It appears likely that the Ground-Based Midcourse (GMD) Defense’s new Long Range Discrimination Radar (LRDR) will operate at S-band instead of at X-band. This raises the question of whether the better range resolution that would have been available at X-band is being sacrificed in order to keep the initial cost of the LRDR down to about $1 billion. Or is there some other reason?
Although the current Ground-Based Midcourse (GMD) national missile defense system nominally provides coverage of all 50 states from limited intercontinental ballistic missile attack, it is well known that the system is severely lacking in its discrimination capabilities. In particular, the primary sensor infrastructure (aside from the infrared seekers on interceptor kill vehicles) for the GMD system consists of five radars — seven within a few years — in the United States, Greenland and Britain that were originally built for ballistic missile early warning purposes. These radars date to the 1970s-1980s, but have subsequently received (or will soon receive) relatively minor upgrades that allow them to detect and track incoming missiles as part of the GMD system. However, the relatively low operating frequency of these radars (about 440 MHz, corresponding to a wavelength of about 0.68 m) limits their bandwidth, resulting in a minimum range resolution of no less than about 5 meters. This low resolution limits these radars to at best being able to only classify objects as potentially threatening (warheads, decoys, booster stages, etc…) or non-threatening (small pieces of debris).
These large early warning radars are supported by forward-deployed TPY-2 X-band radars (in Japan and Turkey) and by S-Band Aegis radars on U.S. Navy ships, which have superior range resolution capabilities, but have limited range and can only observe a North Korean or Iranian missile in the early part of its trajectory.
The only very large radar in the GMD system capable of making high resolution measurements is the Sea-Based X-Band (SBX) radar. This radar, with a 17.8 m diameter antenna, is capable of tracking missile targets at ranges of thousands of kilometers with a theoretical range resolution as low as 0.15 meters, although in actual practice this is probably more like 0.2-0.25 meters. However, the SBX was built primarily for testing purposes and as such has a number of limitations that severely impair its usefulness as an operational radar in the GMD system. Most importantly, it has a very limited electronic field of view (FOV). The electronic FOV is the range of angles over which the radar beam can be steered almost instantaneously, without having to move the radar antenna. A single radar face of a typical phased array radar, such as the U.S. early warning radars, has an electronic FOV of about 120 degrees, while the electronic FOV for the SBX is only about 25 degrees. The small electronic FOV seriously limits the capability of the SBX to deal with multiple targets that are separated by large angles. In addition, the SBX was not built to have the reliability that would be required of an operational system. These deficiencies of the SBX are highlighted in a recent Los Angeles Times article.
In March 2014, at its FY 2015 budget release press conference, the MDA announced that was starting a program to design and deploy a new Long-Range Discrimination Radar (LRDR) for the GMD system. Such a deployment was required by the FY 2014 Defense Authorization Bill of December 2013, which stated that: “The Director of the Missile Defense Agency shall deploy a long-range discriminating radar against long-range ballistic missile threats from the Democratic People’s Republic of Korea. Such radar shall be located at a location optimized to support the defense of the homeland of the United States.” The MDA’s announcement was also consistent with repeated statements by the MDA that improving the discrimination capabilities of the GMD system was one of its top priorities. For example, in July 2013 when MDA Director Admiral Syring was asked in a congressional hearing where he would spend his “next dollars” in order to improve the GMD system, he stated that “I would spend our next dollar on discriminating sensors, meaning radars, big radars west and east, to give us the capability of where I see the threat going in the next five to ten years.”
The LRDR is to be deployed in 2020 in Alaska and is expected to cost about one billion dollars. MDA plans to award a contract for the radar by the end of the current fiscal year. The LRDR will most likely be built at Clear Air Force Station in central Alaska (currently home to a PAVE PAWS early warning radar that is in the process of being incorporated into the GMD system) or at Eareckson Air Station on Shemya Island at the western end of the Aleutian island chain (currently home to the large Cobra Dane radar which has already been incorporated into the GMD system). Once the LRDR is operational, the SBX would most likely be moved to an East Coast location — where it would still suffer from the same limitations it has now.
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. 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 (FFOV) antenna, and that in addition to its electronic-scanning capability, its antenna could be mechanically steered in azimuth or elevation or both (which would be necessary if a LFOV design was chosen — see below for a discussion of FFOV and LFOV radars). It also stated that MDA was interested in “software/hardware reuse and economy-of-scale benefits from existing programs leveraging the current and near-term production base.
