An Alternative Derivation of the Method of Stationary Phase for Multivariate Signals

Loffeld, Otmar

doi:10.1109/tgrs.2011.2174245

Cited by 2 publications

(3 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Equation ( 25) can be asymptotically evaluated by using MSP. This method can be used to obtain an analytical solution for integrals of the following form [33]:…”

Section: Appendixmentioning

confidence: 99%

“…The phase function in (33) and the above derivative are evaluated at the stationary phase point as follows:…”

Section: Appendixmentioning

confidence: 99%

“…The latter expression is obtained using the method of stationary phase (MSP) [33] (see Appendix for more details). Note that unlike the derivation of other versions of RMA [14,17,34,35] in which the magnitude term 1 R is omitted to simplify the extraction process by MSP, we have included it here in the derivation of the above expression to provide a more accurate approximation.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Development of Fast Fourier-Compatible Image Reconstruction for 3D Near-Field Bistatic Microwave Imaging With Dynamic Metasurface Antennas

Molaei

Fromentèze

Skouroliakou

et al. 2022

IEEE Trans. Veh. Technol.

View full text Add to dashboard Cite

Emerging dynamic metasurface antennas (DMAs) technology promises to achieve future wireless communications by reducing hardware costs, physical size and power consumption. Especially in the field of radar imaging, they can be used as an effective alternative platform for modern computational imaging; because they can simplify the physical hardware and increase the data acquisition rate. Fourier transform (FT)-based scene image reconstruction techniques are known as cost-effective computing solutions for the imaging system processing unit. However, due to the physical layer compression in DMAs and the fact that they do not produce uniform radiation patterns, the information provided by them is not compatible with Fourier-based techniques and cannot be applied directly. In this paper, we first introduce a 3D near-field bistatic imaging approach using two one-dimensional (1D) DMAs as a panel-to-panel model in a Mills Cross structure. Then, based on the introduced mathematical model, we derive a Fourier-based algorithm for the image reconstruction problem. The proposed algorithm consists of five main steps: pre-processing (to transfer data provided by the transmitter and receiver DMAs to a set of equivalent spatial measurements), applying FTs to the transferred signal, filtering in the Fourier domain, a simplified interpolation, and applying a 3D inverse FT to retrieve scene information. The results of numerical simulations confirm the satisfactory performance of the proposed approach.

show abstract

“…Equation ( 25) can be asymptotically evaluated by using MSP. This method can be used to obtain an analytical solution for integrals of the following form [33]:…”

Section: Appendixmentioning

confidence: 99%

“…The phase function in (33) and the above derivative are evaluated at the stationary phase point as follows:…”

Section: Appendixmentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation