## 1 Introduction
The eigenspace algorithm divides the signal subspaces by performing eigen-decomposition on the SCM, where the space spanned by eigenvectors corresponding to large eigenvalues is considered to be the subspace of desired signals plus interference, and the space spanned by eigenvectors corresponding to small eigenvalues is considered to be the noise subspace. The actual desired signal SV is guaranteed to fall within the subspace of desired signals plus interference. Therefore, projecting the steering vector of the desired signal, which may contain errors, into the subspace of desired signals plus interference can eliminate these errors, thereby enhancing the robustness of the beamformer. However, under low SNR conditions, the eigenvalues of the SCM are very close to each other, making it difficult to accurately distinguish between the subspace of desired signals plus the interference and the noise subspace. After a thorough study of robust adaptive beamforming algorithms, it was discovered that the primary factor affecting the performance of beamformers is the inclusion of desired signal components in the INCM. [PERSON] initially proposed the reconstruction of the INCM by integrating the Capon spatial spectrum in the interference and noise interval [27]. However, this method estimates the SV using the reconstructed INCM, resulting in low accuracy. An improvement was introduced in [26], where the SV is determined through a convex optimization problem before the INCM reconstruction. This method enhances the accuracy of the reconstruction and reduces the error to an extent, but at the cost of increased complexity. [PERSON] proposed a CMR algorithm based on SVs and power estimation in [25]. The algorithm starts with peak searching in the Capon power spectrum to identify the SVs of all signals, which are subsequently optimized. Next, it uses the approximate orthogonality among the SVs to estimate the power of interference, thus enabling the reconstruction of the interference covariance matrix (ICM). The reconstructed ICM by this algorithm has the same expression form as the theoretical ICM, further eliminating the reconstruction error and enhancing the algorithm performance. [PERSON] suggests employing the SCB algorithm to obtain the noise power and signal covariance matrix in [24]. Then, after eliminating the residual noise, it employs subspace techniques to derive the desired signal SV and reconstructs the ICM through projection transformation. This paper addresses DME interference in LDACS signal reception by proposing a method that combines signal direction estimation and beamforming for interference mitigation. Firstly, it distinguishes between signals and interference by their cyclic frequencies to estimate and identify the directional information of the OFDM signal and DME interference components in the received signal. Then, this directional information is used to estimate the SVs and subsequently reconstruct the INCM. Finally, beamforming is performed to form a high-gain main lobe at the direction of the OFDM signal and deep nulls at the location of DME interference, effectively mitigating DME interference. In our formulation, lowercase letters are used to represent scalars, lowercase boldface letters are used for vectors, and uppercase boldface letters are used for matrices. The symbols \((\cdot)^{*},(\cdot)^{T}\) and \((\cdot)^{H}\) denote conjugate operation, transpose operation, and conjugate transpose operation, respectively. The variable with a superscript like \(\hat{\mathbf{a}}\) denotes the estimated value of that variable.