The use of channel state information (CSI) at the transmitter significantly enhances the performance of wireless communication systems. However, the requirement of CSI feedback places an undue burden on the reverse link, especially in links that employ multiple-input multiple-output (MIMO) and orthogonal frequency division multiplexing (OFDM), where CSI takes the form of a precoding matrix (precoder) for each subcarrier. Typical deployments use quantization and feedback of CSI at certain subcarriers, with interpolation to fill in missing CSI at the transmitter. Past work has used the orthogonal structure of precoders with Flag manifolds for quantization and interpolation of CSI, although interpolation is complicated due to the absence of analytic expressions for geodesics on Flag manifolds. Other approaches have involved the parameterization of the precoder into scalar parameters that are amenable to quantization and interpolation. In this paper, we present efficient methods to quantize and interpolate on Flag manifolds, using both optimal algorithms as well as simplified suboptimal algorithms. Further, we unify these with the parameterization based approaches and show that these translate directly to low-complexity quantization and interpolation on Flag manifolds. Simulations reveal that the proposed precoder quantization and interpolation effectively enhance achievable rates with limited complexity.

中文翻译：

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标记用于 MIMO-OFDM 系统的基于流形的预编码器内插技术

在发射机使用信道状态信息 (CSI) 显着提高了无线通信系统的性能。然而，CSI 反馈的要求给反向链路带来了不适当的负担，尤其是在采用多输入多输出 (MIMO) 和正交频分复用 (OFDM) 的链路中，其中 CSI 采用预编码矩阵的形式（预编码器) 对于每个子载波。典型的部署在某些子载波上使用 CSI 的量化和反馈，并通过内插来填补发射机丢失的 CSI。过去的工作使用带有 Flag 流形的预编码器的正交结构进行 CSI 的量化和插值，尽管由于 Flag 流形上没有测地线的解析表达式，插值很复杂。其他方法涉及将预编码器参数化为适合量化和插值的标量参数。在本文中，我们提出了使用最优算法和简化的次优算法对 Flag 流形进行量化和插值的有效方法。此外，我们将这些与基于参数化的方法统一起来，并表明这些方法可以直接转化为 Flag 流形上的低复杂度量化和插值。模拟表明，所提出的预编码器量化和插值有效地提高了可实现的速率，但复杂度有限。使用最优算法以及简化的次优算法。此外，我们将这些与基于参数化的方法统一起来，并表明这些方法可以直接转化为 Flag 流形上的低复杂度量化和插值。模拟表明，所提出的预编码器量化和插值有效地提高了可实现的速率，但复杂度有限。使用最优算法以及简化的次优算法。此外，我们将这些与基于参数化的方法统一起来，并表明这些方法可以直接转化为 Flag 流形上的低复杂度量化和插值。模拟表明，所提出的预编码器量化和插值有效地提高了可实现的速率，但复杂度有限。