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Enabling Large Intelligent Surfaces with Compressive Sensing and Deep Learning

Abdelrahman Taha, Muhammad Alrabeiah, Ahmed Alkhateeb

arXiv:1904.10136v2cs.ITeess.SP

TL;DR

LIS reflection design needs channel knowledge, but estimating channels across massive arrays creates substantial training overhead. This paper combines a sparse-sensor LIS architecture with compressive sensing and deep learning, and reports near-perfect-channel performance with negligible overhead and fewer than 1% active elements.

  • Problem

    Estimating LIS channels is difficult because the surfaces contain massive numbers of elements, creating large training overhead for reflection-matrix design.

  • Method

    The paper uses a LIS with mostly passive elements and a few active sensors, then applies compressive sensing or deep learning to design reflection matrices from sampled channels.

  • Results

    The proposed solutions approach the perfect-channel upper bound with almost no training overhead when only a few LIS elements are active.

  • Takeaways & Limitations

    Sparse active sensing offers a low-power, low-training-overhead route to LIS reflection-matrix design.

  • Takeaways & Limitations

    Compressive sensing performance becomes limited in scenarios with rich NLOS scattering.

Abstract

from arXiv · show

Employing large intelligent surfaces (LISs) is a promising solution for improving the coverage and rate of future wireless systems. These surfaces comprise a massive number of nearly-passive elements that interact with the incident signals, for example by reflecting them, in a smart way that improves the wireless system performance. Prior work focused on the design of the LIS reflection matrices assuming full knowledge of the channels. Estimating these channels at the LIS, however, is a key challenging problem, and is associated with large training overhead given the massive number of LIS elements. This paper proposes efficient solutions for these problems by leveraging tools from compressive sensing and deep learning. First, a novel LIS architecture based on sparse channel sensors is proposed. In this architecture, all the LIS elements are passive except for a few elements that are active (connected to the baseband of the LIS controller). We then develop two solutions that design the LIS reflection matrices with negligible training overhead. In the first approach, we leverage compressive sensing tools to construct the channels at all the LIS elements from the channels seen only at the active elements. These full channels can then be used to design the LIS reflection matrices with no training overhead. In the second approach, we develop a deep learning based solution where the LIS learns how to optimally interact with the incident signal given the channels at the active elements, which represent the current state of the environment and transmitter/receiver locations. We show that the achievable rates of the proposed compressive sensing and deep learning solutions approach the upper bound, that assumes perfect channel knowledge, with negligible training overhead and with less than 1% of the elements being active.

I. INTRODUCTION

LISs use many nearly passive elements to improve wireless coverage and rate, but channel knowledge is difficult to obtain with massive training overhead. The paper proposes sparse active sensors with compressive sensing and deep learning to design reflection matrices efficiently.

  • Motivation: LISs interact with incident signals through many radiating or sensing elements, potentially improving wireless coverage and rate.Nearly passive implementations such as analog phase shifters are also considered.
  • Challenge: Prior LIS reflection-matrix designs generally assume global channel knowledge, although estimating extremely large-dimensional channels remains challenging.The challenge is linked to the massive number of LIS elements.
  • Challenge: Full channel training or online codebook search can create massive overhead, while fully digital or hybrid architectures impose high hardware complexity and power consumption.Codebooks may need to scale with the number of antennas, and connecting every element to baseband is costly.
  • Contributions: The proposed architecture makes most LIS elements passive and connects only a few randomly distributed active channel sensors to the controller baseband.The active sensors support reflection-matrix design while the remaining elements stay passive.
  • Contributions: Compressive sensing reconstructs full channels from sampled active-element channels, whereas deep learning directly maps sampled channels to reflection matrices.The deep learning approach treats sampled channels as environment descriptors and does not require array-structure knowledge.
  • Results: Both solutions approach the perfect-channel upper bound with only a few active elements and almost no training overhead.The evaluation uses an accurate ray-tracing-based DeepMIMO dataset.

II. SYSTEM AND CHANNEL MODELS

The system models LIS-assisted communication through an interaction matrix applied to transmitter-to-LIS and LIS-to-receiver channels. Practical assumptions restrict the interaction to phase shifts that are shared across OFDM subcarriers.

