Channel estimation is of paramount importance in most communication systems in order to optimize the data rate/energy consumption tradeoff. In modern systems, the possibly large number of transmit/receive antennas and subcarriers makes this task difficult. Designing pilot sequences of reasonable size yielding good performance is thus critical. Classically, the number of pilots is reduced by viewing the channel as a random vector and assuming knowledge of its distribution. In practice, this requires estimating the channel covariance matrix, which can be computationally costly and not adapted to scenarios with high mobility. In this paper, an alternative view is considered, in which the channel is a function of unknown deterministic parameters. In this setting, the problem of designing optimal pilot sequences of smallest possible size is studied for any parametric channel model. To do so, the Cramér-Rao bound (CRB) for this general channel estimation problem is given, highlighting its key dependency on the introduced variation space. Then, the minimal size of pilot sequences and minimal value of the CRB are determined. Moreover, a general strategy to build optimal minimal length power constrained pilots sequences is given, based on an estimation of the variation space. The theoretical results are finally illustrated in a massive MIMO system context. They conveniently allow to retrieve well known previous results, but also to exhibit minimal length optimal pilot sequences for a new strategy based on a nonlinear physical model.

中文翻译：

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信道估计：最佳性能和导频序列的统一视图


为了优化数据速率/能耗权衡，信道估计在大多数通信系统中至关重要。在现代系统中，可能存在大量的发射/接收天线和子载波，使得这项任务变得困难。因此，设计合理大小并产生良好性能的导频序列至关重要。传统上，通过将信道视为随机向量并假设了解其分布来减少导频数量。在实践中，这需要估计信道协方差矩阵，其计算成本可能很高并且不适合高移动性的场景。在本文中，考虑了另一种观点，其中信道是未知确定性参数的函数。在这种情况下，研究了针对任何参数信道模型设计尽可能最小尺寸的最佳导频序列的问题。为此，给出了该一般信道估计问题的 Cramér-Rao 界（CRB），强调了其对引入的变化空间的关键依赖性。然后，确定导频序列的最小尺寸和CRB的最小值。此外，基于变化空间的估计，给出了构建最佳最小长度功率受限导频序列的一般策略。理论结果最终在大规模 MIMO 系统环境中得到说明。它们可以方便地检索以前众所周知的结果，而且还可以为基于非线性物理模型的新策略展示最小长度的最佳导频序列。