An August 2014 update to the LRDR RFI provided additional insight into MDA’s plans for the radar. It asked bidders for the LRDR to provide price estimates for three different LRDR configurations. Significantly, all three of these configurations would have the radar operating in the S-band of radar frequencies (2-4 GHz). One radar configuration would have a single antenna face. Another configuration would have two antenna faces. A third configuration would also have two antenna faces, but only one face would be populated with the modules that transmit and receive the radar energy (T/R modules). The second, inactive face could subsequently be populated with modules if such an upgrade was later determined to be needed. A subsequent RFI update stated that “Both radar faces will be designed to accommodate the same antenna hardware necessary to achieve the same future growth sensitivity.”
At a February 2, 2015 Pentagon press conference on MDA’s FY 2016 budget, Admiral Syring stated that “we’re asking for a two phase capability” for the LRDR.
Phased array radars typically are limited to maximum electronic scan angles of roughly ± 60 degrees because of losses associated with larger scan angles. Phased arrays with maximum scan angles of roughly ±60 degrees are referred to as full field-of-view (FFOV) radars. Such radars have antenna modules spacing of less than about 0.6 λ, where λ is the radar wavelength. For phased-array antennas with larger module spacings, another limitation on the maximum scan angle arises from the need to avoid grating lobes, which are essentially additional main radar beams. Phased array radars with significantly reduced scan angles due to wide module spacings are referred to as limited field of view (LFOV) radars.
For radars which have modules arranged on a square array, such as the SBX, a module spacing of 0.536 λ or less is needed to obtain a ±60 degrees scan angle without producing grating lobes. This corresponds to a maximum allowable antenna area of 0.287λ2 per module. For an antenna with modules arranged on an equilateral triangular array, such as the U.S. early warning radars, this maximum permissible antenna area is 0.332λ2.
For example, a PAVE PAWS early warning radar has 2677 elements arranged in equilateral triangular array with an area of 384 m2. Of these elements, 1792 are actual transmit/receive modules, and the other 685 are dummy elements. The area per element is then 384/2677 = 0.143 m2 = 0.310 λ2 at a wavelength of λ= 0.68 m. This less than the maximum permitted area of 0.332λ2 m2 for a ± 60 degree scan, and thus the PAVE PAWS can achieve a full ±60 degrees scan angle, or even a little more, without producing grating lobes.
On the other hand, the SBX has 45,264 modules on a square array with an area 249 m2. This corresponds to an area per module of 55.0 cm2 and a spacing between of modules of 7.42 cm = 2.35λ assuming a frequency of 9.5 GHz. For radars with widely spaced elements on a square array, the maximum scan angle θM is approximately given by sinθM = ±(0.5λ/d), where d is the module spacing. With the SBX’s module spacing of d = 2.35λ, the maximum electronic scan angle is ±12.3 degrees. Thus the SBX is definitely a LFOV radar.
To get a FFOV of ±60 degrees on the same size antenna, the SBX would have required about (2.35/0.536)2 = 19.2 times more modules, or a total of 45,264 x 19.2 = 869,000 modules. Not only would this have been prohibitively expensive, but it likely would have significantly delayed the deployment of the SBX by years unless costly new module production lines were opened. In addition, it would also have resulted in a radar with much greater capabilities than could ever be used in a missile defense role, given the curvature of the earth and the maximum altitude of ballistic missile trajectories. Alternatively, the SBX could have designed to use the same 45,264 modules but with a 0.536λ module spacing, resulting in an FFOV antenna, but with a diameter of only about 4.1 m. This would have reduced its tracking range, taken to be proportional to the 4th root of the product of its power x aperture area x gain (P-A-G), by a factor of (1 x 19.2 x 19.2)0.25 = 4.4.
For phased arrays using antennas populated with T/R modules, the modules are generally the biggest cost driver of the radar. The above paragraph illustrates how the SBX design, for a given number of modules, trades off its electronic field of view in order to get a larger antenna aperture. The larger antenna gives both a narrower beamwidth (which improves tracking accuracy) and a greater tracking range (or equivalently a higher signal-to noise ratio at a given range) at a price of a limited electronic FOV. This decreased electronic FOV may not be a serious problem for a radar intended for testing, but can be a serious liability for an operational missile defense radar.
