  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.
