When the Akebono (EXOS-D) satellite passed through the plasmasphere, a series of lightning whistlers was observed by its analog wideband receiver (WBA). Recently, we developed an intelligent algorithm to detect lightning whistlers from WBA data. In this study, we analyzed two typical events representing the clear dispersion characteristics of lightning whistlers along the trajectory of Akebono. The event on March 20, 1991 was observed at latitudes ranging from 47.83 (47,83N) to -11.09 (11.09S) and altitudes between ∼2232 and ∼7537 km. The other event on July 12, 1989 was observed at latitudes from 34.94 (34.94N) and -41.89 (41.89S) and altitudes ∼1420–∼7911 km. These events show systematic trends; hence, we can easily determine whether the wave packets of lightning whistlers originated from lightning strikes in the northern or the southern hemispheres. Finally, we approximated the path lengths of these lightning whistlers from the source to the observation points along the Akebono trajectory. In the calculations, we assumed the dipole model as a geomagnetic field and two types of simple electron density profiles in which the electron density is inversely proportional to the cube of the geocentric distance. By scrutinizing the dipole model we propose some models of dispersion characteristic that proportional to the electron density. It was demonstrated that the dispersion D theoretically agrees with observed dispersion trend. While our current estimation is simple, it shows that the difference between our estimation and observation data is mainly due to the electron density profile. Furthermore, the dispersion analysis of lightning whistlers is a useful technique for reconstructing the electron density profile in the Earth's plasmasphere.

Distributed array radars consist of multiple sub-arrays separated by tens to hundreds of wavelengths and can match narrow beamwidths with large-aperture, high-gain antennas. The physical independence of the sub-arrays contributes to significant structure flexibility and is one of the advantages of such radars. However, a typical problem is the grating lobes in the digital beam forming (DBF) beam pattern. Unfortunately, the need to suppress the generation of grating lobes makes the design of acceptable sub-array arrangements very difficult. A sigma-delta beam former direction of arrival (DOA) estimation method is proposed in this study to solve this problem. The proposed method performs DOA estimation by acquiring the difference signals in addition to the sum signals of all sub-arrays. The difference signal is typically used for monopulse DOA estimation in the phased array radar. The sigma-delta beamformer simultaneously has both advantages of DOA estimations using a distributed array with a large aperture length and using a sub-array that is not affected by the grating lobe. The proposed method can improve the DOA estimation accuracy over the conventional method under grating lobe situations and help the distributed array radar achieve flexibility in the sub-array arrangement. Numerical simulations are presented to verify the effectiveness of the proposed DOA estimation method.