The LRDR: (Not) The Best Discrimination Money Can Buy? (January 30, 2019)

Almost three years ago, I wrote a blog post about the then recent announcement that the Long Range Discrimination Radar (LRDR) would operate in the S-Band of radar frequencies.  (S-Band covers the range from 2 to 4 GHz.) I found this development quite surprising. The LRDR was to be the key discrimination sensor for the U.S. Ground-Based Midcourse Defense (GMD) national missile defense system. I had been expecting the LRDR to operate at X-Band (8-12 GHz), which appears to provide a significant advantage in discrimination capability relative to S-Band. At the time, I speculated that this choice may have been made to save money, or that perhaps missile defense flight and intercept testing had shown X-Band did not provide any advantage in discrimination over S-Band in actual practice.

Now we have the answer: It was about cost. According to a 2018 article in the Johns Hopkins APL Technical Digest(The Johns Hopkins Applied Physics Laboratory led the systems engineering portion of the LRDR sensor trade studies, identified performance requirements, siting suitability and developed the LRDR element specification.):

“The choice of S-Band for LRDR was a compromise: S-Band was assessed to provide acceptable performance for much lower cost than an X-Band (~10 GHz) system at the same sensitivity and field of view. Trade study analysis indicated that although discrimination performance at X-Band would be superior, it was not sufficiently better than the performance at S-Band to justify the cost differential.”[1]

Discrimination is not only essential for any midcourse defense, it is the most difficult problem facing any such defense.  As discussed below, two recent government-sponsored studies (by the National Academy of Sciences and the Defense Science Board) had criticized the Missile Defense Agency (MDA) for not taking the discrimination problem seriously enough.  The decision by MDA to deploy the LRDR seemed to be at least a partial response to this criticism. However, while tradeoffs must often be made, MDA’s decision to accept inferior discrimination performance from the LRDR now raises the possibility that it still is not taking the discrimination issue seriously enough.

The two following sections discuss the relative discrimination capabilities and costs of the LRDR at S-Band rather than at X-Band.

Figure 1: LRDR Conceptual Drawing (Image Source: MDA)[2].

Countermeasures, Range Resolution, Discrimination and the GMD system

The most challenging aspect of building an operationally effective ballistic missile defense (BMD) system is dealing with steps (often referred to countermeasures) that a missile attacker could take to defeat the defense.  This is particularly the case for midcourse defenses with interceptors that operate above the atmosphere (exo-atmospheric), such as the Ground-Based Interceptors of the U.S. GMD national missile defense system and the SM-3 interceptors of the U.S. Navy’s Aegis BMD system. The lack of atmosphere makes it possible for attacker to implement a wide range of light weight but potentially very effective countermeasures.[3]

A 2011 report by the U.S. Defense Science Board stated that “The importance of achieving reliable midcourse discrimination cannot be overemphasized” and concluded that “Yet discrimination in the exo-atmosphere is still not a completely solved problem. Robust research and testing of discrimination techniques must remain a high priority.”[4]

A report released the next  year by U.S. National Academy of Sciences similarly concluded that “The hard fact is that no practical missile defense system can avoid the need for midcourse discrimination – that is, the requirement to identify the actual threat objects (warheads) amid the cloud of material accompanying them in the vacuum of space.  This discrimination is not the only challenge for midcourse defense, but it is the most formidable one, and the midcourse discrimination problem must be addressed far more seriously if reasonable confidence is to be achieved.”[5]

At present, there are two primary sources of data that might be used for midcourse discrimination: the infrared seekers on interceptors and surface-based (land or sea) radars.  However, an infrared seeker at best sees each object in a target complex as only a single pixel of light until a very few seconds before an intercept attempt.  For this and other reasons, the burden of the discrimination problem must fall primarily on surface-based radars.

When the GMD system was declared operational in late 2004, it had essentially no discrimination capability.  At that time, its core radar infrastructure consisted of two large phased-array radars, the Cobra Dane radar on Shemya Island at the western end of the Aleutians and the PAVE PAWS early warning radar at Beale Air Force base in California.  These radars were upgraded to give them capabilities to guide interceptors to attacking missiles and are now referred to as Upgraded Early Warning Radars (UEWRs).  Subsequently, four more UEWRs were added (in Britain, Greenland, central Alaska and Massachusetts) were added to this radar core.