Which brings us to the LRDR. I was initially quite surprised to see that the MDA was requesting LRDR price estimates only at S-band, since I was expecting it to be at X-band. Since range resolution is roughly inversely proportional to bandwidth and bandwidth is roughly proportional to frequency, it would be expected that an X-band radar (about 9-10 Ghz) would have a range resolution roughly three times better than an S-band radar (2-4 GHz). (Frequencies much higher than X-band are precluded by atmospheric effects). Thus while an X-band radar might achieve a range resolution of 15-25 cm, an S-band radar might achieve only 50-100 cm, depending on the choice of frequency with S-band. Moreover, the newer U.S. missile defense radars (the TPY-2 and the SBX) already operate at X-band.
However, if the LRDR is strongly cost-constrained, than a large FFOV X-band radar may not be achievable. An X-band FFOV radar with the same range (that is, with the same P-A-G) as the SBX would have roughly 237,000 modules on an antenna with a diameter of about 10.5 meters. (This assumes the X-band modules are arranged as the same triangular array as on a TPY-2 radar antenna and have an average power 60% greater than the modules on the SBX.) It is far from clear that such a radar could be built for one billion dollars. As a point of comparison, a current-production TPY-2 X-band radar, with 25,344 modules, costs about $180 million with the antenna equipment unit alone costing about $140 million. Moreover, to deploy such a radar by 2020 without completely disrupting TPY-2 production would likely require a new module production line. Thus unless the LRDR’s P-A-G is much less than that of the SBX, it may not be possible to build it for $1 billion at X-band if it is a FFOV radar.
In this context, it is useful to compare the National Academy of Sciences (NAS) Report’s proposed “stacked TPY-2” radar proposal. This radar, which the NAS Report refers to as a GBX, has an antenna consisting of two TPY-2 antennas stacked one on top of the other, with 50,688 X-band modules. While it would essentially be a FFOV radar, it would only have about 1% of the power-aperture-gain product of the SBX, although the NAS Panel argues that is sufficient for the discrimination mission. The NAS Report estimates that it would costs between $0.8 and $1.0 billion to develop the GBX, and another $1.6 billion to buy five GBXs. Thus the cost of buying a only single GBX would be somewhat over $1 billion. If the NAS cost estimates are correct, this would suggest that such a stacked TPY-2 would be about the largest FFOV X-band radar that could be bought for $1 billion. For comparison, the NAS estimated the cost of developing and the building SBX to be about $1.4 billion, with another $0.3 billion subsequently spent on radar enhancements. (However, note that the cost of buying and modifying the SBX ocean-going platform for the SBX was itself nearly $0.25 billion, which is included in the above figure.)
Thus if cost is a key driver of the radar’s performance, and a power-aperture-gain product greater than that of a stacked TPY-2 is desired, then it may be necessary to go to a lower frequency or a LFOV antenna, or both. Assume an S-band frequency one third that of X-Band (say 3.17 GHz vs 9.5 GHz) and a FFOV antenna. In this case, for a fixed number of modules, the S-band radar will have an aperture nine times larger than the X-band radar, with about the same gain and beamwidth. All else being equal, the S-band radar would have a tracking range about 90.25 = 1.73 times greater than the X-band radar, or equivalently it would obtain a signal-to-noise ratio nine times greater at a given range. The actual advantage of the S-band radar might be considerably greater than this since the S-band modules are likely to have higher average powers than X-band modules available at the same time, and because the overall radar cross sections of warhead-shaped targets tend to decrease with increasing frequency. These advantages seem likely to overwhelm the additional cost due to the larger S-band antenna size, at least for a fixed, land-based radar.
A choice of S-band could also be consistent with the LRDR RFI’s stated interest in “leveraging the current and near-term production base.” With a 2020 deployment time frame, the LRDR could potentially use the same S-band modules planned for the missile defense antenna of the Navy’s new Aegis Air and Missile Defense Radar (AMDR). The first AMDR-equipped Aegis destroyer is scheduled to be procured in FY 2016 for deployment in about 2023. The S-band part of the AMDR will use new GaN modules that give greater power with less heat dissipation than current GaAs modules. The timing of LRDR and AMDR radars would be consistent with the first batch of the new S-band modules going to the LRDR (and possibly the Space Fence).
