PaperlayerView exact revision on arXiv

Source-linked AI summary

Deep Learning for Optimal Deployment of UAVs with Visible Light Communications

Yining Wang, Mingzhe Chen, Zhaohui Yang, Tao Luo, Walid Saad

arXiv:1912.00752v3eess.SPcs.ITcs.LGmath.IT

TL;DR

The paper addresses UAV deployment that must account for ambient illumination, which interferes with VLC links and affects illumination requirements. It predicts illumination distributions and uses them to optimize UAV deployment and user association, reporting up to 68.9% lower transmit power than a conventional deployment that ignores illumination distribution.

  • Problem

    Existing UAV deployment and ML approaches do not analyze or predict 2D illumination jointly over space and time, although nighttime illumination interferes with VLC links.

    Source: §I · p. 3

  • Method

    The approach combines CNNs, GRUs, and DeCNNs to predict future illumination distributions, then uses physical relaxation and iterative optimization for UAV deployment and user association.

    Source: §I · p. 4

  • Results

    Up to 68.9% reduction in transmit power is reported versus conventional optimal UAV deployment without considering illumination distribution.

    Source: §I · p. 4

  • Takeaways & Limitations

    Predicted illumination distributions inform joint UAV-location and user-association optimization aimed at minimizing transmit power while meeting illumination and communication requirements.

    Source: §I · p. 4, §VI · p. 26

Abstract

from arXiv · show

In this paper, the problem of dynamical deployment of unmanned aerial vehicles (UAVs) equipped with visible light communication (VLC) capabilities for optimizing the energy efficiency of UAV-enabled networks is studied. In the studied model, the UAVs can simultaneously provide communications and illumination to service ground users. Since ambient illumination increases the interference over VLC links while reducing the illumination threshold of the UAVs, it is necessary to consider the illumination distribution of the target area for UAV deployment optimization. This problem is formulated as an optimization problem which jointly optimizes UAV deployment, user association, and power efficiency while meeting the illumination and communication requirements of users. To solve this problem, an algorithm that combines the machine learning framework of gated recurrent units (GRUs) with convolutional neural networks (CNNs) is proposed. Using GRUs and CNNs, the UAVs can model the long-term historical illumination distribution and predict the future illumination distribution. Given the prediction of illumination distribution, the original nonconvex optimization problem can be divided into two sub-problems and is then solved using a low-complexity, iterative algorithm. Then, the proposed algorithm enables UAVs to determine the their deployment and user association to minimize the total transmit power. Simulation results using real data from the Earth observations group (EOG) at NOAA/NCEI show that the proposed approach can achieve up to 68.9% reduction in total transmit power compared to a conventional optimal UAV deployment that does not consider the illumination distribution and user association.

I. INTRODUCTION

The introduction motivates illumination-aware, energy-efficient deployment of VLC-enabled UAVs and presents a prediction-and-optimization framework. Its model treats UAVs as aerial base stations serving users with simultaneous downlink transmission and illumination.

I. INTRODUCTION

  • Prior work omitted energy-aware or joint association optimization –, –, while ML approaches lacked joint spatial-temporal prediction of 2D illumination –[26].Earlier 2D predictors also missed long histories or produced blurry images –.Source: §I · pp. 2–3
  • Nighttime ambient light interferes with VLC links, making service-area illumination distribution relevant to UAV deployment optimization.Source: §I · pp. 3–4, A. Transmission Model · p. 6
  • The paper proposes dynamic location optimization for VLC-enabled UAVs based on predictions of the target area's illumination distribution.Source: §I · p. 4
  • CNNs, GRUs, and DeCNNs analyze long-term spatial-temporal illumination history to predict future distributions.Source: §I · p. 4
  • Given predicted illumination, physical relaxation of user-association constraints yields a convex equivalent solved by a feasible, low-overhead iterative dual-decomposition algorithm.Source: §I · p. 4
  • Up to 68.9% reduction in transmit power is reported versus conventional optimal UAV deployment without considering illumination distribution.Source: §I · p. 4

II. SYSTEM MODEL AND PROBLEM FORMULATION

  • UAVs provide downlink transmission and illumination simultaneously, and act as static aerial base stations after moving to optimal locations.The service area of each UAV is called an aerial cell.Source: §II · p. 5

A. Transmission Model

  • The transmission model uses probabilistic LoS/NLoS VLC channels and excludes outdoor light diffusion and UAV mobility energy consumption.Source: A. Transmission Model · pp. 5, 7

B. Problem Formulation

The formulation jointly chooses UAV locations, user associations, and transmit powers to meet users’ illumination and data-rate requirements while minimizing power. Because ambient illumination varies and affects VLC links, the method predicts its distribution and uses that prediction in deployment optimization.