The inability of the UEWRs to discriminate was acknowledged by the Government Accountability Office in 2004:

“Neither the Cobra Dane radar nor the upgraded early warning radar at Beale is capable of performing rigorous discrimination, a function acheivable only by the X-band radar. Rather, both radars will utilize common “target classification” software that enables them to classify objects as threatening or non-threatening. For example, debris would be classified as non-threatening, but objects like deployment buses and decoy replicas would be classified as threatening.”[6]

A December 2018 Government Accountability Office Report on the Cobra Dane radar indicates this situation remains unchanged today.  It states that the Cobra Dane radar can “Track” and “Classify” missile threats but cannot “Discriminate Missile Threats from Deployed Decoys” or “Determine if a Missile Threat is Successfully Intercepted.”[7]

The most fundamental reason that the UEWRs cannot contribute to discrimination is that they operate at relatively low frequencies (or equivalently, at long radar wavelengths).  The Cobra Dane operates at about 1.2 GHz (wavelength about 23 cm); the other five UEWRs operate at about 0.44 GHz (wavelength about 70 cm).[8]  These low operating frequencies limit the range resolution of these radars to 5 meters or more.  For a phased array radar, its bandwidth β is typically limited to roughly 10% of its operating frequency. The best possible range resolution ΔR is then about ΔR = c/2β, where c is the speed of light.  The UEWRs other than Cobra Dane have a bandwidth of β ≤ 30MHz.  For β = 30 Mhz, this gives ΔR ≥ 5 meters.

The range resolution is the smallest distance along the range axis (the line between the radar and the target) for which the radar can resolve separate objects (or separate features along one object.) The resolution along the other axes is typically much worse. Thus a radar with a range resolution of 5 meters or more can provide little information about the shape of a 2 meter long missile warhead or a similarly-sized decoy or other object other than that which can be gleaned from how its radar cross section varies with time. [Cobra Dane actually can provide a range resolution of about 1.1 m, but only over a very limited range of angles.  Because of its orientation Cobra Dane has never participated in a BMD intercept test.]

As the 2004 GAO report quoted above suggests, much better range resolution, and thus higher quality discrimination data, can be obtained by going to higher frequencies, such as X-Band.  For example, at X-band (~10 GHz, corresponding to a wavelength of about 3 cm), a phased-array radar can achieve a range resolution of about 0.15-0.25 meters.  With such range resolution, multiple features along a 2 meter long object (such a missile warhead) could be resolved.  Moreover, through the use of Doppler measurements, a similar or better resolution can be achieved along an axis perpendicular to the range axis, producing a 2-dimensional image of a target (and with enough time a 3-dimensional image might even be constructed).  While a capability to make such high resolution measurements would not completely solve the discrimination problem, it would clearly be a step in the right direction.

Accordingly, in 2006-2007, the MDA deployed the Sea Based X-Band (SBX) radar.  The SBX is a very large (249 m2 antenna area) phased-array X-Band radar on a self-propelled, semi-submersible sea-going platform. [9]  The SBX, which operates out of Honolulu, is optimized for long-range precision tracking and discrimination, and reportedly has a bandwidth of 1 GHz and range resolution of about 0.25m.[10]  However, the SBX was built initially as a testing asset and it has a number of serious limitations, most notably a very limited electronic scanning field of view (about ±12 degrees) that significantly limits its usefulness as an operational discrimination sensor.  (Many phased array radars have electronic scanning fields of view of about  ±60 degrees.)

Figure 2: The SBX (Image Source: MDA).

In addition, MDA operates five forward-based X-Band radars in Japan (2), Turkey, Israel and Qatar.  These TPY-2 forward-based radars are essentially the same (differing only in software and communications equipment) as the radar in each of the seven U.S. THAAD batteries.  These forward-based radars likely have the same range resolution as the SBX, but have much shorter ranges and can only view the early stages of a missile’s flight towards U.S. territory.

