3.1. Calculations for Possible RCSs
For C0, C1, and C2 UAVs, most dedicated counter-UAV radars use higher carrier frequencies than the L-band, typically the X-band (8–12 GHz) or the Ku/K/Ka/W bands (12–110 GHz). Shorter wavelengths generally provide better angular resolution, target discrimination, and small-target detectability. This study, however, focuses on the IEEE-defined L-band (1–2 GHz) [
20,
21,
22].
Counter-UAS sensing reviews show that many purpose-built UAV detection radars operate in the X-band and higher bands, including the K- and W-band. Frequencies above about 6 GHz are usually better suited to small, slow, low-flying targets. Lower-band radars, however, may be useful in selected architectures; for example, specialized multibeam staring radars. Measurements around 1.5 GHz also show that small-UAV returns depend strongly on scenario and can be confused with birds or other non-UAV movers, which makes geometry- and clutter-aware processing important at lower frequencies [
20,
23].
Idealized Perfect Electric Conductor (PEC) reference shapes provide a more focused first estimate of how small the RCS of UAVs and LUFB payloads may be. In this study, the RCS is reported both in square meters and in decibels relative to one square meter (dBsm). The dBsm scale is useful because radar targets span a large dynamic range and because link-budget terms are commonly handled in decibels. It also provides a compact way to compare how the RCS changes with frequency, aspect angle, polarization, and target type.
The estimates assume a free-space target in air, treated as electromagnetically isolated and not intentionally grounded. RCS values are calculated for ideal orientation: broadside, normal incidence for planar faces, and broadside presentation for cylindrical cells. The geometry is deliberately simplified, with EPS, XPS, and PCB assemblies represented as smooth planar faces.
The monostatic RCS is calculated as [
24]:
The RCS in dBsm is given by [
24]:
where σ is the RCS, A is the area, and λ is the wavelength.
The wavelength is [
24]:
where f is the frequency and c is the speed of light.
The wavelength is calculated from the chosen frequency:
f = 1.5 GHz;
c = 299,792,458 m/s;
λ = 0.19986 m.
Real UAVs and radiosondes are not flat PEC plates, and off-broadside aspects usually reduce RCS substantially. The PEC broadside plate should therefore be read as an idealized reference case, not as a strict physical upper bound.
Commercial micro-UAVs span a wide size range. Representative platforms (e.g., DJI RoboMasterTT) have characteristic dimensions on the order of 100 mm, with central fuselage dimensions about 40 mm [
25].
As noted in
Section 2.1, radiosondes such as the Meteomodem M20 can be even smaller than many commercial micro-UAVs used for comparison. In practice, aspect angle, curvature, and material losses generally reduce the RCS, and the value can change substantially with orientation.
The material estimates in this section are interpreted mainly for the 1.5 GHz L-band case. The additional 26 GHz values are included only as additional references for comparison with published mm wave UAV RCS data.
At the L-band, the examined square facets are electrically small to intermediate. At 1.5 GHz, for example, 50 × 50 mm and 100 × 100 mm plates correspond to approximately 0.25–0.50 wavelengths. In this range, a simple broadside specular plate model is not fully reliable. Induced currents are not uniform, and the return may depend strongly on edge and corner diffraction, aspect angle, polarization, and resonant current modes. For this reason, the broadside PEC plate values are used only as idealized reference estimates, not as operational RCS predictions [
26,
27,
28].
As discussed in
Section 2.1, the main parts of a modern radiosonde are usually EPS, FR-4 PCB laminate, and batteries. Metallic battery cans, such as CR123A-size cells, can dominate backscatter but are excluded from this first-order material-only estimate. Dry EPS generally has permittivity close to air, so a smooth EPS surface reflects very little at 1.5 GHz and most energy passes through it unless the block is large or contains embedded conductors. If the foam becomes wet, its effective permittivity and loss increase, and the surface can become more reflective. FR-4 is a higher-permittivity dielectric, so a bare FR-4 face reflects more than foam. In real PCBs, however, returns are often dominated by copper planes, traces, shielding, and component leads, making the response closer to that of a conductive reflector. Additional calculations were therefore made to estimate possible upper-range radiosonde RCS values.
