Data-Driven Deep MIMO Detection:Network Architectures and Generalization Analysis

TL;DR

This paper proposes inspecting the fully data-driven DeepSIC detection within a Network-of-MLPs architecture, which is composed of multiple interconnected MLPs via outer and inner Directed Acyclic Graphs (DAGs) and reveals that an exponential dependence on the number of iterations for DeepSIC can be eliminated in GNNSIC due to parameter sharing.

Abstract

In practical Multiuser Multiple-Input Multiple-Output (MU-MIMO) systems, symbol detection remains challenging due to severe inter-user interference and sensitivity to Channel State Information (CSI) uncertainty. In contrast to the mostly studied belief propagation-type model-driven methods, which incur high computational complexity, Soft Interference Cancellation (SIC) strikes a good balance between performance and complexity. To further address CSI mismatch and nonlinear effects, the recently proposed data-driven deep neural receivers, such as DeepSIC, leverage the advantages of deep neural networks for interference cancellation and symbol detection, demonstrating strong empirical performance. However, there is still a lack of theoretical underpinning for why and to what extent DeepSIC could generalize with the number of training samples. This paper proposes inspecting the fully data-driven DeepSIC detection within a Network-of-MLPs architecture, which is composed of multiple interconnected MLPs via outer and inner Directed Acyclic Graphs (DAGs). Within such an architecture, DeepSIC can be upgraded as a graph-based message-passing process using Graph Neural Networks (GNNs), termed GNNSIC, with shared model parameters across users and iterations. Notably, GNNSIC achieves excellent expressivity comparable to DeepSIC with substantially fewer trainable parameters, resulting in improved sample efficiency and enhanced user generalization. By conducting a norm-based generalization analysis using Rademacher complexity, we reveal that an exponential dependence on the number of iterations for DeepSIC can be eliminated in GNNSIC due to parameter sharing. Simulation results demonstrate that GNNSIC attains comparable or improved Symbol Error Rate (SER) performance to DeepSIC with significantly fewer parameters and training samples.

Figures (7)

• Figure 1: The internal structure of a GNNSIC network block at the $l$-th iteration. Each user node forms its block input by concatenating the received signal $\boldsymbol{y}$, the channel state $\boldsymbol{h}_i$, and the prior soft symbol estimate $\hat{\boldsymbol{p}}_i^{(l-1)}$, which are processed by a set of MLPs constituting the inner computation graph. Blue dashed lines indicate message exchanges among user nodes induced by the underlying interference graph. This block is repeatedly applied across iterations according to the outer DAG defined by the Network-of-MLPs architecture.
• Figure 2: SER performance versus SNR for GNNSIC, iterative SIC, and DeepSIC over a $6 \times 6$ linear Gaussian channel with perfect CSI ($\sigma_e^2 = 0$) and CSI uncertainty ($\sigma_e^2 = 0.1$).
• Figure 3: SER versus SNR for GNNSIC, iterative SIC, and DeepSIC over a $4 \times 4$ synthetic quantized Gaussian channel with perfect CSI ($\sigma_e^2 = 0$) and CSI uncertainty ($\sigma_e^2 = 0.1$).
• Figure 4: SER versus SNR for GNNSIC, iterative SIC, and DeepSIC over a $4 \times 4$ synthetic Poisson channel with perfect CSI ($\sigma_e^2 = 0$) and CSI uncertainty ($\sigma_e^2 = 0.1$).
• Figure 5: SER versus CSI_NO for GNNSIC and DeepSIC at $\mathrm{SNR} = 10\,\mathrm{dB}$ and $14\,\mathrm{dB}$ on a $6 \times 6$ synthetic linear Gaussian channel.

Theorems & Definitions (8)

• Lemma 1: galanti2023norm
• Lemma 2: Peeling Lemma galanti2023norm
• proof
• Proposition 1
• proof
• Theorem 1
• proof
• Corollary 1