Because ultrawideband (UWB) pulse and antenna lengths are comparable, the antenna will radiate distorted versions of its input pulse in different directions. To design UWB radio devices, it is therefore critical to effectively model pulse distortions. At the University of Alberta in Canada, a method of modeling pulse distortions has been developed by Adrian Eng-Choon Tan, Michael Yan-Wah Chia, Kevin Khee-Meng Chan, and Karumudi Rambabu. Their approach models the antenna’s radiated and received transient fields at various angles. Using this analytical model, designers of UWB radios can gain prior knowledge of the pulse distortion.

This method analytically models the angle-dependent pulse distortion of the planar-aperture antennas used in UWB radios. The antenna’s input pulse is related to its transient radiated fields, while the incident transient fields are related to its outer pulse. As part of this approach, the antenna’s aperture field distribution is estimated from time-domain antenna measurements.

The researchers modeled and compared received pulses from three different antennas—a ridged horn, dielectric load horn, and Vivaldi—with the measured received pulses. A comparison of pulse shape, amplitude, and energy showed good agreement. To evaluate the proposed method, different input pulses were examined.

To estimate the angle-dependent impulse responses, time-domain measurements were conducted in an anechoic chamber. In each measurement, identical antennas were used as transmitting and receiving antennas. The received pulses were recorded with a sampling oscilloscope. A separate measurement also was conducted for the double-ridged horn antenna in an open range.

The least-squares approach was used to perform deconvolution of the measured pulses. As a result, certain conditions had to be met. Both the boresight and off-boresight measured pulses were recorded at the same sampling rate. Their discrete time data also was finite in length. In addition, the pulse data for off-boresight measurements was longer than for that of the boresight pulse measurements. Finally, the impulse response was assumed to be zero outside of its deconvolution data range.

The least-squares approach for deconvolution expresses the convolution process in matrix form. By premultiplying both sides with the transpose of the convolution matrix, the engineers were able to express the impulse response in the form of an inverse Toeplitz matrix. That matrix could then be solved with the conjugate gradient method. See “Modeling the Transient Radiated and Received Pulses of Ultra-Wideband Antennas,” IEEE Transactions On Antennas And Propagation, Jan. 2013, p. 338.