For a non-magnetic dielectric at normal incidence, the reflection coefficient and the power reflectivity are given by [
29]:
To provide best-case, order-of-magnitude monostatic RCS values, idealized geometries are used.
Dielectric-scaled approximation equation (first-order upper bound) [
29]:
These expressions are used as a simple reference framework. The PEC plate gives the broadside specular case, dielectrics are scaled using normal-incidence power reflectivity, and the PCB is represented by an effective coherent conductive area.
Table 3 gives idealized broadside, smooth-face, monostatic RCS reference values. EPS and FR-4 values are obtained by scaling a PEC plate RCS with the normal-incidence power reflectivity |Γ|
2. The reference geometries are the previously used 50 × 50 mm and 100 × 100 mm square plates. These parameters are intended to approximate an idealized upper range for the RCS.
The material calculations in
Table 3 give very low RCS values for the radiosonde-related materials. Dry EPS produces almost no backscatter at 1.5 GHz, while PEC and FR-4 provide broadside reference limits rather than realistic target signatures. The PEC case is an optimistic broadside reference, and real PCBs may exceed the simple FR-4 estimate because of copper traces, ground planes, batteries, antennas, and other conductive components. The dielectric-scaled and PEC flat-plate values should therefore be interpreted only as order-of-magnitude material-contrast indicators. Actual UAVs and radiosonde RCSs may, however, differ substantially because of geometry, conductive parts, moisture, resonances, aspect angle, and polarization.
For the FEM analysis, the RCS of the M20 radiosonde was simulated at 1.5 GHz for multiple aspect angles using Ansys Electromagnetics 2025 R2 (Ansys, Inc., Canonsburg, PA, USA). The analysis also used a simplified electromagnetic model of the radiosonde, shown in
Figure 4.
The FEM model excludes the dry EPS casing because its low dielectric contrast at the L-band should scatter much less than the conductive elements. The model therefore concentrates on the PCB metallization, sensors, antenna, and small metallic parts. As stated previously wet, icy, or moisture-contaminated EPS may change the scattering response. However, returns are often dominated by metallic components, making the response closer to a conductive reflector. This should be examined in later sensitivity studies.
Table 4 lists the nominal material parameters assigned to the conductive components in the simplified FEM model. Copper is used for PCB metallization and sensors, while stainless steel is used for the antenna and small metallic parts. The conductivity values are representative engineering inputs, and the corresponding skin depths at 1.5 GHz and 26 GHz were calculated in Ansys Electromagnetics. Thus,
Table 4 should be read as a modeling-parameter table, not as certified material measurements of the specific radiosonde sample.
Small PCB-mounted components were omitted because their size was not expected to affect the L-band response. The FEM model was solved in Ansys Electromagnetics 2025 R2 using incident plane-wave excitation, Cartesian polarization, and a 1–2 GHz sweep in 10 MHz steps. For conductive parts, skin-depth-based refinement used the values in
Table 4, since surface currents dominate their scattering at 1.5 and 26 GHz. Mesh convergence was checked by repeating the 1.5 GHz and 26 GHz solution with refined meshes and comparing selected monostatic cross-polarized RCS values. The mesh was accepted when changes stayed below 1 dB.
Figure 5 shows six representative aspect directions.
For further, more accurate analyses the 1.5 GHz results were extracted for discussion, presented in
Table 5.
To support the later comparison with published 26–40 GHz UAV RCS measurements, the simplified M20 radiosonde FEM model was also evaluated at 26 GHz. This additional simulation is not part of the RAT-31DL L-band assessment; it provides only a common-frequency reference for comparing radiosonde-like LUFB and UAV scattering levels. The extracted 26 GHz M20 values are presented in
Table 6.
Since the radar is sensitive to cross-polarized returns, the FEM results are relevant for interpreting the radiosonde response. At the same time, the values show that this response can change strongly with target orientation. Therefore, the tabulated RCS values should be read as cross-polarized reference cases, not as one fixed RCS value for the payload.
Estimates for drones can also be calculated by using RCS signatures of drone models measured between 26 GHz and 40 GHz frequencies. Using the reported measurements of Semkin et al. (2020) [
33], the mean RCS values are presented in
Table 7.
