Deep Completion Autoencoders for Radio Map Estimation

Yves Teganya; Daniel Romero

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Deep Completion Autoencoders for Radio Map Estimation

Yves Teganya, Daniel Romero

arXiv:2005.05964v3May 11, 2020eess.SP

TL;DR

Radio map estimation must recover PSD values across locations and frequencies from spatially distributed sensor measurements, while existing interpolation methods do not learn from experience. This paper learns propagation structure from past measurements using a deep completion network, achieving RMSE on the order of 2 dB in experiments with two datasets, at the cost of training data and greater computation.

Problem
Radio map estimation seeks to recover the true PSD map at every location and frequency from measurements collected by distributed spectrum sensors.
Method
The paper learns spatial propagation structure from past measurements and estimates PSD maps with a deep completion network that uses observed measurements and a binary observation mask.
Results
RMSE in the order of 2 dB was attained on two datasets, with the proposed approach outperforming competing methods, especially with few measurements.
Takeaways & Limitations
Learning from past measurements yields estimators requiring fewer measurements to attain target performance than state-of-the-art alternatives.
Takeaways & Limitations
The approach requires a training dataset, which can be costly to obtain from measurements or ray-tracing algorithms, and increases computational demands over traditional interpolation methods.

Abstract

from arXiv · show

Radio maps provide metrics such as power spectral density for every location in a geographic area and find numerous applications such as UAV communications, interference control, spectrum management, resource allocation, and network planning to name a few. Radio maps are constructed from measurements collected by spectrum sensors distributed across space. Since radio maps are complicated functions of the spatial coordinates due to the nature of electromagnetic wave propagation, model-free approaches are strongly motivated. Nevertheless, all existing schemes for radio occupancy map estimation rely on interpolation algorithms unable to learn from experience. In contrast, this paper proposes a novel approach in which the spatial structure of propagation phenomena such as shadowing is learned beforehand from a data set with measurements in other environments. Relative to existing schemes, a significantly smaller number of measurements is therefore required to estimate a map with a prescribed accuracy. As an additional novelty, this is also the first work to estimate radio occupancy maps using deep neural networks. Specifically, a fully convolutional deep completion autoencoder architecture is developed to effectively exploit the manifold structure of this class of maps.

I. INTRODUCTION

Radio occupancy map estimation targets aggregate power across locations without requiring transmitter details, addressing limitations of propagation prediction and interpolation-based methods. The paper introduces data-driven learning from past measurements and a deep neural network formulation for PSD map estimation.

Radio maps represent spatially varying channel metrics including received signal power, interference power, PSD, electromagnetic absorption, and channel gain.
Propagation prediction methods are limited by requirements for known transmitter configurations, interference sensitivity, and high computational complexity over many locations.
Radio occupancy map estimation instead predicts aggregate power without requiring the number, locations, or powers of active transmitters.
The proposed paradigm learns spatial propagation structure from past measurements in different environments to reduce measurements needed for a target accuracy.
The work formulates PSD estimation as tensor completion on a spatial discretization and addresses it with an encoder-decoder completion network.
The paper identifies its novelty as the first data-driven radio occupancy map estimator and the first deep-learning algorithm for this task.

III. DATA-DRIVEN RADIO MAP ESTIMATION

The data-driven formulation uses past measurement records and spatial discretization to convert radio map estimation into a tensor completion problem. Measurements are aggregated on grid points, while observed locations and missing entries are explicitly represented for neural-network processing.

Past measurement records from other geographic areas provide training data for deep learning estimators of radio maps.
Spatial discretization enables feedforward architectures to process radio maps despite the variable number of sensor measurements.
An Ny × Nx grid assigns each measurement location to its nearest grid point, producing a structured representation of the area.
True PSD values across grid points and frequencies are collected into matrices and a tensor representing the true map.
Measurements assigned to each grid point are averaged, while grid points without measurements are marked as misses.
Discretization and measurement errors make sampled entries differ from the corresponding true-map values.

B. Completion Networks for Radio Map Estimation

The section develops completion-network strategies that let neural estimators handle missing spatial measurements and exploit map-side information. Binary masks identify observed locations, while combined masks can reduce parameters without sacrificing performance.

Regular feedforward networks cannot directly accommodate variable input supports, missing entries, or set-valued measurement locations.
Training only on observed entries permits an identity-map solution, so complexity control is required to avoid a useless estimator.
An encoder-decoder completion architecture is used to control the candidate-function family while producing completed maps by evaluating the learned estimator.
A binary observation mask distinguishes missing entries from measured values, particularly when PSDs are represented in logarithmic units such as dBm.
Building and measurement masks can be combined into a single mask, reducing the number of trainable parameters without sacrificing performance.
The framework can express objective tensors in dB units, unlike most listed convex-solver approaches, allowing errors at low-power locations to receive attention.

