IEEE Aerospace and Electronic Systems Magazine - November 2020 - 11

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such cryogenic units. For example, if we need an array
with 100 000 JPAs, and if we cool 100 such devices in
one large cryogenic refrigerator, then we need about 1 000
cryogenic units, and now we are talking about real money.
The SWAP for such refrigerators is also very bad; see [3,
Figure 6]. There are only about five companies in the
world that manufacture and sell such cryogenic units.
However, in the future, we expect this cost to decrease significantly, owing to advances in cryogenic technology, as
well as wider competition in manufacturing such units and
much larger volume production. Such cryogenic units are
also used today for quantum computing and quantum
communications, and hence, we expect that the cost of
cryogenic refrigerators will be substantially reduced in the
future as a result. Unfortunately, even if the cost of such
cryogenic dilution refrigerators was reduced by two orders
of magnitude, the same conclusion would be obtained; in
particular, the QR would still be many orders of magnitude more expensive than the corresponding CR, owing to
the extremely large antennas required to compensate for
the small energy of a photon at X-band, as well as the high
cost of the electronics and other hardware. That is, a very
large reduction in the cost of cryogenic refrigerators is
necessary but not sufficient for cost-effective QR.
The cost for the optimal QR is shown in Fig. 1 plotted against the range from the radar to the target. We
also show the cost of actual real-world CR. Apparently,
the cost of optimal QR is always many orders of magnitude higher than the cost of CR for any range and any
target RCS. This is because we must somehow compensate for the extremely low energy in photons at X-band
as well as the fact that the advantage of QR disappears if
we transmit more than five photons per mode from a single quantum transmit device. In Figure 1, the large variation in the cost for a given range (for both the QR and
CR) is due to the variation in average target RCS, which
varies from stealthy (-40 dBsm) to very large (10 dBsm).
In addition, the cost varies for the CR due to the variation in functionality of the radar system (e.g., phased
array versus dish radars, bandwidth, scan volume, limited
scan versus full scan, system reliability, system availability, etc.). We used the radar range equation to compute
SNR for both the CR and the QR, assuming that the QR
have a 6 dB advantage in SNR relative to the CR with
the same transmit power and the same bandwidth at low
photon flux per mode (see [2] and [16]). The radar range
equation for SNR is extremely well known, and hence,
there is no point in displaying it here; see Skolnik's
Radar Handbook for a very thorough discussion [8]. We
use the standard far-field narrowband approximations to
compute SNR, despite the fact that our optimal QR typically has huge antennas and extremely wide bandwidth;
these approximations are good enough for the purpose of
estimating the radar cost, as long as we include TDUs in
the antenna design.
NOVEMBER 2020

For example, in order to detect and track targets at
1000 km range, a classical X-band radar must transmit
roughly 1 Mw of power (90 dBm) with an antenna of
about 10 m2 area. The corresponding QR would need to
match this power aperture product, minus the 6 dB quantum advantage for search performance. But the QR starts
with a miniscule transmit power per quantum transmit
device (-102 dBm), as shown in the " TRANSMIT
POWER FOR QUANTUM RADAR " section. This is a
186 dB deficit in transmit power that must be overcome
somehow or other. If we only used a bigger antenna to
accomplish this, we would need to use an antenna with the
size of the state of Texas. If we also used a million quantum transmit units in parallel, we would reduce the area of
the antenna to the size of the state of Rhode Island. Amplification of the signal with LNAs also helps, but there is a
practical limit, because we cannot effectively cool LNAs
to 4 K at high signal power levels; it is like putting a heat
source inside your expensive cryogenic refrigerator; also,
it destroys entanglement of the photons.
As shown in Figure 1, the cost of the CR varies by
roughly two orders of magnitude (20 dB) for a given
range, primarily due to the variation in RCS from -40 to
10 dBsm. This is because the SNR is proportional to the
power aperture area squared (PA2), and hence, we must
increase the antenna area by roughly 25 dB to cover the
RCS variation of 50 dB. It turns out that the radar cost
scales linearly with the antenna area, as a crude approximation. But the CR also uses more transmit power to
reduce the cost somewhat. Hence, we see a 20 dB variation in the cost rather than a 25 dB variation. It is interesting that the trends of the cost versus range for CR are very
similar to the optimal QR, as shown in Figure 1. This is
because the actual real-world CRs are designed by radar
system engineers to minimize the cost. However, at a short
range, the variation in the cost for the QR is compressed
because the cost is dominated by the cryogenic refrigerator, and small antennas are relatively cheap, whereas at a
long range, the antennas for the QR are huge and
extremely expensive.
If we consider mm-wave radars, rather than microwave radars, then the energy in a single photon is roughly
an order of magnitude larger, and the maximum bandwidth is also an order of magnitude larger, and hence, the
SNR of the QR is at least 20 dB larger than at X-band.
Also, the transmit antenna gain is another 20 dB higher if
we could use a phased array or dish antenna. But in practice, the optimal QR tend to be MIMO rather than phased
arrays, owing to the random (and hence orthogonal) waveforms radiated from distinct parts of the antenna, resulting
in no increase in transmit antenna gain (despite the higher
frequency). Despite this improvement, the relative cost of
the QR and CR remains roughly the same, because the CR
benefits from 20 dB of higher transmit antenna gain,
whereas the QR does not. That is, the QR is still many

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