The cross-polar channels are clearly lower and more irregular e.g., DJI Matrice 100 (SZ DJI Technology Co., Ltd., Shenzhen, China), consistent with strong polarization sensitivity and shifting scattering contributions across frequencies. These oscillations show that the mean return is frequency-selective and strongly affected by polarization and complex airframe scattering [
33].
To provide an approximate L-band magnitude for illustration only, the 26–40 GHz RCS values can be back-scaled to 1.5 GHz. Conversion is presented for both sigma proportional to f
2 and sigma proportional to f
4. In dB form, the generalized conversion is presented in Equation (7) [
24].
where f
1 is the original frequency (e.g., 26 GHz), f
2 = 1.5 GHz,
n = 2 (represents the first-order specular-like assumption), and
n = 4 (represents an electrically small or Rayleigh-type sensitivity case).
With this model, the band-averaged converted mean estimates are summarized in
Table 8.
The f
4 case lowers the estimated 1.5 GHz RCS by an additional 24.8–28.5 dB relative to the f
2 case. This shows that frequency extrapolation is one of the dominant uncertainty sources in the UAV RCS assessment.
Table 8 summarizes these RCS estimates. These converted values are illustrative only. Real UAVs contain mixed materials, and their dominant L-band scattering mechanisms may differ from those measured at 26–40 GHz.
3.2. Calculation for Possible Radar Horizon
One of the more important physical limitations of low-altitude radar detection is the radar horizon, which is determined by Earth curvature, radar antenna height, target altitude, and atmospheric refraction. For UAVs and radiosonde-type UFB payloads below a few hundred meters, radar horizon can dominate detection range regardless of transmitter power or receiver sensitivity.
In practical terms, this means that increasing radar sensitivity cannot compensate for a target that is still below the local line of sight. For LSS targets, the first question is therefore not only whether the echo is strong enough, but whether the object is geometrically exposed to the antenna at all. This is why the radar-horizon calculation is treated here as a separate limiting condition before the later detectability assessment.
UFBs can rise to 20–40 km, where horizon limits are weaker, but their launch, early ascent, descent, and landing remain affected by terrain, clutter, and low radial velocity.
This section evaluates the height–range relationship for a RAT-31DL-type L-band long-range 3D surveillance radar using the standard 4/3 Earth-radius model. The analysis focuses on low-altitude targets and separates two related but different constraints: smooth-Earth radar-horizon visibility and positive-elevation beam-axis intersection.
The radar horizon distance is approximated by equation [
34]:
where
dkm is the radar horizon distance (km),
hr is the radar antenna elevation AGL (m)
, hc is the target altitude AGL (m),
RE is the Earth radius (m), and
k is the effective Earth radius factor.
The beam-target geometric intersection distance formula by equation [
34]:
where
dθ, km is the last beam-target intersection distance (km),
hc is the target altitude AGL (m),
hr is the radar antenna elevation AGL (m), and
θ is the elevation tilt angle (°).
The calculations assume a 30 m radar antenna height and target altitudes from 60 m to 140 m AGL in 20 m steps. This altitude range generally represents typical low-altitude UAV- and UFB-relevant cases near the small civil-UAV operating ceiling. Very low flights are excluded because local terrain and clutter would dominate practical detection.
Table 9 reports the radar-horizon and beam-axis intersection ranges calculated with Equations (8) and (9).
This choice also keeps the calculation close to the altitude band where geometric effects are most critical. At these heights, even a small change in target altitude or beam elevation can noticeably shift the available range. The values therefore serve mainly to show the sensitivity of low-altitude coverage, rather than to define a fixed operational limit.
For the positive-elevation cases, the values in
Table 9 are not full detection envelopes. They represent only simplified beam-axis intersection ranges. Real coverage also depends on finite beamwidth, beam scheduling, sidelobes, terrain masking, clutter, detection thresholds, tracking logic, and integration gain.
Elevation angles from 2.5° to 20° are used as representative positive-elevation examples rather than confirmed operational RAT-31DL beam positions. This approach is therefore used to show how rapidly low-altitude beam-axis coverage decreases as elevation angle increases.
