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.

翻译：准确检测多输入多输出（MIMO）无线信道中传输的符号，对于实现MIMO技术的优势至关重要。然而，最优MIMO检测的复杂度随MIMO维度呈指数增长，很快变得不切实际。近年来，基于随机采样的贝叶斯推断技术（如马尔可夫链蒙特卡洛（MCMC））与梯度下降（GD）方法相结合，为MIMO检测提供了一个有前景的框架。本文提出通过利用Nesterov梯度加速的MCMC随机游走，高效探索离散搜索空间以逼近最优检测。Nesterov GD引导MCMC在不进行计算昂贵的矩阵求逆和线性搜索的情况下实现高效搜索。所提方法在每次随机游走中执行多次GD，在添加随机扰动前充分逼近搜索空间的重要区域，确保高采样效率。为增强探索能力，通过Nesterov GD轨迹的简单操作派生额外样本，有效补充统计推断的样本列表，提升MIMO检测的整体性能。此外，我们设计了一种提前终止策略以停止不必要的进一步搜索，显著降低复杂度。仿真结果和复杂度分析表明，所提方法在未编码和编码MIMO系统中均表现出卓越性能，能适应实际信道模型，并可良好扩展至大规模MIMO维度。