B. Problem Formulation

  • Each UAV’s minimum transmit power must satisfy the data-rate requirements of its associated users, and meeting the maximum individual power requirement satisfies them all.The formulation first determines each UAV’s minimum transmit power for its associated users’ data-rate and illumination requirements.Source: B. Problem Formulation · p. 7
  • The objective is to select UAV locations, user associations, and transmit powers that meet users’ data-rate and illumination requirements while minimizing transmit power.The optimization includes predicting the illumination distribution and adjusting associations, locations, and powers.Source: B. Problem Formulation · pp. 7–8
  • The constraints require UAV-provided illumination, sufficient data rates, one UAV association per user, and nonoverlapping UAV service areas.Nonoverlapping service areas allow the formulation to ignore interference caused by other UAVs.Source: B. Problem Formulation · p. 8
  • Ambient illumination both interferes with VLC links and reduces users’ illumination requirements, and its distribution varies over time.Vehicle, street, and building lights contribute to the changing nighttime illumination distribution.Source: B. Problem Formulation · p. 8
  • The method integrates GRUs and CNNs to predict future illumination from historical distributions, then uses the predicted illumination in UAV deployment optimization.The prediction model encodes maps with CNNs, predicts features with GRUs, and reconstructs the illumination distribution with a deconvolution network.Source: §III · pp. 8–9

A. CNN for Encoding Illumination Distribution

The model encodes illumination maps into spatial features with CNNs, then uses GRUs to predict future illumination features from their temporal sequence.

A. CNN for Encoding Illumination Distribution

  • CNNs capture spatial correlations between a location’s illumination and that of nearby regions, preserving local illumination changes in their feature representations.The stated motivation is that human activities create strong spatial correlations in illumination.Source: A. CNN for Encoding Illumination… · p. 9
  • The CNN encoder applies convolution and max-pooling layers before flattening the resulting feature maps into a feature vector.Max-pooling compresses feature maps, and its switches are recorded for decoding predicted features later.Source: A. CNN for Encoding Illumination… · pp. 9–10

B. Illumination Distribution Prediction

  • The GRU updates hidden states from the current spatial feature vector and prior hidden state, retaining information about illumination over the input sequence.The hidden states store information related to illumination distributions from time slot 1 through the current time.Source: B. Illumination Distribution Prediction · p. 11
  • After processing the input sequence, the GRU predicts the next time slot’s illumination features from its final hidden state.The GRU output is a feature vector representing the spatial features of the future illumination distribution.Source: B. Illumination Distribution Prediction · pp. 11–12

C. Illumination Distribution Deconvolution Network

The DeCNN reconstructs a complete future illumination map from features predicted by the GRU, using an architecture that mirrors the CNN encoder.

C. Illumination Distribution Deconvolution Network

  • Because GRU predictions contain spatial features rather than a complete illumination map, a DeCNN decodes them into the predicted distribution.The decoder is described as a mirrored CNN encoder comprising unpooling and deconvolutional layers.Source: C. Illumination Distribution… · p. 12
  • Unpooling enlarges sparse feature maps toward the service area’s original size, while deconvolution reconstructs the distribution’s detailed structure using learned weights.The first unpooling layer takes the GRU-predicted feature vector as input.Source: C. Illumination Distribution… · p. 12
  • The integrated prediction process encodes historical maps, predicts future features, decodes the future map, and updates model weights from a loss calculation.Once predicted, the ambient illumination at each user’s location is substituted into the deployment optimization problem.Source: C. Illumination Distribution… · p. 13

D. Integrated GRU and CNN Predictive Model Training

The integrated model is trained on historical illumination sequences, while deployment optimization alternates between UAV placement and power allocation with fixed associations and association selection. The method relates illumination at user locations to UAV transmit-power requirements.