C. Exploiting Structure in the Frequency Domain

The section addresses frequency-domain structure when prior information is unavailable or available through transmission standards. Frequency separation reduces model size and increases effective training examples, while basis expansions model PSD structure and noise power.

1) No Prior Information:: Large frequency dimensions make fully connected networks parameter-heavy and constrain usable depth or width for a fixed training-set size.
1) No Prior Information:: When propagation effects at nearby frequencies are similar, the estimator can operate separately at each frequency to reduce complexity.
Gaussian radial basis functions with a constant white-noise basis function also enable estimation of noise power πB(x) at every location.
1) No Prior Information:: Frequency separation roughly reduces variables by a factor of Nf and multiplies the effective number of training examples by Nf.

2) Output Layers for Parametric PSD Expansions:

The paper uses basis expansion to encode frequency-domain PSD structure, allowing the network to estimate spatial coefficients and reconstruct PSD maps with fewer trainable parameters. This design is suited to wideband settings where propagation can vary across frequencies.

Basis expansion represents the transmit PSD using B−1 given basis functions, including raised-cosine or Gaussian functions.
Assuming channel gain is approximately constant over each basis-function support, the PSD becomes a sum of spatial coefficients weighted by frequency bases.The assumption is reasonable for narrowband bases; wider supports can be split into smaller ones.
The basis expansion can include a constant white-noise basis, enabling estimation of noise power at every location.This is noted as useful for cognitive-radio applications.
The network estimates coefficient maps Π and uses a parameter-free final layer to reconstruct the PSD estimate across frequencies.The final trainable layer has NyNxB neurons instead of NyNxNf.
The coefficient-reduction approach can improve estimation performance for a fixed training size and is particularly suited to wideband communications.Wideband propagation effects may differ substantially across frequencies.

D. Deep Completion Autoencoders

The proposed deep completion autoencoder compresses partially observed radio maps into latent variables and reconstructs the full map using convolutional processing. Its architecture exploits spatial structure while reducing parameter requirements and accommodating different grid sizes.

A completion autoencoder infers latent variables from a subset of input entries and reconstructs the full map when the sampling set preserves sufficient information.If the sampling set lacks sufficient information, reconstruction is impossible regardless of the technique.
The autoencoder is motivated by radio maps lying near a low-dimensional manifold, illustrated by a toy setup identifiable with Nλ = 4 quantities.The four quantities are the x and y coordinates of two sources.
The encoder uses convolutional and pooling layers to reduce parameters, exploit spatial structure, and provide shift-invariant transfer functions.Average pooling gradually condenses information while approximately preserving shift invariance.
The decoder reverses the encoder with convolution-transpose and up-sampling layers to reconstruct the map.Bilinear interpolation or fractional-stride convolutions can implement up-sampling.
The fully convolutional design has no fully connected layers, reduces trainable parameters, and permits reuse for different Nx and Ny values.Fully connected alternatives would generally require a different network for each grid dimension pair.

E. Learning in Real-World Scenarios

For real-world learning, the paper considers synthetic or real training maps and combines them through transfer learning when real data are limited. Synthetic data provide known targets, while real data support adaptation.

A training set can be generated with a mathematical model or simulator that captures propagation structure such as path loss and shadowing.Artificial noise may be added to synthetic measurements to model measurement error.
Synthetic training has the advantage that the true maps are available as ground-truth targets.
The network can be trained on paired incomplete and complete maps, written as {(˘Ψt, Ψt)}T.
If the simulator is sufficiently close to reality, applying the learned estimator to real incomplete maps should produce accurate estimates.

2) Real Training Data:

With real data, complete target maps are generally unavailable, so the paper trains by splitting measurements into input and target subsets and optionally initializes real-data learning from synthetic pretraining. Experiments evaluate RMSE on generated map datasets.

Real training data typically contain incomplete measured tensors but not the corresponding complete maps Ψt.Measurements cannot usually cover every grid point within a sufficiently short interval.
Using all measurements directly can encourage the network to reproduce observed entries, so the method splits measurements into input and target subsets.The subsets may be non-disjoint and can be sampled uniformly without replacement.
Transfer learning first trains on synthetic data and then fine-tunes with real data initialized from the synthetic parameter vector.The procedure combines information from synthetic and real datasets.
Evaluation compares root mean square error, estimated by averaging over a test set of 10^3 maps.The RMSE is defined using the true map, estimated map, measurement noise, and sensor locations.