To get a sense of the range of possibilities, it is interesting to look at some possible S-band radar configurations if the LRDR was required to have the same P-A-G as the SBX. If we assume the S-band modules have twice the average power of the current X-band modules (a complete guess) and a FFOV design with modules arranged on an equilateral triangular array with the same d/λ ratio as the X-Band TPY-2 antenna, then the required antenna would have about 90,500 modules on a diameter of about 19.4 m. (Compare to the 45,264 modules on a 17.8 m diameter for the SBX.)
The LRDR RFI’s explicit mention of a possible LFOV design for the LRDR raises the possibility that the number of modules could be reduced further, although presumably such an LRDR’s electronic FOV would be much wider than that of the SBX. Consider a design with a ± 30 degrees electronic FOV (with the modules on a square array). To have the same P-A-G as the SBX, such a radar would have about 46,200 S-Band modules on a diameter of 23 m. If the design included a second initially unpopulated face, the angular coverage could subsequently be doubled while keeping the initial cost down.
All of the above designs seem likely to exceed $1 billion in cost, suggesting that the LRDR might be built with a P-A-G significantly less than the SBX. Since there is roughly a factor of 100 difference in P-A-G between the SBX and NAS Report’s proposed stacked TPY-2, there is a lot of room for intermediate-sized designs.
While the discussion above is largely speculative, the seeming choice of S-band for the LRDR indicates that achieving the best possible range resolution is not the top priority for the LRDR design. Perhaps the MDA has decided that the range resolution achievable at S-band is adequate for discrimination given the perceived threat. Such a conclusion might be based in part on observations of tests. This would be a surprising conclusion, given that recent Defense Science Board and National Academy of Sciences reports have concluded that discrimination is still an unsolved problem, the same conclusion reached by outside analysts since at least the 1960s, and that it is unlikely that tests have been conducted against anything resembling the full range of possible countermeasures.
Perhaps there is some other reason for preferring S-band over X-band. However, if it a matter of a perceived need to hold the cost of the radar that is driving the frequency choice for the radar, the MDA may be settling for a less-than-optimal discrimination radar.
 The exception being the Cobra Dane radar on Shemya Island in the Aleutians, which was primarily built for gathering intelligence on Soviet ballistic missile tests.
 The radar in Clear, Alaska was not completed until about 2000. However, this radar was built by disassembling a PAVE PAWS radar in Texas that had been deactivated in the 1980s and the reconstructing it in Alaska.
 As originally built, these radars had tracking bandwidths of between 1 and 10 MHz (see my post of April 12, 2012) which would correspond to range resolutions of between 15 and 150 meters. It seems likely that these bandwidths were increased as part of the upgrades involved in incorporating them into the GMD system. However, this increase is limited by the total span of frequencies that the radars can operate over, which is 30 MHz (this span was not changed by the GMD upgrades). This would limit their maximum bandwidth to 30 MHz, corresponding to a range resolution of 5 m.
 The Cobra Dane radar is an exception to the above discussion. It operates at a higher frequency (about 1.3 GHz) than the other radars and has a minimum range resolution of about 1.14 m. (see this post of April 12, 2012 ) However, this high resolution is obtained only within 22.5 degrees of the antenna’s boresite. As noted in the text, Cobra Dane is poorly oriented for observing North Korean missiles, and a missile launched from North Korea towards the U.S. West Coast will never enter the radar’s high resolution part of its field of view.
 U.S. Department of Defense, “Missile Defense Agency Officials Hold a News Briefing on the Missile Defense Agency’s FY 2015 Budget,” March 4, 2014.
 U.S. Congress, National Defense Authorization Act for Fiscal Year 2014, Legislative Text and Joint Explanatory Statement to Accompany H.R. 3304, Public Law 113-66, Section 235, December 2013.
 Hearing of the Defense Subcommittee of the Senate Appropriations Committee, July 17, 2013.
 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
 See the first letter under DRFP Documents, August 8, 2014 at the URL in note 4.
 See round 10 questions and answers at the URL in note 4.
 For the discussion in this paragraph, see section 3.3 of G. Richard Curry, Radar System Performance Modeling, 2nd ed. (Boston, Mass.: Artech House, 2005).
 Theodore C. Cheston and Joe Frank, “Phased Array Radar Antennas,” in Merrill Skolnik, ed., Radar Handbook, 2nd ed. (New York: McGraw-Hill, 1990), p. 7.21.
 Curry, page 33. Curry refers to this as the “acceptable element spacing.”