Low-altitude Signal Processing

Signal processing for unmanned aerial vehicle (UAV) placement, active aerial search, and reliable low-altitude radio mapping.

Why Low-altitude Signal Processing?

Low-altitude wireless systems operate in a difficult middle ground. They are not static like terrestrial cellular networks, and they are not as predictable as satellite links. Unmanned aerial vehicles (UAVs) move in three dimensions (3D), buildings block line-of-sight (LOS) paths, terrestrial base-station beams are tilted for ground users, and many cells may become simultaneously visible in the air. LOS means that the direct propagation path is not blocked; non-line-of-sight (NLOS) means that it is blocked by buildings, terrain, or other scatterers.

Low-altitude signal processing studies the algorithms that make this environment usable: how to find LOS relay positions, how to search without knowing user locations, how to estimate local channel maps while flying, and how to construct per-cell and per-beam radio maps from fifth-generation (5G) synchronization signals.

Our research forms a useful toolbox for the low-altitude economy: geometry-aware placement, active search under unknown user locations, local channel-map estimation, and physical-layer measurement for aerial radio maps.

Low-altitude Scenarios at a Glance

Figure 1. Two representative low-altitude signal-processing scenarios. The left panel, from the 3D urban UAV relay-placement work [1], illustrates how a UAV can move in 3D to escape LOS, obstructed-LOS, and NLOS regions created by buildings and vegetation. The right panel, from the unknown-location active-search work [3], shows a harder setting where the UAV must serve or sense users whose locations and local propagation environment are initially unknown while also maintaining a BS backhaul link.

Figure 1 summarizes the two low-altitude scenarios that motivate this page. In the first scenario, a UAV relay exploits 3D mobility to find a position where the air-to-ground channel avoids building blockage and has useful LOS quality. In the second scenario, the challenge is more exploratory: the UAV must provide sensing or communication service to users at unknown locations, maintain a backhaul link to the BS, and infer the local propagation environment through measurements. Together, these examples show why low-altitude signal processing is both a placement problem and a measurement problem: the UAV must decide where to fly while simultaneously learning which links are reliable.

Problem Statement: Two Core Technical Problems

Many low-altitude problems can be written as geometry-constrained estimation or optimization problems:

x^\star = \arg\max_{x\in\mathcal{D}_{\mathrm{LOS}}} F(g_0(x),g_1(x),\ldots,g_K(x)),

where \(x\) is the UAV position, \(\mathcal{D}_{\mathrm{LOS}}\) is the feasible LOS region, \(g_k(x)\) is the channel gain from the UAV to terminal \(k\), and \(F(\cdot)\) is a communication, sensing, or relaying objective. Channel gain measures how much signal power remains after propagation.

Core problem 1: geometry-aware UAV placement under blockage. The UAV must find a position that gives useful LOS links even though buildings, trees, and terrain create irregular NLOS regions. A brute-force 3D search is too expensive for a flying platform, so the technical question is how to exploit deterministic LOS structure to reduce the search space while retaining optimality or near-optimality guarantees.

Core problem 2: active measurement under unknown users and unknown channels. In many low-altitude sensing and communication tasks, user locations, terrain details, and propagation models are not available in advance. The UAV must therefore learn channel gains, gradients, and link feasibility while it is flying, then use those measurements to update its trajectory and resource-allocation decisions.

When the user locations or propagation model are unknown, the UAV must also learn while moving. A useful abstraction is an equipotential surface,

\mathcal{S}=\{x: F(g(x))=f_0(g_0(x))-F_u(g_u(x),p(x))=0\},

where \(f_0(g_0(x))\) represents the backhaul objective between the UAV and base station (BS), \(F_u(g_u(x),p(x))\) represents the user-side service objective under resource allocation \(p(x)\), and \(g_u(x)\) collects the UAV-user channel gains. A BS is a fixed network node serving users. The surface \(\mathcal{S}\) balances the backhaul link and the service links, so it is a natural place to search for a useful UAV service position.

For low-altitude radio mapping from 5G signals, the received waveform is a superposition of synchronization signal blocks (SSBs) from many BSs and beams. An SSB is a 5G reference block used for cell discovery, beam identification, and channel measurement. The signal-processing task is to separate strong and weak SSB components well enough to produce a trusted radio map rather than only detecting the strongest cell.

Figure 2. Active search on an equipotential surface for users at unknown locations [3]. Panel (a) shows a search trajectory over a non-full-LOS pattern. Panel (b) shows the perturbation-based search geometry: in Phase 1 the UAV descends on the surface to improve the balanced objective, while in Phase 2 it follows a constant-backhaul curve to recover LOS opportunities after entering an NLOS region.

