Phase noise (PN) introduced by the oscillator at the base station and user side severely degrades the channel estimation performance. This paper investigates the impact of PN on downlink compressive channel estimation in massive multiple-input multiple-output (MIMO) systems. Particularly, the downlink compressive channel estimation with PN is modeled as a sparse signal recovery problem with additive correlated perturbation on the pilot matrix, which is a general formulation for both non-synchronous and synchronous PN. Based on this signal model, the performance of the equivalent sensing matrix is analyzed by invoking restricted isometry property (RIP) in compressive sensing. In addition, the upper bound for $l_{1}$ -minimization based channel estimation method and tight channel estimation bound are derived in the framework of RIP and Oracle least square methodology, respectively. Finally, we propose a PN-aware sparse Bayesian learning (PNA-SBL) algorithm to improve the channel estimation performance in the presence of synchronous PN. Simulation results demonstrate our analysis and superiority of the proposed PNA-SBL algorithm.

中文翻译：

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大规模 MIMO 系统中带有相位噪声的下行链路压缩信道估计

基站和用户侧振荡器引入的相位噪声（PN）严重降低了信道估计性能。本文研究了 PN 对大规模多输入多输出 (MIMO) 系统中下行链路压缩信道估计的影响。特别地，使用 PN 的下行链路压缩信道估计被建模为具有导频矩阵上的加性相关扰动的稀疏信号恢复问题，这是非同步和同步 PN 的通用公式。基于该信号模型，通过调用压缩感知中的受限等距特性（RIP）来分析等效感知矩阵的性能。此外，分别在 RIP 和 Oracle 最小二乘法框架中推导出基于 $l_{1}$-最小化的信道估计方法和紧信道估计边界的上限。最后，我们提出了一种 PN 感知稀疏贝叶斯学习 (PNA-SBL) 算法，以在存在同步 PN 的情况下提高信道估计性能。仿真结果证明了我们对所提出的 PNA-SBL 算法的分析和优越性。