference in wireless communication systems, researchers have adopted adaptive techniques such as power allocation, beamforming, and sub-carrier allocation [16]. [PERSON] and [PERSON] have optimized the spectral efficiency by proposing adaptive algorithms for radio resource allocation. This method employs spatial sub-carrier and power allocation techniques to tackle the interference experienced by system users, thereby minimizing its negative impact on overall system performance and effectively maximizing throughput and spectral efficiency [16; 17]. In terms of array antenna interference mitigation, [PERSON] utilized a uniform circular array for signal reception, employing a DOA matrix algorithm to estimate incoming signals and conduct beamforming [18]. Subsequent signal identification is achieved through the application of a power comparator. However, this method tends to perform poorly in scenarios with lower SNRs. To combat high-intensity DME interference, an orthogonal projection algorithm is applied, followed by a blind beamforming method to extract the OFDM direct path signal, as described in [19]. Nevertheless, the effectiveness of the orthogonal projection method diminishes when the power of the interference signal is low. In beamforming, using the sample data matrix as the covariance matrix can mistakenly suppress the desired signal as interference when the SNR increases. To address this issue, a series of robust adaptive beamforming algorithms have been proposed. These include the diagonal loading (DL) algorithm [20; 21], the Eigenspace algorithm [22; 23], and the covariance matrix reconstruction (CMR) algorithm [24; 25; 26; 27]. The diagonal loading algorithm involves adding a diagonal matrix to the sample covariance matrix (SCM), effectively enhancing the robustness of the beamformer by increasing the noise power. However, selecting an appropriate diagonal loading level is challenging; too small a parameter results in minimal performance improvement, while an excessively large parameter can weaken the suppression of interference signals.