Millimeter-Wave Low Altitude UAV ISAC Beam Training and Tracking Technology

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Inspired by information theory, we address beam training and target localization/tracking challenges in millimeter-wave (mmWave) low altitude UAV scenarios. We propose a hierarchical beam training algorithm based on channel coding principles and a UAV tracking algorithm leveraging mmWave radar sensing. Both algorithms exhibit strong robustness and generalization, applicable to static/dynamic scenarios, far-field/near-field conditions, RIS-assisted communications, distributed cell-free networks, and unauthorized UAV intrusion detection. Validated through simulations and hardware tests, our channel-coding beam training improves accuracy via coding gain and error correction, while the radar approach combines Capon beamforming, CFAR detection, and DBSCAN clustering for precise UAV tracking.

Introduction

The low-altitude economy (LAE) represents a pivotal growth sector in future economic development, encompassing commercial, scientific, and public service activities within low-altitude airspace. LAE includes UAV delivery, aerial transportation, agricultural monitoring, inspections, and emergency response. Safe LAE operations require seamless communication/navigation for authorized aircraft and ubiquitous surveillance for unauthorized low altitude UAV targets. Traditional monitoring methods lack the precision and low latency needed for all-weather airspace supervision. Integrated Sensing and Communication (ISAC) technology addresses these challenges by enabling base stations to provide communication/navigation services while monitoring airspace. Millimeter-wave frequencies and MIMO technology facilitate high-precision positioning essential for advanced wireless services. Beam training typically locates static objects, while radar algorithms track dynamic low altitude UAV targets. RIS technology further enhances mmWave ISAC systems by reconfiguring signal propagation to overcome blockages and extend coverage. However, large antenna arrays create narrow beams requiring precise alignment, which introduces significant training overhead—especially in near-field conditions. Existing localization methods often sacrifice real-time performance for accuracy and lack adaptability across complex environments.

System Model

Consider a downlink ISAC mmWave low altitude UAV scenario with one ISAC base station (BS), one RIS, multiple UAVs, and multiple users (Figure 1). The BS employs an M-element uniform planar array (UPA), while each low altitude UAV uses an Nr-antenna UPA. When direct BS-user links are obstructed, an N-element RIS UPA establishes reflective paths. The signal received by user k via direct path is:

$$y_k = \sqrt{P} \mathbf{h}_k \mathbf{v}_k x_k + n_k$$

For RIS-assisted obstructed paths:

$$y_k = \sqrt{P} (\mathbf{g}^H_k \mathbf{\Theta} \mathbf{h}_0) \mathbf{v}_k x_k + n_k$$

where \(x_k \in \mathbb{C}\) and \(\mathbf{v}_k \in \mathbb{C}^{M \times 1}\) are the transmitted signal and beamforming vector; \(\mathbf{h}_k \in \mathbb{C}^{1 \times M}\), \(\mathbf{h}_0 \in \mathbb{C}^{N \times M}\), and \(\mathbf{g}_k \in \mathbb{C}^{N \times 1}\) denote channels; \(P\) is transmit power; \(n_k \sim \mathcal{CN}(0, \sigma_n^2)\) is noise. The RIS reflection matrix is \(\mathbf{\Theta} \triangleq \text{diag}([e^{j\psi_1}, \dots, e^{j\psi_N}])\). Geometric mmWave channels follow:

$$\mathbf{h}_k = \tilde{h}_k \mathbf{a}_B(\phi_k^t, \theta_k^t)$$
$$\mathbf{h}_0 = \tilde{h}_0 \mathbf{a}_B(\phi^t, \theta^t) \mathbf{a}_R(\phi^r, \theta^r)$$
$$\mathbf{g}_k = \tilde{g}_k \mathbf{a}_R(\phi_k^t, \theta_k^t)$$

Near-field steering vectors for an \(N = N_h \times N_v\) UPA are approximated as:

$$\mathbf{a}(\phi, \theta) = \left[1, e^{-j\frac{2\pi}{\lambda_c}\left( d_a \cos\phi + \frac{d_a^2 \sin^2 \phi}{2r} \right)}, \dots \right] \otimes \left[1, e^{-j\frac{2\pi}{\lambda_c}\left( d_a \cos\theta \sin\phi + \frac{d_a^2 (1 – \cos^2\theta \sin^2\phi)}{2r} \right)}, \dots \right]$$

while far-field vectors simplify to:

$$\mathbf{a}(\phi, \theta) = \left[1, e^{j\frac{2\pi}{\lambda_c} d_a \cos\phi}, \dots \right] \otimes \left[1, e^{j\frac{2\pi}{\lambda_c} d_a \cos\theta \sin\phi}, \dots \right]$$