A. Power Map Cartography

Power-map experiments evaluate the proposed network against interpolation and learning alternatives on synthetic and real propagation data. The network performs well with sparse measurements, with larger gains on Wireless InSite maps.

Comparison Setup: The experiments compare the proposed method with kriging, multikernel estimation, matrix completion, and K-nearest neighbors.Competitor parameters were adjusted to approximately yield their best performance.
Wireless InSite Data Set: With |Ω| = 52 measurements, the proposed network already produces a high-quality estimate for a Wireless InSite test map.The network does not reconstruct diffraction, multipath, or antenna-directivity details absent from its Gudmundson training data.
Gudmundson Data Set: On Gudmundson maps, the proposed scheme achieves approximately 30% better RMSE than the next competing alternative.The matrix-completion method is omitted because of its high RMSE over the displayed measurement range.
Wireless InSite Data Set: On Wireless InSite maps, the proposed approach performs roughly 100% and 90% better than the next alternative in the 100 m and 200 m areas, respectively.All five approaches degrade relative to the Gudmundson experiment, indicating that real-map estimation is more challenging in this setting.

3) Hybrid Training:

The paper studies hybrid training and architectural choices for completion autoencoders. Results show benefits from transfer learning, fully convolutional design, and sufficiently deep networks, while latent codes capture structured map variation.

Hybrid Training: Transfer learning yields a significant performance improvement in the hybrid training experiment.The hybrid scheme initializes training with weights obtained from another data set rather than random weights.
Deep Neural Network Design: The architecture study evaluates code length, encoder output-layer type, network depth, and activation function while controlling or examining parameter-count effects.The experiments use RMSE curves across code lengths, measurement counts, and layer counts.
Deep Neural Network Design: The best performance in the depth study occurs around L = 26 layers, while PReLU and LeakyReLU yield roughly the same RMSE overall.PReLU outperforms LeakyReLU for shallow architectures.
Latent Representation: Latent-code perturbations produce maps resembling those in the training set, supporting an interpretation of the code as coordinates on a learned map manifold.The decoder reconstructs two-source maps for the free-space model and maps with noticeable shadowing for Gudmundson-trained codes.

D. PSD Cartography

PSD cartography experiments test the proposed completion autoencoder with frequency-domain structure on Gudmundson and Wireless InSite data. The method outperforms the compared scheme in the reported settings and remains computationally efficient.

Gudmundson Data Set: The proposed output layers outperform the weight-sharing scheme because they exploit prior information in the frequency domain.The proposed output layer is used in the remaining experiments.
Gudmundson Data Set: For |Ω| = 512, the proposed scheme visually estimates PSD-map coefficients and spectra more accurately than the competing algorithm.Its RMSE advantage is especially pronounced for small numbers of measurements.
Wireless InSite Data Set: In a realistic Wireless InSite scenario, the proposed scheme yields a low RMSE, while the competing approach is omitted because of its high RMSE.Training and testing use Wireless InSite maps with random subsets of measurements and noisy PSD values.
Computational Efficiency: For power-map estimation, the proposed method takes 25 · 10^-3 seconds, compared with 10^-1 seconds for kriging and 1.25 seconds for the multikernel method.For PSD-map estimation, its runtime is around 2.12 · 10^-1 seconds versus 6.43 seconds for the competing algorithm.

V. CONCLUSIONS AND DISCUSSION

Data-driven radio map estimation exploits learned propagation structure and the low-dimensional manifold of radio maps to reduce measurement requirements. A deep completion network achieves approximately 2 dB RMSE, while requiring training data and greater computational demands than interpolation approaches.

Learning propagation phenomena from past measurements can require fewer measurements than state-of-the-art alternatives for a target performance.The approach learns spatial structure such as shadowing, reflection, and diffraction from sufficiently realistic datasets.
Radio maps lie close to a low-dimensional manifold, motivating an encoder-decoder deep completion network for PSD-map estimation.
The proposed scheme was evaluated against existing approaches, including the algorithm in [3], through performance comparisons and map-estimation experiments.The supplied figures include PSD reconstructions, performance comparisons, and RMSE results for PSD cartography.
2 dB RMSE was attained in extensive numerical experiments across two datasets, significantly outperforming existing approaches.
Improved performance requires a training dataset and increased computational demands compared with traditional interpolation approaches.Deep neural networks may also require large datasets, whose acquisition through measurements or ray tracing can be costly.