Source-linked AI summary
Unsupervised Learning for Passive Beamforming
Jiabao Gao, Caijun Zhong, Xiaoming Chen, Hai Lin, Zhaoyang Zhang
TL;DR
RIS passive beamforming is difficult because unit-modulus phase constraints make optimal design non-convex, while SDR-based solutions are computationally expensive. The paper trains a customized DNN offline with unsupervised learning for online phase-shift prediction, achieving real-time configuration with substantially lower computation and decent rate performance.
Problem
Unit-modulus constraints make optimal RIS passive beamforming difficult, while conventional SDR-based solutions are computationally expensive for real-time implementation.
Method
A customized DNN is trained offline with an unsupervised loss based on the passive beamforming objective, requiring no labels.
Results
The proposed RISBFNN runs thousands of times faster than SDR while maintaining decent rate performance and enabling real-time phase-shift configuration.
Takeaways & Limitations
Unsupervised learning provides a practical candidate for real-time passive beamforming in RIS-assisted communication systems.
Abstract
from arXiv · showhide
Reconfigurable intelligent surface (RIS) has recently emerged as a promising candidate to improve the energy and spectral efficiency of wireless communication systems. However, the unit modulus constraint on the phase shift of reflecting elements makes the design of optimal passive beamforming solution a challenging issue. The conventional approach is to find a suboptimal solution using the semi-definite relaxation (SDR) technique, yet the resultant suboptimal iterative algorithm usually incurs high complexity, hence is not amenable for real-time implementation. Motivated by this, we propose a deep learning approach for passive beamforming design in RIS-assisted systems. In particular, a customized deep neural network is trained offline using the unsupervised learning mechanism, which is able to make real-time prediction when deployed online. Simulation results show that the proposed approach maintains most of the performance while significantly reduces computation complexity when compared with SDR-based approach.
I. INTRODUCTION
RIS can improve wireless links through low-cost passive reflection, but designing its phase shifts is difficult under unit-modulus constraints. The paper proposes unsupervised deep learning to reduce computation while retaining performance relative to SDR.
- RIS uses low-cost reconfigurable reflecting elements to coherently combine reflected and direct signals, improving intended-user receive strength.Its passive operation distinguishes it from amplify-and-forward relaying and backscatter communication.
- Passive beamforming is critical, but the unit modulus constraint makes deriving an optimal phase-shift solution difficult.
- SDR provides a conventional suboptimal solution, but its computational expense prevents real-time implementation.
- The proposed approach uses a customized DNN with unsupervised learning, avoiding the labelling overhead of supervised learning.The network is trained offline for passive beamforming design.
- The paper evaluates the proposed approach through simulations and organizes its analysis around modeling, conventional methods, learning design, and performance evaluation.
II. SYSTEM MODEL AND PROBLEM FORMULATION
The system comprises an AP, RIS, and single-antenna user, with the received signal combining direct and reflected paths. Given optimal transmit beamforming, RIS phase shifts are optimized under unit-modulus constraints.
- The considered system contains an M-antenna AP, an RIS with N reflecting elements, and a single-antenna user.A controller adjusts RIS phase shifts and coordinates channel-estimation and reflection modes.
- The user receives the superposition of the AP’s direct signal and the RIS-reflected signal.
- The channel model assumes quasi-static flat-fading channels for the direct AP-user, RIS-user, and RIS-AP links.The transmit beamforming vector satisfies a power constraint, and the information symbol has unit power.
- Given the RIS phase matrix, maximum-ratio transmission is the optimal transmit beamforming strategy.
- The RIS phase-shift design maximizes transmission rate subject to |θ_n| = 1 for n = 1, . . . , N.
III. CONVENTIONAL APPROACH
The passive beamforming problem is generally non-convex and difficult to solve optimally. For multi-antenna systems, conventional methods therefore seek suboptimal solutions using SDR.
- Problem P1 is a non-convex QCQP whose optimal solution is intractable except in the single-antenna case.
- For M ≥ 2, conventional passive beamforming uses techniques such as SDR to obtain a suboptimal solution.
- A. Single antenna case: When M = 1, the optimal phase shifts are computed by aligning each reflected component’s phase with the direct-link phase.
B. Multi-antenna case
For the multi-antenna case, the passive beamforming problem is reformulated as a homogeneous QCQP and relaxed into a convex semidefinite problem. Randomization then recovers a suboptimal phase vector.
