本文为西班牙马德里卡洛斯三世大学（作者：Javier C′espedes Mart′ın）的博士论文，共109页。

本文研究了高维多输入多输出（MIMO）系统和高阶M正交幅度调制（QAM）星座的低复杂度推断概率算法。一些现代通信系统正在使用越来越多的天线来最大化频谱效率，在一种新的现象中，称为大规模MIMO。然而，随着天线的数目和/或星座的增长，必须解决几个技术问题，其中一个是符号检测复杂度随系统维数呈指数增长。目前大规模MIMO低复杂度接收机的设计是MIMO中的一个重要研究方向，因为符号检测的指数计算复杂度，不能再依赖于传统的最大后验（MAP）方法。

本文提出了两个主要结论。一方面是一种基于期望传播（EP）算法的低复杂度MIMO检测器，该算法允许在多项式内迭代近似地发射符号的后验分布。该接收器被命名为期望传播检测器（EPD），其解决方案是从最小均方误差（MMSE）的解演变而来，并保持每一次迭代的MMSE复杂度，这是由矩阵求逆所支配的。硬判决符号错误率（SER）的性能显著改善了类似复杂性的最先进的解决方案。另一方面，本文还提出了一种更适合于采用低密度奇偶校验（LDPC）码等信道编码技术的现代通信系统的软推断算法。现代信道解码技术需要每一编码比特的输入对数似然比（LLR）信息。为了获得这些信息，首先必须执行一个软位推断过程。在低维场景中，这可以通过符号后验分布的边缘化来实现。然而，这在高维上是不可行的。虽然EPD可以提供这种概率信息，但在低信噪比（SNR）情况下，其概率估计通常较差。为了解决这一不便，提出了一种基于期望一致性（EC）的新算法，该算法对传统的几种算法如信念传播（BP）算法和期望一致性（EP）算法进行了推广。提出的期望一致性检测器（ECD）算法将推断问题映射为非凸函数上的优化。这种新的方法能够在精度和收敛性之间找到平稳点和折衷，从而产生鲁棒的更新规则。在与EPD相同的复杂成本下，新的建议方法实现了更接近信道容量在中等SNR的性能。结果表明，概率检测精度对整个系统的可实现率有一定的影响。最后，提出了一种改进的ECD算法，采用Turbo接收机结构，将译码器的输出反馈给ECD，在模拟的所有块长度上都获得了性能增益。本文组织结构如下。第一章介绍了MIMO方案，指出了MIMO方案的优势和挑战，并阐述了本文的两个主要方案。最后，揭示了这项工作背后的动机和贡献。第二章和第三章介绍了硬检测的现状和我们的建议，第四章和第五章则介绍了软推断检测。最后，在第六章中可以找到本文的结论和未来的思路。

This Thesis explores low-complexityinference probabilistic algorithms in high-dimensional Multiple-InputMultiple-Output (MIMO) systems and high order M-Quadrature Amplitude Modulation(QAM) constellations. Several modern communications systems are using more andmore antennas to maximize spectral efficiency, in a new phenomena call MassiveMIMO. However, as the number of antennas and/or the order of the constellationgrow several technical issues have to be tackled, one of them is that thesymbol detection complexity grows fast exponentially with the system dimension.Nowadays the design of massive MIMO low-complexity receivers is one importantresearch line in MIMO because symbol detection can no longer rely onconventional approaches such as Maximum a Posteriori (MAP) due to itsexponential computation complexity. This Thesis proposes two main results. Onone hand a hard decision low-complexity MIMO detector based on ExpectationPropagation (EP) algorithm which allows to iteratively approximate withinpolynomial cost the posterior distribution of the transmitted symbols. Thereceiver is named Expectation Propagation Detector (EPD) and its solutionevolves from Minimum Mean Square Error (MMSE) solution and keeps per iterationthe MMSE complexity which is dominated by a matrix inversion. Hard decisionSymbol Error Rate (SER) performance is shown to remarkably improvestate-of-the-art solutions of similar complexity. On the other hand, a soft-inferencealgorithm, more suitable to modern communication systems with channelcodification techniques such as LowDensity Parity-Check (LDPC) codes, is alsopresented. Modern channel decoding techniques need as input Log-Likehood Ratio(LLR) information for each coded bit. In order to obtain that information,firstly a soft bit inference procedure must be performed. In low-dimensionalscenarios, this can be done by marginalization over the symbol posteriordistribution. However, this is not feasible at high-dimension. While EPD couldprovide this probabilistic information, it is shown that its probabilisticestimates are in general poor in the low Signal-to-Noise Ratio (SNR) regime. Inorder to solve this inconvenience a new algorithm based on the ExpectationConsistency (EC) algorithm, which generalizes several algorithms such as BeliefPropagation (BP) and EP itself, was proposed. The proposed algorithm calledExpectation Consistency Detector (ECD) maps the inference problem as anoptimization over a non convex function. This new approach allows to findstationary points and tradeoffs between accuracy and convergence, which leadsto robust update rules. At the same complexity cost than EPD, the new proposalachieves a performance closer to channel capacity at moderate SNR. The resultreveals that the probabilistic detection accuracy has a relevant impact in theachievable rate of the overall system. Finally, a modified ECD algorithm ispresented, with a Turbo receiver structure where the output of the decoder isfed back to ECD, achieving performance gains in all block lengths simulated.The document is structured as follows. In Chapter I an introduction to the MIMOscenario is presented, the advantages and challenges are exposed and the twomain scenarios of this Thesis are set forth. Finally, the motivation behindthis work, and the contributions are revealed. In Chapters II and III the stateof the art and our proposal are presented for Hard Detection, whereas inChapters IV and V are exposed for Soft Inference Detection. Eventually, aconclusion and future lines can be found in Chapter VI.