The results show that the 0° radar-horizon range increases with the square root of target altitude rather than linearly. Increasing the target altitude from 60 m to 140 m extends the theoretical smooth-Earth horizon from approximately 54.5 km to 71.3 km, or by about 16 km. However, even modest positive elevation angles sharply reduce the beam-axis intersection range for low-altitude targets. At the highest examined elevation angle, the beam-axis intersection range becomes extremely short for low-altitude targets. For example, at 20° elevation and 60 m target altitude, the calculated beam-axis intersection distance is only about 80 m. This shows that the main-beam axis reaches the 60 m altitude almost immediately after leaving the radar site. Consequently, such high positive elevation angles are not suitable for maintaining low-altitude beam-axis coverage at operationally relevant ranges in this simplified geometry. This confirms that low-altitude coverage is constrained not only by radar horizon, but also by elevation-beam geometry, as visualized in
Figure 6.
The second, more important part of the calculations focused on the effect of the elevation tilt of the antenna. The RAT-31DL radar uses electronically controlled beamforming in radar elevation, but the direction of each beam determines how far the axis of the main beam intersects the given target altitude. At positive elevation tilt, the main beam rises upwards, so it can only cover low-flying targets for a limited distance.
Figure 7 visualizes the lower and upper positive-elevation boundary cases considered in
Table 9.
The analysis shows that advanced electronic beam steering and signal processing cannot remove fundamental geometric visibility limits. In practice, a target is detectable only if the beam clearance exceeds local terrain, obstacles, and a sufficient safety margin. Terrain masking, forest cover, buildings, towers, hills, near-ground multipath fading, and unusual refraction may therefore reduce or distort the theoretical smooth-Earth coverage.
3.3. Parametric Radar-Equation Detectability Assessment
Because detailed RAT-31DL waveform, receiver, integration, loss, CFAR-threshold, and processing-gain data are not public, this section uses a parametric radar-equation analysis rather than proprietary performance claims. The analysis separates three constraints: thermal-noise-limited detection, clutter-limited detection, and geometry-limited visibility.
For a monostatic radar, the signal-to-noise ratio can be expressed as [
35]:
where P
t is the transmitted power, G
t is the transmit antenna gain, G
r is the receive antenna gain, λ is the radar wavelength, σ is the radar cross-section of the target, G
i is the integration gain or processing gain, R is the radar-to-target range, k
B is the Boltzmann constant, T
0 is the reference noise temperature, B is the receiver bandwidth, F
n is the receiver noise figure expressed as a linear factor, and L is the total system loss factor.
Equation (10) is used only to derive the normalized RCS sensitivity in
Table 10 because the data needed for absolute RAT-31DL SNR, detection range, and probability-of-detection calculations are not public. The resulting values are therefore relative engineering estimates, not operational performance predictions.
With all other parameters fixed, the maximum thermal-noise-limited detection range scales as
The relative range factor in
Table 10 is calculated using a 0 dBsm reference target. Thus, 0 dBsm corresponds to 1 m
2, and each dBsm value is first converted to a linear RCS before applying the fourth-root range law:
Therefore, the relative range factor expresses the fraction of the 0 dBsm target range obtained under otherwise identical radar-equation parameters. This fourth-root dependence is central to engineering interpretation.
Consequently, a long-instrumented range cannot be directly converted into reliable LSS target coverage.
Table 10 shows the detection-range sensitivity in connection with small-target RCSs.
3.4. Software Filtering
Signal processing is central to low-altitude LSS detection because slow UAVs and UFB payloads can fall close to the zero-Doppler clutter region. In this regime, the target return is weak because of small RCSs and is also hard to separate from stationary or slowly varying background returns. Clutter suppression, Doppler filtering, CFAR thresholding, and tracker logic therefore influence whether a low-altitude LSS target is retained or rejected after initial detection.
Moving Target Indication (MTI) suppresses stationary or near-stationary returns and preserves targets with sufficient Doppler shift [
35,
36]. This is effective against fixed ground clutter, but it can create a vulnerability for targets with very low radial velocity. A hovering UAV, a UAV moving tangentially to the radar line of sight, or a wind-drifted radiosonde payload may remain close to the clutter notch. If the processing chain is tuned mainly for conventional aircraft and strong clutter rejection, such targets may be weakened before detection or may fail to form a stable track.
The Doppler shift of a monostatic radar target is given by equation [
24,
35]:
where v
r is the radial velocity, and λ is the radar wavelength.
