Gradient-Based Markov Chain Monte Carlo for MIMO Detection

TL;DR

This work proposes to efficiently approach optimal detection by exploring the discrete search space via MCMC random walk accelerated by Nesterov’s gradient method, achieving exceptional performance in both uncoded and coded MIMO systems, adapts to realistic channel models, and scales well to large MIMO dimensions.

Abstract

Accurately detecting symbols transmitted over multiple-input multiple-output (MIMO) wireless channels is crucial in realizing the benefits of MIMO techniques. However, optimal MIMO detection is associated with a complexity that grows exponentially with the MIMO dimensions and quickly becomes impractical. Recently, stochastic sampling-based Bayesian inference techniques, such as Markov chain Monte Carlo (MCMC), have been combined with the gradient descent (GD) method to provide a promising framework for MIMO detection. In this work, we propose to efficiently approach optimal detection by exploring the discrete search space via MCMC random walk accelerated by Nesterov's gradient method. Nesterov's GD guides MCMC to make efficient searches without the computationally expensive matrix inversion and line search. Our proposed method operates using multiple GDs per random walk, achieving sufficient descent towards important regions of the search space before adding random perturbations, guaranteeing high sampling efficiency. To provide augmented exploration, extra samples are derived through the trajectory of Nesterov's GD by simple operations, effectively supplementing the sample list for statistical inference and boosting the overall MIMO detection performance. Furthermore, we design an early stopping tactic to terminate unnecessary further searches, remarkably reducing the complexity. Simulation results and complexity analysis reveal that the proposed method achieves exceptional performance in both uncoded and coded MIMO systems, adapts to realistic channel models, and scales well to large MIMO dimensions.

Figures (12)

• Figure 1: Block diagram of gradient-based MCMC sampling, where $P$ parallel samplers independently conduct $S$ sample draws to derive the sample list for the final estimate. Init.: Initialization.
• Figure 2: Residual norm from the estimated vector as a function of the number of GD iterations in an ${\text{8}\times\text{8}}$ MIMO system with 16-QAM and ${\text{SNR} = \text{20}\;\text{dB}}$. The naive GD uses the exact line search boyd2004convex to determine the learning rate. The Nesterov's GD and preconditioned GD follow the configurations in nesterov1983method and gowdaMetropolisHastingsRandomWalk2021, respectively.
• Figure 3: BER performance of NAG-MCMC with one GD or multiple GDs per random walk in an uncoded ${\text{8}\times\text{8}}$ MIMO system with 16-QAM under Rayleigh fading channels. The BER curves for MHGD and NAG-MCMC are marked by $P\times S$, representing the number of samplers and sampling iterations, respectively.
• Figure 4: Complexity scalinig behavior with respect to the number of antennas with $N_{\rm t}=N_{\rm r}\in [0,256]$ and 16-QAM modulation.
• Figure 5: BER convergence property with respect to the number of sampling iterations in Rayleigh fading channels.

Theorems & Definitions (3)

• Lemma 1
• Remark 1
• Remark 2