The LRDR will be in S-Band, which extends from 2 to 4 GHz.  The current SPY-1 radar on U.S. Aegis cruisers and destroyers also operates in in S-Band, between 3.1 and 3.5 GHz, and apparently has a bandwidth of about 300-400 MHz.[11]  It is also capable of using Doppler measurement to produce two-dimensional images. Thus, very roughly, we can expect that the LRDR will have a bandwidth about one-third and a range resolution and imaging capability correspondingly about 3 times poorer than what an X-Band version of the LRDR would have had.  This difference seems to be large enough to justify the Johns Hopkins APL paper’s statement that an X-Band version of the LRDR would have discrimination capabilities “superior” to that of the currently planned S-Band LRDR.

The LRDR: Cost at S-Band vs X-Band

MDA’s initial March 2014 LRDR Request for Information (RFI) to industry stated that it was not specifying the operating frequency band for the radar but rather was “looking for recommendations with rationale” based on tradeoffs necessary for the radar to perform its “precision tracking, discrimination and hit assessment” missions.[12]  It also raised the possibility that the radar could have a limited field of view (LFOV) phased-array antenna instead of a full field of view antenna.

According to the 2018 Johns Hopkins APL paper:

“In 2014, the MDA initiated the Long Range Discrimination Radar (LRDR) effort to identify and procure a new midcourse discrimination capability to supplement the existing BMDS.   Key characteristics of the radar include operation at S-Band (~ 3 GHz), wide instantaneous field of view to enable wide-area defense against raids, wide instantaneous bandwidth and a large suite of discrimination features to support robust midcourse discrimination, and high sensitivity to provide this discrimination capability at the long ranges required.”

This establishes two things: That the LRDR will operate at S-Band and that it will have a wide electronic scanning field of view (EFOV), here assumed to be ± 60 degrees.

Each of the two LRDR antenna faces will be populated with large number of GaN transmit/receive (T/R) modules.  For radars of this type, the T/R modules are the primary driver of a radar’s cost.

The requirement for a wide EFOV sets the maximum spacing between the T/R modules.  For an EFOV of ± 60º and a wavelength λ, the spacing between T/R modules in a square array must be 0.536λ or less in order to avoid grating lobes (essentially additional main beams).[13]  This gives an antenna area 0.278λ2 per module.  For an equilateral triangular module arrangement, the area per element is somewhat larger — 0.332λ2 per module.

For short wavelengths and large antenna faces, these module spacing limitations can lead to requirements for very large numbers of modules.  For example, the SBX’s antenna face has an active area of 249 m2.  Assuming a frequency of 9.5 GHz (λ = 3.16 cm), a square module array and an EFOV = ±60º, about 870,000 modules would have been required to fully populate the antenna array, which would have been prohibitively expensive.  In actual practice, the SBX uses a module spacing of about 2.35λ.  Together with the use of other techniques to reduce grating lobes, this spacing reduces the required number of modules to about 45,000, but at the price of a very reduced EFOV of only about ±12º.[14]

Figure 3.  The SBX Antenna Inside its Radome.  Image Source: MDA[15]

The LRDR is intended primarily for precision tracking and discrimination.  For such a radar, a standard figure of merit is its Power-Aperture-Gain (P-A-G) product. Assuming all else (noise figure, system losses, target radar cross section (RCS), etc…) is equal, an X-Band and an S-Band will obtain the same signal-to noise ratio on a target if:

PX*AX*GX = PS*AS*GS,

where PX is the average power of the X-Band radar, AX is its antenna area and GX is its antenna gain.

Since G = 4πA/λ2 and writing the antenna power as P = N*pm, where N is the number of modules and pm is the average power per module, this becomes:

(NX*pmx*AX2)/λX2 = (NS*pms*AS2)/λS2.

Assuming the average powers of the S-Band and X-Band modules are equal (as discussed below, probably not a valid assumption) and noting the antenna area for each module is proportional to λ2, we can solve for NX:

NX = NS*(λS/λ­X)2/3.

