Characteristic basis functions enhanced compressive sensing for solving the bistatic scattering problems of three‐dimensional targets

Abstract

In this letter, the characteristic basis functions (CBFs) are utilized to enhance the compressive sensing (CS) technique to analyze the bistatic scattering problems of three‐dimensional targets. The CS technique can efficiently analyze the bistatic scattering problems by establishing an underdetermined linear equation instead of traditional full‐rank dense impedance matrix equation. However, the CS method is limited to two‐dimensional targets. The reason is that the induced currents of the three‐dimensional target expressed by Rao‐Wilton‐Glisson basis functions are not sparse on the commonly sparse basis, since the field source has no orderly distribution when the target is modeled and discretized by commercial software. In order to solve this problem, the CBFs are used in this letter as the sparse basis to improve the sparsity of the induced currents. The numerical results of different targets are presented to validate the accuracy and efficiency of the proposed method.

High-precision Solution of Monostatic Radar Cross Section based on Compressive Sensing and QR Decomposition Techniques

“…An underdetermined equation is a system of linear equations with more unknowns than equations. For example, Wang proposed two methods to efficiently analyze the three-dimensional bistatic scattering problem [11][12]. The conventional underdetermined equation [13] computation model is not suited for analyzing monostatic electromagnetic scattering problems.…”

Use of the Adaptive Cross Approximation for the Efficient Computation of the Reduced Matrix with the Characteristic Basis Function Method

“…The interest in the use of techniques dealing with Macro Basis Functions (MBFs) [7][8][9][10][11][12][13][14][15][16][17] has increased sharply during the last decade, based on the computational advantages of reducing the effective numerical size of the problems under analysis. This family of methods requires the computation of a new set of basis functions defined on a number of blocks in which the scenario has been previously partitioned.…”

“…The calculation of the reduced matrix can pose an important computational bottleneck for MLFMM-CBFM when considering large blocks, since it is necessary to obtain all the low-level impedance terms inside each block as well as between neighboring blocks. In [15], the CBFs are used as a sparse base over which a Compressive Sensing approach is used to analyze the bistatic RCS of 3D targets. The work described in [16] makes use of CBFs in order to improve the alternating GMRES-Jacobi (AGJ) iterative solver, where the reduced system is built based on the previous iterations.…”

Novel construction of measurement matrix and sparse basis to accelerate compressive sensing for solving wideband RCS of PEC objects

“…The measurement scheme differs from that of the left-multiplied by Gaussian matrix in Chai and Guo, 15 the filling of the MOM impedance matrix is also accelerated under the same advantageous conditions. In Wang et al, 17,18 the characteristic basis functions (CBFs) and characteristic mode basis functions are exploited as sparse basis, respectively, instead of discrete Fourier transform (DFT) in Wang et al, 17 to enhance the sparsity of induced currents. However, these methods are inapplicable to wideband scattering problems.…”