Solution for Wide Band Scattering Problems by Using the Improved Ultra-Wide Band Characteristic Basis Function Method

Abstract

Abstract-The ultra-wide band characteristic basis function method (UCBFM) is an efficient approach for analyzing wide band scattering problems because ultra-wide characteristic basis functions (UCBFs) can be reused for any frequency sample in the range of interest. However, the errors of the radar cross section calculated by using the UCBFs are usually large at low frequency points. To mitigate this problem, an improved UCBFM is presented. Improved UCBFs (IUCBFs) are derived from primary characteristic basis functions and secondary level characteristic basis functions (SCBFs) by applying a singular value decomposition procedure at the highest frequency point. This method fully considers the mutual coupling effects among sub-blocks to obtain the SCBFs. Therefore, the accuracy is improved at lower frequency points because of the higher quantity of current information contained in the IUCBFs. Numerical results demonstrate that the proposed method is accurate and efficient.

Solution of Wideband Scattering Problems Using Hierarchical Ultra-Wideband Characteristic Basis Functions

“…The sphere is divided into 8 blocks, with each block extended by Δ = 0.15λ. Referring to [20], each block is illuminated by multi-angle PWs from 0 • ≤ θ < 180 • and 0 • ≤ φ < 360 • with N θ = 8 and N φ = 8, resulting in a total of 128 PWs. The numbers of UCBFs constructed by using IUCBFM and HUCBFM retained on each block at the highest frequency point are shown in Fig.…”

“…To improve the calculation accuracy of UCBFM at lower frequency points, the construction of UCBFs is improved by considering the mutual coupling effects among sub-blocks. The IUCBFM [20] begins by dividing an object into M blocks. Then, it establishes a model at the highest frequency point and constructs the CBFs by using a series of plane waves (PWs).…”

“…In addition, the number of UCBFs constructed at the highest frequency point is unnecessarily high, and computational complexity increases when applying UCBFs to the lower frequency points. To mitigate these problems, an improved UCBFM (IUCBFM) is proposed in [20] to improve the accuracy at lower frequency points. This improvement is achieved by fully considering the mutual coupling effects among the sub-blocks to obtain the secondary level CBFs (SCBFs).…”

Efficient Computation of Wideband RCS Using Singular Value Decomposition Enhanced Improved Ultrawideband Characteristic Basis Function Method

“…To mitigate these problems, some improved methods have been presented. In [12], the construction of the UCBFs has been improved by fully considering the mutual coupling effects among the subblocks to obtain the secondary level CBFs (SCBFs), such that the improved UCBFs (IUCBFs) contain more current information and improve the calculation accuracy at lower frequency points. In [13], an adaptive IUCBFs construction method has been proposed and the adaptive IUCBFs have been obtained at the highest frequency point in each subband which leads to a smaller number of IUCBFs and significant reduction of solver time at lower frequency band.…”

“…In [14], the unnecessary UCBFs have been removed from the basis set as the frequency is decreased. However, in the generation step of the IUCBFs in [12][13][14], the choice of the number of incident plane waves (PWs) is typically made empirically and the redundant PWs are usually chosen which increases the solving time of the CBFs. To mitigate this problem, singular value decomposition (SVD) is adapted to enhance the efficiency of the CBFs generation in this paper.…”