At 1.5 GHz, λ is 0.2 m. Consequently, even moderate physical motion can produce only a small Doppler shift when the radial component is weak.
Table 11 illustrates this sensitivity and shows why UFBs and tangentially moving UAVs can occupy the same Doppler region as residual ground clutter.
Table 11 shows that radiosonde-type LUFB payloads and tangentially moving or hovering UAVs can remain in the low-Doppler region when their radial velocity component is small. These values should not, however, be read as universal rejection thresholds or as proof that such targets are automatically undetectable.
RAT-31DL-type L-band surveillance radars are designed mainly for conventional aircraft, including fast jet targets with much larger Doppler shifts; low Doppler alone therefore does not rule out detection. For UAVs and radiosonde-type LUFB payloads, however, low Doppler can also reduce robustness when it coincides with a small RCS, low altitude, clutter coupling, and radar-specific filtering or tracker settings. Because RAT-31DL processing parameters are not public, this analysis does not assign a fixed Doppler rejection threshold. Whether slow components are preserved, reduced, or rejected depends on the radar’s PRF, coherent processing interval, Doppler-filter bank, MTI/AMTI notch characteristics, clutter-map configuration, local clutter environment, and tracker logic. Adaptive Moving Target Indication (AMTI) extends the MTI principle by using adaptive filtering and motion compensation to suppress broadened clutter spectra [
35,
36].
Although AMTI is usually discussed in connection with moving-platform radars, the same engineering trade-off appears here. Stronger clutter rejection reduces false alarms, but it can also reduce sensitivity to slow, low RCS targets. This is especially relevant for UFBs, which drift with the wind, and for UAVs whose radial velocity can be small during hovering, orbiting, or cross-range motion.
Constant False Alarm Rate (CFAR) processing adjusts the detection threshold to local noise and clutter. CA-CFAR works well in homogeneous clutter, while OS-CFAR, GO-CFAR, and SO-CFAR are generally more robust near clutter edges or in heterogeneous clutter. In low-altitude surveillance, however, reference cells may contain terrain, vegetation, discrete scatterers, birds, weather returns, or moving vehicles. In such cases, the adaptive threshold can rise and mask weak UAV or UFB echoes [
35,
37].
Low-Doppler-preserving processing, such as low-Doppler maps or zero/near-zero-Doppler channels, can help by retaining returns that conventional clutter-rejection filters might suppress [
35,
37]. Preserving these channels can improve detection of slow LSS targets, but it can also increase false alarms from residual clutter, birds, vegetation, precipitation, and other low-Doppler background sources. The processing configuration must therefore balance detection sensitivity against false alarm control, rather than simply maximize clutter suppression.
At L-band, low-altitude LSS detection is often limited by clutter rather than by receiver noise alone. Relevant clutter sources include terrain, vegetation, buildings, towers, wind turbines, vehicles, precipitation, and biological movers [
12,
20,
23]. Bird clutter is particularly important because birds can occupy altitude, speed, and RCS regimes similar to small UAVs. Multirotor UAVs may be separated by blade-related micro-Doppler components, whereas UFBs normally lack propulsion-induced micro-Doppler and may remain close to zero Doppler. Reliable classification should therefore combine RCS, Doppler, micro-Doppler, trajectory, persistence, and contextual information.
For RAT-31DL-type long-range surveillance radars, public sources describe the general L-band surveillance role but not the detailed MTI, AMTI, CFAR, clutter-map, or tracker parameters [
38]. The discussion above should therefore be read as a physically motivated processing-sensitivity analysis, not as a statement about a specific proprietary radar mode. The operational point remains important. An LSS target may be geometrically visible; however, it may remain difficult to detect or track if it falls into a suppressed Doppler region or if local clutter raises the adaptive detection threshold.
Sensor fusion can reduce these limitations by combining optical, infrared, acoustic, passive RF, mobile radar, and multistatic or networked radar data. These complementary views improve resilience when one sensor is shadowed, clutter-limited, or affected by poor data quality [
20]. In this sense, software filtering should not be treated in isolation. It is one part of a layered LSS surveillance architecture that has to coordinate radar detection, Doppler processing, classification, tracking, and multisensor correlation.