  • System model: The LIS-assisted system contains a transmitter, receiver, and LIS, with the LIS interaction matrix controlling how incident signals are modified.The objective is to adjust this matrix to optimize achievable rate or coverage.
  • Channel representation: The model uses an OFDM system with K subcarriers and defines transmitter-to-LIS and receiver-to-LIS channel vectors at each subcarrier.The transmitters and receivers are single-antenna in the simplified model, with extensions to multi-antenna transceivers noted.
  • Model assumption: The direct transmitter-receiver link is omitted for analysis, representing blocked or negligible-power direct-link scenarios.Under this assumption, the received signal is expressed through the LIS-assisted link.
  • System model: The interaction matrix is diagonal because each LIS element independently multiplies and reflects the incident signal by its interaction factor.The diagonal vector is denoted ψk.
  • Practical assumptions: The paper assumes phase-shifter-only elements, so each interaction factor has unit magnitude and is represented as [ψ]m = e^jφm.The same analog phase shift is applied across all subcarriers.

B. Channel Model

The paper adopts a wideband geometric channel model whose path structure depends on frequency and propagation environment, then formulates reflection-vector selection as a codebook optimization problem. Existing full-estimation and beam-training approaches incur substantial hardware or training costs.

  • Channel model: The wideband geometric model represents channels using multipath clusters with delays, complex coefficients, and azimuth/elevation arrival angles.The delay-domain channel uses the LIS array-response vector, from which frequency-domain subcarrier channels are obtained.
  • Channel model: Channel sparsity depends on propagation conditions: mmWave channels commonly have about 3–5 paths, whereas sub-6 GHz propagation generally has richer scattering.The number of paths also depends on operational frequency and environment.
  • Problem formulation: The objective is to select a reflection beamforming vector ψ from a predefined codebook to maximize achievable rate across the system.Quantized phase-shifter constraints and one vector shared across subcarriers prevent a closed-form solution.
  • Problem formulation: A useful codebook may contain thousands of candidate codewords, making exhaustive reflection-vector search difficult.The codebook size is expected to be on the order of the number of antennas.
  • Existing approaches: Full channel estimation requires complex all-element hardware and orthogonal training, while online exhaustive beam training tests codewords one by one.Both approaches therefore incur prohibitive hardware or training overhead for large LISs.
  • Objective: The paper targets near-optimal achievable rates using low-complexity hardware and low training overhead through compressive sensing and deep learning.The proposed energy-efficient architecture is paired with both design approaches.

IV. LARGE INTELLIGENT SURFACES WITH SPARSE SENSORS: A NOVEL ARCHITECTURE

The proposed sparse-sensor LIS uses mostly passive reflecting elements and a small number of active sensors for channel measurements. These measurements enable low-overhead reflection-vector design, including full-channel recovery under sparse scattering.

  • Architecture: The architecture addresses the hardware complexity and training overhead of designing LIS interaction vectors.The motivation is the difficulty of obtaining full channel vectors with massive LIS antenna arrays.
  • Architecture: The LIS combines M passive reflecting elements with M ≪ M active channel sensors distributed across the surface.The active sensors can operate in sensing or reflection mode, while passive elements remain disconnected from baseband.
  • Channel sensing: Active sensors estimate transmitter-to-LIS and receiver-to-LIS sampled channel vectors using a few pilot signals.One uplink pilot can be received simultaneously by all active elements for each sampled channel.
  • Channel sensing: The sampled vectors select channel entries corresponding to active-element indices, and the overall sampled LIS channel is formed from their elementwise product.A selection matrix represents the active-element sampling operation.
  • Reflection design: The paper develops compressive sensing and deep learning approaches to choose the optimal reflection vector from sampled channels.The two approaches are introduced as alternatives for solving the reflection-design problem without extensive beam training.
  • Compressive sensing: Compressive sensing can recover full channel vectors from active-element samples when channels experience sparse scattering, typically in mmWave and LOS-dominant settings.The recovered vectors can then support reflection-vector design.

A. Recovering Full Channels from Sampled Channels:

The paper exploits sparse scattering and a few active LIS sensors to reconstruct full transmitter and receiver channels from sampled channels. The reconstructed channels then support reflection-beamforming design, with rates approaching the perfect-channel upper bound using only a small fraction of active elements.

  • A. Recovering Full Channels from Sampled Channels:: A few active LIS sensors collect noisy sampled channel vectors during uplink training from the transmitter and receiver.The active-element selection determines the compressive sensing matrix and its properties.
  • A. Recovering Full Channels from Sampled Channels:: The estimated sparse coefficients reconstruct the full channel vector, which is then used to obtain the LIS reflection beamforming vector through offline search.This procedure uses the full channel constructed from the sampled observations rather than directly training every LIS element.
  • A. Recovering Full Channels from Sampled Channels:: Sparse scattering in mmWave and LOS-dominant sub-6 GHz channels yields a small number of paths, enabling sparse channel representations.The channel is modeled using array-response dictionaries over quantized azimuth and elevation directions.
  • A. Recovering Full Channels from Sampled Channels:: The method estimates sparse path coefficients from the sampled channels using a compressive sensing reconstruction problem.Orthogonal matching pursuit is one possible reconstruction algorithm for the sparse vector.
  • A. Recovering Full Channels from Sampled Channels:: The compressive sensing solution approaches the perfect-channel upper bound while requiring only a small fraction of LIS elements to be active.Figure 3 compares achievable rates in mmWave 28GHz and low-frequency 3.5GHz scenarios with the optimal rate R⋆ in (9).

