# Efficient Multipath Clutter Cancellation for UAV Monitoring Using DAB Satellite-Based PBR
## 4 Performance Analysis
### Computational Cost  
Similar to [35], the computational cost is divided into two stages for all ECA versions: adaptive coefficients evaluation and clutter cancellation. For ECA-C/LF-PC, the additional compression for the reference channel is included in the first stage. For simplicity, let \(N\) denote the sampling length within a CPI, \(B\) indicate the total batch number, while \(L\) and \(K\) represent the number of range bins in the target area and suppression region, respectively. In practical applications, the LS estimation is usually solved by matrix factorization and Gaussian elimination rather than inversion and multiplication in (10) for better efficiency and numerical accuracy. If the evaluations are solved with uncompressed signals, a Cholesky factorization of \(\mathbf{C}_{0,b}^{H}\mathbf{C}_{0,b}\) is selected as \(N/B\) is usually significantly larger than \(K\) and the hermitian sampling covariance matrix is positive-definite. On the other hand, for ECA-C/LF-PC, the calculation of \(\mathbf{C}_{0,b}^{H}\mathbf{C}_{0,b}\) and \(\mathbf{C}_{0,b}^{H}\mathbf{s}_{\text{sur},b}\) leads to no size reduction. Thus, a direct LU factorization of \(\mathbf{C}_{0,b}\) is a better choice, although its complexity is about twice that of a Cholesky factorization with the same size. The total overheads within the evaluation stage of different ECA versions are calculated assuming that a complex addition involves two Flops, while a complex multiplication involves six Flops. The results are listed in Table 1, where \(N_{s}\) denotes the sliding window length of ECA-S. The times of products and summations required for the factorization and other matrix calculations can be found in [37; 38]. Similarly, the cost for the cancellation stage is derived as \(8 KLB\) Flops for ECA-C/LF-PC and \(8 KN\) Flops for other versions since the sampling length \(N\) is consistent. Figure 2: Block diagram of the ECA-C/LF with precompression. It can be found that, except for ECA-S, the increased overall Flops of ECA versions with a larger \(B\) can be neglected when \(N\gg K\), as the LS estimation costs much less than the sampling covariance matrix calculation or pulse compression. Standard ECA has the minimum complexity among all versions without precompression for applications with no Doppler extension, as the LS problem is solved only once in each CPI. However, only standard ECA needs an extended clutter base to form a wider notch, which can be achieved with a smaller batch length for ECA-B and ECA-S or filters with a broader passband for ECA-C/LF. Thus, the overall overhead of batched versions is much less in real applications, as the moving clutters cannot be neglected in most scenarios, and a wider notch and a wider notch can improve system robustness [31]. Moreover, a thorough segment can reduce the average overhead at each batch for ECA-B and ECA-ES, which is only valid with \(B<\sqrt{N(1+L/K)}\) for ECA-C/LF-PC and \(B<\sqrt{N(K+3)/2}\) for the non-precompressed version. The above boundaries are rarely reached as the second term in Table 1 cannot be neglected in this case, and the tolerance range seems excessive. It must be noticed that the precompression does not always reduce the total Flops. When \(N\gg L\geq K\), it is appropriate to only count the first term in Table 1, and a vague boundary can be given as  
\[L<\frac{K^{2}+K}{2}. \tag{24}\]  
Since \(L\) and \(K\) have the same order of magnitude in close-range monitoring, the above formulation indicates the computational efficiency of precompression in such applications. In order to better comprehend the above analysis, the total/average Flops of different ECA versions are shown in Figure 3, with \(N=10^{6}\), \(K=50\), \(L=200\), and \(N_{s}=5\times 10^{4}\). The maximum \(B\) of ECA-B and the minimum \(B\) of ECA-S are set at 20 to control the notch width. It should be noted that the curves only represent the trend of a Flops change, as only a few batch numbers can be selected to ensure uniform segmentation.