The Search Radar Equation
2.4 SURVEILLANCE WITH MULTIFUNCTION ARRAY RADAR The multifunction array radar (MFAR) can perform search as well as tracking and The multifunction array radar (MFAR) can perform search as well as tracking and
fire control functions, using one or more planar array faces. Each face may be served by an individual transmitter, or a common transmitter may be switched among faces. Allocation of radar resources in transmitted energy and time is var-ied under software control according to the defense strategy or in response to the threat and environmental conditions. In place of a fixed search volume, as de-scribed in Section 2.2, the MFAR search coverage is commonly divided into
sev-The Search Radar Equation 45 eral sectors, i = 1, 2, … m, with different values of Rmi, angle limits, and frame times tsi, and each sector is allocated some fraction of the resources. To establish requirements for the search fraction of the power-aperture product, the search ra-dar equation is applied separately to each sector, and often to more than one threat condition. For example, there may be a “normal” condition under which a major fraction of the resources is assigned to the search function, and one or more “bat-tle management” conditions requiring diversion of search resources to fire control.
2.4.1 Example of MFAR Search Sectors
A typical search allocation for the normal condition (clear air, low engagement rate) is 50% of the total resources. An example of vertical coverage sectors for a long-range surface-to-air missile (SAM) system for use against aircraft is shown in Figure 2.3. The requirements on each of m = 3 sectors are listed in Table 2.3.
Within each sector, the narrow MFAR beam performs a raster scan with beams spaced by approximately 3, the half-power beamwidth (3 = 1.4 at broadside).
The example assumes that a single array face is used, with azimuth sectors that are within the scan capability of typical array designs. The long-range and horizon sectors use a csc2 envelope, slightly modified to preserve coverage up to the maximum target altitude of the sector. The high-elevation sector is specified to provide coverage to the maximum target altitude at elevations above the long-range sector, without overlapping that coverage. The horizon search sector over-laps the long-range sector, and uses a high revisit rate to guard against
low-Long-range sector High-elevation sector
Horizon sector
Slant range in km
Altitudeinkm
Figure 2.3 Example of vertical coverage sectors for MFAR air defense radar.
altitude threats that might be masked by terrain until they pop up at relatively short range. Its angular extent is minimized to avoid an excessive time allocation.
Each dwell is assumed to use three pulses, providing frequency diversity or alter-natively supporting moving-target indication (MTI).
2.4.2 Advantages and Disadvantages of MFAR Search
An advantage of the MFAR search mode is that tracks can be initiated using vali-dation and multiple track-initiation dwells immediately following the first detec-tion, even when that detection results from a low signal-to-noise ratio with result-ing low sresult-ingle-scan Pd. The range of track initiation is that for which the cumula-tive probability of detection Pc, rather than single-scan Pd, reaches the desired level [7]. This rapid-validation approach is a form of sequential detection [8].
Disadvantages in MFAR search are scan loss and the need to share radar re-sources among the search sectors, including validation dwells and other radar functions. A further disadvantage is that the frequency band must be chosen to accommodate both search and tracking functions, and in general is too high for optimum search and too low for optimum tracking. The sharing of resources is best expressed by applying (2.7) separately to each search sector, using only the fraction of average power allocated to that sector. Similarly, (2.8) will yield the
Table 2.3 Example of MFAR Search Sectors
Requirement Unit Sector
Long-Range High-Elevation Horizon
Maximum range Rm i km 170 89 85
Maximum target altitude Hm i km 30 30 3
Maximum range Rh i at Hm i km 85 42 4
Maximum elevation 2 i deg 20 45 45
Minimum elevation 0 i deg 0 20 0
Azimuth sector Am i deg 90 120 120
Effective elevation sector m deg 14.6 10.2 3.7
Solid angle of sector s i steradian 0.26 0.37 0.13
Frame time ts i s 10 5 1
Dwells per s 38 108 196
Pulses per dwell n 3 3 3
Average dwell time ntr i ms 4.2 2.5 0.31
Sector time fraction TF i 0.159 0.266 0.060
Total search time fraction TF 0.485
The Search Radar Equation 47 required product of receiving aperture and the average power that must be allocat-ed to the sector.
MFAR design normally holds the peak power constant, but permits adjust-ment of transmitted energy per beam through changes in pulsewidth. The same aperture is used for all sectors, but its effective value can be varied by defocusing, to reduce the allocated search time at the expense of increased energy per beam.
MFAR beam broadening and pattern losses L and Lcsc are calculated in the same way as for a scanning-beam 3-D radar. For the coverage shown in Figure 2.3 it can be assumed that Lpe = Lp = 1.24 dB for the long-range and high-altitude sec-tors, because the detection envelope of the narrow scanning beam can be closely matched to the required coverage. For the low-altitude sector, Lpe 1.5 = 1.76 dB because the beamwidth is approximately equal to the sector width.
2.4.3 Example of Search Radar Equation for MFAR
As an example of using the search radar equation, assume that the terms common to the three regions shown in Figure 2.3 are as follows:
Target cross section = 1.0 m2; Detectability factor D0(1) = 15 dB;
Search loss Ls = 20 dB;
Array aperture A = 1.6 m2.
The system temperature, search loss, and other parameters vary as shown in Table 2.4. Other values in the table are obtained from (2.8) and Table 2.3. The example array aperture assumes an X-band radar with broadside beamwidth of 1.4, a broadening factor given by the secant of the off-broadside angle, and use of a fo-cused beam throughout the coverage.
Note that the average powers given by application of (2.8) are averaged over the entire operating time of the radar. The power averaged over a single sector is given by Pav i/TF i for sector i, and that averaged over the search time fraction is Pav/TF = 11.5 kW. A transmitter rated for 10 kW average power would be ade-quate, provided that individual dwells up to 25.3 kW for 2 ms could be support-ed for the horizon sector.
In this example, the fact that the high-elevation sector consumes the largest time fraction while using the least average power suggests that it would be appro-priate to defocus the beamwidths in that sector. Table 2.5 shows the result of in-creasing both beamwidths by a factor of two. The time allocated for search is re-duced, average power in the three search sectors is more uniform, but over the reduced search time fraction it averages twice that for the original allocations. Use of the search radar equation, however, makes this type of trade-off a simple exer-cise.