Assuming the S-Band radar operates at 3.5 GHz (λ = 8.57 cm) and the X-Band at 9.5 GHz (λ = 3.16 cm), then:

NX = 1.94*NS.

Thus the required number of X-band modules would likely be at least twice the number of S-band modules to get a radar with equal sensitivity and EFOV.  The number of modules will be quite large, as in a subsequent post I will argue that number of S-Band modules required for both faces of the LRDR may be as great as 240,000.  The ratio of modules alone suggests that the X-Band version of the radar would cost nearly twice as much as the S-Band version.  This difference could amount to a substantial amount of money as the contract to Lockheed Martin to develop, build and test the LRDR was for $784 million.

Moreover, the actual cost ratio may be significantly higher.  In particular, GaN T/R modules are a relatively new technology compared to the GaS modules used in the SBX or TPY-2 radars.  The LRDR and the Space Fence are the first very large radars to use GaN technology (at least as far as I know).With such new technology, it is likely the average power obtainable from an S-band module will be greater than that from an X-Band module, and the noise figure at S-Band could also be lower.  In addition, over wide ranges of angles, the radar cross sections of warhead-shaped targets tend to decrease as the radar frequency increases. These factors could significantly increase the number of X-Band modules required to get a sensitivity equal to a LRDR radar using S-Band modules.

Thus it seems reasonable to conclude that an X-band version of the LRDR would cost at least twice as much as the currently planned LRDR and it could cost much more.


[1] Kenneth W. O’Haver, Christopher K. Barker, G. Daniel Dockery, and James D. Huffaker, “Radar Development for Air and Missile Defense,” Johns Hopkins APL Technical Digest, Vol. 34, No. 2 (2018), pp. 140-152.  Online at: https://www.jhuapl.edu/techdigest/TD/td3402/34_02_OHaver.pdf.

[2] Missile Defense Agency, “Fiscal Year (FY) 2018 Budget Estimates,” May 15, 2017. Online at: https://www.mda.mil/global/documents/pdf/budgetfy18.pdf.

[3] A.M. Sessler, J.M. Cornwall, B. Dietz, S. Fetter, S. Frankel, R. L. Garwin, K. Gottfried, L. Gronlund, G. N. Lewis, T. A. Postol, and D. C. Wright, Countermeasures: A Technical Evaluation of the Operational Effectiveness of the Planned US National Missile Defense System, Cambridge, Massachusetts: Union of Concerned Scientists /MIT Security Studies Program, 2000, pp 35-37, 145-148. Online at: www.ucsusa.org/sites/default/files/legacy/assets/documents/nwgs/cm_all.pdf.

[4] U.S. Department of Defense, Defense Science Board, Defense Science Board Task Force Report on Science and Technology Issues of Early Intercept Ballistic Missile Defense Feasibility, Washington, D.C.: Defense Science Board, September 2011, p. 5.  Online at: http://www.dtic.mil/docs/citations/ADA552472.

[5] U.S. National Academy of Sciences, National Research Council, Committee on Assessment of Concepts and Systems for U.S. Boost-Phase Missile Defense in Comparison to Other Alternatives, Making Sense of Ballistic Missile Defense: An Assessment of Concepts and Systems for U.S. Boost-Phase Missile Defense in Comparison to Other Alternatives, Washington, D.C.: The National Academies Press, September 2012, p. 10.  Online at: www.nap.edu/catalog.php?record_id=13189.

[6] Government Accountability Office, “Missile Defense: Actions Being Taken to Address Testing Recommendations, but Updated Assessment Needed,” GAO-04-254, February 26, 2004, p. 17. Online at: https://www.gao.gov/assets/250/241487.pdf.

[7] Government Accountability Office, “Missile Defense: Air Force Report to Congress Included Information on the Capabilities, Operational Availability, and Funding Plan for Cobra Dane,” GAO-19-68, December 2018, p. 7 (Table 2).  Online at: https://www.gao.gov/assets/700/696076.pdf.

