Aerospace and Electronic Systems Magazine December 2017 - 42

High-Latitude Application of 3D OTHR Radar
Here, v is the steering vector for the target direction. For a
chosen beamformer and array layout formation, if we write the
transmit and receive gains as a function of the number of elements,
such as Gt(M) and Gr(N), then the objective is to minimize the cost
of the transmit-receive array manifold that has required value of
Gt(M)Gr(N), over all possible M, N, and layout geometries.
The experiments and theoretical considerations [25] suggest
that for large element counts (M,N >> 1), the form of the array gain
is Gt(M) ≈ CM M and Gr(N) ≈ CN N, where CM and CN are constants
that depend on the layout geometry and clutter angular spectrum.
For example, consider a linear array with exponential correlation
function R(X) = exp(-|X|/L), where X is the lag and L is the correlation length. For an array spacing of d, the interelement correlation coefficient is ρ = exp(-d/L) and the array covariance matrix,
assuming N elements, is given by
 1

 ρ
ρ =  ρ2

 
 ρ N −1


ρ
1

ρ2
ρ



ρ N −2

ρ N −3

 ρ N −1 

 ρ N −2 
 ρ N −3  .

 

1 


Figure 4.
(5)

It can be shown [25] for well-correlated clutter ( ρ ≈ 1), large
number of elements ( N  1), and well-resolved clutter and target
vectors that G ≈ 2 N / (1 − ρ ), so CN ≈ 2 / (1 − ρ ). Consider the example ρ = 0.9, so CM = CN = 20. A joint transmit-receive array gain
of 50 dB would require MN ≈ 2,500. If the ratio of the transmit and
receive channel cost is 4, then the minimum cost solution would
involve 25 transmit elements and 100 receive elements. Of course,
one would have to verify that all other performance requirements,
such as azimuth resolution and effective isotropic radiated power,
are satisfied.

EXPERIMENTS
An experimental OTHR was installed at Defence Research and
Development Canada in Ottawa, Canada. Figure 4 shows the
placement of antennas at the site. The OTHR features an array of
eight Beverage antenna elements, laid out in a 4 × 2 configuration,
of which four are available for transmit and four for receive. These
antennas were selected for the experiment for reasons of low cost
because the project was not funded at the time of construction. The
antennas are 150 m long and suspended 6.5 m above the ground.
The antennas generate about 1 dBi of gain at 5 MHz in the direction about 10° counterclockwise from geographic north. Each of
the four transmit antennas can be excited with independent wave
forms at 4-kW peak power and up to 100% duty cycle, and each of
the four receive antennas is connected to a digital radio receiver.
An experiment is described in this section. This experiment
looks at azimuth-elevation beamforming [11], [12]. For experiments on joint transmit-receive beamforming, which will not be
described here, the interested reader is referred to [13], [14].
In the azimuth-elevation beamforming experiment, transmit
antenna TX1 was operated by itself and reception was performed
on antennas RX1 through RX4. The transmitter was operated at
40

Site layout. TX1 through TX4 are the transmit antennas, and RX1
through RX4 are the receive antennas.

50% duty cycle at a frequency of 4.9415 MHz and pulse repetition frequency of 50 Hz. Echoes were obtained of one-hop
ground clutter (a target proxy) and half-hop auroral clutter, as
per Figure 2, over range gates between 1,500 km and 2,000 km
[11]. The ground clutter was extracted by compiling all rangeDoppler cells less than 0.5-Hz Doppler, and the auroral clutter
was extracted as the remaining range-Doppler cells. Direction
of arrival (DOA) was calculated for all ranges and Dopplers
representing each clutter mode, and power-weighted histograms
of the DOAs were compiled [26]. It was shown previously that
these histograms converge to the wave number spectra of the
signals under fairly weak stationarity assumptions [27]. The
ground clutter for two data sets are plotted in Figures 5a and 5b.
The wave number coordinates are normalized to the radar wave
number k = 2π / λ . The OTHR beam is aimed in the y direction at low elevation angle such that the one-hop echo from the
ground is nominally centered around k x / k ≈ 0 and k y / k ≈ 1. If
targets were in the illuminated region, they would return to the
radar in this mode. The illuminated region occupies a continuum
of azimuth and elevation angles. If present, a target echo would,
however, only occupy only a single azimuth and elevation coordinate within this continuum. We arbitrarily choose a hypothetical target location near the center of the wave number spectral
peak for the ground echo at about k x / k  0.15 and k y / k  0.85.
In an auroral clutter control problem, this is the direction for
which we impose the unity gain constraint. The second of the
two modes is spread in Doppler and is the auroral echo. The wave
number spectrum of this mode for the two data sets is shown in
Figures 6a and 6b. In Data Set 1, the difference in angle is pure
elevation, whereas in Data Set 2, there are differences in both
elevation and azimuth. The performance of the beamformer is
characterized by the degree to which the clutter mode is rejected,
while maintaining unity gain on the target. Data Sets 1 and 2 also
vary in the manner in which the clutter is distributed. Data Set
1 is broad in azimuth and likely could be narrowed (sharpened)
by compiling the histogram over a narrower range of Doppler

IEEE A&E SYSTEMS MAGAZINE

DECEMBER 2017

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