D. Integrated GRU and CNN Predictive Model Training

  • Batch gradient descent trains the integrated model’s weights to relate historical illumination sequences to the predicted future distribution.The weights are initialized randomly before training.Source: D. Integrated GRU and CNN Predictive… · p. 13

IV. OPTIMIZATION OF UAV DEPLOYMENT, USER ASSOCIATION, AND POWER EFFICIENCY

  • The deployment algorithm handles the nonconvex problem iteratively, first optimizing UAV deployment and power allocation for fixed associations, then selecting user associations.The UAV positions are assumed unchanged during each prediction period, and deployment is chosen at the beginning of each interval.Source: §IV · p. 14

A. UAV Deployment and Power Efficiency with Fixed User Association

  • With fixed user associations, the deployment and power-efficiency subproblem is convex and can be solved optimally by a dual method.The passage introduces the Lagrange function for that subproblem.Source: A. UAV Deployment and Power Efficiency… · pp. 14–15
  • The resulting subgradient update uses a dynamic step size, and solving the fixed-association problem yields collaborative deployment of multiple UAVs.The stated update uses [a]+ = max(a, 0).Source: A. UAV Deployment and Power Efficiency… · p. 16
  • For given user illumination and data-rate requirements, each UAV’s minimum transmit power depends on illumination at the user’s location.The proposition describes conditions under which each UAV’s transmit power achieves a lower bound.Source: A. UAV Deployment and Power Efficiency… · pp. 16–17

B. User Association and Power Efficiency with Fixed UAV Deployment

With UAV deployment fixed, the paper relaxes binary user association to make the optimization tractable, then solves the dual problem while retaining binary optimal associations. Gradient-based dual updates are iterated with primal optimization to obtain user associations and transmit powers.

B. User Association and Power Efficiency with Fixed UAV Deployment

  • The binary association formulation is relaxed to values in [0, 1] to address its combinatorial complexity.The paper states that the relaxation is later shown not to cause loss of optimality.Source: B. User Association and Power… · p. 17
  • The dual solution retains binary optimal associations, so relaxing the feasible region does not reduce optimality.The original binary formulation is combinatorial and described as essentially impossible to solve even for a modest-sized network.Source: B. User Association and Power… · pp. 17–18
  • Gradient updates to the dual variables are iterated with primal optimization to obtain user associations and transmit powers.The dual-variable update uses a dynamically chosen positive step size.Source: B. User Association and Power… · p. 18

C. Complexity and Overhead of the Proposed Algorithms

The algorithm’s complexity comes from training the integrated GRU–CNN predictor and iteratively updating UAV locations and user associations. After training, UAVs implement an optimization algorithm described as having linear complexity.

C. Complexity and Overhead of the Proposed Algorithms

  • CNN encoder and DeCNN decoder complexity depends on feature-map size and number, while the GRU predictor has complexity O(TDh(N + Dh)).The GRU complexity depends on input time-series length and weight-matrix size; training is performed by the computationally capable BS, so its overhead can be ignored.Source: C. Complexity and Overhead of the… · p. 19
  • UAV deployment costs O(L1D^2U) and user association costs O(L2DU), with L1 and L2 denoting average iterations to convergence.The two optimization subproblems are solved by dual methods.Source: C. Complexity and Overhead of the… · p. 19
  • The UAV-side optimization algorithm has linear complexity and reduces UAV energy consumption.The paper identifies iterative UAV-location and user-association updates as part of the algorithm’s complexity.Source: C. Complexity and Overhead of the… · pp. 18–19

V. SIMULATION RESULTS AND ANALYSIS

The simulations evaluate illumination prediction and UAV deployment using nighttime satellite data, and report lower transmit power with the proposed joint approach. The conclusion describes a GRU–CNN predictor and iterative optimization for deployment and user association.

