# Efficient Multipath Clutter Cancellation for UAV Monitoring Using DAB Satellite-Based PBR
## 3 Suppression Algorithm
The discontinuity of circular filtering limits the suppression performance of clutters with non-orthogonal frequencies. The filter in (18) can be replaced with a linear one to avoid discontinuity and to ameliorate the above problem. Such a process, called ECA-Linear Filter (ECA-LF), can be regarded as a sliding version of ECA-CF with a step size of 1. Unlike ECA-S towards ECA-B, ECA-LF has an equal computational cost to ECA-CF within the same integration time, as the LS estimations can be reused. However, the unavoidable group delay brought by linear filtering deteriorates ECA-LF's real-time performance, which can be alleviated to some extent by asymmetric filter weights [36]. The 2D-CCF is usually calculated using batched 1D-CCF and inter-batch accumulation for efficiency, which resembles the pulse compression and moving target detection (MTD) in traditional pulse radar signal processing. Since the clutter base utilized in ECA-C/LF only contains components with zero Doppler, the 1D-CCF, or pulse compression, can be precalculated before the evaluation stage to reduce data transmission and processing overhead. Such an efficiency improvement can also be attributed to the approximation of the segmented clutter base used in (16) and (17), as otherwise, the separate compression of extended clutter components is unavoidable. It should be noticed that the batch level precompression is not appliable to ECA-B; even only the stationary clutter base is utilized during the suppression. As discussed in Section 4.2, the limited batch number \(B\) cannot form an extensive enough Doppler tolerance range, leading to unacceptable SNR loss for targets with high speed. Assume that the target area contains only the first \(L\) range bins and \(L\geq K\). The multiplied matrix for pulse compression at each batch is denoted as \(\mathbf{R}_{b}\), the partitioned matrix for the first \(K\) range bins of which can be expressed as as follows:  
\[\mathbf{R^{\prime}}_{b}=\mathbf{C}_{0,b}\odot\mathbf{D^{\prime}}, \tag{20}\]  
where \(\mathbf{D^{\prime}}\) contains the first \(K\) columns of the data selection matrix \(\mathbf{D}\), of which the definition is as follows:  
\[\mathbf{D} =\{d_{ij}\}_{i\in[1,N/B],j\in[1,L]}\] \[d_{ij} =\left\{ \begin{array}{ll}1&j\leq i\leq j+N/B-L\\ 0&\text{otherwise}\end{array} \right.. \tag{21}\]  
The estimation of each batch based on compressed signal can be expressed as follow:  
\[\mathbf{\theta}^{\prime}_{0,b}=\left(\mathbf{C}^{H}_{0,b}\mathbf{R^{\prime}}_{b}\mathbf{R^{ \prime}}^{H}_{b}\mathbf{C}_{0,b}\right)^{-1}\mathbf{C}^{H}_{0,b}\mathbf{R^{\prime}}_{b}\bm {R^{\prime}}^{H}_{b}\mathbf{s}_{\text{sur,b}}. \tag{22}\]  
When \(N/B\gg L\), \(\mathbf{R^{\prime}}_{b}\) in the above formulation can be replaced with \(\mathbf{C}_{0,b}\) and  
\[\mathbf{\hat{\theta}}^{\prime}_{0,b} \approx\left(\mathbf{C}^{H}_{0,b}\mathbf{C}_{0,b}\right)^{-1}\mathbf{C}^{H}_{ 0,b}\mathbf{s}_{\text{sur,b}}. \tag{23}\] \[=\mathbf{\hat{\theta}}_{0,b}\]  
Thus, the precompression has little impact on each batch's estimation, while a considerable computation reduction can be achieved for close target detection, which is discussed further in Section 4.1. In practical processing, overlapped data can be included in each batch to complete the signal length to avoid the SNR loss caused by (20). As shown in Figure 2, the processing flow of ECA-C/LF with precompression (ECA-C/LF-PC) can be described as follows:  
1. Signals of two channels are compressed by batches. 2. Least-square estimation of each batch is solved. 3. Coefficients are smoothed with low-pass filters. 4. Clutter component is canceled with the filtered estimations. 5. Two-dimensional cross-correlation function is obtained via inter-batch accumulation. It needs to be re-emphasized that the derivation of ECA-C/LF is based on the assumption of an unchanged reference power. For scenarios where the illuminated power changes shape, the filter's inputs need to be weighted according to the amplitude fluctuation such as in ECA-E [35].