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Planar Diffractive Neural Networks Empowered Communications: A Spatial Modulation Scheme

Xiaokun Teng, Yanqing Ren, Weicong Chen, Wankai Tang, Xiao Li, Shi Jin

TL;DR

The paper introduces planar diffractive neural networks (PDNNs) as on-device, wave-domain signal processors to simplify RF front-ends and reduce digital baseband load. It proposes a PDNN-SSK system with transmitter and receiver PDNNs that jointly perform modulation, beamforming, and non-coherent detection using a single RF chain, and develops a rigorous theory for conditional detection probability and symbol error rate. To overcome the non-convex optimization of PDNN phase configurations, the authors employ a surrogate model-based training approach, demonstrating superior convergence and end-to-end performance. Numerical results validate the theory, reveal fundamental design principles (e.g., deeper structures and stronger coupling, wider PDNNs), and illustrate energy-efficient scaling of modulation order compared to conventional schemes. The work positions PDNNs as a versatile RF computing platform with potential for multi-user, broadband, and sensing-enabled wireless systems.

Abstract

Diffractive neural networks, where signal processing is embedded into wave propagation, promise light-speed and energy-efficient computation. However, existing three-dimensional structures, such as stacked intelligent metasurfaces (SIMs), face critical challenges in implementation and integration. In contrast, this work pioneers planar diffractive neural networks (PDNNs) empowered communications, a novel architecture that performs signal processing as signals propagate through artificially designed planar circuits. To demonstrate the capability of PDNN, we propose a PDNN-based space-shift-keying (PDNN-SSK) communication system with a single radio-frequency (RF) chain and a maximum power detector. In this system, PDNNs are deployed at both the transmitter and receiver to jointly execute modulation, beamforming, and detection. We conduct theoretical analyses to provide the maximization condition of correct detection probability and derive the closed-form expression of the symbol error rate (SER) for the proposed system. To approach these theoretical benchmarks, the phase shift parameters of PDNNs are optimized using a surrogate model-based training approach, which effectively navigates the high-dimensional, non-convex optimization landscape. Extensive simulations verify the theoretical analysis framework and uncover fundamental design principles for the PDNN architecture, highlighting its potential to revolutionize RF front-ends by replacing conventional digital baseband modules with this integrable RF computing platform.

Planar Diffractive Neural Networks Empowered Communications: A Spatial Modulation Scheme

TL;DR

The paper introduces planar diffractive neural networks (PDNNs) as on-device, wave-domain signal processors to simplify RF front-ends and reduce digital baseband load. It proposes a PDNN-SSK system with transmitter and receiver PDNNs that jointly perform modulation, beamforming, and non-coherent detection using a single RF chain, and develops a rigorous theory for conditional detection probability and symbol error rate. To overcome the non-convex optimization of PDNN phase configurations, the authors employ a surrogate model-based training approach, demonstrating superior convergence and end-to-end performance. Numerical results validate the theory, reveal fundamental design principles (e.g., deeper structures and stronger coupling, wider PDNNs), and illustrate energy-efficient scaling of modulation order compared to conventional schemes. The work positions PDNNs as a versatile RF computing platform with potential for multi-user, broadband, and sensing-enabled wireless systems.

Abstract

Diffractive neural networks, where signal processing is embedded into wave propagation, promise light-speed and energy-efficient computation. However, existing three-dimensional structures, such as stacked intelligent metasurfaces (SIMs), face critical challenges in implementation and integration. In contrast, this work pioneers planar diffractive neural networks (PDNNs) empowered communications, a novel architecture that performs signal processing as signals propagate through artificially designed planar circuits. To demonstrate the capability of PDNN, we propose a PDNN-based space-shift-keying (PDNN-SSK) communication system with a single radio-frequency (RF) chain and a maximum power detector. In this system, PDNNs are deployed at both the transmitter and receiver to jointly execute modulation, beamforming, and detection. We conduct theoretical analyses to provide the maximization condition of correct detection probability and derive the closed-form expression of the symbol error rate (SER) for the proposed system. To approach these theoretical benchmarks, the phase shift parameters of PDNNs are optimized using a surrogate model-based training approach, which effectively navigates the high-dimensional, non-convex optimization landscape. Extensive simulations verify the theoretical analysis framework and uncover fundamental design principles for the PDNN architecture, highlighting its potential to revolutionize RF front-ends by replacing conventional digital baseband modules with this integrable RF computing platform.

Paper Structure

This paper contains 18 sections, 4 theorems, 40 equations, 9 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. The Proposed PDNN Empowered Communication System Model
  3. The General Model of PDNN
  4. An Example Design of PDNN layer
  5. PDNN-SSK communication system
  6. Performance Analysis
  7. Conditional Correct Detection Probability
  8. Closed-Form SER Analysis
  9. PDNN Optimization for Optimal Detection
  10. Problem Formulation
  11. Surrogate Model Training
  12. Numerical Results
  13. Simulation Setup
  14. EM Wave Propagation
  15. SER Performance
  16. ...and 3 more sections

Key Result

theorem 1

The CCDP $P_{c,m}$ is monotonically increasing with the desired signal amplitude, $|c_{m,m}|$, and monotonically decreasing with each of the interfering signal amplitudes, $|c_{m',m}|$, for all $m' \neq m$.

Figures (9)

  • Figure 1: PDNN signal processing architecture. (a) General model of signal flow and layer structure. (b) Schematic diagram of an example layer design.
  • Figure 2: The schematic diagram of PDNN-SSK communication system
  • Figure 3: Visualization of the wave-based signal processing in the PDNN-SSK communication system with $L_T=L_R=2$. The vertical strips are 1D heatmaps of the signal amplitude, while the square and diagonal heatmaps illustrate the coupling amplitude matrices and the trained phase shift matrices, respectively.
  • Figure 4: Theoretical and simulated SER performance for modulation orders of $M\in \{4, 16, 64\}$
  • Figure 5: SER performance comparison of the PDNN-SSK modulation scheme with conventional ones for $M\in\{4, 16\}$. For the proposed scheme, both a low-complexity NC detector and an optimal ML detector are evaluated.
  • ...and 4 more figures

Theorems & Definitions (14)

  • remark 1
  • theorem 1: Monotonicity of CCDP
  • proof
  • proposition 1: Optimal Condition for CCDP
  • proof
  • remark 2
  • theorem 2: Accurate closed-form SER
  • proof
  • remark 3
  • proposition 2: Asymptotic closed-form SER
  • ...and 4 more