Aerospace and Electronic Systems Magazine December 2017 - 25

Francis, Cervera, and Frazer
ditive noise scaled to transmitter power are considered. This occurs
when detecting targets against spread-clutter or unwanted targets,
such as meteors, and will not be discussed in this particular case
study but is potentially an important consideration for other user
case studies. We compute
SNR ( dB ) = Tcit + Ptx + σ rcs + G p + Gm - L - n,

(1)

where Tcit is the coherent integration gain in dB relative to 1 second, Ptx is the transmitter power gain in dBW, σrcs is the target RCS
in dB relative to 1 m2, Gp is the base-system propagation path and
array gains generated by ray-tracing, as described previously in
units of dBW per m2 per s per W, Gm is an introduced marginal
system gain (i.e., above the base-system) in dB as described later,
L is the signal processing losses in dB, and n is the combination
of external noise power and receiver noise power in dBW. Spread
Doppler clutter power can also be incorporated although in the scenario discussed in the article; this is an insignificant contribution.
For all targets that are not obscured by clutter, we model the
data processing step of peak detection. Detection is a statistical test
producing the probability of the target signal power being greater
than the threshold within a noise distribution [14]. We use an empirically derived summation of Gaussian and a log-normal distributed noise distribution to encapsulate the short time normal noise
fluctuations and the less probable higher power noise events, such
as lightning. The probability of false alarm is the probability of the
noise power being greater than the threshold.
Once the probability of detection and false alarm are calculated
for each point in space-time, we determine the probability of tracking a target. As we have targets moving through spatially fluctuating SNR values, we also have fluctuations of the probability of
detection. This variation requires an exhaustive search of possible
detections and misses to characterise the ability to initiate a track,
i.e., it is not a simple look-up table of SNR for detection probability to track probability. We choose a characteristic M detections
out of N observations model for tracking [15], where for this case
study, we use M = 7 and N = 10. This model declares the presence
of a track if at least M out of the last N observations detected a
target. This model makes no statement of track accuracy, which is
beyond the scope of this work.
As the probability of detection fluctuates spatially, the target
dynamics and radar revisit rate influence the resultant probability
of tracking. The optimal frequency and subsequent probability of
track can only be achieved by following a path of ground range and
azimuth with the respective carrier frequency that obtains minimum
path loss. Because these radars are observing many targets across a
spatially diverse set of locations, many carrier frequencies are required. This creates a revisit time for observation of a target based on
the spatial location. This case study uses a 30-second revisit time and
target velocity of 600 km/h to determine our observation locations
and the resulting non-uniform sequences of probabilities of detection.

MISSION PERFORMANCE ASSESSMENT
In our approach, there are a number of radar performance assessment metrics computed for each radar location. We use a model of
DECEMBER 2017

track level fusion that maximises the probability of tracking over the
parameter space for each radar. We then recalculate the performance
metrics for the radar network. For brevity, only the network results
are presented. For this study, we assume the network operates the
radars independently but performs data fusion at a track level.
For each radar, we perform the calculations described in the
previous section and apply a 90% probability of target tracking
performance threshold. To help communicate the performance of
the radar network, we condense tracking performance into sets of
characteristic metric values of the typical hours of coverage and
value of each radar contribution in the network. In this case study,
we have chosen our characteristic missions to be the tracking of
commercial aircraft flying into and out of SYD airport from Adelaide (ADL), Brisbane (BNE), Melbourne (MEL), and Hobart
(HBA). Additionally, we wish to assess the tracking performance
for aircraft circling SYD airport in a typical holding pattern.
The analysis for our base-system radar design shows that there is
almost no coverage at low solar activity and only flight specific coverage for medium solar activity. This sensitivity is assessed as not
satisfactory for the mission requirement of tracking flights to SYD.
To investigate what scale of radar sensitivity within the network would achieve the desired mission, we introduce Gm, the
marginal system gain, as a sensitivity-free variable in Equation (1).
We calculate the metrics described in the following section over a
set of radar system sensitivity levels or marginal system gain values. These sensitivity modifications can be incorporated across the
radar design and used to investigate performance stability. For example, doubling of the receive array size or doubling of the transmitter power each achieve incremental 3-dB improvement. We test
an increased sensitivity above the base-system radar sensitivity of
Gm between 0 and 30 dB.

SPATIAL HOUR COVERAGE
We demonstrate the inadequate performance of the base-system
design in Figure 4, where colour represents hours of performance,
with red being no coverage and green being 10+ hours a day. This
image is just one combination of solar state and season but demonstrates the characteristic patchy performance. By comparison when
using an additional marginal system gain of 6 dB, the flights are
consistently covered, as shown in Figure 5.
The BNE flight has almost no track coverage. The difficulty
with tracking the BNE to SYD flight is due to the aspect geometry
of all three radars. The aircrafts in this flight path are either tangential to each radar in the radar network (i.e., lost in the ground
clutter) or have poor target scatter due to the aspect dependency of
target RCS.

MOSTLY-AT-LEAST HOUR COVERAGE
We use the spatial median of hours of coverage for the target missions evaluated for each season and solar state. This is a significant, but robust, data reduction compromise that demonstrates the
performance changes between different levels of solar influence.
This metric value indicates that most of the target flight path will
be covered by the minimum probability of achieving tracking for at

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