B. Simulation Results and Discussion:

Simulations evaluate compressive sensing and deep learning LIS reflection design using ray-tracing channels and sampled observations. The compressive sensing solution approaches optimal rates with few active elements and negligible training overhead, but depends on array geometry and channel sparsity.

  • Simulation setup: Simulations use ray-tracing channels from the DeepMIMO O1 street-and-buildings scenario at 3.5GHz and 28GHz.The LIS uses 16 × 16 antennas at 3.5GHz and 64 × 64 antennas at 28GHz.
  • Compressive sensing evaluation: The compressive sensing evaluation samples channels at randomly selected active elements, reconstructs full channel vectors with OMP, and searches for the LIS interaction vector.Achievable rates are compared with an upper bound assuming perfect full channel knowledge.
  • Compressive sensing results: The compressive sensing solution achieves almost the optimal rate with a small fraction of LIS antennas active.The result demonstrates reduced active hardware and associated power consumption.
  • Training overhead: Offline search for the LIS reflection beamforming vector eliminates beam training, requiring ideally two uplink pilots to estimate sampled channels.The solution therefore has negligible training overhead and is positioned for highly mobile applications.
  • Limitations: Compressive sensing requires a higher active-element ratio at 3.5GHz than at 28GHz because the 3.5GHz scenario has more scattering.Its performance is limited in rich NLOS scattering and depends on sparse channels.
  • Deep learning solution: The deep learning approach treats sampled channel vectors as environment descriptors and learns their mapping to the optimal LIS reflection vector.These descriptors capture a multipath signature and can be obtained with negligible training overhead.

B. Proposed System Operation

The proposed LIS operation has separate learning and prediction phases. It estimates sampled channels at active elements, trains or applies a model, and selects reflection vectors for transmission.

  • System phases: The proposed system operates in learning and prediction phases over channel coherence blocks.The learning phase collects data and trains the model; the prediction phase uses the trained model.
  • Learning phase: During learning, active LIS elements estimate sampled channels from orthogonal uplink pilots transmitted by the transmitter and receiver.These estimates form the sampled channel vectors used by subsequent processing.
  • Learning phase: The LIS exhaustively tests every reflection codeword, receives its achievable-rate feedback, and records the resulting channel-rate pair in dataset D.The highest-rate codeword is used for data transmission during the remainder of the coherence block.
  • Learning phase: After collecting S coherence-block samples, the deep learning model is trained to map sampled channels to predicted achievable rates for all codebook vectors.The model is trained using the entire dataset D.
  • System phases: The deep learning system must retrain and refine its model frequently to account for environmental changes.The paper assumes a phase transition after training but notes that changing environments require further retraining.
  • Prediction phase: During prediction, the LIS estimates sampled channels, predicts rates for candidate vectors, and selects the vector with the highest predicted rate for reflection.The system may instead refine the kB highest-predicted beams online with receiver feedback.

C. Deep Learning Model

The paper uses a supervised MLP to predict achievable rates for LIS reflection codewords from sampled channel descriptors. Its preprocessing and loss design normalize inputs and targets while preserving relevant channel information.

  • Input representation: The model uses sampled channel vectors across K sub-carrier frequencies as environment descriptors, giving each input vector dimensionality KM.Complex entries are converted into real and imaginary components, doubling the input dimensionality for real-valued computation.
  • Input representation: Input samples are normalized by the inverse of the maximum absolute value over the whole dataset.The paper states that this normalization supports learning while preserving distance information encoded in environment descriptors.
  • Target representation: The supervised targets are normalized achievable-rate vectors containing the desired rate for every reflection vector in codebook P.Independent vector normalization avoids bias toward strong responses and gives receivers equal importance regardless of distance from the LIS.
  • Neural network architecture: The network is a Q-layer multilayer perceptron whose hidden structure alternates fully connected and nonlinear layers, with ReLU activations.The final layer is fully connected, and each neuron sees all outputs from the preceding layer.
  • Prediction objective: The model predicts achievable rates for every LIS interaction vector, then selects the vector with the highest predicted rate.This output representation directly supports reflection-beam selection from the codebook.
  • Training loss: Training minimizes mean-squared error between normalized target rates r and predicted rates br over the neural-network parameters.The regression loss is defined through MSE(r,br).

