This letter deals with the application of the expectation propagation (EP) algorithm to turbo equalization. The EP has been successfully applied to obtain either a better approximation at the output of the equalizer or at the output of the channel decoder to better initialize the Gaussian prior used by the equalizer. In this letter we combine both trends to propose a novel double EP-based equalizer that is able to decrease the number of iterations needed, reducing the computational complexity. This novel equalizer is presented in three different implementations: a block design that exploits the whole vector of observations, a Wiener filter-type approach that just uses the observations within a predefined window and a Kalman smoothing filter-type approach that emulates the BCJR behavior. Finally, we include some experimental results to compare the three different implementations and to illustrate their improvements with respect to other EP-based proposals in the literature.

中文翻译：

---

一个基于双 EP 的涡轮均衡方案

这封信涉及期望传播 (EP) 算法在 Turbo 均衡中的应用。EP 已成功应用于在均衡器的输出处或在通道解码器的输出处获得更好的近似，以更好地初始化均衡器使用的高斯先验。在这封信中，我们结合了这两种趋势，提出了一种新型的基于双 EP 的均衡器，该均衡器能够减少所需的迭代次数，降低计算复杂度。这种新颖的均衡器以三种不同的实现方式呈现：利用整个观测向量的块设计、仅使用预定义窗口内的观测的维纳滤波器类型方法和模拟 BCJR 行为的卡尔曼平滑滤波器类型方法。最后，