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 near-optimal 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）无线信道传输的符号是实现MIMO技术优势的关键。然而，最优MIMO检测的复杂度随MIMO维度呈指数增长，很快变得不实用。近年来，随机抽样贝叶斯推断技术（如马尔可夫链蒙特卡洛方法，MCMC）与梯度下降法（GD）相结合，为MIMO检测提供了有前景的框架。本文提出通过Nesterov梯度法加速的MCMC随机游走探索离散搜索空间，以高效逼近最优检测。Nesterov梯度法引导MCMC在避免计算昂贵的矩阵求逆和线搜索的同时实现高效搜索。所提方法在每次随机游走中采用多次梯度下降，在添加随机扰动前充分逼近搜索空间重要区域，保证高采样效率。为增强探索能力，通过简单操作从Nesterov梯度法的轨迹中推导额外样本，有效补充用于统计推断的样本列表，提升整体MIMO检测性能。此外，我们设计早停策略终止不必要的搜索，显著降低复杂度。仿真结果与复杂度分析表明，所提方法在未编码和编码MIMO系统中均能达到近最优性能，适应实际信道模型，并良好扩展至大维度MIMO系统。