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Massive MIMO Detection Based on Belief Propagation in Spatially Correlated Channels

机译：基于信度传播的空间相关信道大规模MIMO检测

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Belief Propagation (BP) is an iterative method to solve inference problems by passing messages in a factor graph. Due to its low complexity and near optimality, the BP algorithm and its variants have been widely applied to solve massive Multiple-Input Multiple-Output (MIMO) detection problems. However, it is worth noting that most of the existing works assume that the channels are spatially independently fading, in which scenario the BP iterations could converge to a fix point even there exist loops in the factor graph. Actually, the practical channels are spatially correlated fading due to the limited-scattering radio environment. Unfortunately, we found that the convergence performance of the BP iterations suffers severe degradation from the spatial correlation. Thus the main work of this paper is to improve the convergence performance of the BP iterations in the massive MIMO detection with the spatially correlated fading channels. In particular, we present two efficient methods, i.e., automatic damping and pre-processing. In the first method, a heuristic damping factor is calculated automatically in each BP iteration from the Kullback-Leibler divergence between the two successive messages, i.e., the current and the previous iterations, and then the calculated damping factor is used to smooth the messages (damping). In the second method, the channel matrices are first pre-processed by a de-correlation matrix, then followed by normal BP algorithms. The de-correlation can also be approximated by fast Fourier transform when the number of receive antennas is a large radix-2 number. The two methods can be used together, exhibiting superior performance over the conventional BP with both analytical spatially-correlated channel models and realistic measured channels in our simulation results.
机译：信念传播（BP）是一种通过在因子图中传递消息来解决推理问题的迭代方法。由于其低复杂度和接近最优性，BP算法及其变体已被广泛应用于解决大规模多输入多输出（MIMO）检测问题。但是，值得注意的是，大多数现有工作都假设信道在空间上是独立衰落的，在这种情况下，即使因子图中存在环路，BP迭代也可能收敛到固定点。实际上，由于有限的散射无线电环境，实际信道在空间上是相关的衰落。不幸的是，我们发现BP迭代的收敛性能受到空间相关性的严重影响。因此，本文的主要工作是在具有空间相关衰落信道的大规模MIMO检测中提高BP迭代的收敛性能。特别是，我们提出了两种有效的方法，即自动阻尼和预处理。在第一种方法中，在每个BP迭代中，根据两个连续消息之间的Kullback-Leibler散度（即当前迭代和先前迭代）自动计算启发式阻尼因子，然后将计算出的阻尼因子用于平滑消息（减震）。在第二种方法中，首先通过去相关矩阵对通道矩阵进行预处理，然后再使用常规的BP算法。当接收天线的数量为大基数2时，也可以通过快速傅立叶变换来近似解相关。这两种方法可以一起使用，在我们的模拟结果中，通过分析空间相关的通道模型和实际的测量通道，均显示出优于常规BP的性能。

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