Aerospace and Electronic Systems Magazine December 2017 - 64

MIMO Methods Applied in Over-the-Horizon Radar

APERTURE RESOLUTION
We were interested in the determining the ability of the chosen
aperture to adequately resolve two propagation modes separated
by a difference in elevation angle and to confirm that it performed
as anticipated at the low elevation take-off angles used in our application.
An estimate of the resolution of the Coondambo transmit array
was obtained on the 1,514 km path to Elliott by opportunistically
exploiting a period of ionospheric change. The elevation angle of
any "high-ray" response versus the elevation angle of the response
from "low ray" propagation for the same layer converges to a single elevation value at the maximum usable frequency (MUF) for
a particular mode. This is because the high ray (1F2h-x) and low
ray (1F2l) paths converge into a single path. This feature of the
ionosphere was exploited by leaving the frequency of operation for
the transmitter system fixed (fc = 9.26MHz) during a period where
the MUF of the ionosphere was higher than that frequency, but
steadily diminishing (as measured using the colocated OIS system)
as the ionosphere changed over time. Such a circumstance allowed
for a steady progression from fully resolvable high-ray and lowray (1F2h-x and 1F2l) responses (separated by over 6° in elevation)
down to unresolvable mode responses (and then eventually no response as the MUF dipped below the operating frequency).
As an approximate measure of resolution, we used an approach
whereby we chose to preserve one mode (say, low-ray) and reject
the companion high-ray mode using the MVDR beamformer. It is
a property of this class of beamformer that as the resolution limits
of the array in use are exceeded the signal to noise preservation
of the wanted mode with respect to the range-Doppler map noise
floor deteriorates.
We examined the performance of the MVDR mode selective
beamformer for the case of preserving the 1F2l as it varied from approximately 19.5° to 22° while rejecting the 1F2h-x mode as it varied
from approximately 26° to 22°. Rejectability was high initially but
decreased as the two modes became closer in elevation angle. As
expected, the adaptive beamformer performance became poor with
the preserved mode signal to noise ratio rapidly decreasing as the
resolution of the transmit array became inadequate with the reducing mode elevation separation. We then designated the resolution
limit as the elevation separation between the two modes such that
the adaptive beamformer no longer enhanced the signal to noise
ratio of the preserved mode compared to the signal to noise ratio
of the preserved mode prior to unwanted mode cancellation. Using
this approach, the estimate of the resolution of the array was 4.8°
at a steer angle of 20°. This compared favorably with a calculated
Rayleigh limit of 4.5° for the operating frequency fc = 9.26 MHz
and a projected aperture of (1,200 m at 20°) of 410 m.

ENERGY BUDGET COMPARISON
MIMO techniques reduce radar sensitivity proportionally to the
waveform set cardinality Kt according to PM = 10 log (Kt), where
PM is the sensitivity penalty in dB. For the Kt = 12 waveforms used
in MSE then PM = 10.8dB. This sensitivity penalty in an element
space MIMO or MISO system compared to a traditional phased
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array transmitter can be understood heuristically in the following
manner. In the following we assume the transmit signal power radiated by each element in the transmit array is the same in both
MIMO and phased array transmit systems.
In the phased array case the waveforms are identical except
for an appropriate time-delay (or phase shift in the narrowband
case) applied to each waveform in order to ensure that the radiated
signal from each element coherently sums in the desired transmit
beam direction. The power in the sum beam is the coherent sum
of all the transmit array element waveform power. For simplicity
assume there are no propagation losses and that a target is in the
beam direction that scatters power toward a receiver without loss.
This sum signal available at the receiver has the same waveform
design as each waveform transmitted in the transmit array and can
be received by a single matched filter at the receiver. The matched
filter achieves signal to noise ratio gain at its output with the signal
to noise ratio given by the waveform power relative to the noise
processed through a single matched filter.
In the MIMO case, the same power is radiated by each element
in the transmit array. No steering is applied and the radiated signals
individually scatter from the target and are received at the receiver.
A bank of matched filters, one per waveform, then recovers the
individual waveforms and a beamformer steering weight applied
to the output of the bank of matched filters. The coherent sum of
the waveform set in the direction of the target is the same as in
the phased array case. However, this has been achieved using K
matched filters rather than one matched filter with a corresponding incoherent summation of the noise output from each matched
filter. The reduced sensitivity of MIMO methods is due to higher
noise from the multiple matched filters rather than reduced total
power scattered by the target. MIMO waveform transmissions can
be interpreted as a particular instantaneous "steering" of a transmit beam, however, it is more useful to ignore this interpretation
and concentrate on the superposition of the radiated waveform
set power from each transmit array element at the target location.
After reception and processing by the bank of matched filters the
power at the target can be coherently summed (albeit observed
over the common to all waveforms in the waveform set path from
target to receiver).
For traditional surveillance radars, the aforementioned penalty
can be recovered by trading surveillance region scan time for extended coherent processing interval. This is generally not possible
in OTHR because beyond certain limits target coherence decreases
as coherent integration time increases. The penalty PM renders
MIMO approaches unsuitable for OTHR target-detection-in-noise
problems since target SNR will decrease by PM and detectability
will decrease accordingly. In limited cases the target may have excess SNR and the PM penalty may not be a concern.
In many cases encountered in OTHR, however, target detectability is limited by clutter of one form or another and not by noise. Clutter is unwanted return scatter from the radar transmission and for
the target-in-clutter detectability case the clutter-to-noise ratio scales
the same as target SNR with reduced radar sensitivity. This means
that target-to-clutter ratio is unchanged with the reduced sensitivity
of MIMO (at least until sensitivity is so reduced that the problem
reverts to the target-in-noise case). MIMO is a useful approach for

IEEE A&E SYSTEMS MAGAZINE

DECEMBER 2017

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