Beam Training for Low Altitude UAV

Channel-Coding Hierarchical Beam Training

We reformulate hierarchical beam training as a channel coding problem to leverage coding gain and error correction. For a codebook size \(J = 2^e\), position index \(\mathbf{u}_{1 \times e} \in \mathcal{U}\) (\(|\mathcal{U}| = 2^e\)) is encoded into codeword \(\mathbf{X} = f(\mathcal{U})\) using function \(f\). After \(n\)-layer beam training, user feedback decodes to \(\hat{\mathbf{u}} = g(\mathbf{y})\). Each layer uses two complementary multi-arm beam codewords \(\mathbf{C}^{(l,1)}\) and \(\mathbf{C}^{(l,2)}\) defined by sub-beam composition vectors:

$$V^{(l,1)}_i = x_i(l), \quad V^{(l,2)}_i = 1 – x_i(l)$$

for \(i = 1,\dots,2^k; l = 1,\dots,n\). This maps layer-\(l\) measurements to the \(l\)-th codeword element. Error correction mechanisms rectify erroneous feedback. Codebook rearrangement minimizes intra-block correlation:

$$D(\mathbf{c}_i, \mathbf{c}_j) = \alpha d_{\text{ang}}(\mathbf{c}_i, \mathbf{c}_j) + (1-\alpha) d_{\text{Hamm}}(E(\mathbf{c}_i), E(\mathbf{c}_j))$$

where \(d_{\text{ang}}\) is angular distance and \(d_{\text{Hamm}}\) is Hamming distance after encoding \(E(\cdot)\).

Hash-Based Multi-Arm Beam Training

For multi-RIS scenarios, we design low-complexity training using \(k\)-wise independent hash functions \(\mathcal{H} = \{f_{h_1}, \dots, f_{h_{|\mathcal{H}|}}\}\). A hash function \(f_h: \mathcal{U} \to \mathcal{X}\) maps single-beam indices \(\mathcal{U} = \{0,1,\dots,J-1\}\) to \(B\) buckets:

$$\mathbf{d}_b = \{ u | f_h(u) = b, u \in \mathcal{U} \} = [d_b^1, d_b^2, \dots, d_b^R]$$

where each multi-arm beam contains \(R = J/B\) single-beams. For \(S\) hashing rounds, each RIS randomly selects \(S\) functions to generate multi-arm codebooks \(\mathbf{C}^1, \mathbf{C}^2, \dots, \mathbf{C}^S\). Scanning requires \(Q = BS\) symbol durations. Users record received power \(\mathbf{P} = [P(1,1), P(1,2), \dots, P(S,B)]\) and SNR. Algorithm 1 demodulates paths by sorting SNRs:

Algorithm 1: Hash-Based Multi-Arm Beam Training

  1. Input: Multi-arm codebooks \(\mathbf{D}^1,\dots,\mathbf{D}^S\), \(\mathbf{C}^1,\dots,\mathbf{C}^S\), rounds \(S\), slots \(Q=BS\), threshold \(\epsilon\)
  2. Output: RIS-user directions \(\gamma_k^i \in \mathcal{U}\)
  3. for \(q = 1 \to Q\):
  4.  BS transmits training symbols; RISs reflect using \(\mathbf{C}^1,\dots,\mathbf{C}^S\)
  5.  User \(k\) records power \(\mathbf{P}\) and computes SNR
  6. \(i = 1\)
  7. while residual power > \(\epsilon\):
  8.  Sort SNRs descending, select slots \(q = \text{index}\{\max_{(i-1)S+1:iS} \mathbf{P}\}\)
  9.  Vote for sub-beams in \(\mathbf{D}(q,:)\)
  10.  \(\gamma_k^i \leftarrow\) highest-vote sub-beam index

Voting identifies optimal RIS-user directions (Figure 2).

mmWave Radar-Based UAV Tracking

Our low altitude UAV detection/tracking framework (Figure 3) comprises range-azimuth map generation, target detection, and point cloud clustering:

Range-Azimuth Map Generation

After range-FFT, static clutter is removed via spectral subtraction. We use Capon beamforming for high-resolution azimuth estimation instead of FFT. For azimuth FoV \(\phi_{\text{FOV}} = 90^\circ\) and step \(\phi_{\text{step}} = 1^\circ\), steering vectors are:

$$\mathbf{a}(\phi_i) = \left[ e^{-j\pi \sin\phi_i}, e^{-j\pi 2 \sin\phi_i}, \dots, e^{-j\pi N_r \sin\phi_i} \right]^T$$

for \(\phi_i = -\phi_{\text{FOV}} + i\phi_{\text{step}}; i=0,\dots,N_A-1\) (\(N_A = 2\phi_{\text{FOV}}/\phi_{\text{step}}\)). The spatial spectrum is:

$$P(\phi) = \frac{1}{\mathbf{a}^H(\phi) \mathbf{R}^{-1} \mathbf{a}(\phi)}$$

where \(\mathbf{R}\) is the covariance matrix.

Target Detection and Clustering

Constant false alarm rate (CFAR) detection adaptively sets thresholds using guard cells (\(l_g = 3\)) and noise cells (\(l_n = 16\)):

$$\theta = \frac{1}{2l_n} \sum_{j \in \mathcal{N}} x(j) + \delta \quad (\delta = 2.5)$$

where \(\mathcal{N} = [i – l_g – l_n, i – l_g – 1] \cup [i + l_g + 1, i + l_g + l_n]\). DBSCAN clusters detected points using density-based connectivity with neighborhood \(\epsilon\) and minimum points \(\text{MinPts}\) (Algorithm 2). The largest cluster represents the low altitude UAV, with its centroid as the position estimate.

Algorithm 2: DBSCAN Clustering

  1. Input: Data points \(\mathbf{D}\)
  2. Output: Clusters \(\mathcal{C}\)
  3. Initialize cluster \(C = 0\); mark all points unvisited
  4. while unvisited \(p \in \mathbf{D}\) exists:
  5.  Mark \(p\) visited
  6.  Retrieve \(\epsilon\)-neighborhood \(N_\epsilon(p)\)
  7.  if \(|N_\epsilon(p)| < \text{MinPts}\):
  8.   Mark \(p\) noise
  9.  else:
  10.   \(C \leftarrow C+1\); add \(p\) to \(C\)
  11.   for \(q \in N_\epsilon(p)\) unvisited:
  12.    Mark \(q\) visited
  13.    if \(|N_\epsilon(q)| \geq \text{MinPts}\):
  14.     Merge \(N_\epsilon(q)\) into \(N_\epsilon(p)\)
  15.    if \(q\) not in any cluster:
  16.     Add \(q\) to \(C\)

Experimental Results

Beam Training Performance

We evaluate channel-coding beam training under near-field conditions. Figure 4 compares Hamming code (\(J=16\)) and convolutional code (\(J=64\)) against exhaustive search. Convolutional coding achieves similar accuracy with 4× lower training overhead. At 5 dB SNR, hash-based multi-arm beam training with \(B=8\) beams attains 97.5% accuracy—20% higher than baselines (Figure 5). Training complexity scales logarithmically with codebook size (Figure 6).

Table 1: Beam Training Accuracy Comparison at 5 dB SNR
Method Beams (\(B\)) Accuracy (%) Overhead (Symbols)
Exhaustive 32 98.0 32
Hierarchical N/A 75.0 10
EIMB 8 77.5 24
Proposed (Hash) 8 97.5 24

UAV Tracking Performance

Using a DJI Mini4 Pro low altitude UAV and TI IWR6843ISK radar, we tested trajectories: horizontal left-right, horizontal front-back, and vertical up-down. Table 2 shows average radial distance errors. Our method achieves decimeter-level precision and outperforms FFT while matching MUSIC with lower computation (Figure 7). Front-back motion exhibits higher errors due to unestimated elevation (Figure 8).

Table 2: Low Altitude UAV Tracking Errors
Trajectory Average Radial Error (m)
Horizontal Left-Right 0.25
Horizontal Front-Back 0.02
Vertical Up-Down 0.19

Conclusion

Our channel-coding beam training algorithm improves accuracy by 20% with logarithmic overhead in multi-RIS low altitude UAV scenarios. The radar-based tracker achieves millimeter-level precision for unauthorized UAV detection. Both algorithms demonstrate robustness across near-field/far-field, static/dynamic, and RIS/cell-free environments. Hardware validation confirms their applicability to real-world low-altitude economy deployments.

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