From Aerial Search to Radio Maps

Step 1: Use LOS geometry to reduce the search space

The UAV-placement papers exploit two structural properties of LOS regions. Upward invariance says that if a UAV has LOS to a user, increasing altitude preserves the LOS condition under broad terrain assumptions. Colinear invariance says that moving away from the user along the same ray can preserve the same obstruction state. These properties turn an otherwise expensive 3D search into a structured search over a plane, a bounded 2D area, or an equipotential surface.

Step 2: Learn local channels while searching

When user locations and channel models are unavailable, the UAV cannot simply optimize from a precomputed map. The unknown-location paper [3] constructs local channel maps from measurements collected along small spiral trajectories. The locally fitted model provides both the channel gain and its spatial gradient, which are needed to keep the UAV near the equipotential surface and choose search directions.

Step 3: Convert measurements into deployment knowledge

The output may be a UAV relay position, a sensing trajectory, a local channel map, or a low-altitude radio map. For 5G radio mapping, physical-layer processing extracts per-cell and per-beam measurements from raw synchronization signals, and these measurements are then converted into power and signal-to-interference-and-noise ratio (SINR) maps. SINR compares desired signal power against interference plus noise.

Theoretical Foundations: Geometry and Equipotential Search

References [1]-[4] in this section refer to the works listed under Ours in the suggested reading.

1. Deterministic LOS structure gives global search guarantees

The 3D urban UAV relay-placement paper [1] does not rely on a probabilistic LOS model. It models propagation regions through deterministic obstruction segments and uses an angular coordinate transform to reduce the 3D placement problem to a 2D proxy search. Under Type-I and Type-II objective functions used for outage minimization and relay-capacity maximization, the proxy cost has enough monotonicity and quasiconvexity structure for the proposed trajectory to converge to the globally optimal 3D UAV position in finite time. The worst-case spatial search length is linear in the target-area scale, while naive exhaustive 3D search scales cubically with spatial resolution.

The geography-aware LOS relaying paper [2] extends this idea to two ground terminals in deep shadow. On the middle-perpendicular plane between the two users, the double-LOS pattern has an ordered structure: if a point is double-LOS, then points vertically above it are also double-LOS; if a point is non-double-LOS, then points vertically below it are also non-double-LOS. This leads to a dynamic trajectory that descends in double-LOS regions and follows circular arcs in non-double-LOS regions. The paper proves global optimality on that 2D plane, with trajectory length bounded by \(2(H_0-H_{\min})+R_0\), where \(H_0\) and \(R_0\) are the initial altitude and initial search radius, and \(H_{\min}\) is the minimum allowed UAV altitude.

2. Bounded 2D search is enough for 3D two-user placement

For the full 3D two-user problem, [2] shows that once an initial double-LOS point \(p_0\) is known, the global optimum must lie in the cap

\mathcal{B}(p_0)=\{p: d_0(p)\le d_0(p_0)\},\qquad d_0(p)=\max\{d_1(p),d_2(p)\},

where \(d_i(p)\) is the UAV distance to user \(i\). Colinear invariance then maps much of this 3D cap to LOS tests on the middle-perpendicular plane and the minimum-altitude horizontal plane. For double-ray and double-stripe LOS patterns, the paper derives closed-form candidate positions from the endpoints of LOS segments. With vertically spaced search lines, the resulting solution has an \(O(\Delta)\) distance gap to the global optimum, where \(\Delta\) is the line spacing, and the total trajectory length scales as \(O(1/\Delta)\). This is the main theoretical reason the algorithm can trade flight distance for certified placement accuracy.

3. Equipotential surfaces turn unknown-location search into constrained dynamics

In the unknown-location paper [3], the UAV must balance a BS backhaul link against communication or sensing service to a cluster of users whose locations are private or unavailable. For a common balancing objective \(f_k(g_k,p_k)=\log_2(1+p_k g_k)\), the paper gives a sufficient condition for the existence of an equipotential surface and shows that, under a log-distance channel model, this surface is a sphere whose center depends on the BS location, the user distribution, and the total power budget.

Even when the surface is not known analytically, the UAV can track it locally. A first-order expansion

F(g(x))\approx F(g(c_0))+\nabla F(g(c_0))^\mathsf{T}G(c_0)(x-c_0)

gives a closed-form local correction direction toward the surface. Here \(c_0\) is the current UAV position and \(G(c_0)\) collects the spatial gradients of the channel gains. Once on the surface, the perturbation analysis in [3] gives an ordinary differential equation (ODE) for the UAV motion that preserves the surface constraint while choosing one of two search-plane normals: one for descending in LOS regions and one for following a constant-backhaul curve in NLOS regions.

4. Spiral measurements have an MSE-optimal design rule

The local channel model in [3] is a first-order polynomial,

\hat g(x)=\hat\alpha+\hat\beta^\mathsf{T}(x-c_0),

where \(\hat\alpha\) estimates the local channel gain and \(\hat\beta\) estimates its spatial gradient. If \(M\) measurements are collected within radius \(r_1\), Theorem 1 shows that the variance of the least-squares estimator is minimized when the measurement points are symmetrically and evenly distributed around \(c_0\). The resulting variance lower bound contains a gain-estimation term proportional to \(1/M\) and a gradient-estimation term proportional to \(1/(M r_1^2)\).