- B. Multi-antenna case: For M ≥ 2, problem P1 is reformulated as a homogeneous QCQP with unit-modulus phase constraints.
- B. Multi-antenna case: The reformulation uses D_h = diag{h_r} and an auxiliary variable t.
- B. Multi-antenna case: Defining Q = θ̄θ̄^H expresses the quadratic objective as tr(RQ), while Q is positive semidefinite and rank one.
- B. Multi-antenna case: Relaxing the rank-one constraint converts the formulation into a convex problem with Q ⪰ 0 and unit diagonal entries.
- B. Multi-antenna case: Randomization extracts a suboptimal solution from the relaxed optimum, followed by normalization to recover the RIS phase vector.
IV. UNSUPERVISED LEARNING BASED APPROACH
Conventional optimization methods can produce suboptimal passive-beamforming solutions with high complexity, motivating a deep-learning framework for problem P1.
- Conventional optimization methods do not guarantee the performance of their suboptimal solutions and generally incur high complexity.
A. Feature Design
The feature design exploits the product structure of the channel matrices and uses an unsupervised objective based directly on the original optimization objective.
- Feature Design: Directly using G, h_r, and h_d as inputs is ineffective and problematic.
- Feature Design: The feature vector uses products of elements from G and h_r, with real and imaginary parts treated as separate features.
- Feature Design: The resulting feature design reduces input dimension while exploiting inherent structural information.
- Loss Function: The loss function is the negative of problem P1's objective rather than supervised-learning mean square error.
- Loss Function: A Lambda layer converts the predicted real phase-shift vector into complex form for loss computation.
C. Network Architecture and training
RISBFNN is a scalable fully connected network trained with stabilization and early-stopping techniques, while performance depends on batch normalization and sufficient training data.
- Network Architecture: RISBFNN contains five fully connected layers with neuron counts proportional to N, ending with a linear phase-shift output layer.
- Training: Adam optimization, learning-rate decay, and early stopping are used to improve training efficiency.
- Training: Without batch normalization and a sufficiently large batch size, training and validation loss cannot decrease.
- Training: A batch size of 5000 and a batch-normalization layer after each fully connected layer work well across various settings.
- Training: 150000 samples suffice for M = 4, N = 8, whereas 350000 are required for M = 4, N = 32.
- Training: The experiments use 800000 training samples, 200000 validation samples, and 10000 testing samples.
V. SIMULATION RESULTS
The simulations use an indoor Rayleigh-fading scenario with distance-dependent path loss and randomized user geometry.
- Simulation Setup: The simulations model all channels using independent Rayleigh small-scale fading in an indoor scenario.
- Simulation Setup: Path loss is computed as 20.4 log10(d/dref) dB with dref = 1m.
- Simulation Setup: The AP-to-RIS distance is set to d_AR = 8m, while d_0 and d_1 are randomly generated within specified uniform ranges.
- Simulation Setup: The simulations use p/σ^2 = 10 dB.
A. Impact of N
Increasing the number of reflecting elements improves performance for both RISBFNN and SDR, while RISBFNN remains near-optimal for single-antenna systems but shows a larger gap in multi-antenna systems as N grows.
- A. Impact of N: Performance improves for both RISBFNN and SDR as the number of reflecting elements N increases.The increase is attributed to enhanced effective gain of the reflecting path.
- A. Impact of N: For the single-antenna case, RISBFNN and SDR performance nearly overlap, indicating near-optimal RISBFNN performance.
- A. Impact of N: In the multi-antenna case, the performance gap between SDR and RISBFNN becomes more significant as N increases.
C. Computation Complexity
RISBFNN has lower stated complexity than SDR, runs thousands of times faster, and is positioned for real-time use when computation must fit within the channel coherence time.
- C. Computation Complexity: RISBFNN has complexity O((64M + 804)N^2), compared with O(N^6.5) for SDR.
- C. Computation Complexity: RISBFNN runs thousands of times faster than SDR in average running-time comparisons on the same Intel i7-8700 CPU.The SDR problem P4 is solved using CVX.
- C. Computation Complexity: The channel coherence time in the considered indoor scenario is 13.77 ms, and passive beamforming computation should not exceed it.The scenario assumes a maximum moving speed of 1.5 m/s and carrier frequency of 2.6 GHz.
- C. Computation Complexity: The SDR approach is described as inapplicable in the considered indoor scenario, making RISBFNN a promising candidate for practical implementation.