VII. SIMULATION RESULTS

The evaluation compares compressive sensing and deep learning reflection beamforming on ray-traced DeepMIMO channels. It examines realistic environmental effects across mmWave and sub-6 GHz settings and varies system and learning parameters.

  • Evaluation scope: Performance is compared at mmWave and sub-6 GHz frequencies using realistic channels whose propagation depends on environmental geometry and materials.The evaluation also investigates the impact of system and machine-learning parameters on deep learning performance.
  • Simulation setup: The simulations evaluate deep learning and compressive sensing reflection beamforming using ray-traced channels from the DeepMIMO dataset.The dataset is generated from the outdoor ray-tracing scenario O1 using Remcom Wireless InSite.
  • Simulation setup: The adopted system contains one LIS reflecting a signal from a transmitter to a receiver, with receiver locations selected on an x-y grid.This setup captures dependence on environment geometry, materials, device locations, and operating frequency.

THE ADOPTED DEEPMIMO DATASET PARAMETERS

The experiments use DeepMIMO ray-traced channels, DFT reflection codebooks, and neural networks trained on sampled channels. Both proposed methods approach the perfect-channel upper bound with few active elements, while their trade-offs depend on channel sparsity and training data.

  • Dataset and system parameters: The default LIS uses 64×64 antennas at 28 GHz and 16×16 antennas at 3.5 GHz, with randomly selected active channel sensors.The transmitter and receiver each have a single antenna, and each LIS element has 3 dBi gain.
  • Channel generation: DeepMIMO channels are generated for candidate receiver locations using transmitter-LIS and receiver-LIS channels, then sampled and noise-corrupted at active elements.The noisy sampled channels are used to design reflection-beamforming vectors through the proposed CS and DL approaches.
  • Reflection codebook: The LIS reflection codebook is constructed from horizontal and vertical DFT codebooks using a Kronecker product.The adopted codebook is DFT_MH ⊗ DFT_MV for the UPA structure.
  • Achievable rates: With M = 4 active antennas out of 4096, deep learning achieves almost 85% of the optimal achievable rate.The two proposed solutions approach the upper bound with 28–36 active antennas, less than 1% of the 4096-element LIS.
  • Achievable rates: At sub-6 GHz, deep learning converges to the upper bound with 4 active elements, whereas compressive sensing requires around 18.The larger deep learning gain occurs where channels are less sparse, but it requires collecting a training dataset.
  • Limitations: Compressive sensing relies on channel sparsity and becomes limited in rich NLOS scattering scenarios.The simulations show that CS requires a higher active-element ratio under less sparse propagation conditions.

C. How much training is needed for the deep learning model?

The deep learning model improves as it sees more sampled user-location data, approaching near-optimal rates with only a small number of active sensors. Larger datasets help especially for multipath channels, while low-power operation remains effective.

  • The learning dataset contains sampled channel vectors captured while the receiver is randomly sampling the x-y grid.
  • With 8 active antennas, the model achieves almost 90% of the optimal rate after training on 10,000 of 53,400 grid points.
  • The deep learning approach gains over compressive sensing as dataset size increases because compressive sensing does not use prior channel-estimation or LIS-interaction observations.
  • With only 8 active receivers, the deep learning solution approaches the perfect-channel upper bound without beam-training overhead for different LIS sizes.
  • Transmit power: At relatively small transmit powers and low SNR regimes, the deep learning solution can still learn and approach the optimal achievable rate.
  • Number of channel paths: As the number of channel paths increases, convergence to the upper bound slows, but a sufficiently large dataset enables learning from multipath channels.

E. Refining the deep learning prediction

The system can refine the deep learning model’s predicted beams by training over a small set of promising candidates. This improves achievable rates, while fully model-based selection removes beam-training overhead but is sensitive to environmental changes.

  • Fully relying on deep learning to determine the reflection beamforming vector eliminates beam-training overhead and can enable highly mobile applications.
  • The fully model-based achievable rates may be sensitive to small environmental changes, motivating refinement in more time-varying settings.
  • The model predicts the most promising kB beams by their rates, then receiver beam training selects the final reflection vector.
  • Refining the most promising kB beams yields higher achievable rates than relying completely on the deep learning model to predict the best beam.
  • The proposed architecture uses few active LIS elements, while compressive sensing reconstructs all channels and deep learning predicts reflection matrices directly from sampled channels.
  • Both solutions achieve near-optimal rates with negligible training overhead and few active elements; deep learning needs fewer active elements but requires enough dataset collection.
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