Carrier frequency offset (CFO) and channel estimation is a classic topic with a large body of prior work using the maximum likelihood (ML) approach together with the Cramér-Rao lower bound (CRLB) analysis. We give the maximum a posteriori probability (MAP) estimation solution, which is particularly useful for tracking. Unlike the ML cases, the corresponding Bayesian CRLB (BCRLB) shows a clear relation with parameters and low complexity algorithms are provided to achieve the BCRLB in almost all SNR range. Among them, the universal algorithm takes a new approach and avoids error floors of the traditional approach. We assume that the time invariant MIMO channel within a packet can have spatial correlation and nonzero mean. The estimation is based on pilot signals. An unexpected result is that the joint MAP estimation is equivalent to an individual MAP estimation of the frequency offset first, again different from the ML results. We provide insight on the pilot/training signal design based on the BCRLB. Unlike past algorithms that trade performance and/or complexity for the accommodation of time varying channels, the MAP solution provides a different route for dealing with time variation. Within a short enough (segment of) packet where the channel and CFO are approximately time invariant, the low complexity algorithm can be employed. Similar to the belief propagation, the estimation of the previous (segment of) packet can serve as the prior knowledge for the next (segment of) packet.

中文翻译：

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具有任意相关信道的 MIMO 系统的最大后验概率 (MAP) 联合精细频偏和信道估计


载波频率偏移 (CFO) 和信道估计是一个经典主题，之前有大量工作使用最大似然 (ML) 方法以及 Cramér-Rao 下界 (CRLB) 分析。我们给出了最大后验概率（MAP）估计解决方案，这对于跟踪特别有用。与 ML 情况不同，相应的贝叶斯 CRLB（BCRLB）显示出与参数的清晰关系，并且提供了低复杂度算法以在几乎所有 SNR 范围内实现 BCRLB。其中，通用算法采用了新的方法，避免了传统方法的错误平台。我们假设数据包内的时不变 MIMO 信道可以具有空间相关性和非零均值。该估计基于导频信号。一个意想不到的结果是，联合 MAP 估计相当于首先对频率偏移进行单独 MAP 估计，这又与 ML 结果不同。我们提供有关基于 BCRLB 的飞行员/训练信号设计的见解。与过去以性能和/或复杂性为代价来适应时变通道的算法不同，MAP 解决方案提供了一种不同的途径来处理时变。在信道和 CFO 近似时不变的足够短的数据包（段）内，可以采用低复杂度算法。与置信传播类似，前一个（段）数据包的估计可以作为下一个（段）数据包的先验知识。