[8] For technical details about the UEWRs, see “Appendix 10: Sensors” of Laura Grego, George N. Lewis, and David Wright, Shielded From Oversight: The Disastrous US Approach to Strategic Missile Defense, Union of Concerned Scientists, July 2016.  Online at: https://www.ucsusa.org/sites/default/files/attach/2016/07/Shielded-from-Oversight-appendix-10.pdf.

[9] For details about the SBX, see “Appendix 2: The Sea Based X-band Radar,” of Laura Grego, George N. Lewis, and David Wright, Shielded From Oversight: The Disastrous US Approach to Strategic Missile Defense, Union of Concerned Scientists, July 2016.  Online at: https://www.ucsusa.org/sites/default/files/attach/2016/07/Shielded-from-Oversight-appendix-2.pdf.

[10] The SBX uses essentially the same radar transmit/receive modules as the THAAD radar (TPY-2), which has a bandwidth of 1 GHz and range resolution of 0.25 m. Philip A. Ingerwesen, William W. Camp and Alan J. Fenn, “Radar Technology for Ballistic Missile Defense,” Lincoln Laboratory Journal, Vol. 13, No. 1 (2002), pp. 109-147 (p. 141).

[11] Ingerwesen, et. al., “Radar Technology for Ballistic Missile Defense,” p. 141 says 300 MHz.  A 1999 Lincoln Laboratory briefing slide shows a “Wideband Waveform Concept for AN/SPY-1 Radar” using a 400 MHz wideband waveform constructed from ten 40 MHz bandwidth pulses frequency jumping from 3.1 to 3.5 GHz.  Eric D. Evans, “Missile Defense Technology (Can BMD Systems Work?)” Mini DTS Course, MIT Lincoln Laboratory, December 10, 1999. (40 MHz was the bandwidth of the Aegis radar when it was initially deployed.)

[12] Missile Defense Agency, “Missile Defense Agency Long Range Discrimination Radar Request for Information,” SN HQ0147-14-R-0002, March 14, 2014. See https://www.fbo.gov/?s=opportunity&mode=form&id=42f1a95465dac067ca3ee0a665adf7f7&tab=core&_cview=1

[13] See Grego, et. al., “Appendix 2,” pp. 4-5.

[14] Grego, et. al., “Appendix 2,”

[15] Online at: https://www.mda.mil/global/images/system/sbx/sbxin.jpg.

Leave a comment

12 Comments

  1. Any indication on the capability of the LRDR to counter antisimulation decoys?

    Reply
    • I think about all we can say based on the available information is that it will be better against such decoys than any of the current very large radars (except the SBX or the smaller TPY-2s). I suspect a properly done anti-simulation decoys will be very hard to discriminate, though. I have seen no evidence that the MDA has ever conducted a flight test using such decoys.

      Reply
  2. corkyboyd

     /  January 31, 2019

    What happened to the GBR-P X band radar on Kwajalein? Wasn’t that destined for the Czech Republic before the prior administration cancelled most of the GB mid course missile defense system for Europe?

    Reply
    • Good question. I haven’t heard anything about the GBR-P for years. I believe it was dismantled for refurbishing prior to being sent to Europe, but of course was never sent. So I assume it is in storage or had simply been scrapped. I doubt if it will ever return as its technology is relatively old – it uses first generation transmit/receive modules, which are much less powerful than the third or later generation modules used in the TPY-2s (and future TPY-2s, if any, will likely move to new GaN technology).

      Reply
  3. mesocyclone

     /  February 8, 2019

    The main focus of this post seems to be on the relative spatial resolution of S and X band, derived from standard theory. I wonder if other techniques may make that parameter less critical.

    One possibility would be using inverse synthetic aperture, using the motion of the warheads, to increase the effective spatial resolution, at least in one dimension, well beyond that possible by pure optics. Another could be the use of spectral signatures of the radar reflections. Who knows what else, but the point is that the improved resolution from reducing the wavelength from S to X bands may not be as important as it would have been with older techniques, before the era of massive parallel computing power.

    Reply
  4. Thanks for your comments.

