Combining the Viterbi Algorithm and Graph Neural Networks for Efficient MIMO Detection

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Which baseline algorithms—such as ZF, MMSE, ML, and DeepMIMO—have you used to compare your model? If all are state-of-the-art, could you please clarify?

Which metrics were employed to assess detection performance, and do these criteria align with industry-standard benchmarking procedures?

The learning curve analysis is clearly provided, but the model training explanation would be strengthened with further evidence supporting the choice of the 125th epoch over nearby epochs.

Although a more thorough examination of the trade-offs between computational complexity and SER across various MIMO sizes and modulation techniques would improve the evaluation, the performance comparison in Figures 9–12 is instructive.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Review Comments on the Paper "Combining Viterbi Algorithm and Graph Neural Networks for Efficient MIMO Detection"(ID: electronics-3576871)

 

In this manuscript, there are some strengths as follows.

1. Innovative Approach: The integration of the Viterbi Algorithm (VA) with Graph Neural Networks (GNNs) for MIMO detection is a novel and promising contribution to the field. The hybrid model effectively leverages the strengths of both techniques.
2. Comprehensive Background: The paper provides a thorough review of traditional MIMO detection methods and recent advancements in deep learning, setting a solid foundation for the proposed work.
3. Clear Methodology: The description of the VA-GNN model is detailed, with clear explanations of the Tanner graph structure, message-passing mechanisms, and the conversion of VA outputs to soft values.
4. Experimental Validation: The paper includes extensive simulations with varying antenna configurations and modulation schemes, demonstrating the model’s superior performance over traditional methods.
5. Practical Relevance: The focus on reducing computational complexity while maintaining detection accuracy addresses a critical challenge in large-scale MIMO systems, making the work highly relevant for real-world applications.

Meantime, there are some weaknesses and suggestions for improvement as follows. 

1. Theoretical Justification: The paper lacks a theoretical analysis of why the VA-GNN combination outperforms standalone methods. Adding a section on the theoretical underpinnings (e.g., convergence guarantees, complexity analysis) would strengthen the work.
2. Comparison with Recent DL Methods: While the paper compares the model with traditional techniques, it omits comparisons with other recent deep learning-based MIMO detectors (e.g., transformer-based models). Including such comparisons would better situate the work in the current research landscape.
3. Ablation Study: The contribution of each component (VA and GNN) to the overall performance is unclear. An ablation study would help quantify their individual impacts and justify the hybrid design.
4. Parameter Sensitivity: The choice of hyperparameters (e.g., \(\alpha\) in soft output conversion, \(D\) in GNN layers) is not thoroughly justified. A sensitivity analysis would provide insights into the robustness of these choices.
5. Computational Complexity: Although the paper claims reduced complexity compared to ML detection, no quantitative complexity analysis (e.g., FLOPs, runtime) is provided. Adding this would make the efficiency claims more concrete.
6. Reproducibility: The description of the training process (e.g., learning rates, batch sizes) and dataset generation (e.g., channel models, SNR ranges) is insufficient for replication. Expanding these details would improve reproducibility.

Additional Recommendations: 

- Visualization: Include visualizations of the Tanner graph or message-passing process to enhance clarity for readers unfamiliar with GNNs. 

- Real-World Data: Validate the model on real-world MIMO channel data (e.g., from 5G/6G testbeds) to demonstrate practical applicability beyond simulations. 

- Future Work: Expand the discussion on adaptive modulation and advanced error correction to outline specific directions for further optimization. 

Overall, the paper presents a compelling and well-executed study with significant potential. Addressing these suggestions would further elevate its rigor, clarity, and impact.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

Reviewer Comments on the Manuscript: electronics-3576871-peer-review-v2

Overall Assessment: 

The manuscript presents a novel approach to MIMO detection by integrating the Viterbi Algorithm (VA) with a Graph Neural Network (GNN). The research is well-motivated, addressing a critical challenge in wireless communication systems, and the proposed method demonstrates promising results. The paper is well-structured, clearly written, and provides sufficient technical details for reproducibility. Below are specific comments and recommendations.

 

Strengths: 

1. Innovative Approach: The combination of VA and GNN for MIMO detection is innovative and leverages the strengths of both techniques. The VA provides a structured initialization, while the GNN refines the signal through iterative message-passing, leading to improved performance.
2. Comprehensive Evaluation: The authors thoroughly evaluate the proposed model under various configurations (e.g., different antenna sizes and modulation schemes) and compare it with state-of-the-art methods. The results demonstrate clear advantages over traditional and some DL-based approaches.
3. Technical Rigor: The mathematical derivations and experimental setup are detailed and rigorous. The transformation of complex-valued MIMO systems into real-valued representations is particularly well-explained.
4. Clarity and Organization: The paper is logically organized, with clear sections and figures that aid understanding. The background and methodology are well-presented, making the work accessible to readers with varying levels of expertise.

 

Minor Comments: 

1. Computational Complexity: While the proposed model achieves superior SER performance, its computational latency is higher than some baseline methods (e.g., ZF, MMSE). The authors should discuss potential optimizations or trade-offs for practical deployment, especially in real-time systems.
2. Generalizability: The experiments are conducted under simulated conditions. Including results from real-world datasets or testbeds (as hinted in the future work) would strengthen the claims about the model's practicality.
3. Hyperparameter Sensitivity: The choice of hyperparameters (e.g., \(\alpha = 1\) for soft output, \(D = 20\) for GNN dimensions) seems arbitrary. A brief discussion or sensitivity analysis would justify these choices.
4. Comparison with Recent Work: The manuscript could benefit from comparing the proposed method with more recent DL-based MIMO detection techniques, such as transformer-based models or hybrid architectures, to better position its contributions.
5. The acronym "VA" is introduced before its full form ("Viterbi Algorithm") in the abstract. Please ensure all acronyms are defined at first use.
6. Figure 8 (learning curves) lacks axis labels for the y-axis ("Accuracy") and x-axis ("Epochs"). Adding these would improve clarity.
7. In Table 2, the latency for ML detection is noted as \(\sim 3.6 \times 10^6\) ms, which seems unusually high. Please verify this value or provide context.

Recommendation: 

The manuscript makes a significant contribution to the field of MIMO detection and is suitable for publication after addressing the minor revisions mentioned above. The proposed Viterbi-GNN model is a promising advancement, and the results are compelling. With slight refinements, this paper would be a valuable addition to the literature. 

 

Final Suggestions: Accept with Minor Revisions 

Overall, this is a strong paper that aligns well with the journal's scope and standards. Congratulations to the authors on their work!

Author Response

Please see the attachment.

Author Response File: Author Response.pdf