Aerospace and Electronic Systems Magazine December 2017 - 39

itude OTHR. The ensemble of techniques under consideration here
is referred to as three-dimensional (3D) OTHR, where the three
dimensions refer to range, azimuth, and elevation. The scope includes the full exploitation of planar antenna arrays on both transmit and receive. Recent cost decreases in high-speed (>100-MHz)
high-dynamic range (>100-dB) software radios enable the deployment of thousands of receive channels and thus the element-level
sampling of a filled planar receive aperture. Similarly on transmit,
digital control of the amplitude and phase of every transmit element allows one to compensate for interelement coupling effects
and operate a filled planar aperture close to grazing.

HIGH-LATITUDE OTHR PHYSICS
Backscatter from plasma consists of the radiation from electrons
accelerated by the incident radar electric fields and, in general
terms, is referred to as Thomson scatter [8]. In an unstructured
thermal ionospheric plasma, detection of Thomson scatter generally requires large radars with a power-aperture product on the order of 1010 Wm2. However, if there exists macroscopic structuring
in the plasma at scale lengths of one half the radar wavelength,
then the Thomson scattering can be enhanced by a Bragg scattering mechanism, and this scatter can be detected by radars with far
smaller power-aperture products. The Thomson scattering volumetric backscatter radar cross section (RCS) of the plasma when
Bragg scattering is included is given by [8]

σ = 4π re2 Sn (−2k ),

(1)

where re is the classical electron radius, Sn is a plasma density fluctuation spectrum, and k is the incident radar wave number.
It is possible to estimate the RCS of the Bragg backscatter by
using models for Sn [9], although experimental measurements are
available from the Polar Fox II experiment [2]. Without delving into
details, we state that this RCS is on the order of approximately −80
dBm2 per m3 near the middle of the high frequency band (around
10 MHz) for representative conditions in the auroral F region. Although this RCS may seem fairly small, the number of cubic meters that are potentially illuminated by a radar is quite large. Let us
consider the radar illumination, prior to applying any sort of beamforming. We consider a field of view that is range gated at intervals
of approximately 10 km, representing a typical radar bandwidth of
approximately 15 kHz. The radar illumination of the irregularities is
DECEMBER 2017

limited to the bottom side of the ionosphere, which may have a vertical depth of about 30 km. Finally, the azimuth extent is potentially
quite large (perhaps 3,000 km), although typically the azimuth extent can be sharpened considerably using Doppler processing prior
to beamforming. This azimuth-Doppler coupling arises due to the
varying angle between the radar look direction and the plasma drift
velocity [10]. To estimate the impact of the sharpening, we make
fairly conservative assumptions of a 5-second integration time (resulting in 0.2-Hz Doppler resolution) and a line-of-sight plasma
drift velocity that changes by 300 m/s over the 3,000-km azimuthal
extent of the illuminated region. At a ∼10-MHz carrier frequency,
these assumptions result in the clutter being spread over approximately 100 Doppler bins. A single Doppler bin, thus, contains the
clutter originating from about 30 km in azimuth.
Based on the previous considerations, the effective resolution
cell volume for the purposes of estimating clutter levels is about
∼10 km (range) × ∼30 km (elevation) × ∼30 km (azimuth), which
is a volume of ∼1013 m3. Combined with a volumetric clutter RCS
of −80 dBm2 per m3, this leads to a total clutter RCS of ∼50 dBm2.
Detecting aircraft with an RCS of 10 dBm2 would require a clutter
suppression of about 50 dB, through beamforming of the Dopplerprocessed data.
Aside from the large clutter RCS, of particular significance here
is the geometry of the target signal ray compared with the clutter
signal ray. Consider, for example, Figure 2: several rays representing wave packets emitted from a radar with a broad elevation beam

Figure 2.

Target and auroral clutter modes for two slant ranges.

IEEE A&E SYSTEMS MAGAZINE

Table of Contents for the Digital Edition of Aerospace and Electronic Systems Magazine December 2017