    I think we have to assume the defense will make use of all of the sensor information and computer processing capabilities available to it. It is known that missile defense radars such as the X-band TPY-2 and the Aegis SPY-1 do use inverse synthetic aperture techniques to obtain small cross-range resolutions (I refer to this as Doppler processing in the post). So it is a certainty that radars such as the LRDR do also. Other techniques, such the time variation of the return from individual scatterers, will also be used. The main point here is that most, if not all, of these techniques work better as the bandwidth increases (and hence range resolution improves), and bandwidth will be significantly better at X-band than at S-band.

    However, signal strength is also very important for these techniques, and for a fixed amount of money to build a radar, you will get significantly better signal strength at S-band than at X-band.

    The most important thing in the post, and the reason I wrote it, is that we now have the people that did the classified trade studies for the LRDR admitting that a X-band would have given superior discrimination performance and that the reason S-band was chosen was to save money.

    Given that discrimination is generally recognized as the most difficult problem for above-the- atmosphere missile defenses, maybe spending the extra money would have been a good idea. Hard to say anything definitive, because we don’t know how big the cost difference would have been to build a X-band LRDR capable of obtaining a signal strength equal to an S-band version. It would almost certainly be at least twice as much and probably much more.

    Reply
  5. Peter

     /  March 7, 2019

    How did you get the cube root in N_x = N_s*(λS/λ­X)^2/3? I was expecting to see the square of the lambdas ratio.

    Reply
  6. Peter,
    I wrote out a derivation, but unfortunately when I paste it into the reply box, it loses all formatting. So I’ll just try to explain it here. If you still have a question, let me know I can try to write it out here or email it to you as a Word file.
    The key point here is that the area of each antenna is given by A = N*k*λ^2 ,
    Where k is a constant that depends on the element arrangement and the required electronic field of view. As discussed earlier in the post, for a square array with a plus or minus 60 degree electronic scan, k = 0.278. Since k will be the same for both S and X band, so we can omit it. Then we have:
    A = N*λ^2 and then A^2 = N^2*λ^4
    Substituting for Ax^2 and As^2 in the equation just above the one you cite:
    (Nx^3*λx^4)/λx^2 = (Ns^3*λs^4)/λs^2
    So then:
    Nx^3*λx^2 = Ns^3*λs^2
    Which gives: Nx = Ns*(λs/λx)^2/3.

    Reply
  7. Peter

     /  March 8, 2019

    Thanks for your answer! I see now where I made the mistake.

    If you don’t mind, one more question. How did you derive the element area as function of lambda from module spacing? It doesn’t appear to be as simple as squaring the distance.

    Reply
  8. Peter,
    No, it isn’t that simple. The problem is that as a phased array radar scans off its boresite, if the element spacing is too large, you will start to get grating lobes, which are essentially additional main beams, which causes all sorts of problems. There are techniques that can be used to suppress these grating lobes such as those used in the Sea-Based X-Band radar (this is why the different sections of the antenna in Figure 3 do not line up exactly, even so its electronic scan is limited to about plus or minus 12 degrees), but it is desirable to avoid the problem altogether. For a full scan angle of plus or minus 60 degrees, with elements on a square grid, the maximum allowable element spacing is about 0.536λ which gives an area per element of 0.287λ^2. (I see in my previous response I mistakenly said 0.278 instead of 0.287.)
    This is not a calculation I did myself, I simply looked up the answer, specifically in Theodore E. Cheston and Joe Frank, “Chapter 7: Phased Array Radar Antennas,” in Merrill I. Skolnik, Radar Handbook, 2nd ed. (1990), pp. 7-17 to 7-21.

    Reply
  9. Simon Petersen

     /  March 25, 2019

    Good article with some interesting perspectives.

    Another element in the comparison between S and X band, which you don’t mention, is attenuation of the radar signal on the two radar bands. Attenuation on X band is significantly higher than on S band.

    Reply
    • Yes, that is true. However, it is not generally a big issue for missile defense at long ranges, because most of the beam propagation is somewhat above the horizon and outside of the atmosphere. Heavy rain might be an issue though.

      Reply

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