Spiral measurement patterns for local channel estimation

Spiral measurement pattern. Two feasible spiral trajectories for collecting local channel measurements around the center \(c_0\) while the UAV advances along direction \(s\) [3]. The blue points indicate symmetric measurement locations used for least-squares channel-gradient estimation, and the trajectory scale is controlled by the measurement radius \(r_1\). These patterns realize the variance-minimizing geometry required by Theorem 1 while remaining flyable as a continuous UAV path.

Theorem 2 then gives the mean squared error (MSE) trade-off for estimating \(\hat g(x)\) at a point \(r_0\) away from \(c_0\):

\mathbb{E}\{(\hat g(x)-g(x))^2\} \lesssim \frac{\sigma^2}{M}\left(1+\frac{3r_0^2}{r_1^2}\right) +\frac{L_g^2}{4}(r_1^2+r_0^2)^2 .

Here \(\sigma^2\) is the measurement-noise variance and \(L_g\) measures the local curvature of the channel map. A larger spiral radius reduces gradient-estimation variance, but too large a radius increases model-bias error because a first-order model no longer matches the curved propagation field. This is the technical basis for the optimal spiral radius used in the search trajectory.

What Performance Advantage Do We Get?

The bracketed references in this section refer to Ours in the suggested reading.

Figure 3. Field-measured low-altitude radio maps from the 5G synchronization-signal measurement paper [4]. The first three panels show received-power maps for representative physical cell identities (PCIs) 45, 47, and 559 at 150 m altitude. PCI is the physical cell identity used by 5G receivers to distinguish cells. The last panel combines detectable cells into an SINR radio map with four link-quality regions: no coverage below -5 dB, low-rate coverage from -5 to 0 dB, medium-rate coverage from 0 to 10 dB, and high-rate coverage above 10 dB.

Based on our real measurements, the power maps show that low-altitude coverage is not a smooth distance-decay field. These irregular regions are consistent with reflected and sidelobe-dominated coverage from terrestrial BSs, whose antennas are designed primarily for ground users rather than aerial receivers. The SINR map is more important for communication performance than power alone. Even when strong power is visible over much of the area, interference from overlapping cells can keep SINR below the high-rate region. The field results in [4] report wide low-rate coverage and medium-rate coverage near main reflection regions, but only limited high-SINR patches. This explains why low-altitude operation needs both measurement-grade radio maps and interference-aware planning: a UAV may hear many BSs clearly, yet still have a poor high-rate link because the strongest reflected components overlap in time, frequency, and space.

Baesd on our results, the reported advantages are complementary:

Scenario	What the method uses	Reported advantage
3D urban UAV relay placement [1]	Deterministic obstruction structure and angular 2D proxy search	Global optimality under the paper's objective classes with linear spatial search length; simulations over Washington DC terrain show strong gains over probabilistic LOS baselines.
Geography-aware LOS relaying [2]	Upward/colinear LOS invariance and bounded 2D search	Above 99% optimality in moderate-density real-city maps; above 96% to 98% of exhaustive 3D performance in denser maps with kilometer-scale search trajectories.
Active search without user locations [3]	Equipotential-surface dynamics plus MSE-designed spiral measurements	Over 95% of exhaustive 3D-search performance with about a 3 km search trajectory, without prior user locations, channel parameters, or terrain model.
Low-altitude 5G radio mapping [4]	Successive waveform reconstruction and multi-burst synchronization-signal processing	Detection and estimation of synchronization signals down to -30 dB SINR in simulations; 150 m field tests produce per-cell and per-beam maps for more than ten overlapping BSs.

These values are tied to the experimental scenarios and baselines in the cited papers and depend on terrain, UAV trajectory limits, measurement bandwidth, interference density, and radio-map resolution.

Why This Research Matters

Low-altitude signal processing makes aerial communication and sensing physically actionable. It connects where a UAV can fly, what signals it can measure, and how those measurements can support reliable links.

For theoretical research, low-altitude signal processing studies geometry-constrained optimization, active sensing, constrained dynamical systems, least-squares design, MSE analysis, and radio-map inference under mobility and blockage. The papers in this folder show how physical structure can reduce otherwise intractable search and estimation problems.

For real industrial applications, reliable low-altitude communications will need practical measurement methods, privacy-preserving search, and deployment-aware optimization before large-scale aerial services can share spectrum safely with terrestrial networks.

For prospective students who are interested in theoretical research, this area offers hands-on problems with visible physical meaning: a UAV trajectory, a blocked link, a 5G signal burst, and a per-beam coverage map. At the same time, the methods involve serious mathematics, including optimization, perturbation analysis, MSE design, ODE-based search, waveform estimation, and radio-map inference.