Estimating the Range of an Aegis Radar against a Missile Warhead Target

By George Lewis and Theodore Postol

In our post of September 21 (https://mostlymissiledefense.com/2012/09/21/ballistic-missile-defense-radar-range-calculations-for-the-antpy-2-x-band-and-nas-proposed-gbx-radars-september-21-2012/), we estimated the range of an AN/TPY-2 X-band radar against a warhead target. For a target radar cross-section of 0.01 m^{2} and with a radar dwell time of 0.1 seconds, we obtained a detection range (assuming S/N = 20) of 870 km and a discrimination range (assuming S/N =100) of 580 km. In this post, we make similar estimates for the Aegis SPY-1 radar, and get significantly shorter ranges of 550 and 370 km, respectively. These numbers seem likely to substantially overestimate an Aegis radar’s actual operation range.

As our starting point, we take the second version of the radar equation from the August 3 post, terms for propagation effects (such as Earth reflections or refraction) and atmospheric attenuation have been neglected and we assume perfect integration, neglect fluctuation losses, and make the standard simplifying assumption that bandwidth-pulse length product = 1:

R_{max} = maximum radar range (m), ρ = antenna aperture efficiency, P_{av} = radar average power (W), A = antenna area (m^{2}), G = antenna gain, n = number of pulses integrated, σ = radar cross section of target (m^{2}), k = Boltzmann’s constant (1.38×10^{-23} J/K), T_{0} = 290 K, F_{N} = receiver noise figure, f_{P} = pulse repetition frequency (Hz), (S/N)_{1} = signal-to noise ratio required as if detection were based only on a single pulse, and L_{S} = system loss.

Below we estimate each parameter and compare to our corresponding estimate for the TPY-2. For additional details on the SPY-1 radar and it parameters, see the post of August 3 (https://mostlymissiledefense.com/2012/08/03/ballistic-missile-defense-the-aegis-spy-1-radar-august-3-2012/).

**P _{av} = 77,000 kW**. (81,000 kW for TPY-2.) This assumes a SPY-1D(V) radar, which is the current production version, with all the power being put out of one antenna face. The radars on the ships that have been so far been upgraded for ballistic missile defense purposes are the somewhat less powerful SPY-1B and SPY-1D versions. The P

_{av}used here is taken to be the power at the output of the transmitter, not the actual power out of the antenna.

**ρ = 0.8.** The same value was assumed for the TPY-2.

**A = 12 m ^{2}.** (9.2 m

^{2}for the TPY-2.)

**G: = 14,600**, using the relationship G = ρ(4πA/λ^{2}), where the wavelength λ = 0.91 m, corresponding to frequency of 3.3 GHz. The corresponding value for the TPY-2 was 103,000.

**n/f _{P} = 0.1.** That, is the total dwell time is 0.1 seconds. The same value was used for the TPY-2 estimates. (An Aegis radar would likely use much shorter pulses than a TPY-2 radar, so both n and f

_{P}would be much larger than the values of n = 20 and f

_{P}= 200 Hz we used for the TPY-2).

**σ = 0.03 m ^{2}.** To account for Aegis’ lower operating frequency, we use a target radar cross section three times higher than the value of σ = 0.01 m

^{2}we used for the TPY-2.

**F _{N} = 4.4 dB = 2.8** (corresponding to a system noise temperature of 800 K). The published noise figure for the Aegis receiver is 4.25 dB =2.66, corresponding to system temperature (excluding the antenna contribution) of 770 K. A value of F

_{N}= 1.4 (corresponding to system temperature of 400 K) was used for the TPY-2.

**S/N = 20 (for detection) or 100 (for discrimination).** These are the same values used for the TPY-2.

**L _{S} = 10 dB = 10.** This was adjusted upward from the value of 8 dB = 6.3 used for the AN/TPY-2 radar to account for the additional waveguide and other “plumbing” losses associated with using a central transmitter rather than an active array antenna.

These values above then give ranges of:

**R _{max} = 550 km (S/N = 20)**

**R _{max} = 370 km (S/N = 100)**

The corresponding results for the TPY-2 radar were 870 and 580 km, respectively.

**Comparison to a published range**

The only public numerical figure on the Aegis detection range (that we have seen) against a specific target is that the SPY-1D(V) “can track golf ball-sized targets at ranges in excess of 165 kilometers.”[1] A golf ball-size (1.68 inches diameter) metallic sphere corresponds to radar cross section of about 0.0025 m^{2} at 3.3 GHz.[2] This statement was made in the context of the soon-to-be deployed SPY-1D(V) radar to detect mortar and artillery shell and small-caliber rockets against a clutter background, so presumably it applies to the D(V) version.

If we simply the scale the 165 km range using a larger radar cross section of 0.03 m^{2} that might be expected of a missile warhead, we get a detection range:

R_{max} = 165 km (0.03/0.0025)^{0.25} = 310 km.

This is much less than our estimate of 550 km, which is not surprising since the 165 km figure is presumably based on much shorter dwell time. The 0.1 second dwell time we used would require the Aegis radar to devote a significant portion of its resources to tracking a single warhead. However, an Aegis radar has many other tasks other than just ballistic missile defense, and in addition, as noted above, we assumed all the radar power was being emitted out of a single radar face. (On Aegis cruisers, one transmitter is shared between two faces. On Aegis destroyers, all four faces share a single transmitter.)

[1] John A. Robinson, “Force Protection from the Sea: Employing the SPY-1D Radar,” *Field Artillery*, March-June 2004, pp. 24-25.

[2] RCS calculated using NASA’s Size Estimation Model. For a discussion of this, see, for example, C.L. Stokely, J.L. Foster, Jr., E.G. Stansbery, J.R. Benbrook and Q. Juarez, “Haystack and HAX Radar Measurements of the Orbital Debris Environment; 2003, NASA Lyndon B. Johnson Space Center, November 2006., pp. 20-22. Available at: http://www.orbitaldebris.jsc.nasa.gov/library/Haystack_HAX_radar2003.pdf.

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/ October 23, 2012The Defense Science Board report concurs that Aegis radars are not up to the job.