We study the expectation propagation (EP) algorithm for symbol detection in massive multiple-input multiple-output (MIMO) systems. The EP detector shows excellent performance but suffers from a high computational complexity due to the matrix inversion, required in each EP iteration to perform marginal inference on a Gaussian system. We propose an inversion-free variant of the EP algorithm by treating inference on the mean and variance as two separate and simpler subtasks: We study the preconditioned conjugate gradient algorithm for obtaining the mean, which can significantly reduce the complexity and increase stability by relying on the Jacobi preconditioner that proves to fit the EP characteristics very well. For the variance, we use a simple approximation based on linear regression of the Gram channel matrix. Numerical studies on the Rayleigh-fading channel and on a realistic 3GPP channel model reveal the efficiency of the proposed scheme, which offers an attractive performance-complexity tradeoff and even outperforms the original EP detector in high multi-user inference cases where the matrix inversion becomes numerically unstable.

翻译：我们研究了大规模多输入多输出（MIMO）系统中用于符号检测的期望传播（EP）算法。EP检测器具有优越的性能，但由于每次EP迭代中需要对高斯系统进行边缘推理而涉及矩阵求逆，导致计算复杂度较高。我们提出了一种无逆矩阵的EP算法变体，将均值和方差的推理处理为两个独立且更简单的子任务：研究了用于求解均值的预条件共轭梯度算法，该算法通过采用Jacobi预条件子显著降低了复杂度并提高了稳定性，且该预条件子被证明非常符合EP特性。对于方差，我们基于Gram信道矩阵的线性回归使用了简单近似。在瑞利衰落信道和真实3GPP信道模型上的数值研究表明，所提方案具有高效的性能-复杂度折衷，并且在多用户干扰较大导致矩阵求逆数值不稳定的场景中，其性能甚至优于原始EP检测器。