V. SIMULATION RESULTS AND ANALYSIS

  • As more historical illumination distributions are input, prediction accuracy increases because the model extracts more time-varying information.The predictions begin at zero at the first time step.Source: Figure 3 · p. 20, §V · pp. 20–21
  • The CNN encoder extracts boundary and shading features, GRUs predict next-slot features, and DeCNN layers reconstruct the illumination map from coarse to fine.The simulations train the predictor on average-radiance composite nighttime satellite images from EOG at NOAA/NCEI because no public UAV-collected illumination dataset is available.Source: §V · pp. 20–22
  • The proposed model’s average prediction MSE is 6.01 × 10−4 on training data and 6.03 × 10−4 on test data, with up to 46.5% and 53.6% lower MSE than GMM-and-GRU and conventional autoencoder models, respectively.MSE decreases as the input illumination series grows; the autoencoder’s MSE remains constant because it uses only the last input time slot.Source: Figure 5 · p. 22, §V · p. 23
  • 37.4% lower transmit power on average is reported versus center deployment as user count varies; reductions reach 31.3% versus user-association-only optimization and 15.5% versus deployment-only optimization.The proposed algorithm is also within 2.8% of optimization using actual illumination distributions.Source: Figure 6 · p. 23, §V · p. 24
  • 68.9% lower transmit power is achieved versus conventional optimal deployment without illumination distribution and user association as UAV height varies.The proposed algorithm’s power increases with height, but its user-association strategy limits the increase by assigning users to fewer UAVs at high altitudes.Source: Figure 7 · p. 24, §V · pp. 25–26
  • The proposed iterative algorithm is within 1.5% of exhaustive search, while its deployment gain becomes less significant as more users make their distribution more uniform.The paper attributes the smaller gain to the optimal UAV position becoming fixed when enough users are considered.Source: §V · p. 25
  • In the illustrated 80 m × 80 m deployment, one UAV serves users in the bright area while other UAVs serve scattered users, minimizing total transmit power.The paper explains that the brightest area usually determines the maximum illumination requirement among a UAV’s associated users.Source: §V · p. 26

VI. CONCLUSION

  • The conclusion frames the method as joint dynamic optimization of UAV locations and user association, using predicted illumination and an iterative solution to minimize transmit power while meeting user requirements.The original nonconvex problem is reformulated as convex through physical relaxation of user association.Source: §VI · p. 26

APPENDIX

The appendix supports convergence of the iterative algorithm and derives an optimal illumination choice and a lower bound on UAV transmit power.

A. Proof of Theorem 1

  • The convex subproblem is solved optimally at each iteration by the dual method, and the algorithm for the full problem converges because total transmit power is bounded below by zero.The proof also uses a first-order Taylor expansion to relate the iterative constraint to the original constraint.Source: A. Proof of Theorem 1 · p. 27

B. Proof of Proposition 1

  • The proof derives the illumination at each user that minimizes the associated UAV's transmit power, then uses it to obtain a lower bound on minimum UAV transmit power.It compares the power needed to meet users' illumination and data-rate requirements.Source: B. Proof of Proposition 1 · p. 28

C. Proof of Theorem 2

The proof uses the dual problem to obtain optimal user-association and UAV-power solutions.

C. Proof of Theorem 2

  • The dual objective is linear in the association variables, so the optimal association selects the UAV with the smallest association coefficient for each user.The passage states that this user's selected association coefficient is 1.Source: C. Proof of Theorem 2 · p. 29
  • The proof obtains the optimal UAV transmit power by differentiating the dual objective with respect to power.The stated power solution is infinite when 1 minus the sum of the corresponding association coefficients is nonpositive.Source: C. Proof of Theorem 2 · p. 29

D. Proof of Lemma 1

The proof accounts for encoder and decoder complexity through their constituent CNN operations and the symmetry between the two networks.

D. Proof of Lemma 1

  • Each max-pooling layer divides its input feature map into square regions and retains the most robust feature from each region.The stated complexity per layer is O(S_m^2).Source: D. Proof of Lemma 1 · p. 30
  • The flatten layer rewrites its input feature map, and its complexity is included in the encoder's total complexity.The passage identifies the flatten operation as a separate component of the complexity analysis.Source: D. Proof of Lemma 1 · p. 30
  • The CNN encoder's complexity is derived from its convolutional, max-pooling, and flatten layers; the decoder has matching complexity by symmetry.The decoder uses deconvolutional and unpooling layers corresponding to the encoder operations.Source: D. Proof of Lemma 1 · pp. 29–30

E. Proof of Lemma 2

The proof analyzes the GRU predictor's computational cost across its gate operations, input sequence, and output prediction.

E. Proof of Lemma 2

  • The reset gate, candidate hidden state, and update gate each have complexity O(ND_h + D_h^2) per input.The proof states that candidate-state and update-gate calculations share this complexity with the reset gate.Source: E. Proof of Lemma 2 · p. 30
  • The GRU iteratively updates hidden states across the input illumination sequence to extract temporal features.The passage then gives a total complexity for temporal feature extraction across the sequence.Source: E. Proof of Lemma 2 · p. 30
  • The output illumination-distribution prediction has complexity O(ND_h).The stated output cost depends on the size of the representation.Source: E. Proof of Lemma 2 · p. 31
Loading 1912.00752v3…